cs user al simulations - gromacs
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GR
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9747
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Gro
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ivPreface
&D
isclaimer
This
manualis
notcomplete
andhas
nopretention
tobe
sodue
tolack
oftime
ofthecontributors
–our
firstpriorityis
toim
provethe
software.
Itism
eantasa
sourceofinform
ationand
referencesforthe
GR
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AC
Suser.
Itcoversboth
thephysicalbackground
ofMD
simulations
ingeneraland
detailsof
theG
RO
MA
CS
software
inparticular.
The
manualis
continuouslybeing
worked
on,w
hichin
some
casesm
ightmean
theinform
ationis
notentirelycorrect.
When
citingthis
documentin
anyscientific
publicationplease
referto
itas:
vander
Spoel,D
.,A.R
.vanB
uuren,E.A
pol,P.J.Meulenhoff,D
.P.Tielem
an,A
.L.T.M.S
ijbers,B.H
ess,K.A
.Feenstra,E
.Lindahl,R.van
Drunen
andH
.J.C.
Berendsen,G
rom
acs
Use
rM
an
ua
lversio
n3
.0,
Nijenborgh
4,9747A
GG
roningen,The
Netherlands.
Internet:w
ww
.gromacs.org(2001)
or,ifyouuse
BibTeX
,youcan
directlycopy
thefollow
ing:
@M
an
ua
l{gm
x30
,title
="G
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{U}se
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Any
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Any
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welcom
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themby
e-mailtogrom
acs@grom
acs.org.
Groningen,A
ugust10,2001.
Departm
entofBiophysicalC
hemistry
University
ofGroningen
Nijenborgh
49747
AG
Groningen
The
Netherlands
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11
3.2.
1S
ome
usef
ulbo
xty
pes.
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13
3.2.
2C
ut-o
ffre
stric
tions
..
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.14
3.3
The
grou
pco
ncep
t..
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.14
3.4
Mol
ecul
arD
ynam
ics
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15
3.4.
1In
itial
cond
ition
s.
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.15
3.4.
2N
eigh
bor
sear
chin
g..
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.18
3.4.
3C
ompu
tefo
rces.
..
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20
3.4.
4U
pdat
eco
nfigu
ratio
n..
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21
3.4.
5Te
mpe
ratu
reco
uplin
g..
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.21
3.4.
6P
ress
ure
coup
ling.
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.23
3.4.
7O
utpu
tste
p..
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.26
3.5
She
llm
olec
ular
dyna
mic
s..
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28
3.5.
1O
ptim
izat
ion
ofth
esh
ellp
ositi
ons..
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.28
viiiC
on
ten
ts
3.6C
onstraintalgorithms.
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.28
3.6.1S
HA
KE
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.29
3.6.2LIN
CS
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.29
3.7S
imulated
Annealing.
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.31
3.8S
tochasticD
ynamics.
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.32
3.9B
rownian
Dynam
ics.
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.32
3.10E
nergyM
inimization
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33
3.10.1S
teepestDescent..
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33
3.10.2C
onjugateG
radient...
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33
3.11N
ormalM
odeA
nalysis..
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.34
3.12F
reeenergy
calculations..
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34
3.13E
ssentialDynam
icsS
ampling.
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36
3.14P
arallelization..
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37
3.14.1M
ethodsofparallelization.
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37
3.14.2M
Don
aring
ofprocessors...
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39
3.15P
arallelMolecular
Dynam
ics..
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42
3.15.1D
omain
decomposition.
..
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42
3.15.2D
omain
decomposition
fornon-bonded
forces.
..
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..
43
3.15.3P
arallelPP
PM
..
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.44
3.15.4P
arallelsorting..
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.45
4F
orcefields
47
4.1N
on-bondedinteractions.
..
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.48
4.1.1T
heLennard-Jones
interaction...
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48
4.1.2B
uckinghampotential.
..
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49
4.1.3C
oulomb
interaction..
..
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50
4.1.4C
oulomb
interactionw
ithreaction
field..
..
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..
50
4.1.5M
odifiednon-bonded
interactions..
..
..
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..
.51
4.1.6M
odifiedshort-range
interactionsw
ithE
wald
summ
ation.
..
..
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..
53
4.2B
ondedinteractions.
..
..
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54
4.2.1B
ondstretching.
..
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54
4.2.2M
orsepotentialbond
stretching..
..
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55
4.2.3C
ubicbond
stretchingpotential.
..
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..
.56
4.2.4H
armonic
anglepotential..
..
..
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..
56
Index
τT
22εr
501-4
interaction59,85
Aaccelerategroup
15A
FM
pulling103
All-hydrogen
forcefield77
Am
dahl’slaw
38A
nglerestraint
62angle
vibration56
annealing,simulated
seesim
ulatedannealing
atomse
eparticletype
80D
umm
y∼se
eDum
my
atomdum
my∼
seedum
my
atomunited∼
seeunited
atomautocorrelation
function137
average,ensemble
seeensem
bleaverage
BBerendsen
temperature
coupling22
bondshellse
eparticlestretching
54bonded
parameter
83B
orn-Oppenheim
er4
Boundary
Conditions,P
eriodicse
ePeriodic
Boundary
Conditions
boundaryconditions,P
eriodicse
ePeriodic
boundaryconditions
Brow
nianD
ynamics
32B
uckingham49
buildingblock
82,86
Ccenter-of-mass
velocity17
Charge
Group
70
chargegroup
19,121chem
istry,computational
seecom
putationalchemistry
citingiv
coefficient,diffusionse
ediffusioncoefficient
combination
rule85
compressibility
24com
putationalchemistry
1C
onjugateG
radient33
conjugategradient
117connection
85constant,dielectric
seedielectric
constantC
onstraint28,85
constraint4
Constraintforce
100103
constraints126
convention,polymer
seepolym
erconvention
correlation137
Coulom
b50,66
couplingP
ressure∼se
ePressure
couplingS
urfacetension∼
seeS
urfacetension
couplingTem
perature∼se
eTemperature
couplingtem
perature∼se
etemperature
couplingC
ovarianceanalysis
145cut-off
51,70,121,122
DData
Parallel
37D
atabase86
databasehydrogen∼
seehydrogen
database
24
0B
iblio
gra
ph
yC
on
ten
tsix
4.2.
5C
osin
eba
sed
angl
epo
tent
ial
..
..
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..
57
4.2.
6Im
prop
erdi
hedr
als.
..
..
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..
57
4.2.
7P
rope
rdi
hedr
als.
..
..
..
..
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..
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..
.57
4.2.
8S
peci
alin
tera
ctio
ns..
..
..
..
..
..
..
..
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..
.60
4.2.
9P
ositi
onre
stra
ints.
..
..
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..
.61
4.2.
10A
ngle
rest
rain
ts..
..
..
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..
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..
.62
4.2.
11D
ista
nce
rest
rain
ts..
..
..
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..
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..
.62
4.3
Fre
een
ergy
inte
ract
ions.
..
..
..
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..
66
4.3.
1S
oft-
core
inte
ract
ions.
..
..
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..
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..
..
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..
.68
4.4
Met
hods
..
..
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..
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..
.69
4.4.
1E
xclu
sion
san
d1-
4In
tera
ctio
ns...
..
..
..
..
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..
69
4.4.
2C
harg
eG
roup
s...
..
..
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..
.70
4.4.
3T
reat
men
tofc
ut-o
ffs.
..
..
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..
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..
.70
4.5
Dum
my
atom
s..
..
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..
71
4.6
Long
Ran
geE
lect
rost
atic
s..
..
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..
.74
4.6.
1E
wal
dsu
mm
atio
n..
..
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74
4.6.
2P
ME
..
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..
75
4.6.
3P
PP
M.
..
..
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..
..
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..
..
..
..
..
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..
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..
..
.75
4.6.
4O
ptim
izin
gF
ourie
rtr
ansf
orm
s..
..
..
..
..
..
..
..
..
..
..
.76
4.7
All-
hydr
ogen
forc
efiel
d..
..
..
..
..
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..
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..
.77
4.8
GR
OM
OS
-96
note
s..
..
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.77
4.8.
1T
heG
RO
MO
S-9
6fo
rce
field.
..
..
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..
.77
4.8.
2G
RO
MO
S-9
6fil
es.
..
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..
78
5To
polo
gies
79
5.1
Intr
oduc
tion
..
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..
.79
5.2
Par
ticle
type
..
..
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..
.79
5.2.
1A
tom
type
s..
..
..
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..
.80
5.2.
2D
umm
yat
oms
..
..
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..
.81
5.3
Par
amet
erfil
es.
..
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..
82
5.3.
1A
tom
s..
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..
82
5.3.
2B
onde
dpa
ram
eter
s..
..
..
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..
.83
5.3.
3N
on-b
onde
dpa
ram
eter
s..
..
..
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..
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..
84
5.3.
41-
4in
tera
ctio
ns.
..
..
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..
85
xC
on
ten
ts
5.3.5E
xclusions.
..
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85
5.4C
onstraints.
..
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85
5.5D
atabases..
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86
5.5.1R
esiduedatabase.
..
..
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..
.86
5.5.2H
ydrogendatabase.
..
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88
5.5.3Term
inidatabase..
..
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89
5.6F
ileform
ats.
..
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..
91
5.6.1Topology
file.
..
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.91
5.6.2M
olecule.itpfile
..
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96
5.6.3Ifdefoption
..
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..
.98
5.6.4F
reeenergy
calculations..
..
..
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..
99
5.6.5C
onstraintforce..
..
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.100
5.6.6C
oordinatefile
..
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.101
6S
pecialTopics103
6.1C
alculatingpotentials
ofmean
force:the
pullcode...
..
..
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..
.103
6.1.1O
verview.
..
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.103
6.1.2U
sage..
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..104
6.1.3O
utput.
..
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..107
6.1.4Lim
itations.
..
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..107
6.1.5Im
plementation.
..
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..108
6.1.6F
uturedevelopm
ent...
..
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..
..108
6.2R
emoving
fastestdegreesoffreedom
..
..
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..
108
6.2.1H
ydrogenbond-angle
vibrations...
..
..
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..
.109
6.2.2O
ut-of-planevibrations
inarom
aticgroups..
..
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..
110
6.3V
iscositycalculation
..
..
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..111
6.4U
serspecified
potentialfunctions...
..
..
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..
.113
6.5R
unningG
RO
MA
CS
inparallel.
..
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.114
7R
unparam
etersand
Program
s115
7.1O
nlineand
htmlm
anuals..
..
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..115
7.2F
iletypes
..
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..115
7.3R
unP
arameters.
..
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..117
7.3.1G
eneral..
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.117
7.3.2P
reprocessing..
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..117
Bib
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..
..
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..
..
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..
..
..
..
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..
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..
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..
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..
.120
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9E
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san
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..
..
..
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..1
20
7.3.
10Te
mpe
ratu
reco
uplin
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..
..
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..
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.123
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11P
ress
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coup
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..
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.123
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12S
imul
ated
anne
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g..
..
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..1
25
7.3.
13Ve
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tion.
..
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..1
25
7.3.
14B
onds
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..1
26
7.3.
15E
nerg
ygr
oup
excl
usio
ns..
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..1
27
7.3.
16N
MR
refin
emen
t..
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..1
27
7.3.
17F
ree
Ene
rgy
Per
turb
atio
n..
..
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..1
28
7.3.
18N
on-e
quili
briu
mM
D.
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.128
7.3.
19E
lect
ricfie
lds.
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.129
7.3.
20U
ser
defin
edth
ingi
es..
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..1
29
7.4
Pro
gram
sby
topi
c..
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..1
29
8A
naly
sis
133
8.1
Gro
ups
inA
naly
sis..
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..1
33
8.1.
1D
efau
ltG
roup
s..
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.134
8.2
Look
ing
atyo
urtr
ajec
tory
..
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.135
8.3
Gen
eral
prop
ertie
s..
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..1
35
8.4
Rad
iald
istr
ibut
ion
func
tions
..
..
..
..
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..1
36
8.5
Cor
rela
tion
func
tions
..
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..1
37
8.5.
1T
heor
yof
corr
elat
ion
func
tions
..
..
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..
137
8.5.
2U
sing
FF
Tfo
rco
mpu
tatio
nof
the
AC
F..
..
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..
139
8.5.
3S
peci
alfo
rms
ofth
eA
CF.
..
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.139
8.5.
4S
ome
App
licat
ions
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.139
8.5.
5M
ean
Squ
are
Dis
plac
emen
t..
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140
8.6
Bon
ds,a
ngle
san
ddi
hedr
als.
..
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.140
8.7
Rad
ius
ofgy
ratio
nan
ddi
stan
ces..
..
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..1
43
xiiC
on
ten
ts
8.8R
ootmean
squaredeviations
instructure
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144
8.9C
ovarianceanalysis.
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..145
8.10H
ydrogenbonds.
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..147
8.11P
roteinrelated
items.
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.148
8.12Interface
relateditem
s...
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.150
8.13C
hemicalshifts.
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..151
ATechnicalD
etails153
A.1
Installation.
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..153
A.2
Single
orD
oubleprecision.
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..153
A.3
Porting
GR
OM
AC
S.
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..154
A.3.1
Multi-processor
Optim
ization..
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.155
A.4
Environm
entVariables..
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.155
BS
ome
implem
entationdetails
157
B.1
Single
Sum
Virialin
GR
OM
AC
S..
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157
B.1.1
Virial.
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..157
B.1.2
Virialfrom
non-bondedforces...
..
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.158
B.1.3
The
intramolecular
shift(mol-shift)..
..
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.158
B.1.4
Virialfrom
CovalentB
onds...
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159
B.1.5
Virialfrom
Shake.
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.160
B.2
Optim
izations.
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.160
B.2.1
InnerLoops
forW
ater..
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.160
B.2.2
Fortran
Code.
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.161
B.3
Com
putationofthe
1.0/sqrtfunction..
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B.3.1
Introduction..
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B.3.2
General.
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..161
B.3.3
Applied
tofloating
pointnumbers.
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162
B.3.4
Specification
ofthelookup
table..
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163
B.3.5
Separate
exponentandfraction
computation
..
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164
B.3.6
Implem
entation..
..
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.165
B.4
Tabulatedfunctions.
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..165
CLong
rangecorrections
167
C.1
Dispersion.
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.167
Bib
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.218
E.55
grompp
..
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.218
E.56
highway
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.220
E.57
makendx
..
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..220
E.58
mdrun
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..221
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23
4A
pp
en
dix
E.
Ma
nu
alP
age
sC
on
ten
tsxv
E.5
9m
kan
gndx
..
..
..
..
..
..
..
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..
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..
..
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..
.222
E.6
0ng
mx
..
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..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..2
22
E.6
1nm
run
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..2
23
E.6
2op
tions
..
..
..
..
..
..
..
..
..
..
..
..
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..
..
..
..
..
..
..2
23
E.6
3pd
b2gm
x.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.224
E.6
4pr
oton
ate
..
..
..
..
..
..
..
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..
..
..
..
..2
25
E.6
5tp
bcon
v.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..2
26
E.6
6tr
jcat
..
..
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..
.226
E.6
7tr
jcon
v.
..
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.227
E.6
8tr
jord
er.
..
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..2
28
E.6
9w
heel
..
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..2
29
E.7
0x2
top
..
..
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..
..
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..
..
..
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..
..
..
..
..2
29
E.7
1xm
drun
..
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..
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..
..
..
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..
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..
..
..
..
..
..
..
..
..
.230
E.7
2xp
m2p
s.
..
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..
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..2
31
E.7
3xr
ama
..
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..
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..
..2
32
Bib
liogr
aphy
235
Inde
x24
1
xviC
on
ten
tsE
.73
.xra
ma
23
3
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
23
2A
pp
en
dix
E.
Ma
nu
alP
age
s
sele
cted
toco
mbi
neth
em
atric
es.
Inth
isca
se,
ane
wco
lor
map
will
bege
nera
ted
with
are
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adie
ntfo
rne
gativ
enu
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rsan
da
blue
for
posi
tive.
Ifth
eco
lor
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ngan
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labe
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both
mat
rices
are
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lege
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tosh
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long
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List
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3.1
Per
iodi
cbo
unda
ryco
nditi
ons
intw
odi
men
sion
s...
..
..
..
..
..
..
..
.12
3.2
Arh
ombi
cdo
deca
hedr
onan
dtr
unca
ted
octa
hedr
on(a
rbitr
ary
orie
ntat
ions
)..
..
13
3.3
The
glob
alM
Dal
gorit
hm.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.16
3.4
AM
axw
ellia
ndi
strib
utio
n,ge
nera
ted
from
rand
omnu
mbe
rs.
..
..
..
..
..
.17
3.5
Grid
sear
chin
two
dim
ensi
ons.
The
arro
ws
are
the
box
vect
ors.
..
..
..
..
..
19
3.6
The
Leap
-Fro
gin
tegr
atio
nm
etho
d...
..
..
..
..
..
..
..
..
..
..
..
.21
3.7
The
MD
upda
teal
gorit
hm.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
27
3.8
The
thre
epo
sitio
nup
date
sne
eded
for
one
time
step
..
..
..
..
..
..
..
..
.30
3.9
Fre
een
ergy
cycl
es..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
35
3.10
The
inte
ract
ion
mat
rix..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
40
3.11
Inte
ract
ion
mat
rices
for
diffe
rentN
..
..
..
..
..
..
..
..
..
..
..
..
.40
3.12
The
Par
alle
lMD
algo
rithm
...
..
..
..
..
..
..
..
..
..
..
..
..
..
.41
3.13
Dat
aflo
win
arin
gof
proc
esso
rs.
..
..
..
..
..
..
..
..
..
..
..
..
..
42
3.14
Inde
xin
the
coor
dina
tear
ray..
..
..
..
..
..
..
..
..
..
..
..
..
..
.43
4.1
The
Lenn
ard-
Jone
sin
tera
ctio
n...
..
..
..
..
..
..
..
..
..
..
..
..
.48
4.2
The
Buc
king
ham
inte
ract
ion..
..
..
..
..
..
..
..
..
..
..
..
..
..
.49
4.3
The
Cou
lom
bin
tera
ctio
nw
ithan
dw
ithou
trea
ctio
nfie
ld.
..
..
..
..
..
..
.50
4.4
The
Cou
lom
bF
orce
,Shi
fted
For
cean
dS
hift
Fun
ctio
nS
(r),
..
..
..
..
..
..
53
4.5
Bon
dst
retc
hing
...
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.54
4.6
The
Mor
sepo
tent
ialw
ell,
with
bond
leng
th0.
15nm
...
..
..
..
..
..
..
.56
4.7
Ang
levi
brat
ion.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.57
4.8
Impr
oper
dihe
dral
angl
es...
..
..
..
..
..
..
..
..
..
..
..
..
..
..
58
4.9
Impr
oper
dihe
dral
pote
ntia
l...
..
..
..
..
..
..
..
..
..
..
..
..
..
58
4.10
Pro
per
dihe
dral
angl
e...
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
59
4.11
Ryc
kaer
t-B
elle
man
sdi
hedr
alpo
tent
ial.
..
..
..
..
..
..
..
..
..
..
..
.60
xviiiL
istofF
igu
res
4.12P
ositionrestraintpotential..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
61
4.13D
istanceR
estraintpotential...
..
..
..
..
..
..
..
..
..
..
..
..
..
63
4.14S
oft-coreinteractions
atλ
=0.5,w
ithC
A6=C
A12
=C
B6=C
B12
=1.
..
..
..
.68
4.15A
toms
alongan
alkanechain.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
69
4.16D
umm
yatom
construction....
..
..
..
..
..
..
..
..
..
..
..
..
..
72
6.1S
chematic
pictureofpulling
alipid
outofalipid
bilayerw
ithA
FM
pulling.V
rup
isthe
velocityatw
hichthe
springis
retracted,Z
link
isthe
atomto
which
thespring
isattached
andZsp
rin
gis
thelocation
ofthespring..
..
..
..
..
..
..
..
.104
6.2O
verviewof
thedifferent
referencegroup
possibilities,applied
tointerface
sys-tem
s.C
isthe
referencegroup.
The
circlesrepresent
thecenter
ofm
assof
2groups
plusthe
referencegroup,and
dc
isthe
referencedistance...
..
..
..
.105
6.3D
umm
yatom
constructionsfor
hydrogenatom
s..
..
..
..
..
..
..
..
..
.109
6.4D
umm
yatom
constructionsfor
aromatic
residues..
..
..
..
..
..
..
..
..
111
8.1T
hew
indowofn
gm
xshow
inga
boxofw
ater...
..
..
..
..
..
..
..
..
.136
8.2D
efinitionofslices
ingrd
f..
..
..
..
..
..
..
..
..
..
..
..
..
..
.137
8.3gO
O(r)
forO
xygen-Oxygen
ofSP
C-w
ater....
..
..
..
..
..
..
..
..
..
138
8.4M
eanS
quareD
isplacementofS
PC
-water.
..
..
..
..
..
..
..
..
..
..
.141
8.5D
ihedralconventions...
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..142
8.6O
ptionsofg
sga
ng
le.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..142
8.7A
minim
umdistance
matrix
fora
peptide[
3]..
..
..
..
..
..
..
..
..
..
144
8.8G
eometricalH
ydrogenbond
criterion....
..
..
..
..
..
..
..
..
..
..
147
8.9Insertion
ofwater
intoan
H-bond..
..
..
..
..
..
..
..
..
..
..
..
..
147
8.10A
nalysisofthe
secondarystructure
elements
ofapeptide
intim
e..
..
..
..
..
149
8.11D
efinitionofthe
dihedralanglesφandψ
oftheprotein
backbone...
..
..
..
149
8.12R
amachandran
plotofasm
allprotein..
..
..
..
..
..
..
..
..
..
..
..
149
8.13H
elicalwheelprojection
oftheN
-terminalhelix
ofHP
r..
..
..
..
..
..
..
.150
B.1
IEE
Esingle
precisionfloating
pointformat.
..
..
..
..
..
..
..
..
..
.162
E.7
2.
xpm
2p
s2
31
theusualoutputw
illbew
rittento
file.W
henrunning
with
MP
I,asignalto
oneofthe
mdrun
processesis
sufficient,thissignalshould
notbesentto
mpirun
orthe
mdrun
processthatis
theparentofthe
others.
Files
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-otra
j.trrO
utputF
ullprecisiontrajectory:
trrtrj
-xtra
j.xtcO
utput,Opt.
Com
pressedtrajectory
(portablexdr
format)
-cco
nfo
ut.g
roO
utputG
enericstructure:
grog96
pdb-e
en
er.e
dr
Output
Generic
energy:edr
ene-g
md
.log
Output
Logfile
-dg
dl
dg
dl.xvg
Output,O
pt.xvgr/xm
grfile
-tab
leta
ble
.xvgInput,O
pt.xvgr/xm
grfile
-reru
nre
run
.xtcInput,O
pt.G
enerictrajectory:
xtctrr
trjgrog96
pdb-e
isa
m.e
di
Input,Opt.
ED
sampling
input-e
osa
m.e
do
Output,O
pt.E
Dsam
plingoutput
-jw
ha
m.g
ctInput,O
pt.G
eneralcouplingstuff
-job
am
.gct
Input,Opt.
Generalcoupling
stuff-ffo
ut
gct.xvg
Output,O
pt.xvgr/xm
grfile
-de
vou
td
evia
tie.xvg
Output,O
pt.xvgr/xm
grfile
-run
av
run
ave
r.xvgO
utput,Opt.
xvgr/xmgr
file-p
ip
ull.p
pa
Input,Opt.
Pullparam
eters-p
op
ullo
ut.p
pa
Output,O
pt.P
ullparameters
-pd
pu
ll.pd
oO
utput,Opt.
Pulldata
output-p
np
ull.n
dx
Input,Opt.
Indexfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-de
ffnm
stringS
etthedefaultfilenam
efor
allfileoptions
-np
int1
Num
berofnodes,m
ustbethe
same
asused
forgrom
pp-v
booln
oB
eloud
andnoisy
-com
pa
ctbool
yes
Write
acom
pactlogfile
-mu
ltibool
no
Do
multiple
simulations
inparallel(only
with
-np>1)
-gla
sbool
no
Do
glasssim
ulationw
ithspeciallong
rangecorrections
-ion
izebool
no
Do
asim
ulationincluding
theeffectofan
X-R
aybom
bardmenton
yoursystem
E.72
xpm2ps
xpm2ps
makes
abeautifulcolor
plotofanX
PixelM
apfile.
Labelsand
axiscan
bedisplayed,w
henthey
aresupplied
inthe
correctm
atrixform
at.M
atrixdata
may
begenerated
byprogram
ssuch
asdo
dssp,grm
sor
gm
dmat.
Param
etersare
setinthem2
pfile
optionallysupplied
with-d
i.
Reasonable
defaultsare
provided.S
ettingsforthe
y-axisdefaultto
thoseforthe
x-axis.F
ontnames
havea
defaultinghierarchy:
titlefont->
legendfont;titlefont->
(xfont->yfont->
ytickfont)->
xtickfont,e.g.setting
titlefontsetsallfonts,setting
xfontsetsyfont,ytickfontand
xtickfont.
With
-f2a
2ndm
atrixfile
canbe
supplied,both
matrix
filesw
illberead
simultaneously
andthe
upperleft
halfof
thefirst
one(-f
)is
plottedtogether
with
thelow
erright
halfof
thesecond
one(
-f2).
The
diagonalwillcontain
valuesfrom
them
atrixfile
selectedw
ith-d
iag
.P
lottingofthe
diagonalvaluescan
besuppressed
altogetherby
setting-d
iag
ton
on
e.
With
-com
bin
ean
alternativeoperation
canbe
23
0A
pp
en
dix
E.
Ma
nu
alP
age
s
-kt
real
40
0A
ngle
forc
eco
nsta
nt(k
J/m
ol/r
ad2 )-k
pre
al5
Dih
edra
lang
lefo
rce
cons
tant
(kJ/
mol
/rad2 )
-ne
xcl
int
3N
umbe
rof
excl
usio
ns-H
14
bool
no
Use
3rd
neig
hbou
rin
tera
ctio
nsfo
rhy
drog
enat
oms
-alld
ihbo
oln
oG
ener
ate
allp
rope
rdi
hedr
als
-ro
un
dbo
olye
sR
ound
offm
easu
red
valu
es-p
airs
bool
yes
Out
put1
-4in
tera
ctio
ns(p
airs
)in
topo
logy
file
-na
me
strin
gIC
EN
ame
ofyo
urm
olec
ule
•T
heat
omty
pese
lect
ion
ispr
imiti
ve.
Virt
ually
noch
emic
alkn
owle
dge
isus
ed
•P
erio
dic
boun
dary
cond
ition
ssc
rew
upth
ebo
ndin
g
•N
oim
prop
erdi
hedr
als
are
gene
rate
d
•T
heat
oms
toat
omty
petr
ansl
atio
nta
ble
isin
com
plet
e(f
fG43
a1.n
2tfil
ein
the
$GM
XLI
Bdi
rect
ory)
.P
leas
eex
tend
itan
dse
ndth
ere
sults
back
toth
eG
RO
MA
CS
crew
.
E.7
1xm
drun
xmdr
unis
the
expe
rimen
talM
Dpr
ogra
m.
New
feat
ures
are
test
edin
this
prog
ram
befo
rebe
ing
impl
emen
ted
inth
ede
faul
tm
drun
.C
urre
ntly
unde
rin
vest
igat
ion
are:
pola
rizib
ility
,gl
ass
sim
ulat
ions
,F
ree
ener
gype
r-tu
rbat
ion,
X-R
aybo
mba
rdm
ents
and
para
lleli
ndep
ende
ntsi
mul
atio
ns.It
read
sth
eru
nin
put
file
(-s
)an
ddi
strib
utes
the
topo
logy
over
node
sif
need
ed.
The
coor
dina
tes
are
pass
edar
ound
,so
that
com
puta
tions
can
begi
n.F
irsta
neig
hbor
listi
sm
ade,
then
the
forc
esar
eco
mpu
ted.
The
forc
esar
egl
obal
lysu
mm
ed,a
ndth
eve
loci
ties
and
posi
tions
are
upda
ted.
Ifne
cess
ary
shak
eis
perf
orm
edto
cons
trai
nbo
ndle
ngth
san
d/or
bond
angl
es.
Tem
pera
ture
and
Pre
ssur
eca
nbe
cont
rolle
dus
ing
wea
kco
uplin
gto
aba
th.
mdr
unpr
oduc
esat
leas
tthr
eeou
tput
file,
plus
one
log
file
(-g
)pe
rno
de.
The
traj
ecto
ryfil
e(
-o),
cont
ains
coor
dina
tes,
velo
citie
san
dop
tiona
llyfo
rces
.T
hest
ruct
ure
file
(-c
)co
ntai
nsth
eco
ordi
nate
san
dve
loci
ties
ofth
ela
stst
ep.
The
ener
gyfil
e(
-e)
cont
ains
ener
gies
,the
tem
pera
ture
,pre
ssur
e,et
c,a
loto
fthe
seth
ings
are
also
prin
ted
inth
elo
gfil
eof
node
0.O
ptio
nally
coor
dina
tes
can
bew
ritte
nto
aco
mpr
esse
dtr
ajec
tory
file
(-x
).
Whe
nru
nnin
gin
para
llelw
ithP
VM
oran
old
vers
ion
ofM
PIt
he-np
optio
nm
ustb
egi
ven
toin
dica
teth
enu
mbe
rof
node
s.
The
optio
n-d
gd
lis
only
used
whe
nfr
eeen
ergy
pert
urba
tion
istu
rned
on.
With
-re
run
anin
putt
raje
ctor
yca
nbe
give
nfo
rw
hich
forc
esan
den
ergi
esw
illbe
(re)
calc
ulat
ed.
Nei
gh-
bor
sear
chin
gw
illbe
perf
orm
edfo
rev
ery
fram
e,un
less
nst
list
isze
ro(s
eeth
e.md
pfil
e).
ED
(ess
entia
ldyn
amic
s)sa
mpl
ing
issw
itche
don
byus
ing
the
-ei
flag
follo
wed
byan
.ed
ifil
e.T
he.e
di
file
can
bepr
oduc
edus
ing
optio
nsin
the
essd
ynm
enu
ofth
eW
HAT
IFpr
ogra
m.
mdr
unpr
oduc
esa
.ed
ofil
eth
atco
ntai
nspr
ojec
tions
ofpo
sitio
ns,v
eloc
ities
and
forc
eson
tose
lect
edei
genv
ecto
rs.
The
-tab
leop
tion
can
beus
edto
pass
mdr
una
form
atte
dta
ble
with
user
-defi
ned
pote
ntia
lfun
ctio
ns.
The
file
isre
adfr
omei
ther
the
curr
entd
irect
ory
orfr
omth
eG
MX
LIB
dire
ctor
y.A
num
ber
ofpr
efor
mat
ted
tabl
esar
epr
esen
ted
inth
eG
MX
LIB
dir,
for
6-8,
6-9,
6-10
,6-
11,
6-12
Lenn
ard
Jone
spo
tent
ials
with
norm
alC
oulo
mb.
The
optio
ns-p
i,-
po
,-p
d,-
pn
are
used
for
pote
ntia
lofm
ean
forc
eca
lcul
atio
nsan
dum
brel
lasa
mpl
ing.
See
man
ual.
Whe
nm
drun
rece
ives
aT
ER
Msi
gnal
,itw
illse
tnst
eps
toth
ecu
rren
tste
ppl
uson
e.W
hen
mdr
unre
ceiv
esa
US
R1
sign
al,
itw
illse
tns
teps
toth
ene
xtm
ultip
leof
nstx
out
afte
rth
ecu
rren
tst
ep.
Inbo
thca
ses
all
List
ofTa
bles
1.1
Typi
calv
ibra
tiona
lfre
quen
cies
...
..
..
..
..
..
..
..
..
..
..
..
..
.3
2.1
Bas
icun
itsus
edin
GR
OM
AC
S..
..
..
..
..
..
..
..
..
..
..
..
..
.8
2.2
Der
ived
units
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
8
2.3
Som
eP
hysi
calC
onst
ants.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.9
2.4
Red
uced
Lenn
ard-
Jone
squ
antit
ies
..
..
..
..
..
..
..
..
..
..
..
..
.9
3.1
The
cubi
cbo
x,th
erh
ombi
cdo
deca
hedr
onan
dth
etr
unca
ted
octa
hedr
on.
..
..
.13
3.2
The
num
ber
ofin
tera
ctio
nsbe
twee
npa
rtic
les...
..
..
..
..
..
..
..
..
.40
4.1
Con
stan
tsfo
rR
ycka
ert-
Bel
lem
ans
pote
ntia
l(kJ
mol
−1).
..
..
..
..
..
..
..
59
4.2
Par
amet
ers
for
the
diffe
rent
func
tiona
lfor
ms
ofth
eno
n-bo
nded
inte
ract
ions
..
..
71
5.1
Par
ticle
type
sin
GR
OM
AC
S..
..
..
..
..
..
..
..
..
..
..
..
..
..
80
5.2
Sta
ticat
omty
pepr
oper
ties
inG
RO
MA
CS.
..
..
..
..
..
..
..
..
..
..
83
5.3
The
topo
logy
(*.to
p)
file.
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.92
5.4
The
mol
ecul
ede
finiti
on..
..
..
..
..
..
..
..
..
..
..
..
..
..
..
.93
7.1
The
GR
OM
AC
Sfil
ety
pes
and
how
they
can
beus
edfo
rin
put/o
utpu
t..
..
..
.11
6
xxL
istofTa
ble
sE
.69
.w
he
el
22
9
ofthefirstn
waters
ism
ade,theordered
trajectorycan
beused
with
anyG
romacs
programto
analyzethe
nclosestw
aters.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-oo
rde
red
.xtcO
utputG
enerictrajectory:
xtctrr
trjgrog96
pdb
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-na
int3
Num
berofatom
sin
am
olecule-d
aint
1A
tomused
forthe
distancecalculation
E.69
wheel
wheelplots
ahelicalw
heelrepresentationofyour
sequence.The
inputsequenceis
inthe
.datfilew
herethe
firstlinecontains
thenum
berofresidues
andeach
consecutiveline
containsa
residuename.
Files
-fn
nn
ice.d
at
InputG
enericdata
file-o
plo
t.ep
sO
utputE
ncapsulatedP
ostScript(tm
)file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-r0int
1T
hefirstresidue
number
inthe
sequence-ro
t0real
0R
otatearound
anangle
initially(90
degreesm
akessense)
-Tstring
Plota
titlein
thecenter
ofthew
heel(mustbe
shorterthan
10characters,
oritw
illoverwrite
thew
heel)-n
nbool
yes
Togglenum
bers
E.70
x2top
x2topgenerates
aprim
itivetopology
froma
coordinatefile.
The
programassum
esallhydrogens
arepresent
when
definingthe
hybridizationfrom
theatom
name
andthe
number
ofbonds.T
heprogram
canalso
make
anrtp
entry,which
youcan
thenadd
tothe
rtpdatabase.
Files
-fco
nf.g
roInput
Generic
structure:gro
g96pdb
tprtpb
tpa-o
ou
t.top
Output,O
pt.Topology
file-r
ou
t.rtpO
utput,Opt.
Residue
Typefile
usedby
pdb2gmx
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int0
Setthe
nicelevel-kb
real4
00
00
0B
ondedforce
constant(kJ/mol/nm 2)
22
8A
pp
en
dix
E.
Ma
nu
alP
age
s
Usi
ng-t
run
ctr
jcon
vca
ntr
unca
te.tr
jin
plac
e,i.e
.w
ithou
tcop
ying
the
file.
Thi
sis
usef
ulw
hen
aru
nha
scr
ashe
ddu
ring
disk
I/O(o
nem
ore
disk
full)
,or
whe
ntw
oco
ntig
uous
traj
ecto
ries
mus
tbe
conc
aten
ated
with
outh
ave
doub
lefr
ames
.
trjc
at
ism
ore
suita
ble
for
conc
aten
atin
gtr
ajec
tory
files
.
Opt
ion
-du
mp
can
beus
edto
extr
acta
fram
eat
orne
aron
esp
ecifi
ctim
efr
omyo
urtr
ajec
tory
.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-otr
ajo
ut.xt
cO
utpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put,
Opt
.S
truc
ture
+m
ass(
db):
tpr
tpb
tpa
gro
g96
pdb
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-f
rfr
am
es.
nd
xIn
put,
Opt
.In
dex
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-t
uen
ump
sT
ime
unit:
ps
,fs
,ns
,us
,ms,
s,m
orh
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
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kip
int
1O
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ery
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ame
-dt
time
0O
nly
writ
efr
ame
whe
ntM
OD
dt=
first
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mp
time
-1D
ump
fram
ene
ares
tspe
cifie
dtim
e(p
s)-t
0tim
e0
Sta
rtin
gtim
e(p
s)(d
efau
lt:do
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hang
e)-t
ime
ste
ptim
e0
Cha
nge
time
step
betw
een
inpu
tfra
mes
(ps)
-pb
cen
umn
on
eP
BC
trea
tmen
t:no
ne
,wh
ole
,in
bo
xor
no
jum
p-u
ren
umre
ctU
nit-
cell
repr
esen
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n:re
ct,t
ric
orco
mp
act
-ce
nte
rbo
oln
oC
ente
rat
oms
inbo
x-b
ox
vect
or0
00
Siz
efo
rne
wcu
bic
box
(def
ault:
read
from
inpu
t)-s
hift
vect
or0
00
All
coor
dina
tes
will
besh
ifted
byfr
amen
r*sh
ift-f
itbo
oln
oF
itm
olec
ule
tore
fstr
uctu
rein
the
stru
ctur
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oln
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rogr
essi
vefit
,to
the
prev
ious
fitte
dst
ruct
ure
-nd
ec
int
3P
reci
sion
for
.xtc
and
.gro
writ
ing
innu
mbe
rof
deci
mal
plac
es-v
el
bool
yes
Rea
dan
dw
rite
velo
citie
sif
poss
ible
-fo
rce
bool
no
Rea
dan
dw
rite
forc
esif
poss
ible
-tru
nc
time
-1T
runc
ate
inpu
ttrj
file
afte
rth
istim
e(p
s)-e
xec
strin
gE
xecu
teco
mm
and
for
ever
you
tput
fram
ew
ithth
efr
ame
num
ber
asar
-gu
men
t-a
pp
bool
no
App
end
outp
ut-s
plit
time
0S
tart
writ
ing
new
file
whe
ntM
OD
split
=fir
sttim
e(p
s)-s
ep
bool
no
Writ
eea
chfr
ame
toa
sepa
rate
.gro
or.p
dbfil
e
E.6
8tr
jord
er
trjo
rder
orde
rsm
olec
ules
acco
rdin
gto
the
smal
lest
dist
ance
toat
oms
ina
refe
renc
egr
oup.
Itw
illas
kfo
ra
grou
pof
refe
renc
eat
oms
and
agr
oup
ofm
olec
ules
.F
orea
chfr
ame
ofth
etr
ajec
tory
the
sele
cted
mol
ecul
esw
illbe
reor
dere
dac
cord
ing
toth
esh
orte
stdi
stan
cebe
twee
nat
omnu
mbe
r-d
ain
the
mol
ecul
ean
dal
lthe
atom
sin
the
refe
renc
egr
oup.
All
atom
sin
the
traj
ecto
ryar
ew
ritte
nto
the
outp
uttr
ajec
tory
.
trjo
rder
can
beus
eful
for
e.g.
anal
yzin
gth
en
wat
ers
clos
est
toa
prot
ein.
Inth
atca
seth
ere
fere
nce
grou
pw
ould
beth
epr
otei
nan
dth
egr
oup
ofm
olec
ules
wou
ldco
nsis
tofa
llth
ew
ater
atom
s.W
hen
anin
dex
grou
p
Cha
pter
1
Intro
duct
ion
1.1
Com
puta
tiona
lChe
mis
try
and
Mol
ecul
arM
odel
ing
GR
OM
AC
Sis
anen
gine
tope
rfor
mm
olec
ular
dyna
mic
ssi
mul
atio
nsan
den
ergy
min
imiz
atio
n.T
hese
are
two
ofth
em
any
tech
niqu
esth
atbe
long
toth
ere
alm
ofco
mpu
tatio
nalc
hem
istr
yan
dm
olec
ular
mod
elin
g.Co
mp
uta
tion
alC
he
mis
tryis
just
ana
me
toin
dica
teth
eus
eof
com
puta
tiona
lte
chni
ques
inch
emis
try,
rang
ing
from
quan
tum
mec
hani
csof
mol
ecul
esto
dyna
mic
sof
larg
eco
mpl
exm
olec
ular
aggr
egat
es.
Mo
lecu
lar
mo
de
lingi
ndic
ates
the
gene
ralp
roce
ssof
desc
ribin
gco
mpl
exch
emic
alsy
stem
sin
term
sof
are
alis
ticat
omic
mod
el,
with
the
aim
toun
ders
tand
and
pred
ictm
acro
scop
icpr
oper
ties
base
don
deta
iled
know
ledg
eon
anat
omic
scal
e.O
ften
mol
ecul
arm
odel
ing
isus
edto
desi
gnne
wm
ater
ials
,for
whi
chth
eac
cura
tepr
edic
tion
ofph
ysic
alpr
oper
ties
ofre
alis
ticsy
stem
sis
requ
ired.
Mac
rosc
opic
phys
ical
prop
ertie
sca
nbe
dist
ingu
ishe
din
(a)
sta
tice
qu
ilib
riu
mp
rop
ert
ies,s
uch
asth
ebi
ndin
gco
nsta
ntof
anin
hibi
tor
toan
enzy
me,
the
aver
age
pote
ntia
len
ergy
ofa
syst
em,
orth
era
dial
dist
ribut
ion
func
tion
ina
liqui
d,an
d(
b)d
yna
mic
or
no
n-e
qu
ilib
riu
mp
rop
ert
ies,su
chas
the
visc
osity
ofa
liqui
d,di
ffusi
onpr
oces
ses
inm
embr
anes
,th
edy
nam
ics
ofph
ase
chan
ges,
reac
tion
kine
tics,
orth
edy
nam
ics
ofde
fect
sin
crys
tals
.T
hech
oice
ofte
chni
que
depe
nds
onth
equ
estio
nas
ked
and
onth
efe
asib
ility
ofth
em
etho
dto
yiel
dre
liabl
ere
sults
atth
epr
esen
tsta
teof
the
art.
Idea
lly,t
he(r
elat
ivis
tic)
time-
depe
nden
tSch
rod
inge
req
uatio
nde
scrib
esth
epr
oper
ties
ofm
olec
ular
syst
ems
with
high
accu
racy
,bu
tan
ythi
ngm
ore
com
plex
than
the
equi
libriu
mst
ate
ofa
few
atom
sca
nnot
beha
ndle
dat
this
ab
initi
ole
vel.
Thu
sap
prox
imat
ions
are
man
dato
ry;
the
high
erth
eco
mpl
exity
ofa
syst
eman
dth
elo
nger
the
time
span
ofth
epr
oces
ses
ofin
tere
stis
,the
mor
ese
vere
appr
oxim
atio
nsar
ere
quire
d.A
tace
rtai
npo
int(
reac
hed
very
muc
hea
rlier
than
one
wou
ldw
ish)
thea
bin
itio
appr
oach
mus
tbe
augm
ente
dor
repl
aced
bye
mp
iric
alp
aram
eter
izat
ion
ofth
em
odel
used
.W
here
sim
ulat
ions
base
don
phys
ical
prin
cipl
esof
atom
icin
tera
ctio
nsst
illfa
ildu
eto
the
com
plex
ityof
the
syst
em(a
sis
unfo
rtun
atel
yst
illth
eca
sefo
rth
epr
edic
tion
ofpr
otei
nfo
ldin
g;bu
t:th
ere
isho
pe!)
mol
ecul
arm
odel
ing
isba
sed
entir
ely
ona
sim
ilarit
yan
alys
isof
know
nst
ruct
ural
and
chem
ical
data
.T
heQ
SA
Rm
etho
ds(Q
uant
itativ
eS
truc
ture
-Act
ivity
Rel
atio
ns)
and
man
yho
mol
ogy-
base
dpr
otei
nst
ruct
ure
pred
ictio
nsbe
long
toth
ela
tter
cate
gory
.
Mac
rosc
opic
prop
ertie
sar
eal
way
sen
sem
ble
aver
ages
over
are
pres
enta
tive
stat
istic
alen
sem
ble
2C
ha
pte
r1
.In
trod
uctio
n
(eitherequilibrium
ornon-equilibrium
)of
molecular
systems.
For
molecular
modeling
thishas
two
importantconsequences:
•T
heknow
ledgeof
asingle
structure,even
ifit
isthe
structureof
theglobal
energym
in-im
um,
isnot
sufficient.It
isnecessary
togenerate
arepresentative
ensemble
ata
giventem
perature,inorder
tocom
putem
acroscopicproperties.
Butthis
isnotenough
tocom
putetherm
odynamic
equilibriumproperties
thatare
basedon
freeenergies,
suchas
phaseequi-
libria,bindingconstants,solubilities,relative
stabilityofm
olecularconform
ations,etc.T
hecom
putationof
freeenergies
andtherm
odynamic
potentialsrequires
specialextensionsof
molecular
simulation
techniques.
•W
hilem
olecularsim
ulationsin
principleprovide
atomic
detailsof
thestructures
andm
o-tions,
suchdetails
areoften
notrelevant
forthe
macroscopic
propertiesof
interest.T
hisopens
thew
ayto
simplify
thedescription
ofinteractionsand
averageover
irrelevantdetails.T
hescience
ofstatistical
mechanics
providesthe
theoreticalfram
ework
forsuch
simpli-
fications.T
hereis
ahierarchy
ofm
ethodsranging
fromconsidering
groupsof
atoms
asone
unit,describing
motion
ina
reducednum
berof
collectivecoordinates,
averagingover
solventm
oleculesw
ithpotentials
ofm
eanforce
combined
with
stochasticdynam
ics[
4],to
me
sosco
pic
dyn
am
icsdescribingdensities
ratherthan
atoms
andfluxes
asresponse
totherm
odynamic
gradientsrather
thanvelocities
oraccelerations
asresponse
toforces
[5].
For
thegeneration
ofarepresentative
equilibriumensem
bletw
om
ethodsare
available:(
a)M
on
teC
arlo
simu
latio
nsand
(b)Mo
lecu
larD
yna
mics
simu
latio
ns.F
orthegeneration
ofnon-equilibriumensem
blesand
forthe
analysisofdynam
icevents,
onlythe
secondm
ethodis
appropriate.W
hileM
onteC
arlosim
ulationsare
more
simple
thanM
D(they
donotrequire
thecom
putationofforces),
theydo
notyieldsignificantly
betterstatisticsthan
MD
ina
givenam
ountofcomputertim
e.T
here-fore
MD
isthe
more
universaltechnique.Ifa
startingconfiguration
isvery
farfrom
equilibrium,
theforces
may
beexcessively
largeand
theM
Dsim
ulationm
ayfail.
Inthose
casesa
robuste
ne
rgy
min
imiza
tionis
required.A
notherreason
toperform
anenergy
minim
izationis
therem
ovalofallkinetic
energyfrom
thesystem
:if
several’snapshots’fromdynam
icsim
ulationsm
ustbe
com-
pared,energym
inimization
reducesthe
thermal’noise’in
thestructures
andpotentialenergies,so
thattheycan
becom
paredbetter.
1.2M
olecularD
ynamics
Sim
ulations
MD
simulations
solveN
ewton’s
equationsofm
otionfor
asystem
ofN
interactingatom
s:
mi ∂
2ri
∂t 2
=F
i ,i=
1...N
.(1.1)
The
forcesare
thenegative
derivativesofa
potentialfunctionV
(r1 ,r
2 ,...,rN
):
Fi =
−∂V
∂r
i(1.2)
The
equationsare
solvedsim
ultaneouslyin
small
time
steps.T
hesystem
isfollow
edfor
some
time,
takingcare
thatthe
temperature
andpressure
remain
atthe
requiredvalues,
andthe
coor-dinates
arew
rittento
anoutput
fileat
regularintervals.
The
coordinatesas
afunction
oftim
e
E.6
7.
trjconv
22
7
E.67
trjconv
trjconvcan
converttrajectoryfiles
inm
anyw
ays:1.from
oneform
attoanother
2.selectasubsetofatom
s3.rem
oveperiodicity
fromm
olecules4.keep
multim
ericm
oleculestogether
5.centeratom
sin
thebox
6.fitatoms
toreference
structure7.reduce
thenum
beroffram
es8.change
thetim
estamps
ofthefram
es(
-t0and
-time
step
)
The
programtrjca
tcan
concatenatem
ultipletrajectory
files.
Currently
sevenform
atsare
supportedfor
inputandoutput:
.xtc,.trr
,.trj,.g
ro,.g
96
,.pd
band
.g8
7.
The
fileform
atsare
detectedfrom
thefile
extension.T
heprecision
of.xtc
and.g
rooutput
istaken
fromthe
inputfilefor.xtc
,.g
roand
.pd
b,
andfrom
the-nd
ec
optionfor
otherinputform
ats.T
heprecision
isalw
aystaken
from-nd
ec
,when
thisoption
isset.
Allother
formats
havefixed
precision..trr
and.trj
outputcanbe
singleor
doubleprecision,depending
onthe
precisionofthe
trjconvbinary.
Note
thatvelocitiesare
onlysupported
in.trr
,.trj,.g
roand
.g9
6files.
Option
-ap
pcan
beused
toappend
outputtoan
existingtrajectory
file.N
ochecks
areperform
edto
ensureintegrity
ofthe
resultingcom
binedtrajectory
file..pdb
filesw
ithallfram
esconcatenated
canbe
viewed
with
rasm
ol
-nm
rpd
b.
Itis
possibleto
selectpart
ofyour
trajectoryand
write
itout
toa
newtrajectory
filein
orderto
savedisk
space,e.g.
forleaving
outthe
water
froma
trajectoryof
aprotein
inw
ater.A
LWAY
Sput
theoriginal
trajectoryon
tape!W
erecom
mend
touse
theportable
.xtcform
atfor
youranalysis
tosave
diskspace
andto
haveportable
files.
There
aretw
ooptions
forfitting
thetrajectory
toa
referenceeither
foressentialdynam
icsanalysis
orfor
whatever.
The
firstoptionis
justplainfitting
toa
referencestructure
inthe
structurefile,the
secondoption
isa
progressivefit
inw
hichthe
firsttim
eframe
isfitted
tothe
referencestructure
inthe
structurefile
toobtain
andeach
subsequenttim
eframe
isfitted
tothe
previouslyfitted
structure.T
hisw
aya
continuoustrajectory
isgenerated,
which
might
notbe
thecase
when
usingthe
regularfit
method,
e.g.w
henyour
proteinundergoes
largeconform
ationaltransitions.
Option
-pb
csets
thetype
ofperiodic
boundarycondition
treatment.w
ho
leputs
theatom
sin
thebox
andthen
makes
brokenm
oleculesw
hole(a
runinput
fileis
required).in
bo
xputs
allthe
atoms
inthe
box.n
oju
mp
checksif
atoms
jump
acrossthe
boxand
thenputs
themback.
This
hasthe
effectthat
allm
oleculesw
illremain
whole
(providedthey
were
whole
inthe
initialconformation),note
thatthisensures
acontinuous
trajectorybutm
oleculesm
aydiffuse
outofthebox.
The
startingconfiguration
forthisprocedure
istaken
fromthe
structurefile,ifone
issupplied,otherw
iseitis
thefirstfram
e.-p
bc
isignored
when-fit
of-pfit
isset,in
thatcasem
oleculesw
illbem
adew
hole.
Option
-ur
setsthe
unitcellrepresentationforoptions
wh
ole
andin
bo
xof-p
bc
.A
llthreeoptions
givedifferent
resultsfor
triclincboxes
andidenticalresults
forrectangular
boxes.re
ctis
theordinary
brickshape.tric
isthe
triclinicunitcell.co
mp
act
putsallatom
satthe
closestdistancefrom
thecenter
ofthebox.
This
canbe
usefulforvisualizing
e.g.truncated
octahedrons.
Option
-cen
ter
centersthe
systemin
thebox.
The
usercan
selectthegroup
which
isused
todeterm
inethe
geometricalcenter.
Use
option-pbc
wh
ole
inaddition
to-ce
nte
rw
henyou
want
allmolecules
inthe
boxafter
thecentering.
With
-dt
itispossible
toreduce
thenum
beroffram
esin
theoutput.
This
optionrelies
onthe
accuracyof
thetim
esin
yourinputtrajectory,so
iftheseare
inaccurateuse
the-tim
este
poption
tom
odifythe
time
(thiscan
bedone
simultaneously).
22
6A
pp
en
dix
E.
Ma
nu
alP
age
s
E.6
5tp
bcon
v
tpbc
onv
can
edit
run
inpu
tfile
sin
two
way
s.
1st.
bycr
eatin
ga
run
inpu
tfile
for
aco
ntin
uatio
nru
nw
hen
your
sim
ulat
ion
has
cras
hed
due
toe.
g.a
full
disk
,orb
ym
akin
ga
cont
inua
tion
run
inpu
tfile
.N
ote
that
afr
ame
with
coor
dina
tes
and
velo
citie
sis
need
ed,
whi
chm
eans
that
whe
nyo
une
ver
writ
eve
loci
ties,
you
can
not
use
tpbc
onv
and
you
have
tost
art
the
run
agai
nfr
omth
ebe
ginn
ing.
2nd.
bycr
eatin
ga
tpx
file
for
asu
bset
ofyo
uror
igin
altp
xfil
e,w
hich
isus
eful
whe
nyo
uw
antt
ore
mov
eth
eso
lven
tfro
myo
urtp
xfil
e,or
whe
nyo
uw
antt
om
ake
e.g.
apu
reC
atp
xfil
e.W
AR
NIN
G:t
his
tpx
file
isno
tful
lyfu
nctio
nal.
File
s-s
top
ol.t
pr
Inpu
tG
ener
icru
nin
put:
tpr
tpb
tpa
-ftr
aj.t
rrIn
put,
Opt
.F
ullp
reci
sion
traj
ecto
ry:
trr
trj
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-o
tpxo
ut.tp
rO
utpu
tG
ener
icru
nin
put:
tpr
tpb
tpa
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t0
Set
the
nice
leve
l-t
ime
real
-1C
ontin
uefr
omfr
ame
atth
istim
e(p
s)in
stea
dof
the
last
fram
e-e
xte
nd
real
0E
xten
dru
ntim
eby
this
amou
nt(p
s)-u
ntil
real
0E
xten
dru
ntim
eun
tilth
isen
ding
time
(ps)
-un
con
stra
ine
dbo
olye
sF
ora
cont
inuo
ustr
ajec
tory
,th
eco
nstr
aint
ssh
ould
not
beso
lved
befo
reth
efir
stst
ep(d
efau
lt)
E.6
6tr
jcat
trjc
atco
ncat
enat
esse
vera
linp
uttr
ajec
tory
files
inso
rted
orde
r.In
case
ofdo
uble
time
fram
esth
eon
ein
the
late
rfil
eis
used
.B
ysp
ecify
ing-s
ettim
eyo
uw
illbe
aske
dfo
rth
est
artt
ime
ofea
chfil
e.T
hein
putfi
les
are
take
nfr
omth
eco
mm
and
line,
such
that
aco
mm
and
like
trjc
at
-ofix
ed
.trr
*.tr
rsh
ould
doth
etr
ick.
File
s-o
tra
jou
t.xt
cO
utpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-bre
al-1
Firs
ttim
eto
use
-ere
al-1
Last
time
tous
e-d
tre
al0
Onl
yw
rite
fram
ew
hen
tMO
Ddt
=fir
sttim
e-p
rec
int
3P
reci
sion
for
.xtc
and
.gro
writ
ing
innu
mbe
rof
deci
mal
plac
es-v
el
bool
yes
Rea
dan
dw
rite
velo
citie
sif
poss
ible
-se
ttim
ebo
oln
oC
hang
est
artin
gtim
ein
tera
ctiv
ely
-so
rtbo
olye
sS
ortt
raje
ctor
yfil
es(n
otfr
ames
)
1.2
.M
ole
cula
rD
yna
mic
sS
imu
latio
ns
3
type
ofw
aven
umbe
rty
peof
bond
vibr
atio
n(c
m−
1)
C-H
,O-H
,N-H
stre
tch
3000
–350
0C
=C
,C=
O,
stre
tch
1700
–200
0H
OH
bend
ing
1600
C-C
stre
tch
1400
–160
0H
2C
Xsc
iss,
rock
1000
–150
0C
CC
bend
ing
800–
1000
O-H···O
libra
tion
400–
700
O-H···O
stre
tch
50–
200
Tabl
e1.
1:Ty
pica
lvib
ratio
nalf
requ
enci
es(w
aven
umbe
rs)
inm
olec
ules
and
hydr
ogen
-bon
ded
liq-
uids
.C
ompa
rekT/h
=20
0cm
−1
at30
0K
.
repr
esen
tatr
aje
cto
ryof
the
syst
em.
Afte
rin
itial
chan
ges,
the
syst
emw
illus
ually
reac
han
eq
ui-
libriu
mst
ate.
By
aver
agin
gov
eran
equi
libriu
mtr
ajec
tory
man
ym
acro
scop
icpr
oper
ties
can
beex
trac
ted
from
the
outp
utfil
e.
Itis
usef
ulat
this
poin
tto
cons
ider
the
limita
tions
ofM
Dsi
mul
atio
ns.
The
user
shou
ldbe
awar
eof
thos
elim
itatio
nsan
dal
way
spe
rfor
mch
ecks
onkn
own
expe
rimen
talp
rope
rtie
sto
asse
ssth
eac
cura
cyof
the
sim
ulat
ion.
We
listt
heap
prox
imat
ions
belo
w.
The
sim
ulat
ions
are
clas
sica
lU
sing
New
ton’
seq
uatio
nof
mot
ion
auto
mat
ical
lyim
plie
sth
eus
eof
cla
ssic
alm
ech
an
icsto
desc
ribe
the
mot
ion
ofat
oms.
Thi
sis
allr
ight
for
mos
tat
oms
atno
rmal
tem
pera
ture
s,bu
tth
ere
are
exce
ptio
ns.
Hyd
roge
nat
oms
are
quite
light
and
the
mot
ion
ofpr
oton
sis
som
etim
esof
esse
ntia
lqua
ntum
mec
hani
calc
hara
cter
.F
orex
ampl
e,a
prot
onm
aytu
nn
elth
roug
ha
po-
tent
ialb
arrie
rin
the
cour
seof
atr
ansf
erov
era
hydr
ogen
bond
.S
uch
proc
esse
sca
nnot
bepr
oper
lytr
eate
dby
clas
sica
ldyn
amic
s!H
eliu
mliq
uid
atlo
wte
mpe
ratu
reis
anot
here
xam
ple
whe
recl
assi
calm
echa
nics
brea
ksdo
wn.
Whi
lehe
lium
may
notd
eepl
yco
ncer
nus
,the
high
freq
uenc
yvi
brat
ions
ofco
vale
ntbo
nds
shou
ldm
ake
usw
orry
!T
hest
atis
tical
mec
hani
csof
acl
assi
calh
arm
onic
osci
llato
rdi
ffers
appr
ecia
bly
from
that
ofa
real
quan
tum
osci
llato
r,w
hen
the
reso
nanc
efr
eque
ncyν
appr
oxim
ates
orex
ceed
sk BT/h
.N
owat
room
tem
per-
atur
eth
ew
aven
umbe
rσ=
1/λ
=ν/c
atw
hichhν
=k
BT
isap
prox
imat
ely
200
cm−1.
Thu
sal
lfre
quen
cies
high
erth
an,s
ay,1
00cm−1
are
susp
ecto
fmis
beha
vior
incl
assi
cals
im-
ulat
ions
.T
his
mea
nsth
atpr
actic
ally
allb
ond
and
bond
-ang
levi
brat
ions
are
susp
ect,
and
even
hydr
ogen
-bon
ded
mot
ions
astr
ansl
atio
nalo
rlib
ratio
nalH
-bon
dvi
brat
ions
are
beyo
ndth
ecl
assi
call
imit
(see
Tabl
e1.1)
.W
hatc
anw
edo
?
Wel
l,ap
artf
rom
real
quan
tum
-dyn
amic
alsi
mul
atio
ns,w
eca
ndo
eith
erof
two
thin
gs:
(a)
Ifw
epe
rfor
mM
Dsi
mul
atio
nsus
ing
harm
onic
osci
llato
rsfo
rbo
nds,
we
shou
ldm
ake
corr
ectio
nsto
the
tota
lint
erna
lene
rgyU
=E
kin
+E
potan
dsp
ecifi
che
atCV
(and
toen
trop
yS
and
free
ener
gyAorG
ifth
ose
are
calc
ulat
ed).
The
corr
ectio
nsto
the
ener
gyan
dsp
ecifi
che
atof
aon
e-di
men
sion
alos
cilla
tor
with
freq
uenc
yν
are:
[6]
UQ
M=U
cl+kT
( 1 2x−
1+
x
ex−
1
)(1
.3)
4C
ha
pte
r1
.In
trod
uctio
n
CQ
MV
=C
clV
+k (
x2e
x
(ex−
1)2−
1 ),
(1.4)
where
x=hν/kT
.T
heclassicaloscillator
absorbstoo
much
energy(
kT
),while
thehigh-
frequencyquantum
oscillatoris
inits
groundstate
atthezero-pointenergy
levelof12 hν.
(b)W
ecan
treatthebonds
(andbond
angles)as
con
strain
tsinthe
equationofm
otion.T
herationalbehind
thisis
thata
quantumoscillator
inits
groundstate
resembles
aconstrained
bondm
oreclosely
thana
classicaloscillator.
Agood
practicalreason
forthis
choiceis
thatthe
algorithmcan
uselarger
time
stepsw
henthe
highestfrequencies
arerem
oved.In
practicethe
time
stepcan
bem
adefourtim
esas
largew
henbonds
areconstrained
thanw
henthey
areoscillators
[7].G
RO
MA
CS
hasthis
optionfor
thebonds,and
forthe
bondangles.
The
flexibilityofthe
latteris
ratheressentialto
allowfor
therealistic
motion
andcoverage
ofconfigurationalspace[
7].
Electrons
arein
theground
stateIn
MD
we
useaco
nse
rvativeforce
fieldthatis
afunction
ofthepositions
ofatoms
only.T
hism
eansthat
theelectronic
motions
arenot
considered:the
electronsare
supposedto
adjusttheir
dynamics
infinitelyfast
when
theatom
icpositions
change(theB
orn
-Op
pe
nh
eim
er
approximation),and
remain
intheir
groundstate.
This
isreally
allright,almostalw
ays.B
utof
course,electron
transferprocesses
andelectronically
excitedstates
cannot
betreated.
Neither
canchem
icalreactionsbe
treatedproperly,
butthereare
otherreasons
toshy
away
fromreactions
forthe
time
being.
Force
fieldsare
approximate
Force
fieldsprovide
theforces.
They
arenotreally
apartofthe
simulation
method
andtheir
parameters
canbe
user-modified
asthe
needarises
orknow
ledgeim
proves.B
utthe
formof
theforces
thatcan
beused
ina
particularprogram
issubject
tolim
itations.T
heforce
fieldthat
isincorporated
inG
RO
MA
CS
isdescribed
inC
hapter4.
Inthe
presentversion
theforce
fieldis
pair-additive(apartfrom
long-rangecoulom
bforces),itcannotincorporate
polarizabilities,and
itdoes
notcontain
fine-tuningof
bondedinteractions.
This
urgesthe
inclusionof
some
limitations
inthis
listbelow
.F
orthe
restit
isquite
usefuland
fairlyreliable
forbio
macro-m
oleculesin
aqueoussolution!
The
forcefield
ispair-additive
This
means
thatallnon
-bo
nd
edforces
resultfromthe
sumofnon-bonded
pairinteractions.
Non
pair-additiveinteractions,
them
ostimportantexam
pleofw
hichis
interactionthrough
atomic
polarizability,are
representedbye
ffective
pa
irp
ote
ntia
ls.O
nlyaverage
nonpair-
additivecontributions
areincorporated.
This
alsom
eansthat
thepair
interactionsare
notpure,i.e.,they
arenotvalid
forisolatedpairs
orforsituationsthatdifferappreciably
fromthe
testsystem
son
which
them
odelsw
ereparam
eterized.In
fact,the
effectivepair
potentialsare
notthat
badin
practice.B
utthe
omission
ofpolarizability
alsom
eansthat
electronsin
atoms
donotprovide
adielectric
constantasthey
should.F
orexam
ple,realliquid
alkaneshave
adielectric
constantofslightlym
orethan
2,which
reducethe
long-rangeelectrostatic
interactionbetw
een(partial)
charges.T
husthe
simulations
willexaggerate
thelong-range
Coulom
bterm
s.Luckily,the
nextitemcom
pensatesthis
effectabit.
Long-rangeinteractions
arecut-off
Inthis
versionG
RO
MA
CS
always
usesa
cut-offradius
forthe
Lennard-Jonesinteractions
E.6
4.
pro
ton
ate
22
5
-ncle
an
.nd
xO
utput,Opt.
Indexfile
-qcle
an
.pd
bO
utput,Opt.
Generic
structure:gro
g96pdb
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int0
Setthe
nicelevel-m
erg
ebool
no
Merge
multiple
chainsinto
onem
olecule-in
ter
booln
oS
etthenext6
optionsto
interactive-ss
booln
oInteractive
SS
bridgeselection
-ter
booln
oInteractive
terminiselection,iso
charged-lys
booln
oInteractive
Lysineselection,iso
charged-a
spbool
no
InteractiveA
sparticA
cidselection,iso
charged-g
lubool
no
InteractiveG
lutamic
Acid
selection,isocharged
-his
booln
oInteractive
Histidine
selection,isochecking
H-bonds
-an
gle
real1
35
Minim
umhydrogen-donor-acceptor
anglefor
aH
-bond(degrees)
-dist
real0
.3M
aximum
donor-acceptordistance
fora
H-bond
(nm)
-un
abool
no
Select
aromatic
ringsw
ithunited
CH
atoms
onP
henylalanine,T
rypto-phane
andTyrosine
-sort
boolye
sS
orttheresidues
accordingto
database-H
14
booln
oU
se1-4
interactionsbetw
eenhydrogen
atoms
-ign
hbool
no
Ignorehydrogen
atoms
thatarein
thepdb
file-a
lldih
booln
oG
enerateallproper
dihedrals-d
um
my
enumn
on
eC
onvertatoms
todum
my
atoms:n
on
e,h
ydro
ge
ns
oraro
ma
tics-h
ea
vyhbool
no
Make
hydrogenatom
sheavy
-de
ute
rate
booln
oC
hangethe
mass
ofhydrogensto
2am
u
E.64
protonate
pro
ton
ate
reads(a)
conformation(s)
andadds
allm
issinghydrogens
asdefined
inffg
mx2
.hd
b.
Ifonly
-sis
specified,thisconform
ationw
illbeprotonated,ifalso
-fis
specified,theconform
ation(s)w
illbe
readfrom
thisfile
which
canbe
eithera
singleconform
ationor
atrajectory.
Ifapdb
fileis
supplied,residuenam
esm
ightnotcorrespondto
tothe
GR
OM
AC
Snam
ingconventions,in
which
casethese
residuesw
illprobablynotbe
properlyprotonated.
Ifanindex
fileis
specified,pleasenote
thattheatom
numbers
shouldcorrespond
tothe
protonatedstate.
Files
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-f
traj.xtc
Input,Opt.
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput,O
pt.Index
file-o
pro
ton
ate
d.xtc
Output
Generic
trajectory:xtc
trrtrjgro
g96pdb
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int0
Setthe
nicelevel-b
time
-1F
irstframe
(ps)to
readfrom
trajectory-e
time
-1Lastfram
e(ps)
toread
fromtrajectory
-dt
time
-1O
nlyuse
frame
when
tMO
Ddt=
firsttime
(ps)
22
4A
pp
en
dix
E.
Ma
nu
alP
age
s
E.6
3pd
b2gm
x
Thi
spr
ogra
mre
ads
apd
bfil
e,le
tsyo
uch
oose
afo
rcefi
eld,
read
sso
me
data
base
files
,ad
dshy
drog
ens
toth
em
olec
ules
and
gene
rate
sco
ordi
nate
sin
Gro
mac
s(G
rom
os)
form
atan
da
topo
logy
inG
rom
acs
form
at.
The
sefil
esca
nsu
bseq
uent
lybe
proc
esse
dto
gene
rate
aru
nin
putfi
le.
Not
eth
ata
pdb
file
isno
thin
gm
ore
than
afil
efo
rmat
,and
itne
edno
tnec
essa
rily
cont
ain
apr
otei
nst
ruct
ure.
Eve
ryki
ndof
mol
ecul
efo
rw
hich
ther
eis
supp
ort
inth
eda
taba
seca
nbe
conv
erte
d.If
ther
eis
nosu
ppor
tin
the
data
base
,you
can
add
ityo
urse
lf.
The
prog
ram
has
limite
din
telli
genc
e,it
read
sa
num
ber
ofda
taba
sefil
es,
that
allo
wit
tom
ake
spec
ial
bond
s(C
ys-C
ys,
Hem
e-H
is,
etc.
),if
nece
ssar
yth
isca
nbe
done
man
ually
.T
hepr
ogra
mca
npr
ompt
the
user
tose
lect
whi
chki
ndof
LYS
,A
SP,
GLU
,C
YS
orH
ISre
sidu
esh
ew
ants
.F
orLY
Sth
ech
oice
isbe
twee
nLY
S(t
wo
prot
ons
onN
Z)
orLY
SH
(thr
eepr
oton
s,de
faul
t),
for
AS
Pan
dG
LUun
prot
onat
ed(d
efau
lt)or
prot
onat
ed,
for
HIS
the
prot
onca
nbe
eith
eron
ND
1(H
ISA
),on
NE
2(H
ISB
)or
onbo
th(H
ISH
).B
yde
faul
tthe
sese
lect
ions
are
done
auto
mat
ical
ly.
For
His
,th
isis
base
don
anop
timal
hydr
ogen
bond
ing
conf
orm
atio
n.H
ydro
gen
bond
sar
ede
fined
base
don
asi
mpl
ege
omet
riccr
iteriu
m,
spec
ified
byth
em
axim
umhy
drog
en-d
onor
-acc
epto
ran
gle
and
dono
r-ac
cept
ordi
stan
ce,w
hich
are
setb
y-a
ng
lean
d-d
ist
resp
ectiv
ely.
Opt
ion
-me
rge
will
ask
ifyo
uw
antt
om
erge
cons
ecut
ive
chai
nsin
toon
em
olec
ule,
this
can
beus
eful
for
conn
ectin
gch
ains
with
adi
sulfi
debr
igde
.
pdb2
gmx
will
also
chec
kth
eoc
cupa
ncy
field
ofth
epd
bfil
e.If
any
ofth
eoc
cupa
ncci
esar
eno
ton
e,in
dica
ting
that
the
atom
isno
tres
olve
dw
elli
nth
est
ruct
ure,
aw
arni
ngm
essa
geis
issu
ed.
Whe
na
pdb
file
does
noto
rigin
ate
from
anX
-Ray
stru
ctur
ede
term
inat
ion
allo
ccup
ancy
field
sm
aybe
zero
.E
ither
way
,it
isup
toth
eus
erto
verif
yth
eco
rrec
tnes
sof
the
inpu
tdat
a(r
ead
the
artic
le!)
.
Dur
ing
proc
essi
ngth
eat
oms
will
bere
orde
red
acco
rdin
gto
Gro
mac
sco
nven
tions
.W
ith-n
anin
dex
file
can
bege
nera
ted
that
cont
ains
one
grou
pre
orde
red
inth
esa
me
way
.T
his
allo
ws
you
toco
nver
taG
rom
ostr
ajec
tory
and
coor
dina
tefil
eto
Gro
mos
.T
here
ison
elim
itatio
n:re
orde
ring
isdo
neaf
ter
the
hydr
ogen
sar
est
rippe
dfr
omth
ein
puta
ndbe
fore
new
hydr
ogen
sar
ead
ded.
Thi
sm
eans
that
you
shou
ldno
tuse
-ig
nh
.
The
.gro
and
.g9
6fil
efo
rmat
sdo
nots
uppo
rtch
ain
iden
tifier
s.T
here
fore
itis
usef
ulto
ente
ra
pdb
file
nam
eat
the-o
optio
nw
hen
you
wan
tto
conv
erta
mul
ticha
inpd
bfil
e.
-so
rtw
illso
rtal
lres
idue
sac
cord
ing
toth
eor
deri
nth
eda
taba
se,s
omet
imes
this
isne
cess
ary
toge
tcha
rge
grou
psto
geth
er.
-alld
ihw
illge
nera
teal
lpro
per
dihe
dral
sin
stea
dof
only
thos
ew
ithas
few
hydr
ogen
sas
poss
ible
,thi
sis
usef
ulfo
rus
ew
ithth
eC
harm
mfo
rcefi
eld.
The
optio
n-d
um
my
rem
oves
hydr
ogen
and
fast
impr
oper
dihe
dral
mot
ions
.A
ngul
aran
dou
t-of
-pla
nem
otio
nsca
nbe
rem
oved
bych
angi
nghy
drog
ens
into
dum
my
atom
san
dfix
ing
angl
es,
whi
chfix
esth
eir
posi
tion
rela
tive
tone
ighb
orin
gat
oms.
Add
ition
ally
,all
atom
sin
the
arom
atic
rings
ofth
est
anda
rdam
ino
acid
s(i.
e.P
HE
,T
RP,
TY
Ran
dH
IS)
can
beco
nver
ted
into
dum
my
atom
s,el
min
atin
gth
efa
stim
prop
erdi
hedr
alflu
ctua
tions
inth
ese
rings
.N
ote
that
inth
isca
seal
loth
erhy
drog
enat
oms
are
also
conv
erte
dto
dum
my
atom
s.T
hem
ass
ofal
lato
ms
that
are
conv
erte
din
todu
mm
yat
oms,
isad
ded
toth
ehe
avy
atom
s.
Als
osl
owin
gdo
wn
ofdi
hedr
alm
otio
nca
nbe
done
with-h
ea
vyh
done
byin
crea
sing
the
hydr
ogen
-mas
sby
afa
ctor
of4.
Thi
sis
also
done
for
wat
erhy
drog
ens
tosl
owdo
wn
the
rota
tiona
lmot
ion
ofw
ater
.T
hein
crea
sein
mas
sof
the
hydr
ogen
sis
subt
ract
edfr
omth
ebo
nded
(hea
vy)
atom
soth
atth
eto
talm
ass
ofth
esy
stem
rem
ains
the
sam
e.R
efer
ence
Fee
nstr
aet
al.,
J.C
ompu
t.C
hem
.20
,786
(199
9).
File
s-f
eiw
it.p
db
Inpu
tG
ener
icst
ruct
ure:
gro
g96
pdb
tpr
tpb
tpa
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nf.g
roO
utpu
tG
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icst
ruct
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gro
g96
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-pto
po
l.to
pO
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tTo
polo
gyfil
e-i
po
sre
.itp
Out
put
Incl
ude
file
for
topo
logy
1.3
.E
ne
rgy
Min
imiz
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nd
Se
arc
hM
eth
od
s5
and
som
etim
esal
sofo
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oulo
mb.
Due
toth
em
inim
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age
conv
entio
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nly
one
imag
eof
each
part
icle
inth
epe
riodi
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unda
ryco
nditi
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isco
nsid
ered
for
apa
irin
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fran
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the
box
size
.T
hati
sst
illpr
etty
big
for
larg
esy
stem
s,an
dtr
oubl
eis
only
expe
cted
for
syst
ems
cont
aini
ngch
arge
dpa
rtic
les.
But
then
real
bad
thin
gsm
ayha
ppen
,lik
eac
cum
ulat
ion
ofch
arge
sat
the
cut-
offb
ound
ary
orve
ryw
rong
ener
gies
!F
orsu
chsy
stem
syo
ush
ould
cons
ider
usin
gon
eof
the
impl
emen
ted
long
-ran
geel
ectr
osta
tical
gorit
hms.
Bou
ndar
yco
nditi
ons
are
unna
tura
lS
ince
syst
emsi
zeis
smal
l(ev
en10
,000
part
icle
sis
smal
l),a
clus
ter
ofpa
rtic
les
will
have
alo
tof
unw
ante
dbo
unda
ryw
ithits
envi
ronm
ent
(vac
uum
).T
his
we
mus
tav
oid
ifw
ew
ish
tosi
mul
ate
abu
lksy
stem
.S
ow
eus
epe
riodi
cbo
unda
ryco
nditi
ons,
toav
oid
real
phas
ebo
unda
ries.
But
liqui
dsar
eno
tcr
ysta
ls,
soso
met
hing
unna
tura
lre
mai
ns.
Thi
site
mis
men
tione
din
the
last
plac
ebe
caus
eit
isth
ele
aste
vilo
fall.
For
larg
esy
stem
sth
eer
rors
are
smal
l,bu
tfor
smal
lsys
tem
sw
itha
loto
fint
erna
lspa
tialc
orre
latio
n,th
epe
riodi
cbo
unda
ries
may
enha
nce
inte
rnal
corr
elat
ion.
Inth
atca
se,b
ewar
ean
dte
stth
ein
fluen
ceof
syst
emsi
ze.
Thi
sis
espe
cial
lyim
port
ant
whe
nus
ing
latti
cesu
ms
for
long
-ran
geel
ectr
osta
tics,
sinc
eth
ese
are
know
nto
som
etim
esin
trod
uce
extr
aor
derin
g.
1.3
Ene
rgy
Min
imiz
atio
nan
dS
earc
hM
etho
ds
As
men
tione
din
sec.1
.1,i
nm
any
case
sen
ergy
min
imiz
atio
nis
requ
ired.
GR
OM
AC
Spr
ovid
esa
sim
ple
form
oflo
cale
nerg
ym
inim
izat
ion,
theste
ep
est
de
sce
nt
met
hod.
The
pote
ntia
lene
rgy
func
tion
ofa
(mac
ro)m
olec
ular
syst
emis
ave
ryco
mpl
exla
ndsc
ape
(or
hyp
er
surf
ace
)in
ala
rge
num
ber
ofdi
men
sion
s.It
has
one
deep
est
poin
t,th
eg
lob
al
min
imu
man
da
very
larg
enu
mbe
rofl
oca
lm
inim
a,w
here
all
deriv
ativ
esof
the
pote
ntia
len
ergy
func
tion
with
resp
ect
toth
eco
ordi
nate
sar
eze
roan
dal
lse
cond
deriv
ativ
esar
eno
nneg
ativ
e.T
hem
atrix
ofse
cond
deriv
ativ
es,
whi
chis
calle
dth
eHe
ssia
nm
atr
ix,ha
sno
nneg
ativ
eei
genv
alue
s;on
lyth
eco
llect
ive
coor
dina
tes
that
corr
espo
ndto
tran
slat
ion
and
rota
tion
(for
anis
olat
edm
olec
ule)
have
zero
eige
nval
ues.
Inbe
twee
nth
elo
calm
inim
ath
ere
are
sad
dle
po
ints,
whe
reth
eH
essi
anm
atrix
has
only
one
nega
tive
eige
nval
ue.
The
sepo
ints
are
the
mou
ntai
npa
sses
thro
ugh
whi
chth
esy
stem
can
mig
rate
from
one
loca
lmin
imum
toan
othe
r.
Kno
wle
dge
ofal
lloc
alm
inim
a,in
clud
ing
the
glob
alon
e,an
dof
alls
addl
epo
ints
wou
lden
able
usto
desc
ribe
the
rele
vant
stru
ctur
esan
dco
nfor
mat
ions
and
thei
rfr
eeen
ergi
es,
asw
ell
asth
edy
nam
ics
ofst
ruct
ural
tran
sitio
ns.
Unf
ortu
nate
ly,t
hedi
men
sion
ality
ofth
eco
nfigu
ratio
nals
pace
and
the
num
ber
oflo
calm
inim
ais
sohi
ghth
atit
isim
poss
ible
tosa
mpl
eth
esp
ace
ata
suffi
cien
tnu
mbe
rof
poin
tsto
obta
ina
com
plet
esu
rvey
.In
part
icul
ar,
nom
inim
izat
ion
met
hod
exis
tsth
atgu
aran
tees
the
dete
rmin
atio
nof
the
glob
alm
inim
um.
How
ever
,gi
ven
ast
artin
gco
nfigu
ratio
n,it
ispo
ssib
leto
find
then
ea
rest
loca
lm
inim
um.
Nea
rest
inth
isco
ntex
tdo
esno
tal
way
sim
ply
near
est
ina
geom
etric
alse
nse
(i.e.
,th
ele
ast
sum
ofsq
uare
coor
dina
tedi
ffere
nces
),bu
tm
eans
the
min
imum
that
can
bere
ache
dby
syst
emat
ical
lym
ovin
gdo
wn
the
stee
pest
loca
lgr
adie
nt.
Fin
ding
this
near
est
loca
lmin
imum
isal
ltha
tG
RO
MA
CS
can
dofo
ryo
u,so
rry!
Ifyo
uw
ant
tofin
dot
her
min
ima
and
hope
todi
scov
erth
egl
obal
min
imum
inth
epr
oces
s,th
ebe
stad
vice
isto
expe
rimen
twith
tem
pera
ture
-cou
pled
MD
:run
your
syst
emat
ahi
ghte
mpe
ratu
refo
ra
whi
lean
d
6C
ha
pte
r1
.In
trod
uctio
n
thenquench
itslow
lydow
nto
therequired
temperature;
dothis
repeatedly!If
something
asa
melting
orglass
transitiontem
peratureexists,
itis
wise
tostay
forsom
etim
eslightly
belowthat
temperature
andcooldow
nslow
lyaccording
tosom
eclever
scheme,
aprocess
calledsim
ula
ted
an
ne
alin
g.S
inceno
physicaltruthis
required,youcan
useyour
phantasyto
speedup
thisprocess.
One
trickthatoften
works
isto
make
hydrogenatom
sheavier
(mass
10or
so):although
thatwill
slowdow
nthe
otherwise
veryrapid
motions
ofhydrogenatom
s,itwillhardly
influencethe
slower
motions
inthe
systemw
hileenabling
youto
increasethe
time
stepby
afactor
of3or
4.You
canalso
modify
thepotentialenergy
functionduring
thesearch
procedure,e.g.
byrem
ovingbarriers
(remove
dihedralanglefunctions
orreplace
repulsivepotentials
byso
ftco
repotentials[8]),
butalw
aystake
careto
restorethe
correctfunctionsslow
ly.T
hebestsearch
method
thatallows
ratherdrastic
structuralchangesis
toallow
excursionsinto
four-dimensionalspace
[9],butthis
requiressom
eextra
programm
ingbeyond
thestandard
capabilitiesofG
RO
MA
CS
.
Three
possibleenergy
minim
izationm
ethodsare:
•T
hosethat
requireonly
functionevaluations.
Exam
plesare
thesim
plexm
ethodand
itsvariants.
Astep
ism
adeon
thebasis
ofthe
resultsof
previousevaluations.
Ifderivative
information
isavailable,such
methods
areinferior
tothose
thatusethis
information.
•T
hosethat
usederivative
information.
Since
thepartialderivatives
ofthe
potentialenergyw
ithrespect
toall
coordinatesare
known
inM
Dprogram
s(these
areequal
tom
inusthe
forces)this
classofm
ethodsis
verysuitable
asm
odificationofM
Dprogram
s.
•T
hosethat
usesecond
derivativeinform
ationas
well.
These
methods
aresuperior
intheir
convergenceproperties
nearthe
minim
um:
aquadratic
potentialfunctionis
minim
izedin
onestep!
The
problemis
thatforNparticles
a3N×
3N
matrix
mustbe
computed,stored
andinverted.
Apart
fromthe
extraprogram
ming
toobtain
secondderivatives,
form
ostsystem
sof
interestthis
isbeyond
theavailable
capacity.T
hereare
intermediate
methods
buildingup
theH
essianm
atrixon
thefly,
butthey
alsosuffer
fromexcessive
storagere-
quirements.
So
GR
OM
AC
Sw
illshyaw
ayfrom
thisclass
ofmethods.
The
stee
pe
std
esce
ntmethod,
availablein
GR
OM
AC
S,
isof
thesecond
class.It
simply
takesa
stepin
thedirection
ofthe
negativegradient
(hencein
thedirection
ofthe
force),w
ithoutany
considerationofthe
historybuiltup
inprevious
steps.T
hestep
sizeis
adjustedsuch
thatthesearch
isfastbutthe
motion
isalw
aysdow
nhill.T
hisis
asim
pleand
sturdy,butsomew
hatstupid,method:
itsconvergence
canbe
quiteslow
,especially
inthe
vicinityof
thelocal
minim
um!
The
fasterconvergingco
nju
ga
teg
rad
ien
tm
eth
od(see
e.g.[10])
usesgradient
information
fromprevious
steps.In
general,steepestdescentsw
illbringyou
closeto
thenearestlocalm
inimum
veryquickly,
while
conjugategradients
bringsyouveryclose
tothe
localminim
um,butperform
sw
orsefaraw
ayfrom
them
inimum
.
E.6
1.
nm
run
22
3
E.61
nmrun
nmrun
buildsa
Hessian
matrix
fromsingle
conformation.
For
usualNorm
alModes-like
calculations,make
surethat
thestructure
providedis
properlyenergy-m
inimised.
The
generatedm
atrixcan
bediagonalized
byg
nmeig.
Files
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-mh
essia
n.m
txO
utputH
essianm
atrix-g
nm
.log
Output
Logfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-np
int1
Num
berofnodes,m
ustbethe
same
asused
forgrom
pp-v
booln
oVerbose
mode
-com
pa
ctbool
yes
Write
acom
pactlogfile
E.62
options
AllG
RO
MA
CS
programs
have6
standardoptions,ofw
hichsom
eare
hiddenby
default:
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int0
Setthe
nicelevel
•O
ptionalfilesare
notusedunless
theoption
isset,in
contrasttonon
optionalfiles,where
thedefault
filenam
eis
usedw
henthe
optionis
notset.
•A
llGR
OM
AC
Sprogram
sw
illacceptfileoptions
withouta
fileextension
orfilename
beingspecified.
Insuch
casesthe
defaultfilenam
esw
illbe
used.W
ithm
ultipleinput
filetypes,
suchas
genericstructure
format,
thedirectory
will
besearched
forfiles
ofeach
typew
iththe
suppliedor
defaultnam
e.W
henno
suchfile
isfound,or
with
outputfilesthe
firstfiletype
willbe
used.
•A
llGR
OM
AC
Sprogram
sw
iththe
exceptionofmd
run
,n
mru
nand
en
eco
nv
checkif
thecom
-m
andline
optionsare
valid.Ifthis
isnotthe
case,theprogram
willbe
halted.
•E
numerated
options(enum
)shouldbe
usedw
ithone
oftheargum
entslisted
inthe
optiondescription,
theargum
entmay
beabbreviated.
The
firstmatch
tothe
shortestargumentin
thelistw
illbeselected.
•Vector
optionscan
beused
with
1or
3param
eters.W
henonly
oneparam
eteris
suppliedthe
two
othersare
alsosetto
thisvalue.
•F
orm
anyG
RO
MA
CS
programs,the
time
optionscan
besupplied
indifferenttim
eunits,depending
onthe
settingofthe-tu
option.
•A
llGR
OM
AC
Sprogram
scan
readcom
pressedor
g-zippedfiles.
There
might
bea
problemw
ithreading
compressed.xtc
,.trrand
.trjfiles,butthese
willnotcom
pressvery
wellanyw
ay.
•M
ostG
RO
MA
CS
programs
canprocess
atrajectory
with
lessatom
sthan
therun
inputor
structurefile,butonly
ifthetrajectory
consistsofthe
firstnatom
softhe
runinputor
structurefile.
•M
anyG
RO
MA
CS
programs
willaccept
the-tuoption
toset
thetim
eunits
touse
inoutput
files(e.g.
forxmg
rgraphs
orxpm
matrices)
andin
alltime
options.
22
2A
pp
en
dix
E.
Ma
nu
alP
age
s
-nic
ein
t1
9S
etth
eni
cele
vel
-de
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mst
ring
Set
the
defa
ultfi
lena
me
for
allfi
leop
tions
-np
int
1N
umbe
rof
node
s,m
ustb
eth
esa
me
asus
edfo
rgr
ompp
-vbo
oln
oB
elo
udan
dno
isy
-co
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act
bool
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Writ
ea
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E.5
9m
kan
gndx
mk
angn
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akes
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for
calc
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gle
dist
ribut
ions
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Itus
esa
run
inpu
tfile
(.tp
x)
for
the
defin
ition
sof
the
angl
es,d
ihed
rals
etc.
File
s-s
top
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pr
Inpu
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put:
tpr
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Out
put
Inde
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Oth
erop
tions
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oln
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info
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quit
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Set
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l-t
ype
enum
an
gle
Type
ofan
gle:
an
gle
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96
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si
E.6
0ng
mx
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xis
the
Gro
mac
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Thi
spr
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aru
nin
put
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and
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and
plot
sa
3Dst
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ure
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urm
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ule
onyo
urst
anda
rdX
Win
dow
scre
en.
No
need
for
ahi
ghen
dgr
aphi
csw
orks
tatio
n,it
even
wor
kson
Mon
ochr
ome
scre
ens.
The
follo
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gfe
atur
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vebe
enim
plem
ente
d:3D
view
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atio
n,tr
ansl
atio
nan
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your
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ecul
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oms,
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atio
nof
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hard
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MIT
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ealX
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owco
mpu
tatio
nalb
ox.
Som
eof
the
mor
eco
mm
onX
com
man
dlin
eop
tions
can
beus
ed:
-bg,
-fg
chan
geco
lors
,-fo
ntfo
ntna
me,
chan
ges
the
font
.
File
s-f
tra
j.xtc
Inpu
tG
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Gen
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Opt
.In
dex
file
Oth
erop
tions
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oln
oP
rinth
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Set
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l-b
time
-1F
irstf
ram
e(p
s)to
read
from
traj
ecto
ry-e
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hen
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Ddt
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•B
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k
•S
ome
times
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psco
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ithou
tago
odre
ason
Cha
pter
2
Defi
nitio
nsan
dU
nits
2.1
Not
atio
n
The
follo
win
gco
nven
tions
for
mat
hem
atic
alty
pese
tting
are
used
thro
ugho
utth
isdo
cum
ent:
Item
Not
atio
nE
xam
ple
Vect
orB
old
italic
ri
Vect
orLe
ngth
Italic
r i
We
defin
eth
elow
erc
ase
subs
crip
tsi,j,k
andl
tode
note
part
icle
s:ri
isth
ep
osi
tion
vect
oro
fpa
rtic
lei,
and
usin
gth
isno
tatio
n:
rij
=r
j−
ri
(2.1
)
r ij
=|r
ij|
(2.2
)
The
forc
eon
part
iclei
isde
note
dby
Fi
and
Fij
=fo
rce
oni
exer
ted
byj
(2.3
)
Ple
ase
note
that
we
chan
ged
nota
tion
asof
ver.
2.0
tor
ij=
rj−
ri
sinc
eth
isis
the
nota
tion
com
mon
lyus
ed.
Ifyo
uen
coun
ter
aner
ror,
letu
skn
ow.
2.2
MD
units
GR
OM
AC
Sus
esa
cons
iste
ntse
tof
units
that
prod
uce
valu
esin
the
vici
nity
ofun
ityfo
rm
ost
rele
vant
mol
ecul
arqu
antit
ies.
Let
usca
llth
emMD
un
its.
The
basi
cun
itsin
this
syst
emar
enm
,ps
,K,e
lect
ron
char
ge(e
)an
dat
omic
mas
sun
it(u
),se
eTa
ble
2.1.
Con
sist
entw
ithth
ese
units
are
ase
tofd
eriv
edun
its,g
iven
inTa
ble
2.2.
The
elec
tric
conv
ersi
onfa
ctorf
=1
4πε o
=13
8.93
548
5(9)
kJm
ol−
1nm
e−2.
Itre
late
sth
em
echa
nica
lqua
ntiti
esto
the
elec
tric
alqu
antit
ies
asin
V=fq2 r
orF
=fq2 r2
(2.4
)
8C
ha
pte
r2
.D
efin
ition
sa
nd
Un
its
Quantity
Sym
bolU
nitlength
rnm
=10−
9m
mass
mu
(atomic
mass
unit)=1.6605402(10)×10
−27
kg(1/12
ofthem
assofa
Catom
)1.6605402(10)×
10−
27
kgtim
et
ps=10−
12
scharge
qe
=electronic
charge=1.60217733(49)×
10−
19
Ctem
peratureT
K
Table2.1:
Basic
unitsused
inG
RO
MA
CS
.Num
bersin
parenthesesgive
accuracy.
Quantity
Sym
bolU
nitenergy
E,V
kJm
ol −1
Force
FkJ
mol −
1nm
−1
pressurep
kJm
ol −1
nm−
3=
1030/N
AV
Pa
1.660
54×
106
Pa=
16.6054B
arvelocity
vnm
ps −1
=1000
m/s
dipolem
oment
µe
nmelectric
potentialΦ
kJm
ol −1
e −1
=0.010
364272(3)
Voltelectric
fieldE
kJm
ol −1
nm−
1e −
1=
1.036427
2(3)×10
7V
/m
Table2.2:
Derived
units
Electric
potentialsΦand
electricfieldsE
areinterm
ediatequantities
inthe
calculationofenergies
andforces.
They
donotoccur
insideG
RO
MA
CS
.Iftheyare
usedin
evaluations,thereis
achoice
ofequationsand
relatedunits.
We
recomm
endstrongly
tofollow
theusualpractice
toinclude
thefactorf
inexpressions
thatevaluateΦandE
:
Φ(r)
=f ∑
j
qj
|r−
rj |
(2.5)
E(r)
=f ∑
j
qj(r−
rj )
|r−
rj | 3
(2.6)
With
thesedefinitionsqΦ
isan
energyandqE
isa
force.T
heunits
arethose
givenin
Table2.2:
about10m
Vfor
potential.T
husthe
potentialofanelectronic
chargeata
distanceof1
nmequals
f≈
140units≈
1.4V.(exactvalue:
1.439965V
)
Note
thattheseunits
arem
utuallyconsistent;changing
anyofthe
unitsis
likelyto
produceincon-
sistenciesand
isthereforestro
ng
lyd
iscou
raged!In
particular:ifA
areused
insteadofnm
,theunit
oftim
echanges
to0.1
ps.If
thekcal/m
ol(=4.184
kJ/mol)
isused
insteadof
kJ/molfor
energy,the
unitoftime
becomes
0.488882ps
andthe
unitoftemperature
changesto
4.184K
.Butin
bothcases
allelectricalenergiesgo
wrong,because
theyw
illstillbecom
putedin
kJ/mol,expecting
nmas
theunitoflength.
Although
carefulrescalingofcharges
may
stillyieldconsistency,
itisclear
thatsuchconfusions
mustbe
rigidlyavoided.
Interm
softhe
MD
unitsthe
usualphysicalconstantstake
ondifferentvalues,
seeTable
2.3.A
llquantities
areper
mol
ratherthan
perm
olecule.T
hereis
nodistinction
between
Boltzm
ann’sconstantk
andthe
gasconstant
R:
theirvalue
is0.008314
51kJ
mol −
1K−
1.
E.5
8.
md
run
22
1
E.58
mdrun
The
mdrun
programperform
sM
olecularD
ynamics
simulations.
Itreads
therun
inputfile
(-s
)and
dis-tributes
thetopology
overnodes
ifneeded.
The
coordinatesare
passedaround,
sothat
computations
canbegin.
Firsta
neighborlistism
ade,thenthe
forcesare
computed.
The
forcesare
globallysum
med,and
thevelocities
andpositions
areupdated.
Ifnecessaryshake
isperform
edto
constrainbond
lengthsand/or
bondangles.
Temperature
andP
ressurecan
becontrolled
usingw
eakcoupling
toa
bath.
mdrun
producesatleastthree
outputfile,plusone
logfile
(-g
)per
node.T
hetrajectory
file(
-o),contains
coordinates,velocitiesand
optionallyforces.
The
structurefile
(-c
)contains
thecoordinates
andvelocities
ofthelaststep.
The
energyfile
(-e
)contains
energies,thetem
perature,pressure,etc,alotofthese
thingsare
alsoprinted
inthe
logfile
ofnode0.
Optionally
coordinatescan
bew
rittento
acom
pressedtrajectory
file(-x
).
When
runningin
parallelwith
PV
Mor
anold
versionofM
PIthe
-np
optionm
ustbegiven
toindicate
thenum
berofnodes.
The
option-dg
dl
isonly
usedw
henfree
energyperturbation
isturned
on.
With
-reru
nan
inputtrajectorycan
begiven
forw
hichforces
andenergies
willbe
(re)calculated.N
eigh-bor
searchingw
illbeperform
edfor
everyfram
e,unlessn
stlistis
zero(see
the.md
pfile).
ED
(essentialdynamics)
sampling
issw
itchedon
byusing
the-e
iflag
followed
byan.e
di
file.T
he.e
di
filecan
beproduced
usingoptions
inthe
essdynm
enuofthe
WH
ATIF
program.
mdrun
producesa
.ed
ofile
thatcontainsprojections
ofpositions,velocitiesand
forcesonto
selectedeigenvectors.
The
-tableoption
canbe
usedto
passm
druna
formatted
tablew
ithuser-defined
potentialfunctions.T
hefile
isread
fromeither
thecurrentdirectory
orfrom
theG
MX
LIBdirectory.
Anum
berofpreform
attedtables
arepresented
inthe
GM
XLIB
dir,for
6-8,6-9,
6-10,6-11,
6-12Lennard
Jonespotentials
with
normal
Coulom
b.
The
options-pi
,-po
,-pd
,-pn
areused
forpotentialofm
eanforce
calculationsand
umbrella
sampling.
See
manual.
When
mdrun
receivesa
TE
RM
signal,itwillsetnsteps
tothe
currentstepplus
one.W
henm
drunreceives
aU
SR
1signal,
itw
illset
nstepsto
thenext
multiple
ofnstxout
afterthe
currentstep.
Inboth
casesall
theusualoutputw
illbew
rittento
file.W
henrunning
with
MP
I,asignalto
oneofthe
mdrun
processesis
sufficient,thissignalshould
notbesentto
mpirun
orthe
mdrun
processthatis
theparentofthe
others.
Files
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-otra
j.trrO
utputF
ullprecisiontrajectory:
trrtrj
-xtra
j.xtcO
utput,Opt.
Com
pressedtrajectory
(portablexdr
format)
-cco
nfo
ut.g
roO
utputG
enericstructure:
grog96
pdb-e
en
er.e
dr
Output
Generic
energy:edr
ene-g
md
.log
Output
Logfile
-dg
dl
dg
dl.xvg
Output,O
pt.xvgr/xm
grfile
-tab
leta
ble
.xvgInput,O
pt.xvgr/xm
grfile
-reru
nre
run
.xtcInput,O
pt.G
enerictrajectory:
xtctrr
trjgrog96
pdb-e
isa
m.e
di
Input,Opt.
ED
sampling
input-e
osa
m.e
do
Output,O
pt.E
Dsam
plingoutput
-pi
pu
ll.pp
aInput,O
pt.P
ullparameters
-po
pu
llou
t.pp
aO
utput,Opt.
Pullparam
eters-p
dp
ull.p
do
Output,O
pt.P
ulldataoutput
-pn
pu
ll.nd
xInput,O
pt.Index
file
Other
options-h
booln
oP
rinthelpinfo
andquit
22
0A
pp
en
dix
E.
Ma
nu
alP
age
s
-tim
ere
al-1
Take
fram
eat
orfir
staf
ter
this
time.
-np
int
1G
ener
ate
stat
usfil
efo
r#
node
s-s
hu
ffle
bool
no
Shu
ffle
mol
ecul
esov
erno
des
-so
rtbo
oln
oS
ortm
olec
ules
acco
rdin
gto
Xco
ordi
nate
-rm
du
mb
ds
bool
yes
Rem
ove
cons
tant
bond
edin
tera
ctio
nsw
ithdu
mm
ies
-lo
ad
strin
gR
elea
tive
load
capa
city
ofea
chno
deon
apa
ralle
lmac
hine
.B
esu
reto
use
quot
esar
ound
the
strin
g,w
hich
shou
ldco
ntai
na
num
ber
for
each
node
-ma
xwa
rnin
t1
0N
umbe
rof
war
ning
saf
ter
whi
chin
putp
roce
ssin
gst
ops
-ch
eck
14
bool
no
Rem
ove
1-4
inte
ract
ions
with
outV
ande
rW
aals
E.5
6hi
ghw
ay
high
way
isth
egr
omac
shi
ghw
aysi
mul
ator
.It
isan
X-w
indo
ws
gadg
etth
atsh
ows
a(p
erio
dic)
auto
bahn
with
aus
erde
fined
num
ber
ofca
rs.
Fog
can
betu
rned
onor
offt
oin
crea
seth
enu
mbe
rof
cras
hes.
Nic
efo
ra
back
grou
ndC
PU
-eat
er
File
s-f
hig
hw
ay.
da
tIn
put
Gen
eric
data
file
-aa
uto
.da
tIn
put
Gen
eric
data
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t0
Set
the
nice
leve
l-b
time
-1F
irstf
ram
e(p
s)to
read
from
traj
ecto
ry-e
time
-1La
stfr
ame
(ps)
tore
adfr
omtr
ajec
tory
-dt
time
-1O
nly
use
fram
ew
hen
tMO
Ddt
=fir
sttim
e(p
s)
E.5
7m
ake
ndx
Inde
xgr
oups
are
nece
ssar
yfo
ral
mos
tev
ery
grom
acs
prog
ram
.A
llth
ese
prog
ram
sca
nge
nera
tede
faul
tin
dex
grou
ps.
You
ON
LYha
veto
use
mak
endx
whe
nyo
une
edS
PE
CIA
Lin
dex
grou
ps.
The
reis
ade
faul
tin
dex
grou
pfo
rth
ew
hole
syst
em,9
defa
ulti
ndex
grou
psar
ege
nera
ted
for
prot
eins
,ade
faul
tind
exgr
oup
isge
nera
ted
for
ever
yot
her
resi
due
nam
e.
Whe
nno
inde
xfil
eis
supp
lied,
also
mak
endx
will
gene
rate
the
defa
ultg
roup
s.W
ithth
ein
dex
edito
ryo
uca
nse
lect
onat
om,
resi
due
and
chai
nna
mes
and
num
bers
,yo
uca
nus
eN
OT,
AN
Dan
dO
R,y
ouca
nsp
litgr
oups
into
chai
ns,r
esid
ues
orat
oms.
You
can
dele
tean
dre
nam
egr
oups
.
The
atom
num
berin
gin
the
edito
ran
dth
ein
dex
file
star
tsat
1.
File
s-f
con
f.g
roIn
put
Gen
eric
stru
ctur
e:gr
og9
6pd
btp
rtp
btp
a-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-oin
de
x.n
dx
Out
put
Inde
xfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t0
Set
the
nice
leve
l
2.3
.R
ed
uce
du
nits
9
Sym
bol
Nam
eVa
lue
NA
VA
voga
dro’
snu
mbe
r6.
022
1367(
36)×
1023
mol−
1
Rga
sco
nsta
nt8.
314
510(
70)×
10−
3kJ
mol−
1K−
1
kB
Bol
tzm
ann’
sco
nsta
ntid
emh
Pla
nck’
sco
nsta
nt0.
399
03132
(24)
kJm
ol−
1ps
hD
irac’
sco
nsta
nt0.
063
50780
7(38
)kJ
mol−
1ps
cve
loci
tyof
light
299
792.
458
nm/p
s
Tabl
e2.
3:S
ome
Phy
sica
lCon
stan
ts
Qua
ntity
Sym
bol
Rel
atio
nto
SI
Leng
thr∗
rσ−
1
Mas
sm∗
mM−
1
Tim
et∗
tσ−
1√ ε/
MTe
mpe
ratu
reT∗
k BTε−
1
Ene
rgy
E∗
Eε−
1
For
ceF∗
Fσε−
1
Pre
ssur
eP∗
Pσ
3ε−
1
Velo
city
v∗v√ M
/εD
ensi
tyρ∗
Nσ
3V−
1
Tabl
e2.
4:R
educ
edLe
nnar
d-Jo
nes
quan
titie
s
2.3
Red
uced
units
Whe
nsi
mul
atin
gLe
nnar
d-Jo
nes
(LJ)
syst
ems
itm
ight
bead
vant
ageo
usto
use
redu
ced
units
(i.e
.,se
ttingε i
i=σ
ii=m
i=k
B=
1fo
ron
ety
peof
atom
s).
Thi
sis
poss
ible
.W
hen
spec
ifyin
gth
ein
put
inre
duce
dun
its,
the
outp
utw
illal
sobe
inre
duce
dun
its.
The
reis
one
exce
ptio
n:th
ete
mp
era
ture,
whi
chis
expr
esse
din0.0
0831
451
redu
ced
units
.T
his
isa
cons
eque
nce
ofth
eus
eof
Bol
tzm
ann’
sco
nsta
ntin
the
eval
uatio
nof
tem
pera
ture
inth
eco
de.
Thu
sno
tT
,bu
tkBT
isth
ere
duce
dte
mpe
ratu
re.
AG
RO
MA
CS
tem
pera
ture
T=
1m
eans
are
duce
dte
mpe
ratu
reof
0.00
8...
units
;if
are
duce
dte
mpe
ratu
reof
1is
requ
ired,
the
GR
OM
AC
Ste
mpe
ratu
resh
ould
be12
0.27
17.
InTa
ble
2.4
quan
titie
sar
egi
ven
for
LJpo
tent
ials
:
VL
J=
4ε
[ ( σ r
) 12−( σ r
) 6](2
.7)
10
Ch
ap
ter
2.
De
finitio
ns
an
dU
nits
E.5
5.
gro
mp
p2
19
grompp
callsthe
c-preprocessorto
resolveincludes,
macros
etcetera.To
specifya
macro-preprocessor
otherthan
/lib/cpp(such
asm
4)you
canput
aline
inyour
parameter
filespecifying
thepath
tothat
cpp.S
pecifying-pp
willgetthe
pre-processedtopology
filew
rittenout.
Ifyoursystem
doesnothave
ac-preprocessor,you
canstilluse
grompp,butyou
donothave
accessto
thefeatures
fromthe
cpp.C
omm
andline
optionsto
thec-preprocessor
canbe
givenin
the.m
dp
file.S
eeyour
localmanual(m
ancpp).
When
usingposition
restraintsa
filew
ithrestraint
coordinatescan
besupplied
with
-r,
otherwise
con-straining
willbe
donerelative
tothe
conformation
fromthe-c
option.
Starting
coordinatescan
beread
fromtrajectory
with
-t.
The
lastfram
ew
ithcoordinates
andvelocities
willbe
read,unless
the-time
optionis
used.N
otethatthese
velocitiesw
illnotbeused
when
ge
nve
l=
yes
inyour.m
dp
file.Ifyou
wantto
continuea
crashedrun,itis
easierto
usetp
bco
nv
.
When
preparingan
inputfilefor
parallelm
dru
nitm
aybe
advantageousto
partitionthe
simulation
systemover
thenodes
ina
way
inw
hicheach
nodehas
asim
ilaram
ountof
work.
The
-shuffleoption
doesjust
that.F
ora
singleprotein
inw
aterthis
doesnot
make
adifference,
however
fora
systemw
hereyou
havem
anycopies
ofdifferentmolecules
(e.g.liquid
mixture
orm
embrane/w
atersystem
)the
optionis
definitelya
must.
Afurther
optimization
forparallelsystem
sis
the-sort
optionw
hichsorts
molecules
accordingto
coor-dinates.
This
mustalw
aysbe
usedin
conjunctionw
ith-sh
uffle
,however
sortingalso
works
when
youhave
onlyone
molecule
type.
Using
the-mo
rseoption
grompp
canconvert
theharm
onicbonds
inyour
topologyto
morse
potentials.T
hism
akesit
possibleto
breakbonds.
For
thisoption
tow
orkyou
needan
extrafile
inyour
$GM
XLIB
with
dissociationenergy.
Use
the-debug
optionto
getm
oreinform
ationon
thew
orkingsof
thisoption
(lookfor
MO
RS
Ein
thegrom
pp.logfile
usingless
orsom
ethinglike
that).
By
defaultallbonded
interactionsw
hichhave
constantenergy
dueto
dumm
yatom
constructionsw
illberem
oved.If
thisconstant
energyis
notzero,
thisw
illresult
ina
shiftin
thetotal
energy.A
llbonded
interactionscan
bekeptby
turningoff-rm
du
mb
ds
.A
dditionally,allconstraintsfor
distancesw
hichw
illbe
constantanyw
aybecause
ofdum
my
atomconstructions
will
berem
oved.If
anyconstraints
remain
which
involvedum
my
atoms,a
fatalerrorw
illresult.
Toverify
yourrun
inputfile,pleasem
akenotice
ofallwarnings
onthe
screen,andcorrectw
herenecessary.
Do
alsolook
atthecontents
ofthemdo
ut.m
dp
file,thiscontains
comm
entlines,asw
ellasthe
inputthatg
rom
pp
hasread.
Ifin
doubtyou
canstart
grompp
with
the-d
eb
ug
optionw
hichw
illgiveyou
more
information
ina
filecalled
grompp.log
(alongw
ithrealdebug
info).F
inally,youcan
seethe
contentsofthe
runinputfile
with
thegm
xdu
mp
program.
Files
-fg
rom
pp
.md
pInput
grompp
inputfilew
ithM
Dparam
eters-p
om
do
ut.m
dp
Output
grompp
inputfilew
ithM
Dparam
eters-c
con
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21
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each
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non
the
num
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and
bond
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na
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and
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Max
wel
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ted.
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sore
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para
met
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for
the
mdr
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g.nu
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s,tim
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asN
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Dpa
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hich
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neta
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Eve
ntua
llya
bina
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that
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serv
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the
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the
MD
prog
ram
.
grom
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eat
omna
mes
from
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topo
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file.
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nam
esin
the
coor
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gene
rate
war
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sw
hen
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atch
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.N
ote
that
the
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nam
esar
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atio
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only
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atom
type
sar
eus
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nera
ting
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ract
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para
met
ers.
Cha
pter
3
Alg
orith
ms
3.1
Intro
duct
ion
Inth
isch
apte
rw
efir
stgi
vede
scrib
etw
oge
nera
lcon
cept
sus
edin
GR
OM
AC
S:
pe
rio
dic
bo
un
da
ryco
nd
itio
ns(
sec.
3.2)
and
theg
rou
pco
nce
pt(s
ec.3
.3).
The
MD
algo
rithm
isde
scrib
edin
sec.3.
4:fir
sta
glob
alfo
rmof
the
algo
rithm
isgi
ven,
whi
chis
refin
edin
subs
eque
ntsu
bsec
tions
.T
he(s
impl
e)E
M(E
nerg
yM
inim
izat
ion)
algo
rithm
isde
scrib
edin
sec.
3.10
.S
ome
othe
ral
gorit
hms
for
spec
ialp
urpo
sedy
nam
ics
are
desc
ribed
afte
rth
is.
Inth
efin
alse
c.3.
14of
this
chap
ter
afe
wpr
inci
ples
are
give
non
whi
chpa
ralle
lizat
ion
ofG
RO
MA
CS
isba
sed.
The
para
lleliz
atio
nis
hard
lyvi
sibl
efo
rth
eus
eran
dis
ther
efor
eno
ttre
ated
inde
tail.
Afe
wis
sues
are
ofge
nera
lin
tere
st.
Inal
lca
ses
the
syst
em
mus
tbe
defin
ed,
cons
istin
gof
mol
ecul
es.
Mol
ecul
esag
ain
cons
ist
ofpa
rtic
les
with
defin
edin
tera
ctio
nfu
nctio
ns.
The
deta
iled
desc
riptio
nof
theto
po
log
yoft
hem
olec
ules
and
ofth
eforc
efie
ldan
dth
eca
lcul
atio
nof
forc
esis
give
nin
chap
ter4.
Inth
epr
esen
tcha
pter
we
desc
ribe
othe
ras
pect
sof
the
algo
rithm
,suc
has
pair
listg
ener
atio
n,up
date
ofve
loci
ties
and
posi
tions
,co
uplin
gto
exte
rnal
tem
pera
ture
and
pres
sure
,co
nser
vatio
nof
cons
trai
nts.
Thea
na
lysi
soft
heda
tage
nera
ted
byan
MD
sim
ulat
ion
istr
eate
din
chap
ter8
.
3.2
Per
iodi
cbo
unda
ryco
nditi
ons
The
clas
sica
lway
tom
inim
ize
edge
effe
cts
ina
finite
syst
emis
toap
ply
pe
rio
dic
bo
un
da
ryco
nd
i-tio
ns.
The
atom
sof
the
syst
emto
besi
mul
ated
are
puti
nto
asp
ace-
fillin
gbo
x,w
hich
issu
rrou
nded
bytr
ansl
ated
copi
esof
itsel
f(F
ig.3.1)
.T
hus
ther
ear
eno
boun
darie
sof
the
syst
em;
the
artif
act
caus
edby
unw
ante
dbo
unda
ries
inan
isol
ated
clus
ter
isno
wre
plac
edby
the
artif
act
ofpe
riodi
cco
nditi
ons.
Ifa
crys
tali
ssi
mul
ated
,su
chbo
unda
ryco
nditi
ons
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red
(alth
ough
mot
ions
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rally
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ricte
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perio
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mot
ions
with
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elen
gths
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Ifon
ew
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sto
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csy
stem
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solu
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,the
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tyby
itsel
fcau
ses
erro
rs.
The
erro
rsca
nbe
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uate
dby
com
parin
gva
rious
syst
emsi
zes;
they
are
expe
cted
tobe
less
seve
reth
anth
eer
rors
resu
lting
from
anun
natu
ralb
ound
ary
with
vacu
um.
12
Ch
ap
ter
3.
Alg
orith
ms
j’j’
i’i’
i’i’
j’
i’i’
y
x
y
x
j’j’
i’
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i’i
i’
j’j’
j’
j
i’i’
i’
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i’i’
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j’j’
j
Figure
3.1:P
eriodicboundary
conditionsin
two
dimensions.
There
areseveralpossible
shapesfor
space-fillingunitcells.
Som
e,asthe
rho
mb
icd
od
eca
he
dro
nand
thetrun
cate
do
ctah
ed
ron[11]
approacha
sphericalshape
betterthan
acubic
boxand
aretherefore
more
economicalfor
studyingan
(approximately
spherical)m
acromolecule
insolution,
sinceless
solventmolecules
arerequired
tofillthe
boxgiven
am
inimum
distancebetw
eenm
acro-m
olecularim
ages.H
owever,
aperiodic
systembased
onthe
rhombic
dodecahedronor
truncatedoctahedron
isequivalentto
aperiodic
systembased
ona
triclinic
unitcell.T
helatter
shapeis
them
ostgeneralspace-filling
unitcell;
itcom
prisesallpossible
space-fillingshapes
[12].
Therefore
GR
OM
AC
Sis
basedon
thetriclinic
unitcell.
GR
OM
AC
Suses
periodicboundary
conditions,com
binedw
iththe
min
imu
mim
ageco
nven
tion
:only
one-
thenearest
-im
ageof
eachparticle
isconsidered
forshort-range
non-bondedinter-
actionterm
s.F
orlong-range
electrostaticinteractions
thisis
notalw
aysaccurate
enough,and
GR
OM
AC
Stherefore
alsoincorporates
latticesum
methods
likeE
wald
Sum
,PM
Eand
PP
PM
.
Grom
acssupports
triclinicboxes
ofanyshape.
The
boxis
definedby
the3
boxvectorsa
,bandc.
The
boxvectors
mustsatisfy
thefollow
ingconditions:
ay
=a
z=bz
=0
(3.1)
ax>
0,
by>
0,
cz>
0(3.2)
|bx |≤
12a
x ,|c
x |≤12a
x ,|c
y |≤12by
(3.3)
Equations
(3.1)can
always
bestatisfied
byrotating
thebox.
Equations
(3.2)
and(3.3)
canalw
aysbe
statisfiedby
addingand
subtractingbox
vectors.
Even
when
simulating
usinga
triclinicbox,G
RO
MA
CS
always
putsthe
particlesin
abrick
shapedvolum
e,forefficiency
reasons.T
hisis
illustratedin
Fig.
3.1for
a2-dim
ensionalsystem.
So
from
E.5
2.
gen
pr
21
7
Files
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atopology
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Asingle
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constantmay
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WA
RN
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olecules,therefore
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oleculetypein
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energyfile
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dr
)andprints
outusefulinform
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.
Option
-cchecks
forpresence
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boxin
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).If
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peraturew
illbecalculated
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.
The
programw
illcompare
runinput(
.tpr
,.tpb
or.tpa
)files
when
both-s1and
-s2are
supplied.
21
6A
pp
en
dix
E.
Ma
nu
alP
age
s
•M
olec
ules
mus
tbe
who
lein
the
initi
alco
nfigu
ratio
ns.
•A
tthe
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ent-
cion
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orks
whe
nin
sert
ing
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E.5
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ncon
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othe
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akes
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nm
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ake
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putfi
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Van
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isfil
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f.g
roIn
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Gen
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xtc
trr
trjg
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6pd
b
Oth
erop
tions
-hbo
oln
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rinth
elp
info
and
quit
-nic
ein
t0
Set
the
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xve
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11
1N
umbe
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or0
00
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bool
no
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bool
no
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rtbo
oln
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ivid
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bloc
kson
this
num
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us-n
mo
lat
int
3N
umbe
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spe
rm
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ule,
assu
med
tost
art
from
0.If
you
set
this
wro
ng,i
twill
scre
wup
your
syst
em!
-ma
xro
tve
ctor9
09
09
0M
axim
umra
ndom
rota
tion
-re
nu
mb
er
bool
no
Ren
umbe
rre
sidu
es
•T
hepr
ogra
msh
ould
allo
wfo
rra
ndom
disp
lace
men
toff
latti
cepo
ints
.
E.5
1ge
nion
geni
onre
plac
esso
lven
tmol
ecul
esby
mon
oato
mic
ions
atth
epo
sitio
nof
the
first
atom
sw
ithth
em
ostf
avor
-ab
leel
ectr
osta
ticpo
tent
ialo
rat
rand
om.
The
pote
ntia
lis
calc
ulat
edon
alla
tom
s,us
ing
norm
alG
RO
MA
CS
part
icle
base
dm
etho
ds(in
cont
rast
toot
her
met
hods
base
don
solv
ing
the
Poi
sson
-Bol
tzm
ann
equa
tion)
.T
hepo
tent
iali
sre
calc
ulat
edaf
ter
ever
yio
nin
sert
ion.
Ifsp
ecifi
edin
the
run
inpu
tfil
e,a
reac
tion
field
orsh
iftfu
nctio
nca
nbe
used
.T
hegr
oup
ofso
lven
tmol
ecul
essh
ould
beco
ntin
uous
and
allm
olec
ules
shou
ldha
veth
esa
me
num
ber
ofat
oms.
The
user
shou
ldad
dth
eio
nm
olec
ules
toth
eto
polo
gyfil
ean
din
clud
eth
efil
eio
ns.
itp.
Ion
nam
esfo
rG
rom
os96
shou
ldin
clud
eth
ech
arge
.
The
pote
ntia
lcan
bew
ritte
nas
B-f
acto
rsin
apd
bfil
e(f
orvi
sual
isat
ion
usin
ge.
g.ra
smol
).T
heun
itof
the
pote
ntia
lis
0.00
1kJ
/(m
ole)
.
For
larg
erio
ns,e
.g.
sulfa
tew
ere
com
men
ded
tous
ege
nbox
.
3.2
.P
erio
dic
bo
un
da
ryco
nd
itio
ns
13
Fig
ure
3.2:
Arh
ombi
cdo
deca
hedr
onan
dtr
unca
ted
octa
hedr
on(a
rbitr
ary
orie
ntat
ions
).
box
type
imag
ebo
xbo
xve
ctor
sbo
xve
ctor
angl
esdi
stan
cevo
lum
ea
bc
6bc
6ac
6ab
d0
0cu
bic
dd
30
d0
90◦
90◦
90◦
00
d
rhom
bic
d0
1 2d
dode
cahe
dron
d1 2
√2d
30
d1 2d
60◦
60◦
90◦
(xy-
squa
re)
≈0.
71d
30
01 2
√2d
rhom
bic
d1 2d
1 2d
dode
cahe
dron
d1 2
√2d
30
1 2
√3d
1 6
√3d
60◦
60◦
60◦
(xy-
hexa
gon)
≈0.
71d
30
01 3
√6d
trun
cate
dd
1 3d
-1 3d
octa
hedr
ond
4 9
√3d
30
2 3
√2d
1 3
√2d
≈71◦
≈71◦
≈71◦
≈0.
77d
30
01 3
√6d
Tabl
e3.
1:T
hecu
bic
box,
the
rhom
bic
dode
cahe
dron
and
the
trun
cate
doc
tahe
dron
.
the
outp
uttr
ajec
tory
itm
ight
seem
like
the
sim
ulat
ion
was
done
ina
rect
angu
larb
ox.
The
prog
ram
trjc
on
vca
nbe
used
toco
nver
tthe
traj
ecto
ryto
adi
ffere
ntun
it-ce
llre
pres
enta
tion.
Itis
also
poss
ible
tosi
mul
ate
with
out
perio
dic
boun
dary
cond
ition
s,bu
tit
ism
ore
effic
ient
tosi
mul
ate
anis
olat
edcl
uste
rof
mol
ecul
esin
ala
rge
perio
dic
box,
sinc
efa
stgr
idse
arch
ing
can
only
beus
edin
ape
riodi
csy
stem
.
3.2.
1S
ome
usef
ulbo
xty
pes
The
thre
em
ost
usef
ulbo
xty
pes
for
sim
ulat
ions
ofso
lvat
edsy
stem
sar
ede
scrib
edin
Tabl
e3.
1.T
herh
ombi
cdo
deca
hedr
on(F
ig.
3.2)
isth
esm
alle
stan
dm
ostr
egul
arsp
ace-
fillin
gun
itce
ll.E
ach
ofth
e12
imag
ece
llsis
atth
esa
me
dist
ance
.T
hevo
lum
eis
71%
ofth
evo
lum
eof
acu
bic
box
with
the
sam
eim
age
dist
ance
.T
his
save
sab
out
29%
ofC
PU
-tim
ew
hen
sim
ulat
ing
asp
heric
alor
flexi
ble
mol
ecul
ein
solv
ent.
Arh
ombi
cdo
deca
hedr
onca
nha
vetw
odi
ffere
ntor
ient
atio
ns,
whi
lefu
lfilli
ngeq
uatio
ns(3.
1).
The
prog
ram
ed
itco
nf
prod
uces
the
orie
ntat
ion
whi
chha
sa
14
Ch
ap
ter
3.
Alg
orith
ms
squarecross-section
with
thexy-plane.
This
orientationw
aschosen
becausethe
firsttw
obox
vectorscoincide
with
thex
andy-axis,
which
iseasier
tocom
prehend.T
heother
orientationcan
beusefulfor
simulations
ofmem
braneproteins.
Inthis
casethe
cross-sectionw
iththe
xy-planeis
ahexagon,w
hichhas
anarea
which
is14%
smaller
thanthe
areaofa
squarew
iththe
same
image
distance.T
heheight
ofthe
box(
cz )
shouldbe
changedto
obtainan
optimalspacing.
This
boxshape
doesnotonly
saveC
PU
-time,italso
resultsin
am
oreuniform
arrangementofthe
proteins.
3.2.2C
ut-offrestrictions
The
minim
umim
ageconvention
implies
thatthecut-offradius
usedto
truncatenon-bonded
inter-actions
mustnotexceed
halftheshortestbox
vectorfor
gridsearch:
Rc<
12m
in(‖a‖,‖b‖,‖c‖),
(3.4)
otherwise
more
thanone
image
would
bew
ithinthe
cut-offdistanceofthe
force.W
hena
macro-
molecule,
suchas
aprotein,
isstudied
insolution,
thisrestriction
doesnot
suffice.In
principlea
singlesolventm
oleculeshould
notbeable
to‘see’both
sidesofthe
macrom
olecule.T
hism
eansthatthe
lengthofeach
boxvector
mustexceed
thelength
ofthem
acromolecule
inthe
directionof
thatedgep
lus
two
times
thecut-off
radiusRc .
Itis
comm
onto
comprom
isein
thisrespect,
andm
akethe
solventlayersom
ewhatsm
allerin
orderto
reducethe
computationalcost.
For
efficiencyreasons
thecut-offw
ithsim
plesearch
intriclinic
boxes(grid
searchalw
aysuses
eq.(
3.4))is
more
restriced:
Rc<
12m
in(ax ,b
y ,cz )
(3.5)
Each
unitcell
(cubic,rectangular
ortriclinic)
issurrounded
by26
translatedim
ages.T
husa
particularim
agecan
always
beidentified
byan
indexpointing
toone
of27tra
nsla
tion
vecto
rsandconstructed
byapplying
atranslation
with
theindexed
vector(see3.4.3).
3.3T
hegroup
concept
Inthe
GR
OM
AC
SM
Dand
analysisprogram
sone
usesg
rou
psofatom
sto
performcertain
actionson.
The
maxim
umnum
berof
groupsis
256,but
everyatom
canonly
belongto
fourdifferent
groups,oneofeach
ofthefollow
ingkinds:
T-couplinggroup
The
temperature
couplingparam
eters(reference
temperature,
time
constant,num
berof
degreesof
freedom,
see3.4.4)
canbe
definedfor
eachT-coupling
groupsepa-
rately.F
orexam
ple,in
asolvated
macrom
oleculethe
solvent(that
tendsto
producem
oreheating
byforce
andintegration
errors)canbe
coupledw
itha
shortertime
constanttoa
baththan
am
acromolecule,
ora
surfacecan
bekept
coolerthan
anadsorbing
molecule.
Many
differentT-couplinggroups
may
bedefined.
Freeze
groupA
toms
thatbelong
toa
freezegroup
arekept
stationaryin
thedynam
ics.T
hisis
usefulduringequilibration,
e.g.to
avoidthat
badlyplaced
solventm
oleculesw
illgiveun-
reasonablekicks
toprotein
atoms,although
thesam
eeffectcan
alsobe
obtainedby
puttinga
restrainingpotentialon
theatom
sthat
must
beprotected.
The
freezeoption
canbe
used
E.4
9.
gen
bo
x2
15
E.49
genbox
Genbox
cando
oneof3
things:
1)G
eneratea
boxofsolvent.
Specify
-csand
-box.O
rspecify
-csand
-cpw
itha
structurefile
with
abox,
butwithoutatom
s.
2)S
olvatea
soluteconfiguration,
eg.a
protein,in
abath
ofsolvent
molecules.
Specify-cp
(solute)and
-cs(solvent).
The
boxspecified
inthe
solutecoordinate
file(
-cp)
isused,
unless-bo
xis
set,w
hichalso
centersthe
solute.T
heprogramed
itcon
fhas
more
sophisticatedoptions
tochange
thebox
andcenter
thesolute.
Solventm
oleculesare
removed
fromthe
boxw
herethe
distancebetw
eenany
atomofthe
solutem
olecule(s)and
anyatom
ofthe
solventm
oleculeis
lessthan
thesum
ofthe
VanderWaals
radiiofboth
atoms.
Adatabase
(vd
wra
dii.d
at
)ofVanderW
aalsradiiis
readby
theprogram
,atoms
notinthe
databaseare
assigneda
defaultdistance-vd
w.
3)Insertanum
ber(-nmo
l)ofextra
molecules
(-ci)atrandom
positions.T
heprogram
iteratesuntiln
mo
lm
oleculeshave
beeninserted
inthe
box.To
testwhether
aninsertion
issuccessfulthe
same
VanderWaals
criteriumis
usedas
forrem
ovalofsolvent
molecules.
When
noappropriately
sizedholes
(holesthat
canhold
anextra
molecule)
areavailable
theprogram
triesfor
-nm
ol
*-try
times
beforegiving
up.Increase
-tryifyou
haveseveralsm
allholesto
fill.
The
defaultsolventisS
imple
PointC
hargew
ater(S
PC
),with
coordinatesfrom
$G
MX
LIB
/spc2
16
.gro
.O
thersolvents
arealso
supported,asw
ellasm
ixedsolvents.
The
onlyrestriction
tosolventtypes
isthata
solventmolecule
consistsofexactly
oneresidue.
The
residueinform
ationin
thecoordinate
filesis
used,andshould
thereforebe
more
orless
consistent.In
practicethis
means
thattw
osubsequent
solventm
oleculesin
thesolvent
coordinatefile
shouldhave
differentresidue
number.
The
boxof
soluteis
builtby
stackingthe
coordinatesread
fromthe
coordinatefile.
This
means
thatthese
coordinatesshould
beequlibrated
inperiodic
boundaryconditions
toensure
agood
alignmentofm
oleculeson
thestacking
interfaces.
The
programcan
optionallyrotate
thesolute
molecule
toalign
thelongestm
oleculeaxis
alonga
boxedge.
This
way
theam
ountof
solventm
oleculesnecessary
isreduced.
Itshould
bekept
inm
indthat
thisonly
works
forshort
simulations,
aseg.
analpha-helicalpeptide
insolution
canrotate
over90
degrees,w
ithin500
ps.In
generalitistherefore
betterto
make
am
oreor
lesscubic
box.
Setting
-shelllargerthan
zerow
illplacea
layerofw
aterofthe
specifiedthickness
(nm)
aroundthe
solute.H
int:itis
agood
ideato
puttheprotein
inthe
centerofa
boxfirst(using
editconf).
Finally,genbox
willoptionally
remove
linesfrom
yourtopologyfile
inw
hicha
numberofsolventm
oleculesis
alreadyadded,and
addsa
linew
iththe
totalnumber
ofsolventmolecules
inyour
coordinatefile.
Files-cp
pro
tein
.gro
Input,Opt.
Generic
structure:gro
g96pdb
tprtpb
tpa-cs
spc2
16
.gro
Input,Opt.,Lib.Generic
structure:gro
g96pdb
tprtpb
tpa-ci
inse
rt.gro
Input,Opt.
Generic
structure:gro
g96pdb
tprtpb
tpa-o
ou
t.gro
Output
Generic
structure:gro
g96pdb
-pto
po
l.top
In/Out,O
pt.Topology
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-bo
xvector
00
0box
size-n
mo
lint
0no
ofextram
oleculesto
insert-try
int1
0try
inserting-nm
ol*-trytim
es-se
ed
int1
99
7random
generatorseed
-vdw
dreal
0.1
05
defaultvdwaals
distance-sh
ell
real0
thicknessofoptionalw
aterlayer
aroundsolute
21
4A
pp
en
dix
E.
Ma
nu
alP
age
s
-ot
tem
p.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-e
kre
kro
t.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-co
mbo
oln
oP
lotd
ata
for
the
com
ofea
chgr
oup
-mo
lbo
oln
oIn
dex
cont
ains
mol
ecul
enu
mbe
rsis
oat
omnu
mbe
rs-n
oju
mp
bool
no
Rem
ove
jum
psof
atom
sac
ross
the
box
-xbo
olye
sP
lotX
-com
pone
nt-y
bool
yes
Plo
tY-c
ompo
nent
-zbo
olye
sP
lotZ
-com
pone
nt-le
nbo
oln
oP
lotv
ecto
rle
ngth
E.4
8g
vela
cc
gve
lacc
com
pute
sth
eve
loci
tyau
toco
rrel
atio
nfu
nctio
n.W
hen
the
-sop
tion
isus
ed,
the
mom
entu
mau
toco
rrel
atio
nfu
nctio
nis
calc
ulat
ed.
With
optio
n-m
ol
the
mom
entu
mau
toco
rrel
atio
nfu
nctio
nof
mol
ecul
esis
calc
ulat
ed.
Inth
isca
seth
ein
dex
grou
psh
ould
cons
isto
fmol
ecul
enu
mbe
rsin
stea
dof
atom
num
bers
.
File
s-f
tra
j.trr
Inpu
tF
ullp
reci
sion
traj
ecto
ry:
trr
trj
-sto
po
l.tp
rIn
put,
Opt
.S
truc
ture
+m
ass(
db):
tpr
tpb
tpa
gro
g96
pdb
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-o
vac.
xvg
Out
put
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-m
ol
bool
no
Cal
cula
teva
cof
mol
ecul
es-a
cfle
nin
t-1
Leng
thof
the
AC
F,de
faul
tis
half
the
num
ber
offr
ames
-no
rma
lize
bool
yes
Nor
mal
ize
AC
F-P
enum
0O
rder
ofLe
gend
repo
lyno
mia
lfor
AC
F(0
indi
cate
sno
ne):
0,1
,2or
3-f
itfn
enum
no
ne
Fit
func
tion:
no
ne
,exp
,ae
xp,e
xpe
xpor
vac
-ncs
kip
int
0S
kip
Npo
ints
inth
eou
tput
file
ofco
rrel
atio
nfu
nctio
ns-b
eg
infit
real
0T
ime
whe
reto
begi
nth
eex
pone
ntia
lfito
fthe
corr
elat
ion
func
tion
-en
dfit
real
-1T
ime
whe
reto
end
the
expo
nent
ialfi
toft
heco
rrel
atio
nfu
nctio
n,-1
istil
lth
een
d
3.4
.M
ole
cula
rD
yna
mic
s1
5
onon
eor
two
coor
dina
tes
ofan
atom
,th
ereb
yfr
eezi
ngth
eat
oms
ina
plan
eor
ona
line.
Man
yfr
eeze
grou
psca
nbe
defin
ed.
Acc
eler
ate
grou
pO
nea
chat
omin
an’a
ccel
erat
egr
oup’
anac
cele
ratio
na
gw
illbe
impo
sed.
Thi
sis
equi
vale
ntto
anex
tern
alfo
rce.
Thi
sfe
atur
em
akes
itpo
ssib
leto
driv
eth
esy
stem
into
ano
n-eq
uilib
rium
stat
ean
den
able
sto
perf
orm
non-
equi
libriu
mM
Dto
obta
intr
ansp
ort
prop
ertie
s.
Ene
rgy
mon
itor
grou
pM
utua
lint
erac
tions
betw
een
alle
nerg
ym
onito
rgro
ups
are
com
pile
ddu
r-in
gth
esi
mul
atio
n.T
his
isdo
nese
para
tely
for
Lenn
ard-
Jone
san
dC
oulo
mb
term
s.In
prin
-ci
ple
upto
256
grou
psco
uld
bede
fined
,but
that
wou
ldle
adto
256
×25
6ite
ms!
Bet
ter
use
this
conc
epts
parin
gly.
All
non-
bond
edin
tera
ctio
nsbe
twee
npa
irsof
ener
gym
onito
rgr
oups
can
beex
clud
ed(s
eese
c.7.
3.1)
.P
airs
ofpa
rtic
les
from
excl
uded
pairs
ofen
ergy
mon
itor
grou
psar
eno
tpu
tin
toth
epa
irlis
t.T
his
can
resu
ltin
asi
gnifi
cant
spee
dup
for
sim
ulat
ions
whe
rein
tera
ctio
nsw
ithin
orbe
twee
npa
rts
ofth
esy
stem
are
notr
equi
red.
The
use
ofgr
oups
inan
alys
ispr
ogra
ms
isde
scrib
edin
chap
ter
8.
3.4
Mol
ecul
arD
ynam
ics
Agl
obal
flow
sche
me
for
MD
isgi
ven
inF
ig.3.3.
Eac
hM
Dor
EM
run
requ
ires
asin
puta
seto
fin
itial
coor
dina
tes
and
-op
tiona
lly-
initi
alve
loci
ties
ofal
lpar
ticle
sin
volv
ed.
Thi
sch
apte
rdo
esno
tdes
crib
eho
wth
ese
are
obta
ined
;for
the
setu
pof
anac
tual
MD
run
chec
kth
eon
line
man
uala
tw
ww
.gro
mac
s.or
g.
3.4.
1In
itial
cond
ition
s
Topo
logy
and
forc
efie
ld
The
syst
emto
polo
gy,
incl
udin
ga
desc
riptio
nof
the
forc
efie
ld,
mus
tbe
load
ed.
The
seite
ms
are
desc
ribed
inch
apte
r4.A
llth
isin
form
atio
nis
stat
ic;i
tis
neve
rm
odifi
eddu
ring
the
run.
Coo
rdin
ates
and
velo
citie
s
The
n,be
fore
aru
nst
arts
,th
ebo
xsi
zean
dth
eco
ordi
nate
san
dve
loci
ties
ofal
lpar
ticle
sar
ere
-qu
ired.
The
box
size
isde
term
ined
byth
ree
vect
ors
(nin
enu
mbe
rs)
b1,b
2,b
3,w
hich
repr
esen
tthe
thre
eba
sis
vect
ors
ofth
epe
riodi
cbo
x.W
hile
inth
epr
esen
tve
rsio
nof
GR
OM
AC
Son
lyre
ctan
-gu
lar
boxe
sar
eal
low
ed,
thre
enu
mbe
rssu
ffice
,bu
tth
eus
eof
thre
eve
ctor
sal
read
ypr
epar
esfo
rar
bitr
ary
tric
linic
boxe
sto
beim
plem
ente
din
ala
ter
vers
ion.
Ifth
eru
nst
arts
att=t 0
,th
eco
ordi
nate
satt
=t 0
mus
tbe
know
n.T
hele
ap
-fro
ga
lgo
rith
m,
used
toup
date
the
time
step
with∆t
(see
3.4.
4),
requ
ires
that
the
velo
citie
sm
ust
bekn
own
att
=t 0−
∆t
2.
Ifve
loci
ties
are
not
avai
labl
e,th
epr
ogra
mca
nge
nera
tein
itial
atom
icve
loci
ties
16
Ch
ap
ter
3.
Alg
orith
ms
TH
EG
LOB
AL
MD
ALG
OR
ITH
M
1.Inputinitialconditions
PotentialinteractionV
asa
functionofatom
positionsP
ositionsrofallatom
sin
thesystem
Velocitiesv
ofallatoms
inthe
system⇓
repeat2,3,4requirednum
berofsteps:
2.C
ompute
forces
The
forceon
anyatom
Fi =
−∂V
∂ri
iscom
putedby
calculatingthe
forcebetw
eennon-bonded
atompairs:
Fi = ∑
jF
ij
plusthe
forcesdue
tobonded
interactions(w
hichm
aydepend
on1,
2,3,or4
atoms),plus
restrainingand/or
externalforces.T
hepotentialand
kineticenergies
andthe
pressuretensor
arecom
puted.⇓
3.U
pdateconfiguration
The
movem
entoftheatom
sis
simulated
bynum
ericallysolving
New
ton’sequations
ofmotion
d2r
i
dt 2=
Fi
mi
ordr
i
dt=
vi ;
dv
i
dt
=F
i
mi
⇓4.ifrequired:O
utputstepw
ritepositions,velocities,energies,tem
perature,pressure,etc.
Figure
3.3:T
heglobalM
Dalgorithm
E.4
7.
gtra
j2
13
When
thebox
iscubic,
onecan
usethe
option-o
c,
which
averagesthe
tcaf’sover
allk-vectorsw
iththe
same
length.T
hisresults
inm
oreaccurate
tcaf’s.B
oththe
cubictcaf’s
andfits
arew
rittento
-oc
The
cubiceta
estimates
arealso
written
to-o
v.
With
option-m
ol
thetransverse
currentisdeterm
inedofm
oleculesinstead
ofatoms.
Inthis
casethe
indexgroup
shouldconsistofm
oleculenum
bersinstead
ofatomnum
bers.
The
k-dependentviscositiesin
the-ovfile
shouldbe
fittedto
eta(k)=
eta0(1
-a
k2)
toobtain
theviscosity
atinfinitew
avelength.
NO
TE
:make
sureyou
write
coordinatesand
velocitiesoften
enough.T
heinitial,
non-exponential,partof
theautocorrelation
functionis
veryim
portantforobtaining
agood
fit.
Files
-ftra
j.trrInput
Fullprecision
trajectory:trr
trj-s
top
ol.tp
rInput,O
pt.S
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-ot
tran
scur.xvg
Output,O
pt.xvgr/xm
grfile
-oa
tcaf
all.xvg
Output
xvgr/xmgr
file-o
tcaf.xvg
Output
xvgr/xmgr
file-o
ftca
ffit.xvg
Output
xvgr/xmgr
file-o
ctca
fcu
b.xvg
Output,O
pt.xvgr/xm
grfile
-ov
visck.xvg
Output
xvgr/xmgr
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-m
ol
booln
oC
alculatetcafofm
olecules-k3
4bool
no
Also
usek=
(3,0,0)and
k=(4,0,0)
-wt
real5
Exponentialdecay
time
forthe
TC
AF
fitweights
E.47
gtraj
gtrajplots
coordinates,velocities,forcesand/or
thebox.
With
-com
thecoordinates,velocities
andforces
arecalculated
forthe
centerof
mass
ofeach
group.W
hen-m
ol
isset,
thenum
bersin
theindex
fileare
interpretedas
molecule
numbers
andthe
same
procedureas
with
-com
isused
foreach
molecule.
Option
-ot
plotsthe
temperature
ofeach
group,provided
velocitiesare
presentin
thetrajectory
file.This
implies
-com
.
Option
-ekr
plotsthe
rotationalkineticenergy
ofeachgroup,provided
velocitiesare
presentinthe
trajec-tory
file.T
hisim
plies-com
.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-ox
coo
rd.xvg
Output,O
pt.xvgr/xm
grfile
-ov
velo
c.xvgO
utput,Opt.
xvgr/xmgr
file-o
ffo
rce.xvg
Output,O
pt.xvgr/xm
grfile
-ob
bo
x.xvgO
utput,Opt.
xvgr/xmgr
file
21
2A
pp
en
dix
E.
Ma
nu
alP
age
s
E.4
5g
sorie
nt
gso
rient
anal
yzes
solv
ento
rient
atio
nar
ound
solu
tes.
Itca
lcul
ates
two
angl
esbe
twee
nth
eve
ctor
from
one
orm
ore
refe
renc
epo
sitio
nsto
the
first
atom
ofea
chso
lven
tmol
ecul
e:th
eta1
:th
ean
gle
with
the
vect
orfr
omth
efir
stat
omof
the
solv
entm
olec
ule
toth
em
idpo
intb
etw
een
atom
s2
and
3.th
eta2
:th
ean
gle
with
the
norm
alof
the
solv
entp
lane
,defi
ned
byth
esa
me
thre
eat
oms.
The
refe
renc
eca
nbe
ase
tof
atom
sor
the
cent
erof
mas
sof
ase
tof
atom
s.T
hegr
oup
ofso
lven
tat
oms
shou
ldco
nsis
tof
3at
oms
per
solv
ent
mol
ecul
e.O
nly
solv
ent
mol
ecul
esbe
twee
n-r
min
and
-rm
ax
are
cons
ider
edea
chfr
ame.
-o:
angl
edi
strib
utio
nof
thet
a1.
-no
:an
gle
dist
ribut
ion
ofth
eta2
.
-ro
:<
cos(
thet
a1)>
and<
3cos
2(t
heta
2)-1>
asa
func
tion
ofth
edi
stan
ce.
-ro
:th
esu
mov
eral
lsol
vent
mol
ecul
esw
ithin
dist
ance
rof
cos(
thet
a1)
and
3cos
2(t
heta
2)-1
asa
func
tion
ofr.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-oso
ri.x
vgO
utpu
txv
gr/x
mgr
file
-no
sno
r.xv
gO
utpu
txv
gr/x
mgr
file
-ro
sord
.xvg
Out
put
xvgr
/xm
grfil
e-c
osc
um
.xvg
Out
put
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-c
om
bool
no
Use
the
cent
erof
mas
sas
the
refe
renc
epo
stio
n-r
min
real
0M
inim
umdi
stan
ce-r
ma
xre
al0
.5M
axim
umdi
stan
ce-n
bin
int
20
Num
ber
ofbi
ns
E.4
6g
tcaf
gtc
afco
mpu
tes
tran
vers
ecu
rren
taut
ocor
rela
tions
.T
hese
are
used
toes
timat
eth
esh
ear
visc
osity
eta.
For
deta
ilsse
e:P
alm
er,J
CP
49(1
994)
pp35
9-36
6.
Tra
nsve
rse
curr
ents
are
calc
ulat
edus
ing
the
k-ve
ctor
s(1
,0,0
)an
d(2
,0,0
)ea
chal
soin
the
y-an
dz-
dire
ctio
n,(1
,1,0
)an
d(1
,-1,
0)ea
chal
soin
the
2ot
her
plai
ns(t
hese
vect
ors
are
noti
ndep
ende
nt)
and
(1,1
,1)
and
the
3ot
her
box
diag
onal
s(a
lso
noti
ndep
ende
nt).
For
each
k-ve
ctor
the
sine
and
cosi
near
eus
ed,i
nco
mbi
natio
nw
ithth
eve
loci
tyin
2pe
rpen
dicu
lar
dire
ctio
ns.
Thi
sgi
ves
ato
talo
f16
*2*2
=64
tran
sver
secu
rren
ts.
One
auto
corr
elat
ion
isca
lcul
ated
fitte
dfo
rea
chk-
vect
or,w
hich
give
s16
tcaf
’s.
Eac
hof
thes
etc
af’s
isfit
ted
tof(
t)=
exp(
-v)(
cosh
(Wv)
+1/
Wsi
nh(W
v)),
v=
-t/(
2ta
u),W
=sq
rt(1
-4
tau
eta/
rho
k2),
whi
chgi
ves
16ta
u’s
and
eta’
s.T
hefit
wei
ghts
deca
yw
ithtim
eas
exp(
-t/w
t),t
hetc
afan
dfit
are
calc
ulat
edup
totim
e5*
wt.
The
eta’
ssh
ould
befit
ted
to1
-a
eta(
k)k
2,f
rom
whi
chon
eca
nes
timat
eth
esh
ear
visc
osity
atk=
0.
3.4
.M
ole
cula
rD
yna
mic
s1
7
0�
Vel
ocity
�
0.0
Probability �
Fig
ure
3.4:
AM
axw
ellia
ndi
strib
utio
n,ge
nera
ted
from
rand
omnu
mbe
rs.
v i,i
=1...3N
from
aM
axw
ellia
ndi
strib
utio
n(F
ig.3.
4)at
agi
ven
abso
lute
tem
pera
tureT:
p(v
i)=√ m
i
2πkT
exp(−m
iv2 i
2kT
)(3
.6)
whe
rek
isB
oltz
man
n’s
cons
tant
(see
chap
ter
2).
Toac
com
plis
hth
is,n
orm
ally
dist
ribut
edra
ndom
num
bers
are
gene
rate
dby
addi
ngtw
elve
rand
omnu
mbe
rsR
kin
the
rang
e0≤R
k<
1an
dsu
btra
ctin
g6.
0fr
omth
eir
sum
.T
here
sult
isth
enm
ultip
lied
byth
est
anda
rdde
viat
ion
ofth
eve
loci
tydi
strib
utio
n√ kT/m
i.S
ince
the
resu
lting
tota
lene
rgy
will
notc
orre
spon
dex
actly
toth
ere
quire
dte
mpe
ratu
reT,a
corr
ectio
nis
mad
e:fir
stth
ece
nter
-of-
mas
sm
otio
nis
rem
oved
and
then
allv
eloc
ities
are
scal
edsu
chth
atth
eto
tale
nerg
yco
rres
pond
sex
actly
toT
(see
eqn.3
.12)
.
Cen
ter-
of-m
ass
mot
ion
The
cent
er-o
f-m
ass
velo
city
isno
rmal
lyse
tto
zero
atev
ery
step
.N
orm
ally
ther
eis
none
text
erna
lfo
rce
actin
gon
the
syst
eman
dth
ece
nter
-of-
mas
sve
loci
tysh
ould
rem
ain
cons
tant
.In
prac
tice,
how
ever
,th
eup
date
algo
rithm
deve
lops
ave
rysl
owch
ange
inth
ece
nter
-of-
mas
sve
loci
ty,
and
thus
inth
eto
talk
inet
icen
ergy
ofth
esy
stem
,spe
cial
lyw
hen
tem
pera
ture
coup
ling
isus
ed.
Ifsu
chch
ange
sar
eno
tque
nche
d,an
appr
ecia
ble
cent
er-o
f-m
ass
mot
ion
deve
lops
even
tual
lyin
long
runs
,an
dth
ete
mpe
ratu
rew
illbe
sign
ifica
ntly
mis
inte
rpre
ted.
The
sam
em
ayha
ppen
due
toov
eral
lro
tatio
nalm
otio
n,bu
ton
lyw
hen
anis
olat
edcl
uste
ris
sim
ulat
ed.
Inpe
riodi
csy
stem
sw
ithfil
led
boxe
s,th
eov
eral
lrot
atio
nalm
otio
nis
coup
led
toot
her
degr
ees
offr
eedo
man
ddo
esno
tgiv
ean
ypr
oble
ms.
18
Ch
ap
ter
3.
Alg
orith
ms
3.4.2N
eighborsearching
As
mentioned
inchapter4,
internalforcesare
eithergenerated
fromfixed
(static)lists,
orfrom
dynamics
lists.T
helatter
concernnon-bonded
interactionsbetw
eenany
pairof
particles.W
hencalculating
thenon-bonded
forces,it
isconvenient
tohave
allparticlesin
arectangular
box.A
sshow
nin
Fig.3.1,
itis
possibleto
transforma
triclinicbox
intoa
rectangularbox.
The
outputcoordinates
arealw
aysin
arectangular
box,evenw
hena
dodecahedronor
triclinicbox
was
usedfor
thesim
ulation.E
quations(
3.1)ensure
thatwe
canresetparticles
ina
rectangularbox
byfirst
shiftingthem
with
boxvectorc,then
withb
andfinally
witha
.E
quations(3.3)ensure
thatwe
canfind
the14
nearesttriclinic
images
within
alinear
combination
which
doesnot
involvem
ultiplesofbox
vectors.
Pair
listsgeneration
The
non-bondedpair
forcesneed
tobe
calculatedonly
forthose
pairsi,j
forw
hichthe
distancerij
betweeni
andthe
nearestimage
ofj
isless
thana
givencut-offradiusRc .
Som
eofthe
particlepairs
thatfulfillthiscriterion
areexcluded,w
hentheir
interactionis
alreadyfully
accountedfor
bybonded
interactions.G
RO
MA
CS
employs
ap
air
listthat
containsthose
particlepairs
forw
hichnon-bonded
forcesm
ustbecalculated.
The
pairlistcontains
theparticle
numbers
andan
indexfor
theim
agedisplacem
entvectors
thatm
ustbe
appliedto
obtainthe
nearestim
age,for
allparticlepairs
thathave
anearest-im
agedistance
lessthanrsh
ort
.T
helist
isupdated
everynstliststeps,
wheren
stlistis
typically10
forthe
GR
OM
AC
Sforcefield
and5
forthe
GR
OM
OS
-96forcefield.
There
isan
optionto
calculatethe
totalnon-bondedforce
oneach
particledue
toall
particlein
ashellaround
thelist-cutoff,
i.e,atadistance
betweenrsh
ort
andrlo
ng
.T
hisforce
iscalculated
duringthe
pairlistupdate
andretained
duringn
stliststeps.
Tom
akethe
neighborlistallparticlesthatare
close(i.e.w
ithinthe
cut-off)toa
givenparticle
must
befound.
This
searching,usually
calledneighbor
searching(N
S),
involvesperiodic
boundaryconditions
anddeterm
iningtheim
age(see
sec.3.2).W
ithoutperiodic
boundaryconditions
asim
pleO
(N2)
algorithmm
ustbe
used.W
ithperiodic
boundaryconditions
agrid
searchcan
beused,w
hichisO
(N).
Sim
plesearch
Due
toequations
(3.1)and
(3.5),the
vectorrij
connectingim
agesw
ithinthe
cut-offRccan
befound
byconstructing:
r′′′
=r
j −r
i(3.7)
r′′
=r′′′−
a∗
rou
nd
(r ′′′z/c
z ))(3.8)
r′
=r′′−
b∗
rou
nd
(r ′′y /by )
(3.9)
rij
=r′−
c∗
rou
nd
(r ′x /a
x )(3.10)
When
distancesbetw
eenany
two
particlesin
atriclinic
boxare
needed,m
anyshifts
ofcombina-
tionsofbox
vectorsneed
tobe
consideredto
findthe
nearestimage.
E.4
4.
gsg
an
gle
21
1
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-so
lsizereal
0.1
4R
adiusofthe
solventprobe(nm
)-n
do
tsint
24
Num
berofdots
persphere,m
oredots
means
more
accuracy-q
ma
xreal
0.2
The
maxim
umcharge
(e,absolutevalue)
ofahydrophobic
atom-m
ina
rea
real0
.5T
hem
aximum
charge(e,absolute
value)ofa
hydrophobicatom
-skipint
1D
oonly
everynth
frame
-pro
tbool
yes
Outputthe
proteinto
theconnelly
pdbfile
too
E.44
gsgangle
Com
putethe
angleand
distancebetw
eentw
ogroups.
The
groupsare
definedby
anum
berofatom
sgiven
inan
indexfile
andm
aybe
two
orthree
atoms
insize.
The
anglescalculated
dependon
theorder
inw
hichthe
atoms
aregiven.
Giving
forinstance
56
willrotate
thevector
5-6w
ith180
degreescom
paredto
giving6
5.
Ifthreeatom
sare
given,thenorm
alonthe
planespanned
bythose
threeatom
sw
illbecalculated,using
theform
ulaP
1P2
xP
1P3.
The
cosofthe
angleis
calculated,usingthe
inproductofthetw
onorm
alizedvectors.
Here
isw
hatsome
ofthefile
optionsdo:
-oa:A
nglebetw
eenthe
two
groupsspecified
inthe
indexfile.
Ifa
groupcontains
threeatom
sthe
normal
tothe
planedefined
bythose
threeatom
sw
illbeused.
Ifagroup
containstw
oatom
s,thevector
definedby
thosetw
oatom
sw
illbeused.
-od:D
istancebetw
eentw
ogroups.
Distance
istaken
fromthe
centerofone
groupto
thecenter
oftheother
group.-od1:
Ifoneplane
andone
vectoris
given,thedistances
foreach
oftheatom
sfrom
thecenter
oftheplane
isgiven
seperately.-od2:
For
two
planesthis
optionhas
nom
eaning.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput
Indexfile
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-oa
sga
ng
le.xvg
Output
xvgr/xmgr
file-o
dsg
dist.xvg
Output
xvgr/xmgr
file-o
d1
sgd
ist1.xvg
Output
xvgr/xmgr
file-o
d2
sgd
ist2.xvg
Output
xvgr/xmgr
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files
21
0A
pp
en
dix
E.
Ma
nu
alP
age
s
-acf
len
int
-1Le
ngth
ofth
eA
CF,
defa
ulti
sha
lfth
enu
mbe
rof
fram
es-n
orm
aliz
ebo
olye
sN
orm
aliz
eA
CF
-Pen
um0
Ord
erof
Lege
ndre
poly
nom
ialf
orA
CF
(0in
dica
tes
none
):0
,1,2
or3
-fitf
nen
umn
on
eF
itfu
nctio
n:n
on
e,e
xp,a
exp
,exp
exp
orva
c-n
cski
pin
t0
Ski
pN
poin
tsin
the
outp
utfil
eof
corr
elat
ion
func
tions
-be
gin
fitre
al0
Tim
ew
here
tobe
gin
the
expo
nent
ialfi
toft
heco
rrel
atio
nfu
nctio
n-e
nd
fitre
al-1
Tim
ew
here
toen
dth
eex
pone
ntia
lfito
fthe
corr
elat
ion
func
tion,
-1is
till
the
end
E.4
2g
saltb
r
gsa
ltbr
plot
sth
edi
ffere
nce
betw
een
allc
ombi
natio
nof
char
ged
grou
psas
afu
nctio
nof
time.
The
grou
psar
eco
mbi
ned
indi
ffere
ntw
ays.
Am
inim
umdi
stan
ceca
nbe
give
n,(e
g.th
ecu
t-of
f),
then
grou
psth
atar
ene
ver
clos
erth
anth
atdi
stan
cew
illno
tbe
plot
ted.
Out
put
will
bein
anu
mbe
rof
fixed
filen
ames
,m
in-m
in.x
vg,m
in-p
lus.
xvg
and
plus
-plu
s.xv
g,or
files
for
ever
yin
divi
dual
ion-
pair
ifse
lect
ed
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tre
al1
00
0tr
unc
dist
ance
-se
pbo
oln
oU
sese
para
tefil
esfo
rea
chin
tera
ctio
n(m
aybe
MA
NY
)
E.4
3g
sas
gsa
sco
mpu
tes
hydr
opho
bic
and
tota
lsol
vent
acce
ssib
lesu
rfac
ear
ea.
As
asi
deef
fect
the
Con
nolly
surf
ace
can
bege
nera
ted
asw
elli
na
pdb
file
whe
reth
eno
des
are
repr
esen
ted
asat
oms
and
the
vert
ices
conn
ectin
gth
ene
ares
tno
des
asC
ON
EC
Tre
cord
s.T
hear
eaca
nbe
plot
ted
per
atom
and
per
resi
due
asw
ell(
optio
n-a
o).
Inco
mbi
natio
nw
ithth
ela
tter
optio
nanit
pfil
eca
nbe
gene
rate
d(o
ptio
n-i)
whi
chca
nbe
used
tore
stra
insu
rfac
eat
oms.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a-o
are
a.x
vgO
utpu
txv
gr/x
mgr
file
-rre
sare
a.x
vgO
utpu
txv
gr/x
mgr
file
-qco
nn
elly
.pd
bO
utpu
t,O
pt.
Pro
tein
data
bank
file
-ao
ato
ma
rea
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-i
surf
at.itp
Out
put,
Opt
.In
clud
efil
efo
rto
polo
gy
3.4
.M
ole
cula
rD
yna
mic
s1
9
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Fig
ure
3.5:
Grid
sear
chin
two
dim
ensi
ons.
The
arro
ws
are
the
box
vect
ors.
Grid
sear
ch
The
grid
sear
chis
sche
mat
ical
lyde
pict
edin
Fig
.3.
5.A
llpa
rtic
les
are
puto
nth
eN
Sgr
id,w
ithth
esm
alle
stsp
acin
g≥R
c/2
inea
chof
the
dire
ctio
ns.
Inth
edi
rect
ion
ofea
chbo
xve
ctor
,a
part
icle
iha
sth
ree
imag
es.
For
each
dire
ctio
nth
eim
age
may
be-1
,0or
1,co
rres
pond
ing
toa
tran
slat
ion
over
-1,
0or
+1
box
vect
or.
We
dono
tse
arch
the
surr
ound
ing
NS
grid
cells
for
neig
hbor
sof
ian
dth
enca
lcul
ate
the
imag
e,bu
tra
ther
cons
truc
tth
eim
ages
first
and
then
sear
chne
ighb
ors
corr
espo
ndin
gto
that
imag
eofi.
As
can
been
seen
inF
ig.
3.5,
for
som
eim
ages
ofith
esa
me
grid
cell
mig
htbe
sear
ched
.T
his
isno
ta
prob
lem
,si
nce
atm
ost
one
imag
ew
ill“s
ee”
the
j-pa
rtic
le,
due
toth
em
inim
umim
age
conv
entio
n.F
orev
ery
part
icle
,le
ssth
an12
5(5
3)
neig
hbor
ing
cells
are
sear
ched
.T
here
fore
,th
eal
gorit
hmsc
ales
linea
rw
ithth
enu
mbe
rof
part
icle
s.A
lthou
ghth
epr
efac
tor
isla
rge
the
scal
ing
beha
vior
mak
esth
eal
gorit
hmfa
rsu
perio
rov
erth
est
anda
rdO
(N2)
algo
rithm
whe
nth
enu
mbe
rof
part
icle
sex
ceed
sa
few
hund
red.
The
grid
sear
chis
equa
llyfa
stfo
rre
ctan
gula
ran
dtr
iclin
icbo
xes.
Thu
sfo
rm
ost
prot
ein
and
pept
ide
sim
ulat
ions
the
rhom
bic
dode
cahe
dron
will
beth
epr
efer
able
box
shap
e.
Cha
rge
grou
ps
Whe
reap
plic
able
,nei
ghbo
rsea
rchi
ngis
carr
ied
outo
nth
eba
sis
ofch
arg
eg
rou
ps.A
char
gegr
oup
isa
smal
lset
ofne
arby
atom
sth
atha
vene
tcha
rge
zero
.C
harg
egr
oups
are
defin
edin
the
mol
ecul
arto
polo
gy.
Ifth
ene
ares
tim
age
dist
ance
betw
een
the
geo
me
tric
alc
en
terso
fthe
atom
sof
two
char
gegr
oups
isle
ssth
anth
ecu
toff
radi
us,a
llat
ompa
irsbe
twee
nth
ech
arge
grou
psar
ein
clud
edin
the
pair
list.
Thi
spr
oced
ure
avoi
dsth
ecr
eatio
nof
char
ges
due
toth
eus
eof
acu
t-of
f(w
hen
one
char
geof
adi
pole
isw
ithin
rang
ean
dth
eot
her
not)
,whi
chca
nha
vedi
sast
rous
cons
eque
nces
for
the
beha
vior
ofth
eC
oulo
mb
inte
ract
ion
func
tion
atdi
stan
ces
near
the
cut-
offr
adiu
s.If
mol
ecul
argr
oups
have
full
char
ges
(ions
),ch
arge
grou
psdo
nota
void
adve
rse
cut-
offe
ffect
s,an
dyo
ush
ould
cons
ider
usin
gon
eof
the
latti
cesu
mm
etho
dssu
pplie
dby
GR
OM
AC
S[
13].
Ifap
prop
riate
lyco
nstr
ucte
dsh
iftfu
nctio
nsar
eus
edfo
rth
eel
ectr
osta
ticfo
rces
,no
char
gegr
oups
20
Ch
ap
ter
3.
Alg
orith
ms
areneeded.
Such
shiftfunctionsare
implem
entedin
GR
OM
AC
S(see
chapter4)
butmustbe
usedw
ithcare:
inprinciple
theyshould
becom
binedw
itha
latticesum
forlong-range
electrostatics.
3.4.3C
ompute
forces
Potentialenergy
When
forcesare
computed,
thepotential
energyof
eachinteraction
termis
computed
asw
ell.T
hetotalpotentialenergy
issum
med
forvarious
contributions,suchas
Lennard-Jones,Coulom
b,and
bondedterm
s.Itis
alsopossible
tocom
putethese
contributionsfor
gro
up
sofatoms
thatareseparately
defined(see
sec.3.3).
Kinetic
energyand
temperature
The
temperature
isgiven
bythe
totalkineticenergy
oftheN
-particlesystem
:
Ekin
=12
N∑i=1
mi v
2i(3.11)
From
thisthe
absolutetem
peratureT
canbe
computed
using:
12N
df kT
=E
kin
(3.12)
where
kis
Boltzm
ann’sconstant
andNdf
isthe
number
ofdegrees
offreedom
which
canbe
computed
from:
Ndf
=3N
−N
c −N
com
(3.13)
Here
Nc
isthe
numberofco
nstra
intsim
posedon
thesystem
.W
henperform
ingm
oleculardynam-
icsN
com
=3
additionaldegreesof
freedomm
ustbe
removed,
becausethe
threecenter-of-m
assvelocities
areconstants
ofthe
motion,
which
areusually
setto
zero.W
hensim
ulatingin
vacuo,the
rotationaround
thecenter
ofm
asscan
alsobe
removed,
inthis
caseN
com
=6.
When
more
thanone
temperature
couplinggroup
isused,the
number
ofdegreesoffreedom
forgroup
iis:
Nidf
=(3N
i−N
ic ) 3N−N
c −N
com
3N−N
c(3.14)
The
kineticenergy
canalso
bew
rittenas
atensor,w
hichis
necessaryfor
pressurecalculation
ina
triclinicsystem
,orsystem
sw
hereshear
forcesare
imposed:
Ekin
=12
N∑i
mi v
i ⊗v
i(3.15)
Pressure
andvirial
The
pressuretensorPis
calculatedfrom
thedifference
between
kineticenergy
Ekin
andthe
virialΞ
P=
2V(E
kin−
Ξ)
(3.16)
E.4
1.
gro
tacf
20
9
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-qe
iwit.p
db
Input,Opt.
Protein
databank
file-o
qb
fac.p
db
Output,O
pt.P
roteindata
bankfile
-ox
xave
r.pd
bO
utput,Opt.
Protein
databank
file-o
rmsf.xvg
Output
xvgr/xmgr
file-o
drm
sde
v.xvgO
utput,Opt.
xvgr/xmgr
file-o
cco
rrel.xvg
Output,O
pt.xvgr/xm
grfile
-dir
rmsf.lo
gO
utput,Opt.
Logfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-re
sbool
no
Calculate
averagesfor
eachresidue
-an
isobool
no
Com
puteanisotropic
termperature
factors
E.41
grotacf
grotacf
calculatesthe
rotationalcorrelationfunction
form
olecules.T
hreeatom
s(i,j,k)
must
begiven
inthe
indexfile,defining
two
vectorsijand
jk.T
herotationalacfis
calculatedas
theautocorrelation
functionofthe
vectorn
=ijx
jk,i.e.the
crossproductofthe
two
vectors.S
incethree
atoms
spana
plane,theorder
ofthethree
atoms
doesnotm
atter.O
ptionally,controlledby
the-d
switch,you
cancalculate
therotational
correlationfunction
forlinear
molecules
byspecifying
two
atoms
(i,j)in
theindex
file.
EX
AM
PLE
S
grotacf-P
1-nparm
2-fft-n
index-o
rotacf-x-P1
-faexpfit-x-P
1-beginfit2.5
-endfit20.0
This
willcalculate
therotationalcorrelation
functionusing
afirst
orderLegendre
polynomialof
theangle
ofavector
definedby
theindex
file.T
hecorrelation
functionw
illbefitted
from2.5
pstill20.0
psto
atw
oparam
eterexponential
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-nin
de
x.nd
xInput
Indexfile
-oro
tacf.xvg
Output
xvgr/xmgr
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-d
booln
oU
seindex
doublets(vectors)
forcorrelation
functioninstead
oftriplets
(planes)-a
ver
boolye
sA
verageover
molecules
20
8A
pp
en
dix
E.
Ma
nu
alP
age
s
0.6
inth
isca
se)
can
bege
nera
ted,
byde
faul
tave
ragi
ngov
ereq
uiva
lent
hydr
ogen
s(a
lltr
iple
tsof
hydr
ogen
sna
med
*[12
3]).
Add
ition
ally
alis
tof
equi
vale
ntat
oms
can
besu
pplie
d(
-eq
uiv
),ea
chlin
eco
ntai
ning
ase
tofe
quiv
alen
tato
ms
spec
ified
asre
sidu
enu
mbe
ran
dna
me
and
atom
nam
e;e.
g.:
3S
ER
HB
13
SE
RH
B2
Res
idue
and
atom
nam
esm
ust
exac
tlym
atch
thos
ein
the
stru
ctur
efil
e,in
clud
ing
case
.S
peci
fyin
gno
n-se
quen
tiala
tom
sis
unde
fined
.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-eq
uiv
eq
uiv
.da
tIn
put,
Opt
.G
ener
icda
tafil
e-o
dis
trm
sd.x
vgO
utpu
txv
gr/x
mgr
file
-rm
srm
sdis
t.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e-s
clrm
ssca
le.x
pm
Out
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
-me
an
rmsm
ea
n.x
pm
Out
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
-nm
r3n
mr3
.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e-n
mr6
nm
r6.x
pm
Out
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
-no
en
oe
.da
tO
utpu
t,O
pt.
Gen
eric
data
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-n
leve
lsin
t4
0D
iscr
etiz
erm
sin
#le
vels
-ma
xre
al-1
Max
imum
leve
lin
mat
rices
-su
mh
bool
yes
aver
age
dist
ance
over
equi
vale
nthy
drog
ens
E.4
0g
rmsf
grm
sfco
mpu
tes
the
root
mea
nsq
uare
fluct
uatio
n(R
MS
F,i.e
.st
anda
rdde
viat
ion)
ofat
omic
posi
tions
afte
rfir
stfit
ting
toa
refe
renc
efr
ame.
With
optio
n-o
qth
eR
MS
Fva
lues
are
conv
erte
dto
B-f
acto
rva
lues
,whi
char
ew
ritte
nto
apd
bfil
ew
ithth
eco
ordi
nate
s,of
the
stru
ctur
efil
e,or
ofa
pdb
file
whe
n-q
issp
ecifi
ed.
Opt
ion-o
xw
rites
the
B-f
acto
rsto
afil
ew
ithth
eav
erag
eco
ordi
nate
s.
With
the
optio
n-o
dth
ero
otm
ean
squa
rede
viat
ion
with
resp
ectt
oth
ere
fere
nce
stru
ctur
eis
calc
ulat
ed.
With
the
optio
nan
iso
grm
sfw
illco
mpu
tean
isot
ropi
cte
mpe
ratu
refa
ctor
san
dth
enit
will
also
outp
utav
erag
eco
ordi
nate
san
da
pdb
file
with
AN
ISO
Ure
cord
s(c
orre
sond
ing
toth
e-o
qor
-ox
optio
n).
Ple
ase
note
that
the
Uva
lues
are
orie
ntat
ion
depe
nden
t,so
befo
reco
mpa
rison
with
expe
rimen
tald
ata
you
shou
ldve
rify
that
you
fitto
the
expe
rimen
talc
oord
inat
es.
Whe
na
pdb
inpu
tfile
ispa
ssed
toth
epr
ogra
man
dth
e-a
nis
ofla
gis
seta
corr
elat
ion
plot
ofth
eU
ijw
illbe
crea
ted,
ifan
yan
isot
ropi
cte
mpe
ratu
refa
ctor
sar
epr
esen
tin
the
pdb
file.
With
optio
n-d
irth
eav
erag
eM
SF
(3x3
)m
atrix
isdi
agon
aliz
ed.
Thi
ssh
ows
the
dire
ctio
nsin
whi
chth
eat
oms
fluct
uate
the
mos
tand
the
leas
t.
File
s
3.4
.M
ole
cula
rD
yna
mic
s2
1
12
0t
xv
x
Fig
ure
3.6:
The
Leap
-Fro
gin
tegr
atio
nm
etho
d.T
heal
gorit
hmis
calle
dLe
ap-F
rog
beca
use
ran
dv
are
leap
ing
like
frog
sov
erea
chot
hers
back
.
whe
reV
isth
evo
lum
eof
the
com
puta
tiona
lbox
.T
hesc
alar
pres
sure
P,
whi
chca
nbe
used
for
pres
sure
coup
ling
inth
eca
seof
isot
ropi
csy
stem
s,is
com
pute
das
:
P=
trac
e(P
)/3
(3.1
7)
The
viria
lΞte
nsor
isde
fined
as
Ξ=−
1 2
∑ i<j
rij⊗
Fij
(3.1
8)
Inse
c.B
.1th
eim
plem
enta
tion
inG
RO
MA
CS
ofth
evi
rialc
ompu
tatio
nis
desc
ribed
.
3.4.
4U
pdat
eco
nfigu
ratio
n
The
GR
OM
AC
SM
Dpr
ogra
mut
ilize
sth
eso
-cal
ledlea
p-f
rog
algo
rithm
[14]
for
the
inte
grat
ion
ofth
eeq
uatio
nsof
mot
ion.
The
leap
-fro
gal
gorit
hmus
espo
sitio
nsr
attim
et
and
velo
citie
svat
timet−
∆t
2;i
tupd
ates
posi
tions
and
velo
citie
sus
ing
the
forc
esF
(t)
dete
rmin
edby
the
posi
tions
attim
et:
v(t
+∆t 2)
=v(t−
∆t 2)+
F(t
)m
∆t
(3.1
9)
r(t
+∆t)
=r(t
)+
v(t
+∆t 2)∆t
(3.2
0)
The
algo
rithm
isvi
sual
ized
inF
ig.3.6.
Itis
equi
vale
ntto
the
Verle
t[15]
algo
rithm
:
r(t
+∆t)
=2r
(t)−
r(t−
∆t)
+F
(t)
m∆t2
+O
(∆t4
)(3
.21)
The
algo
rithm
isof
third
orde
rinr
and
istim
e-re
vers
ible
.S
eere
f.[
16]
for
the
mer
itsof
this
algo
rithm
and
com
paris
onw
ithot
her
time
inte
grat
ion
algo
rithm
s.
The
equa
tions
ofm
otio
nar
em
odifi
edfo
rte
mpe
ratu
reco
uplin
gan
dpr
essu
reco
uplin
g,an
dex
-te
nded
toin
clud
eth
eco
nser
vatio
nof
cons
trai
nts,
allo
fwhi
char
ede
scrib
edbe
low
.
3.4.
5Te
mpe
ratu
reco
uplin
g
For
seve
ralr
easo
ns(d
riftd
urin
geq
uilib
ratio
n,dr
iftas
are
sult
offo
rce
trun
catio
nan
din
tegr
atio
ner
rors
,hea
ting
due
toex
tern
alor
fric
tiona
lfor
ces)
,iti
sne
cess
ary
toco
ntro
lthe
tem
pera
ture
ofth
esy
stem
.G
RO
MA
CS
can
use
eith
erth
ew
ea
kco
up
lings
chem
eof
Ber
ends
en[
17]o
rth
eex
tend
eden
sem
ble
Nose
-Hoo
ver
sche
me
[18,1
9].
22
Ch
ap
ter
3.
Alg
orith
ms
Berendsen
temperature
coupling
The
Berendsen
algorithmm
imics
weak
couplingw
ithfirst-order
kineticsto
anexternalheatbath
with
giventem
peratureT0 .
See
ref.[20]
fora
comparison
with
theN
ose-Hoover
scheme.
The
effectof
thisalgorithm
isthat
adeviation
ofthe
systemtem
peraturefromT
0is
slowly
correctedaccording
todTdt
=T
0 −T
τ(3.22)
which
means
thata
temperature
deviationdecays
exponentiallyw
itha
time
constantτ.
This
method
ofcouplinghas
theadvantage
thatthestrength
ofthecoupling
canbe
variedand
adaptedto
theuser
requirement:
forequilibration
purposesthe
couplingtim
ecan
betaken
quiteshort(e.g.
0.01ps),butfor
reliableequilibrium
runsitcan
betaken
much
longer(e.g.0.5
ps)in
which
caseithardly
influencesthe
conservativedynam
ics.
The
heatflowinto
oroutofthe
systemis
effectedby
scalingthe
velocitiesofeach
particleevery
stepw
itha
time-dependentfactor
λ,given
by
λ= [1
+∆t
τT {
T0
T(t−
∆t
2)−
1 }]1/2
(3.23)
The
parameterτ
Tis
closeto,
butnot
exactlyequal
tothe
time
constantτ
ofthe
temperature
coupling(eqn.3.22):
τ=
2CVτT/N
df k(3.24)
where
CV
isthe
totalheat
capacityof
thesystem
,k
isB
oltzmann’s
constant,andN
dfis
thetotal
number
ofdegrees
offreedom
.T
hereason
thatτ6=τT
isthat
thekinetic
energychange
causedby
scalingthe
velocitiesis
partlyredistributed
between
kineticand
potentialenergyand
hencethe
changein
temperature
isless
thanthe
scalingenergy.
Inpractice,the
ratioτ/τ
Tranges
from1
(gas)to
2(harm
onicsolid)
to3
(water).
When
we
usethe
term’tem
peraturecoupling
time
constant’,w
em
eanthe
parameterτT
.N
otethat
inpractice
thescaling
factorλislim
itedto
therange
of0.8<
=λ<
=1.25,
toavoid
scalingby
verylarge
numbers
which
may
crashthe
simulation.
Innorm
aluse,λwillalw
aysbe
much
closerto
1.0.
Strictly,forcom
putingthe
scalingfactorthe
temperature
Tis
neededattim
et,butthisis
notavail-able
inthe
algorithm.
Inpractice,
thetem
peratureat
theprevious
time
stepis
used(as
indicatedin
eqn.3.23),which
isperfectly
allrightsincethe
couplingtim
econstantis
much
longerthan
onetim
estep.
The
Berendsen
algorithmis
stableup
toτT≈
∆t.
Nos
e-Hoover
temperature
coupling
The
Berendsen
weak
couplingalgorithm
isextrem
elyefficientfor
relaxinga
systemto
thetarget
temperature,
butonce
yoursystem
hasreached
equilibriumit
might
bem
oreim
portantto
probea
correctcanonicalensem
ble.T
hisis
unfortunatelynot
thecase
forthe
weak
couplingschem
e,although
thedifference
isusually
negligible.
Toenable
canonicalensemble
simulations,
GR
OM
AC
Salso
supportsthe
extended-ensemble
ap-proach
firstproposedby
Nose[18]and
laterm
odifiedby
Hoover[19].
The
systemH
amiltonian
isextended
byintroducing
atherm
alreservoirand
afriction
termin
theequations
ofm
otion.T
he
E.3
9.
grm
sdist
20
7
Allthe
structuresare
fittedpairw
ise.
With
-f2,the
’otherstructures’are
takenfrom
asecond
trajectory.
Option
-bin
doesa
binarydum
pofthe
comparison
matrix.
Option
-bm
producesa
matrix
ofaveragebond
angledeviations
analogouslyto
the-m
option.O
nlybonds
between
atoms
inthe
comparison
groupare
considered.
Files
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-f
traj.xtc
InputG
enerictrajectory:
xtctrr
trjgrog96
pdb-f2
traj.xtc
Input,Opt.
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput,O
pt.Index
file-o
rmsd
.xvgO
utputxvgr/xm
grfile
-mir
rmsd
mir.xvg
Output,O
pt.xvgr/xm
grfile
-aa
vgrp
.xvgO
utput,Opt.
xvgr/xmgr
file-d
istrm
sd-d
ist.xvgO
utput,Opt.
xvgr/xmgr
file-m
rmsd
.xpm
Output,O
pt.X
PixM
apcom
patiblem
atrixfile
-bin
rmsd
.da
tO
utput,Opt.
Generic
datafile
-bm
bo
nd
.xpm
Output,O
pt.X
PixM
apcom
patiblem
atrixfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-tuenum
ps
Tim
eunit:p
s,fs
,ns
,us
,ms,s
,morh
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-w
ha
tenum
rmsd
Structuraldifference
measure:
rmsd
,rho
orrho
sc-p
bc
boolye
sP
BC
check-fit
boolye
sF
ittoreference
structure-p
rev
int0
Com
parew
ithprevious
frame
-split
booln
oS
plitgraphw
heretim
eis
zero-skip
int1
Only
write
everynr-th
frame
tom
atrix-skip
2int
1O
nlyw
riteevery
nr-thfram
eto
matrix
-ma
xreal
-1M
aximum
levelincom
parisonm
atrix-m
inreal
-1M
inimum
levelincom
parisonm
atrix-b
ma
xreal
-1M
aximum
levelinbond
anglem
atrix-b
min
real-1
Minim
umlevelin
bondangle
matrix
-nle
vels
int8
0N
umber
oflevelsin
them
atrices
E.39
grm
sdist
grm
sdistcom
putesthe
rootm
eansquare
deviationof
atomdistances,
which
hasthe
advantagethat
nofit
isneeded
likein
standardR
MS
deviationas
computed
byg
rms.
The
referencestructure
istaken
fromthe
structurefile.
The
rmsd
attime
tiscalculated
asthe
rms
ofthedifferences
indistance
between
atom-pairs
inthe
referencestructure
andthe
structureattim
et.
grm
sdistcanalso
producem
atricesofthe
rms
distances,rms
distancesscaled
with
them
eandistance
andthe
mean
distancesand
matrices
with
NM
Raveraged
distances(1/r
3and
1/r 6averaging).
Finally,
listsof
atompairs
with
1/r 3and1/r 6
averageddistance
belowthe
maxim
umdistance
(-m
ax
,which
willdefaultto
20
6A
pp
en
dix
E.
Ma
nu
alP
age
s
Ifa
run
inpu
tfil
eis
supp
lied
(-s),
excl
usio
nsde
fined
inth
atfil
ear
eta
ken
into
acco
unt
whe
nca
lcul
atin
gth
erd
f.T
heop
tion-
cut
ism
eant
asan
alte
rnat
ive
way
toav
oid
intr
amol
ecul
arpe
aks
inth
erd
fplo
t.It
isho
wev
erbe
tter
tosu
pply
aru
nin
put
file
with
ahi
gher
num
ber
ofex
clus
ions
.F
oreg
.be
nzen
ea
topo
logy
with
nrex
clse
tto
5w
ould
elim
inat
eal
lint
ram
olec
ular
cont
ribut
ions
toth
erd
f.N
ote
that
alla
tom
sin
the
sele
cted
grou
psar
eus
ed,a
lso
the
ones
that
don’
thav
eLe
nnar
d-Jo
nes
inte
ract
ions
.
Opt
ion
-cn
prod
uces
the
cum
ulat
ive
num
ber
rdf.
Tobr
idge
the
gap
betw
een
theo
ryan
dex
perim
ent
stru
ctur
efa
ctor
sca
nbe
com
pute
d(o
ptio
n-s
q).
The
algo
rithm
uses
FF
T,th
egr
idsp
acin
gof
whi
chis
dete
rmin
edby
optio
n-g
rid
.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put,
Opt
.S
truc
ture
+m
ass(
db):
tpr
tpb
tpa
gro
g96
pdb
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-o
rdf.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e-s
qsq
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-cn
rdf
cn.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-h
qh
q.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-im
ag
esq
.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-b
inre
al0
.00
1B
inw
idth
(nm
)-c
om
bool
no
RD
Fw
ithre
spec
tto
the
cent
erof
mas
sof
first
grou
p-c
ut
real
0S
hort
estd
ista
nce
(nm
)to
beco
nsid
ered
-fa
de
real
0F
rom
this
dist
ance
onw
ards
the
RD
Fis
tran
form
edby
g’(r
)=
1+
[g(r
)-1]
exp(
-(r/
fade
-1)2
tom
ake
itgo
to1
smoo
thly
.If
fade
is0.
0no
thin
gis
done
.-g
rid
real
0.0
5G
ridsp
acin
g(in
nm)
for
FF
Ts
whe
nco
mpu
ting
stru
ctur
efa
ctor
s-n
leve
lin
t2
0N
umbe
rof
diffe
rent
colo
rsin
the
diffr
actio
nim
age
-wa
vere
al0
.1W
avel
engt
hfo
rX
-ray
s/N
eutr
ons
for
scat
terin
g.0.
1nm
corr
espo
nds
toro
ughl
y12
keV
E.3
8g
rms
grm
sco
mpa
res
two
stru
ctur
esby
com
putin
gth
ero
otm
ean
squa
rede
viat
ion
(RM
SD
),th
esi
ze-in
depe
nden
t’rh
o’si
mila
rity
para
met
er(r
ho)
orth
esc
aled
rho
(rho
sc),
refe
renc
eM
aior
ov&
Crip
pen,
PR
OT
EIN
S22
,27
3(1
995)
.T
his
isse
lect
edby-w
ha
t.
Eac
hst
ruct
ure
from
atr
ajec
tory
(-f
)is
com
pare
dto
are
fere
nce
stru
ctur
efr
oma
run
inpu
tfil
eby
leas
t-sq
uare
sfit
ting
the
stru
ctur
eson
top
ofea
chot
her.
The
refe
renc
est
ruct
ure
ista
ken
from
the
stru
ctur
efil
e(-
s).
With
optio
n-m
iral
soa
com
paris
onw
ithth
em
irror
imag
eof
the
refe
renc
est
ruct
ure
isca
lcul
ated
.
Opt
ion
-pre
vpr
oduc
esth
eco
mpa
rison
with
apr
evio
usfr
ame.
Opt
ion
-mpr
oduc
esa
mat
rixin.
xpm
form
atof
com
paris
onva
lues
ofea
chst
ruct
ure
inth
etr
ajec
tory
with
resp
ect
toea
chot
her
stru
ctur
e.T
his
file
can
bevi
sual
ized
with
for
inst
ance
xvan
dca
nbe
conv
erte
dto
post
scrip
twith
xpm
2p
s.
3.4
.M
ole
cula
rD
yna
mic
s2
3
fric
tion
forc
eis
prop
ortio
nalt
oth
epr
oduc
tof
each
part
icle
’sve
loci
tyan
da
fric
tion
para
met
erξ.
Thi
sfr
ictio
npa
ram
eter
(or
’hea
tbat
h’va
riabl
e)is
afu
llydy
nam
icqu
antit
yw
ithits
own
equa
tion
ofm
otio
n;th
etim
ede
rivat
ive
isca
lcul
ated
from
the
diffe
renc
ebe
twee
nth
ecu
rren
tkin
etic
ener
gyan
dth
ere
fere
nce
tem
pera
ture
.
Inth
efo
rmul
atio
nof
Hoo
ver,
the
part
icle
s’eq
uatio
nsof
mot
ion
inF
ig.
3.3
are
repl
aced
by
d2r
i
dt2
=F
i
mi−ξ
dri
dt,
(3.2
5)
whe
reth
eeq
uatio
nof
mot
ion
for
the
heat
bath
para
met
erξ
is
dξ dt=
1 Q(T
−T
0).
(3.2
6)
The
refe
renc
ete
mpe
ratu
reis
deno
ted
T0,
whi
leT
isth
ecu
rren
tm
omen
tary
tem
pera
ture
ofth
esy
stem
.T
hest
reng
thof
the
coup
ling
isde
term
ined
byth
eco
nsta
ntQ
(usu
ally
calle
dth
e’m
ass
para
met
er’o
fthe
rese
rvoi
r)in
com
bina
tion
with
the
refe
renc
ete
mpe
ratu
re.
Inou
rop
inio
n,th
em
ass
para
met
eris
aso
mew
hata
wkw
ard
way
ofde
scrib
ing
coup
ling
stre
ngth
,es
peci
ally
due
toits
depe
nden
ceon
refe
renc
ete
mpe
ratu
re(a
ndso
me
impl
emen
tatio
nsev
enin
-cl
ude
the
num
ber
ofde
gree
sof
free
dom
inyo
ursy
stem
whe
nde
finin
gQ
).To
mai
ntai
nth
eco
u-pl
ing
stre
ngth
,you
wou
ldha
veto
chan
geQpr
opor
tiona
lto
your
chan
gein
refe
renc
ete
mpe
ratu
re.
For
this
reas
on,w
epr
efer
tole
tthe
GR
OM
AC
Sus
erw
ork
with
the
perio
dτ T
ofth
eos
cilla
tions
ofki
netic
ener
gybe
twee
nth
esy
stem
and
the
rese
rvoi
rin
stea
d.It
isdi
rect
lyre
late
dto
Qan
dT
0as
Q=τ
2 TT
0
4π2.
(3.2
7)
Thi
spr
ovid
esa
muc
hm
ore
intu
itive
way
ofse
lect
ing
the
Nos
e-H
oove
rco
uplin
gst
reng
th(s
imila
rto
the
wea
kco
uplin
gre
laxa
tion)
,an
din
addi
tionτ T
isin
depe
nden
tof
syst
emsi
zean
dre
fere
nce
tem
pera
ture
.
Itis
how
ever
impo
rtan
tto
keep
the
diffe
renc
ebe
twee
nth
ew
eak
coup
ling
sche
me
and
the
Nos
e-H
oove
ral
gorit
hmin
min
d:U
sing
wea
kco
uplin
gyo
uge
ta
stro
ngly
dam
ped
exp
on
en
tialre
lax-
atio
n,w
hile
the
Nos
e-H
oove
rap
proa
chpr
oduc
esanos
cilla
tory
rela
xatio
n.T
heac
tual
time
itta
kes
tore
lax
with
Nose
-Hoo
ver
coup
ling
isse
vera
ltim
esla
rger
than
the
perio
dof
the
osci
llatio
nsth
atyo
use
lect
.T
hese
osci
llatio
ns(in
cont
rast
toex
pone
ntia
lrel
axat
ion)
also
mea
nsth
atth
etim
eco
nsta
ntno
rmal
lysh
ould
be4–
5tim
esla
rger
than
the
rela
xatio
ntim
eus
edw
ithw
eak
coup
ling,
buty
our
mile
age
may
vary
.
3.4.
6P
ress
ure
coup
ling
Inth
esa
me
spiri
tas
the
tem
pera
ture
coup
ling,
the
syst
emca
nal
sobe
coup
led
toa
’pre
ssur
eba
th’.
GR
OM
AC
Ssu
ppor
tsbo
thth
eB
eren
dsen
algo
rithm
[17
]th
atsc
ales
coor
dina
tes
and
box
vect
ors
ever
yst
ep,a
ndth
eex
tend
eden
sem
ble
Par
rinel
lo-R
ahm
anap
proa
ch.
Bot
hof
thes
eca
nbe
com
bine
dw
ithan
yof
the
tem
pera
ture
coup
ling
met
hods
abov
e.
24
Ch
ap
ter
3.
Alg
orith
ms
Berendsen
pressurecoupling
The
Berendsen
algorithmrescales
thecoordinates
andbox
vectorsevery
stepw
itha
matrix
µ,
which
hasthe
effectof
afirst-order
kineticrelaxation
ofthe
pressuretow
ardsa
givenreference
pressureP0 :
dPdt=
P0 −
Pτp
(3.28)
The
scalingm
atrixµis
givenbyµ
ij=δij −
∆t
3τpβ
ij {P
0ij −
Pij (t)}
(3.29)
Here
βis
theisotherm
alcom
pressibilityof
thesystem
.In
most
casesthis
will
bea
diagonalm
atrix,with
equalelements
onthe
diagonal,thevalue
ofwhich
isgenerally
notknown.
Itsufficesto
takea
roughestim
atebecause
thevalue
ofβ
onlyinfluences
thenon-criticaltim
econstant
ofthe
pressurerelaxation
withoutaffecting
theaverage
pressureitself.
For
water
at1atm
and300
Kβ
=4.6
×10−
10
Pa −
1=
4.6×
10−
5B
ar −1,w
hichis7.6
×10−
4M
Dunits
(seechapter2).
Most
otherliquids
havesim
ilarvalues.
When
scalingcom
pletelyanisotropically,
thesystem
hasto
berotated
inorder
toobey
thebox
restriction(
3.1).T
hisrotation
isapproxim
atedin
firstorderin
thescaling,w
hichis
usuallyless
than10−
4.T
heactualscaling
matrixµ
′is:
µ′=
µxx
µxy
+µ
yx
µxz+µ
zx
0µ
yy
µyz+µ
zy
00
µzz
(3.30)
The
velocitiesare
neitherscaled
norrotated.
InG
RO
MA
CS
,the
Berendsen
scalingcan
alsobe
doneisotropically,
which
means
thatinstead
ofP
adiagonalm
atrixw
ithelem
entsof
sizetrace(P
)/3is
used.F
orsystem
sw
ithinterfaces,
semi-isotropic
scalingcan
beuseful.
Inthis
casethex/y-directions
arescaled
isotropicallyand
thez
directionis
scaledindependently.
The
compressibility
inthex/y
orz-direction
canbe
settozero,to
scaleonly
inthe
otherdirection(s).
Ifyou
allowfullanisotropic
deformations
anduse
constraintsyou
might
haveto
scaleslow
eror
decreaseyour
timestep
toavoid
errorsfrom
theconstraintalgorithm
s.
Parrinello-R
ahman
pressurecoupling
Incases
where
thefluctuations
inpressure
orvolum
eare
important
pe
rse(e.g.
tocalculate
ther-m
odynamic
properties)it
might
atleast
theoreticallybe
aproblem
thatthe
exactensem
bleis
notw
ell-definedfor
thew
eakcoupling
scheme.
Forthis
reason,GR
OM
AC
Salso
supportsconstant-pressure
simulations
usingthe
Parrinello-R
ahman
approach[21,22],which
issim
ilarto
theN
ose-Hoover
temperature
coupling.W
iththe
Parrinello-
Rahm
anbarostat,
thebox
vectorsas
representedby
them
atrixb
obeythe
matrix
equationof
motion 1
1The
boxm
atrixrepresentationbin
GR
OM
AC
Scorresponds
tothe
transposeofthe
boxm
atrixrepresentation
hin
thepaper
byN
oseand
Klein.
Because
ofthis,some
ofourequations
willlook
slightlydifferent.
E.3
6.
gra
ma
20
5
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput
Indexfile
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-op
ote
ntia
l.xvgO
utputxvgr/xm
grfile
-oc
cha
rge
.xvgO
utputxvgr/xm
grfile
-of
field
.xvgO
utputxvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
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ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-d
stringZ
Takethe
normalon
them
embrane
indirection
X,Y
orZ
.-sl
int1
0C
alculatepotential
asfunction
ofboxlength,
dividingthe
boxin
#nrslices.
-cbint
0D
iscardfirst#nr
slicesofbox
forintegration
-ceint
0D
iscardlast#nr
slicesofbox
forintegration
-tzreal
0T
ranslateallcoordinates<distance>
inthe
directionofthe
box-sp
he
rical
booln
oC
alculatesphericalthingie
•D
iscardingslices
forintegration
shouldnotbe
necessary.
E.36
gram
a
gram
aselects
theP
hi/Psidihedralcom
binationsfrom
yourtopology
fileand
computes
theseas
afunction
oftime.
Using
simple
Unix
toolssuch
asgrep
youcan
selectoutspecificresidues.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-ora
ma
.xvgO
utputxvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files
E.37
grdf
The
structureof
liquidscan
bestudied
byeither
neutronor
X-ray
scattering.T
hem
ostcom
mon
way
todescribe
liquidstructure
isby
aradial
distributionfunction.
How
ever,this
isnot
easyto
obtainfrom
ascattering
experiment.
grdf
calculatesradial
distributionfunctions
indifferent
ways.
The
normal
method
isaround
a(set
of)particle(s),the
otherm
ethodis
aroundthe
centerofm
assofa
setofparticles.
20
4A
pp
en
dix
E.
Ma
nu
alP
age
s
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-o
en
sem
ble
.xtc
Out
put
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-te
mp
real
30
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mpe
ratu
rein
Kel
vin
-se
ed
int
-1R
ando
mse
ed,-
1ge
nera
tes
ase
edfr
omtim
ean
dpi
d-n
um
int
10
0N
umbe
rof
stru
ctur
esto
gene
rate
-first
int
7F
irste
igen
vect
orto
use
(-1
isse
lect
)-la
stin
t-1
Last
eige
nvec
tor
tous
e(-
1is
tillt
hela
st)
E.3
4g
orde
r
Com
pute
the
orde
rpa
ram
eter
per
atom
for
carb
onta
ils.
For
atom
ithe
vect
ori-1
,i+
1is
used
toge
ther
with
anax
is.
The
inde
xfil
eha
sto
cont
ain
agr
oup
with
alle
quiv
alen
tato
ms
inal
ltai
lsfo
rea
chat
omth
eor
der
para
met
erha
sto
beca
lcul
ated
for.
The
prog
ram
can
also
give
alld
iago
nale
lem
ents
ofth
eor
der
tens
oran
dev
enca
lcul
ate
the
deut
eriu
mor
der
para
met
erS
cd(d
efau
lt).
Ifth
eop
tion
-szo
nly
isgi
ven,
only
one
orde
rte
nsor
com
pone
nt(s
peci
fied
byth
e-d
optio
n)is
give
nan
dth
eor
der
para
met
erpe
rsl
ice
isca
lcul
ated
asw
ell.
If-s
zonl
yis
nots
elec
ted,
alld
iago
nale
lem
ents
and
the
deut
eriu
mor
der
para
met
eris
give
n.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-nin
de
x.n
dx
Inpu
tIn
dex
file
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a-o
ord
er.
xvg
Out
put
xvgr
/xm
grfil
e-o
dd
eu
ter.
xvg
Out
put
xvgr
/xm
grfil
e-o
ssl
ice
d.x
vgO
utpu
txv
gr/x
mgr
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-d
enum
zD
irect
ion
ofth
eno
rmal
onth
em
embr
ane:z,x
ory
-sl
int
1C
alcu
late
orde
rpa
ram
eter
asfu
nctio
nof
boxl
engt
h,di
vidi
ngth
ebo
xin
#nr
slic
es.
-szo
nly
bool
no
Onl
ygi
veS
zel
emen
tofo
rder
tens
or.
(axi
sca
nbe
spec
ified
with
-d)
-un
sat
bool
no
Cal
cula
teor
derp
aram
eter
sfo
runs
atur
ated
carb
ons.
Not
eth
atth
isca
nnot
bem
ixed
with
norm
alor
der
para
met
ers.
E.3
5g
pote
ntia
l
Com
pute
the
elec
tros
tatic
alpo
tent
iala
cros
sth
ebo
x.T
hepo
tent
iali
scal
cula
ted
byfir
stsu
mm
ing
the
char
ges
per
slic
ean
dth
enin
tegr
atin
gtw
ice
ofth
isch
arge
dist
ribut
ion.
Per
iodi
cbo
unda
ries
are
not
take
nin
toac
-co
unt.
Ref
eren
ceof
pote
ntia
lis
take
nto
beth
ele
ftsi
deof
the
box.
It’s
also
poss
ible
toca
lcul
ate
the
pote
ntia
lin
sphe
rical
coor
dina
tes
asfu
nctio
nof
rby
calc
ulat
ing
ach
arge
dist
ribut
ion
insp
heric
alsl
ices
and
twic
ein
tegr
atin
gth
em.
epsi
lonris
take
nas
1,2
ism
ore
appr
opria
tein
man
yca
ses
3.4
.M
ole
cula
rD
yna
mic
s2
5
db2
dt2
=V
W−
1b′−
1(P
−P
ref
).(3
.31)
The
volu
me
ofth
ebo
xis
deno
tedV,a
ndW
isa
mat
rixpa
ram
eter
that
dete
rmin
esth
est
reng
thof
the
coup
ling.
The
mat
ricesP
andP
ref
are
the
curr
enta
ndre
fere
nce
pres
sure
s,re
spec
tivel
y.
The
equa
tions
ofm
otio
nfo
rth
epa
rtic
les
are
also
chan
ged,
just
asfo
rth
eN
ose-
Hoo
ver
coup
ling.
Inm
ostc
ases
you
wou
ldco
mbi
neth
eP
arrin
ello
-Rah
man
baro
stat
with
the
Nos
e-H
oove
rth
erm
o-st
at,b
utto
keep
itsi
mpl
ew
eon
lysh
owth
eP
arrin
ello
-Rah
man
mod
ifica
tion
here
:
d2r
i
dt2
=F
i
mi−
Mdr
i
dt,
(3.3
2)
M=
b−
1
[ bdb′
dt+
db dtb′] b
′−1.
(3.3
3)
The
(inve
rse)
mas
spa
ram
eter
mat
rixW−
1de
term
ines
the
stre
ngth
ofth
eco
uplin
g,an
dho
wth
ebo
xca
nbe
defo
rmed
.T
hebo
xre
stric
tion
(3.
1)w
illbe
fulfi
lled
auto
mat
ical
lyif
the
corr
espo
ndin
gel
emen
tsof
W−
1ar
eze
ro.
Sin
ceth
eco
uplin
gst
reng
thal
sode
pend
son
the
size
ofyo
urbo
x,w
epr
efer
toca
lcul
ate
itau
tom
atic
ally
inG
RO
MA
CS
.You
only
have
topr
ovid
eth
eap
prox
imat
eis
othe
rmal
com
pres
sibi
litie
sβan
dth
epr
essu
retim
eco
nsta
ntτ pin
the
inpu
tfile
(Lis
the
larg
est
box
mat
rixel
emen
t):
( W−
1) ij
=4π
2β
ij
3τ2 pL.
(3.3
4)
Just
asfo
rth
eN
ose-H
oove
rth
erm
osta
t,yo
ush
ould
real
ize
that
the
Par
rinel
lo-R
ahm
antim
eco
n-st
ant
isn
ote
quiv
alen
tto
the
rela
xatio
ntim
eus
edin
the
Ber
ends
enpr
essu
reco
uplin
gal
gorit
hm.
Inm
ostc
ases
you
will
need
tous
ea
4–5
times
larg
ertim
eco
nsta
ntw
ithP
arrin
ello
-Rah
man
cou-
plin
g.If
your
pres
sure
isve
ryfa
rfr
omeq
uilib
rium
,the
Par
rinel
lo-R
ahm
anco
uplin
gm
ayre
sult
inve
ryla
rge
box
osci
llatio
nsth
atco
uld
even
cras
hyo
urru
n.In
that
case
you
wou
ldha
veto
incr
ease
the
time
cons
tant
,or
(bet
ter)
use
the
wea
kco
uplin
gsc
hem
eto
reac
hth
eta
rget
pres
sure
,and
then
switc
hto
Par
rinel
lo-R
ahm
anco
uplin
gon
ceth
esy
stem
isin
equi
libriu
m.
Sur
face
tens
ion
coup
ling
Whe
na
perio
dic
syst
emco
nsis
tsof
mor
eth
anon
eph
ase,
sepa
rate
dby
surf
aces
whi
char
epa
r-al
lelt
oth
exy
-pla
ne,
the
surf
ace
tens
ion
and
the
z-co
mpo
nent
ofth
epr
essu
reca
nbe
coup
led
toa
pres
sure
bath
.P
rese
ntly
,th
ison
lyw
orks
with
the
Ber
ends
enpr
essu
reco
uplin
gal
gorit
hmin
GR
OM
AC
S.T
heav
erag
esu
rfac
ete
nsio
nγ(t
)ca
nbe
calc
ulat
edfr
omth
edi
ffere
nce
betw
een
the
norm
alan
dth
ela
tera
lpre
ssur
e:
γ(t
)=
1 n
∫ L z 0
{ Pzz(z,t
)−P
xx(z,t
)+P
yy(z,t
)2
} dz(3
.35)
=L
z n
{ Pzz(t
)−P
xx(t
)+P
yy(t
)2
}(3
.36)
26
Ch
ap
ter
3.
Alg
orith
ms
where
Lz
isthe
heightofthebox
andnis
thenum
berofsurfaces.
The
pressurein
thez-direction
iscorrected
byscaling
theheightofthe
boxw
ithµ
z :
∆P
zz
=∆t
τp{P
0zz −
Pzz (t)}
(3.37)
µzz
=1
+β
zz ∆P
zz
(3.38)
This
issim
ilarto
normalpressure
coupling,except
thatthe
power
ofone
thirdis
missing.
The
pressurecorrection
inthe
z-directionis
thenused
toget
thecorrect
convergencefor
thesurface
tensionto
thereference
valueγ0 .T
hecorrection
factorfor
thebox-length
inthe
x/y-directionis:
µx/y
=1
+∆t
2τpβ
x/y (
nγ
0
µzz L
z− {
Pzz (t)
+∆P
zz −
Pxx (t)
+P
yy (t)
2
})(3.39)
The
valueofβ
zz
ism
orecritical
thanw
ithnorm
alpressure
coupling.N
ormally
anincorrect
compressibility
willjust
scaleτp ,
butw
ithsurface
tensioncoupling
itaffects
theconvergence
ofthe
surfacetension.
Whenβz
zis
settozero
(constantboxheight),
∆P
zis
alsosetto
zero,which
isnecessary
forobtaining
thecorrectsurface
tension.
The
complete
updatealgorithm
The
complete
algorithmfor
theupdate
ofvelocities
andcoordinates
isgiven
inF
ig.3.7.
The
SH
AK
Ealgorithm
ofstep4
isexplained
below.
GR
OM
AC
Shas
aprovision
to”freeze”
(preventm
otionof)
selectedparticles,
which
must
bedefined
asa
’freezegroup’.
This
isim
plemented
usinga
free
zefa
ctorf
g ,w
hichis
avector,
anddiffers
foreachfre
ezeg
rou
p(seesec.3.3).
This
vectorcontains
onlyzero
(freeze)or
one(don’t
freeze).W
henw
etake
thisfreeze
factorand
theexternalacceleration
ah
intoaccountthe
updatealgorithm
forthe
velocitiesbecom
es:
v(t+∆t2)
=f
g ∗λ∗ [v(t−
∆t2)+
F(t)m
∆t+
ah ∆
t ](3.40)
where
gand
hare
groupindices
which
differper
atom.
3.4.7O
utputstep
The
important
outputof
theM
Drun
isthetra
jecto
ryfile
na
me
.trjw
hichcontains
particlecoordinates
and-optionally-
velocitiesat
regularintervals.
Since
thetrajectory
filesare
lengthy,one
shouldnotsave
everystep!
Toretain
allinformation
itsufficesto
write
afram
eevery
15steps,
sinceatleast30
stepsare
made
perperiod
ofthehighestfrequency
inthe
system,and
Shannon’s
sampling
theoremstates
thattw
osam
plesper
periodof
thehighest
frequencyin
aband-lim
itedsignal
containall
availableinform
ation.B
utthat
stillgives
verylong
files!S
o,if
thehighest
frequenciesare
notofinterest,10or
20sam
plesper
psm
aysuffice.
Be
aware
ofthedistortion
ofhigh-frequency
motions
bythestro
bo
scop
ice
ffect,calleda
liasin
g:higherfrequenciesare
mirrored
with
respecttothe
sampling
frequencyand
appearas
lower
frequencies.
E.3
2.
gn
me
ig2
03
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-tuenum
ps
Tim
eunit:p
s,fs
,ns
,us
,ms,s
,morh
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-typ
eenum
no
Com
putediffusion
coefficientinone
direction:n
o,x
,yorz
-late
ral
enumn
oC
alculatethe
lateraldiffusionin
aplane
perpendicularto:
no
,x,y
orz-n
gro
up
int1
Num
berofgroups
tocalculate
MS
Dfor
-mw
boolye
sM
assw
eightedM
SD
-tresta
rttim
e0
Tim
ebetw
eenrestarting
pointsin
trajectory(ps)
-be
gin
fittim
e0
Starttim
efor
fittingthe
MS
D(ps)
-en
dfit
time
-1E
ndtim
efor
fittingthe
MS
D(ps),-1
istillend
E.32
gnm
eig
gnm
eigcalculates
theeigenvectors/values
ofa(H
essian)matrix,w
hichcan
becalculated
with
nm
run
.T
heeigenvectors
arew
rittento
atrajectory
file(
-v).
The
structureis
written
firstw
itht=
0.T
heeigenvectors
arew
rittenas
frames
with
theeigenvector
number
astim
estamp.
The
eigenvectorscan
beanalyzed
with
ga
na
eig
.A
nensem
bleofstructures
canbe
generatedfrom
theeigenvectors
with
gn
me
ns.
Files
-fh
essia
n.m
txInput
Hessian
matrix
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-o
eig
en
val.xvg
Output
xvgr/xmgr
file-v
eig
en
vec.trr
Output
Fullprecision
trajectory:trr
trj
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-mbool
yes
Divide
elements
ofH
essianby
productof
sqrt(mass)
ofinvolved
atoms
priorto
diagonalization.T
hisshould
beused
for’N
ormalM
odes’analy-sis
-firstint
1F
irsteigenvectorto
write
away
-last
int1
00
Lasteigenvectorto
write
away
E.33
gnm
ens
gn
me
ns
generatesan
ensemble
aroundan
averagestructure
ina
subspacew
hichis
definedby
aset
ofnorm
almodes
(eigenvectors).T
heeigenvectors
areassum
edto
bem
ass-weighted.
The
positionalong
eacheigenvector
israndom
lytaken
froma
Gaussian
distributionw
ithvariance
kT/eigenvalue.
By
defaultthe
startingeigenvector
isset
to7,
sincethe
firstsix
normal
modes
arethe
translationaland
rotationaldegreesoffreedom
.
Files
-ve
ige
nve
c.trrInput
Fullprecision
trajectory:trr
trj-e
eig
en
val.xvg
Inputxvgr/xm
grfile
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb
20
2A
pp
en
dix
E.
Ma
nu
alP
age
s
E.3
0g
mor
ph
gm
orph
does
alin
ear
inte
rpol
atio
nof
conf
orm
atio
nsin
orde
rto
crea
tein
term
edia
tes.
Ofc
ours
eth
ese
are
com
plet
ely
unph
ysic
al,b
utth
atyo
um
aytr
yto
just
ifyyo
urse
lf.O
utpu
tis
inth
efo
rmof
age
neric
traj
ecto
ry.
The
num
ber
ofin
term
edia
tes
can
beco
ntro
lled
with
the
-nin
term
flag.
The
first
and
last
flag
corr
espo
ndto
the
way
ofin
terp
olat
ing:
0co
rres
pond
sto
inpu
tstr
uctu
re1
whi
le1
corr
espo
nds
toin
puts
truc
utre
2.If
you
spec
ifyfir
st<
0or
last>
1ex
trap
olat
ion
will
beon
the
path
from
inpu
tstr
uctu
rex1
tox2
.In
gene
ralt
heco
ordi
nate
sof
the
inte
rmed
iate
x(i)
outo
fNto
tali
nter
mid
ates
corr
espo
ndto
:
x(i)
=x1
+(fi
rst+
(i/(N
-1))
*(la
st-fi
rst)
)*(x
2-x1
)
Fin
ally
the
RM
SD
with
resp
ectt
obo
thin
puts
truc
ture
sca
nbe
com
pute
dif
expl
icitl
yse
lect
ed(-
orop
tion)
.In
that
case
anin
dex
file
may
bere
adto
sele
ctw
hatg
roup
RM
Sis
com
pute
dfr
om.
File
s -f1
con
f1.g
roIn
put
Gen
eric
stru
ctur
e:gr
og9
6pd
btp
rtp
btp
a-f
2co
nf2
.gro
Inpu
tG
ener
icst
ruct
ure:
gro
g96
pdb
tpr
tpb
tpa
-oin
term
.xtc
Out
put
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b-o
rrm
s-in
term
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t0
Set
the
nice
leve
l-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-nin
term
int
11
Num
ber
ofin
term
edia
tes
-first
real
0C
orre
spon
dsto
first
gene
rate
dst
ruct
ure
(0is
inpu
tx0,
see
abov
e)-la
stre
al1
Cor
resp
onds
tola
stge
nera
ted
stru
ctur
e(1
isin
putx
1,se
eab
ove)
-fit
bool
yes
Do
ale
asts
quar
esfit
ofth
ese
cond
toth
efir
stst
ruct
ure
befo
rein
terp
olat
-in
g
E.3
1g
msd
gm
sdco
mpu
tes
the
mea
nsq
uare
disp
lace
men
t(M
SD
)of
atom
sfr
omth
eir
initi
alpo
sitio
ns.
Thi
spr
ovid
esan
easy
way
toco
mpu
teth
edi
ffusi
onco
nsta
ntus
ing
the
Ein
stei
nre
latio
n.T
hedi
ffusi
onco
nsta
ntis
calc
u-la
ted
byle
ast
squa
res
fittin
ga
stra
ight
line
thro
ugh
the
MS
Dfr
om-be
gin
fitto
-en
dfit
.A
ner
ror
estim
ate
give
n,w
hich
isth
edi
ffere
nce
ofth
edi
ffusi
onco
effic
ient
sob
tain
edfr
omfit
sov
erth
etw
oha
lfsof
the
fitin
terv
al.
Opt
ion
-mo
lpl
ots
the
MS
Dfo
rm
olec
ules
,th
isim
plie
s-mw
,i.e
.fo
rea
chin
idiv
idua
lmol
ecul
ean
diffu
-si
onco
nsta
ntis
com
pute
d.W
hen
usin
gan
inde
xfil
e,it
shou
ldco
ntai
nm
olec
ule
num
bers
inst
ead
ofat
omnu
mbe
rs.
Usi
ngth
isop
tion
one
also
gets
anac
cura
teer
ror
estim
ate
base
don
the
stat
istic
sbe
twee
nin
divi
d-ua
lmol
ecul
es.
Sin
ceon
eus
ually
isin
tere
sted
inse
lf-di
ffusi
onat
infin
itedi
lutio
nth
isis
prob
ably
the
mos
tus
eful
num
ber.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-om
sd.x
vgO
utpu
txv
gr/x
mgr
file
-mo
ld
iffm
ol.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e
3.4
.M
ole
cula
rD
yna
mic
s2
7
TH
EU
PD
ATE
ALG
OR
ITH
M
Giv
en:
Pos
ition
srof
alla
tom
sat
timet
Velo
citie
svof
alla
tom
sat
timet−
∆t
2A
ccel
erat
ions
F/m
onal
lato
ms
attim
et.(F
orce
sar
eco
mpu
ted
disr
egar
ding
any
cons
trai
nts)
Tota
lkin
etic
ener
gyan
dvi
rial
⇓1.
Com
pute
the
scal
ing
fact
orsλan
dµ
acco
rdin
gto
eqns
.3.23
and
3.29
⇓2.
Upd
ate
and
scal
eve
loci
ties:v′=λ(v
+a∆t)
⇓3.
Com
pute
new
unco
nstr
aine
dco
ordi
nate
s:r′=
r+
v′ ∆t
⇓4.
App
lyco
nstr
aint
algo
rithm
toco
ordi
nate
s:co
nstr
ain(
r′→
r′′ ;
r)
⇓5.
Cor
rect
velo
citie
sfo
rco
nstr
aint
s:v=
(r′′−
r)/
∆t
⇓6.
Sca
leco
ordi
nate
san
dbo
x:r=µr′′ ;
b=µb
Fig
ure
3.7:
The
MD
upda
teal
gorit
hm
28
Ch
ap
ter
3.
Alg
orith
ms
3.5S
hellmolecular
dynamics
GR
OM
AC
Scan
simulate
polarizabilityusing
theshell
model
ofD
ickand
Overhauser
[23].
Insuch
models
ashellparticle
representingthe
electronicdegrees
offreedomis
attachedto
anucleus
bya
spring.T
hepotential
energyis
minim
izedw
ithrespect
tothe
shellposition
atevery
stepof
thesim
ulation(see
below).
Succesfullapplications
ofshellm
odelsin
GR
OM
AC
Shave
beenpublished
forN2
[24]andw
ater[25].
3.5.1O
ptimization
oftheshellpositions
The
forceFS
ona
shellparticleScan
bedecom
posedinto
two
components:
FS
=F
bond
+F
nb
(3.41)
whereF
bond
denotesthe
componentrepresenting
thepolarization
energy,usuallyrepresented
bya
harmonic
potentialandFnb
isthe
sumofC
oulomb
andVan
derW
aalsinteractions.
Ifwe
assume
thatFnb
isalm
ostconstantwe
cananalytically
derivethe
optimalposition
oftheshell,i.e.
where
FS
=0.
Ifwe
havethe
shellSconnected
toatom
Aw
ehave
Fbo
nd
=k
b (xS−
xA)
(3.42)
Inan
iterativesolver,
we
havepositionsxS (n)
where
nis
theiteration
count.W
enow
haveit
iterationn
:
Fnb
=F
S−k
b (xS (n)−
xA)
(3.43)
andthe
optimalposition
forthe
shellsxS (n+
1)thus
follows
from
FS−k
b (xS (n)−
xA)+k
b (xS (n
+1)−
xA)
=0
(3.44)
ifwe
write
∆x
S=
xS (n
+1)−
xS (n)
(3.45)
we
finallyobtain
∆x
S=
FS/k
b(3.46)
which
thenyields
thealgorithm
tocom
putethe
nexttrialinthe
optimization
ofshellpositions:
xS (n
+1)
=x
S (n)+
FS/k
b(3.47)
3.6C
onstraintalgorithms
Constraints
canbe
imposed
inG
RO
MA
CS
usingLIN
CS
(default)or
thetraditional
SH
AK
Em
ethod.
E.2
8.
gm
dm
at
20
1
E.28
gm
dmat
gm
dmatm
akesdistance
matrices
consistingofthe
smallestdistance
between
residuepairs.
With
-frames
thesedistance
matrices
canbe
storedas
afunction
oftime,to
beable
tosee
differencesin
tertiarystructure
asa
funcionof
time.
Ifyou
chooseyour
optionsunw
ise,this
may
generatea
largeoutput
file.D
efaultonly
anaveraged
matrix
overthe
whole
trajectoryis
output.A
lsoa
countofthenum
berofdifferentatom
iccontacts
between
residuesoverthe
whole
trajectorycan
bem
ade.T
heoutputcan
beprocessed
with
xpm2ps
tom
akea
PostS
cript(tm)
plot.F
iles-f
traj.xtc
InputG
enerictrajectory:
xtctrr
trjgrog96
pdb-s
top
ol.tp
rInput
Structure+
mass(db):
tprtpb
tpagro
g96pdb
-nin
de
x.nd
xInput,O
pt.Index
file-m
ea
nd
m.xp
mO
utputX
PixM
apcom
patiblem
atrixfile
-fram
es
dm
f.xpm
Output,O
pt.X
PixM
apcom
patiblem
atrixfile
-no
nu
m.xvg
Output,O
pt.xvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-treal
1.5
truncdistance
-nle
vels
int4
0D
iscretizedistance
in#
levels
E.29
gm
indist
gm
indistcom
putesthe
distancebetw
eenone
groupand
anum
berof
othergroups.
Both
them
inimum
distanceand
thenum
berofcontacts
within
agiven
distanceare
written
totw
oseparate
outputfiles.
With
option-p
ithe
minim
umdistance
ofa
groupto
itsperiodic
image
isplotted.
This
isuseful
forchecking
ifa
proteinhas
seenits
periodicim
ageduring
asim
ulation.O
nlyone
shiftin
eachdirection
isconsidered,giving
atotalof26
shifts.Italso
plotsthe
maxim
umdistance
within
thegroup
andthe
lengthsofthe
threebox
vectors.T
hisoption
isvery
slow.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
Input,Opt.
Structure+
mass(db):
tprtpb
tpagro
g96pdb
-nin
de
x.nd
xInput,O
pt.Index
file-o
dm
ind
ist.xvgO
utputxvgr/xm
grfile
-on
nu
mco
nt.xvg
Output
xvgr/xmgr
file-o
atm
-pa
ir.ou
tO
utputG
enericoutputfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-m
atrix
booln
oC
alculatehalfa
matrix
ofgroup-groupdistances
-dreal
0.6
Distance
forcontacts
-pi
booln
oC
alculatem
inimum
distancew
ithperiodic
images
20
0A
pp
en
dix
E.
Ma
nu
alP
age
s
8.A
vera
geC
alph
a-C
alph
adi
hedr
alan
gle
(file
phi-a
hx.x
vg).
9.A
vera
geP
hian
dP
sian
gles
(file
phip
si.x
vg).
10.E
llipt
icity
at22
2nm
acco
rdin
gtoH
irsta
nd
Bro
oks
File
s-s
top
ol.t
pr
Inpu
tG
ener
icru
nin
put:
tpr
tpb
tpa
-nin
de
x.n
dx
Inpu
tIn
dex
file
-ftr
aj.x
tcIn
put
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b-t
og
tra
j.g8
7O
utpu
t,O
pt.
Gro
mos
-87
AS
CII
traj
ecto
ryfo
rmat
-cz
zco
nf.g
roO
utpu
tG
ener
icst
ruct
ure:
gro
g96
pdb
-co
wa
ver.
gro
Out
put
Gen
eric
stru
ctur
e:gr
og9
6pd
b
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-r
0in
t1
The
first
resi
due
num
ber
inth
ese
quen
ce-q
bool
no
Che
ckat
ever
yst
epw
hich
part
ofth
ese
quen
ceis
helic
al-F
bool
yes
Togg
lefit
toa
perf
ecth
elix
-db
bool
no
Prin
tdeb
ugin
fo-e
vbo
oln
oW
rite
ane
w’tr
ajec
tory
’file
for
ED
-ah
xsta
rtin
t0
Firs
tres
idue
inhe
lix-a
hxe
nd
int
0La
stre
sidu
ein
helix
E.2
7g
lie
glie
com
pute
sa
free
ener
gyes
timat
eba
sed
onan
ener
gyan
alys
isfr
om.
One
need
san
ener
gyfil
ew
ithth
efo
llow
ing
com
pone
nts:
Cou
l(A
-B)
LJ-S
R(A
-B)
etc.
File
s-f
en
er.
ed
rIn
put
Gen
eric
ener
gy:
edr
ene
-olie
.xvg
Out
put
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-E
ljre
al0
Lenn
ard-
Jone
sin
tera
ctio
nbe
twee
nlig
and
and
solv
ent
-Eq
qre
al0
Cou
lom
bin
tera
ctio
nbe
twee
nlig
and
and
solv
ent
-Clj
real
0.1
81
Fac
tor
inth
eLI
Eeq
uatio
nfo
rLe
nnar
d-Jo
nes
com
pone
ntof
ener
gy-C
real
0F
acto
rin
the
LIE
equa
tion
for
Cou
lom
bco
mpo
nent
ofen
ergy
-lig
an
dst
ring
no
ne
Nam
eof
the
ligan
din
the
ener
gyfil
e
3.6
.C
on
stra
inta
lgo
rith
ms
29
3.6.
1S
HA
KE
The
SH
AK
E[2
6]al
gorit
hmch
ange
sa
seto
func
onst
rain
edco
ordi
nate
sr′
toa
seto
fcoo
rdin
ates
r′′
that
fulfi
lla
listo
fdis
tanc
eco
nstr
aint
s,us
ing
ase
tr
asre
fere
nce:
SH
AK
E(r
′→
r′′ ;
r)
Thi
sac
tion
isco
nsis
tent
with
solv
ing
ase
tofL
agra
nge
mul
tiplie
rsin
the
cons
trai
ned
equa
tions
ofm
otio
n.S
HA
KE
need
sato
lera
nce
TO
L;it
will
cont
inue
until
allc
onst
rain
tsar
esa
tisfie
dw
ithin
are
lativ
eto
lera
nceT
OL.
An
erro
rm
essa
geis
give
nif
SH
AK
Eca
nnot
rese
tthe
coor
dina
tes
beca
use
the
devi
atio
nis
too
larg
e,or
ifa
give
nnu
mbe
rof
itera
tions
issu
rpas
sed.
Ass
ume
the
equa
tions
ofm
otio
nm
ustf
ulfil
lK
holo
nom
icco
nstr
aint
s,ex
pres
sed
as
σk(r
1...r
N)
=0;
k=
1...K
(3.4
8)
(e.g
.(r
1−
r2)2−b2
=0)
.T
hen
the
forc
esar
ede
fined
as
−∂ ∂r
i
( V+
K ∑ k=
1
λkσ
k
)(3
.49)
whe
reλ
kar
eLa
gran
gem
ultip
liers
whi
chm
ust
beso
lved
tofu
lfill
the
cons
trai
nteq
uatio
ns.
The
seco
ndpa
rtof
this
sum
dete
rmin
esth
eco
nst
rain
tfo
rce
sGi,
defin
edby
Gi=−
K ∑ k=
1
λk∂σ
k
∂r
i(3
.50)
The
disp
lace
men
tdu
eto
the
cons
trai
ntfo
rces
inth
ele
apfr
ogor
Verle
tal
gorit
hmis
equa
lto
(Gi/m
i)(∆t)
2.
Sol
ving
the
Lagr
ange
mul
tiplie
rs(a
ndhe
nce
the
disp
lace
men
ts)
requ
ires
the
so-
lutio
nof
ase
tofc
oupl
edeq
uatio
nsof
the
seco
ndde
gree
.T
hese
are
solv
edite
rativ
ely
byS
HA
KE
.F
orth
esp
ecia
lcas
eof
rigid
wat
erm
olec
ules
,tha
tofte
nm
ake
upm
ore
than
80%
ofth
esi
mul
atio
nsy
stem
we
have
impl
emen
ted
the
SE
TT
LEal
gorit
hm[
27](
sec.
5.4)
.
3.6.
2LI
NC
S
The
LIN
CS
algo
rithm
LIN
CS
isan
algo
rithm
that
rese
tsbo
nds
toth
eirc
orre
ctle
ngth
saf
tera
nun
cons
trai
ned
upda
te[
28].
The
met
hod
isno
n-ite
rativ
e,as
ital
way
sus
estw
ost
eps.
Alth
ough
LIN
CS
isba
sed
onm
atric
es,
nom
atrix
-mat
rixm
ultip
licat
ions
are
need
ed.
The
met
hod
ism
ore
stab
lean
dfa
ster
than
SH
AK
E,
but
itca
non
lybe
used
with
bond
cons
trai
nts
and
isol
ated
angl
eco
nstr
aint
s,su
chas
the
prot
onan
gle
inO
H.B
ecau
seof
itsst
abili
tyLI
NC
Sis
espe
cial
lyus
eful
for
Bro
wni
andy
nam
ics.
LIN
CS
has
two
para
met
ers,
whi
char
eex
plai
ned
inth
esu
bsec
tion
para
met
ers.
The
LIN
CS
form
ulas
We
cons
ider
asy
stem
ofNpa
rtic
les,
with
posi
tions
give
nby
a3Nve
ctor
r(t
).F
orm
olec
ular
dyna
mic
sth
eeq
uatio
nsof
mot
ion
are
give
nby
New
ton’
sla
w
d2r
dt2
=M
−1F
(3.5
1)
30
Ch
ap
ter
3.
Alg
orith
ms
� �� �
� �� �
������������
� �� �
����
������������
� � �
�������
�������
�������
���������
���������
���������
���������
���������
���������
���������
���������
���������
���������
���������
���������
unconstrainedupdate
correction forrotational
lengthening
projecting outforces w
orkingalong the bonds
θ
d
ld
pd
Figure
3.8:T
hethree
positionupdates
neededfor
onetim
estep.
The
dashedline
isthe
oldbond
oflengthd,the
solidlines
arethe
newbonds.
l=d
cosθ
andp
=(2d
2−l 2)
12.
where
Fis
the3Nforce
vectorandM
isa3N
×3N
diagonalmatrix,containing
them
assesof
theparticles.
The
systemis
constrainedbyK
time-independentconstraintequations
gi (r)
=|r
i1 −r
i2 |−d
i =0
i=
1,...,K(3.52)
Ina
numerical
integrationschem
eLIN
CS
isapplied
afteran
unconstrainedupdate,
justlike
SH
AK
E.T
healgorithm
works
intw
osteps
(seefigure
Fig.
3.8).In
thefirststep
theprojections
ofthe
newbonds
onthe
oldbonds
areset
tozero.
Inthe
secondstep
acorrection
isapplied
forthe
lengtheningof
thebonds
dueto
rotation.T
henum
ericsfor
thefirst
stepand
thesecond
stepare
verysim
ilar.A
complete
derivationofthe
algorithmcan
befound
in[
28].O
nlya
shortdescriptionofthe
firststepis
givenhere.
Anew
notationis
introducedfor
thegradientm
atrixofthe
constraintequationsw
hichappears
onthe
righthandside
oftheequation
Bhi =
∂gh
∂ri
(3.53)
Notice
thatBis
aK×
3Nm
atrix,itcontainsthe
directionsofthe
constraints.T
hefollow
ingequa-
tionshow
show
thenew
constrainedcoordinates
rn+
1are
relatedto
theunconstrained
coordinatesr
unc
n+
1
rn+
1=
(I−
TnB
n )runc
n+
1+
Tnd
=
runc
n+
1 −M
−1B
n (BnM
−1B
Tn ) −1(B
nr
unc
n+
1 −d)
(3.54)
where
T=
M−
1BT(B
M−
1BT) −
1.T
hederivation
ofthis
equationfrom
eqns.3.51
and3.52
canbe
foundin
[28].
This
firststepdoes
notsettherealbond
lengthsto
theprescribed
lengths,buttheprojection
ofthenew
bondsonto
theold
directionsofthe
bonds.To
correctfortherotation
ofbondi,the
projectionofthe
bondon
theold
directionis
settopi = √
2d
2i −l 2i
(3.55)
where
liis
thebond
lengthafter
thefirstprojection.
The
correctedpositions
are
r∗n+
1=
(I−
TnB
n )rn+
1+
Tnp
(3.56)
E.2
6.
gh
elix
19
9
insertioninto
hydrogenbonds.
Ordering
isidenticalto
thatin-h
bn
indexfile.
-da
:w
riteoutthe
number
ofdonorsand
acceptorsanalyzed
foreach
timefram
e.T
hisis
especiallyusefull
when
using-she
ll.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-nin
de
x.nd
xInput,O
pt.Index
file-g
hb
on
d.lo
gO
utput,Opt.
Logfile
-sel
sele
ct.nd
xInput,O
pt.Index
file-n
um
hb
nu
m.xvg
Output
xvgr/xmgr
file-a
ch
ba
c.xvgO
utput,Opt.
xvgr/xmgr
file-d
isth
bd
ist.xvgO
utput,Opt.
xvgr/xmgr
file-a
ng
hb
an
g.xvg
Output,O
pt.xvgr/xm
grfile
-hx
hb
he
lix.xvgO
utput,Opt.
xvgr/xmgr
file-h
bn
hb
on
d.n
dx
Output,O
pt.Index
file-h
bm
hb
ma
p.xp
mO
utput,Opt.
XP
ixMap
compatible
matrix
file-d
ad
an
um
.xvgO
utput,Opt.
xvgr/xmgr
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-ins
booln
oA
nalyzesolventinsertion
-areal
60
Cutoffangle
(degrees,Donor
-H
ydrogen-
Acceptor)
-rreal
0.2
5C
utoffradius(nm
,Hydrogen
-A
cceptor)-a
bin
real1
Binw
idthangle
distribution(degrees)
-rbin
real0
.00
5B
inwidth
distancedistribution
(nm)
-nita
ccbool
yes
Regard
nitrogenatom
sas
acceptors-sh
ell
real-1
when
>0,
onlycalculate
hydrogenbonds
within
#nm
shellaroundone
particle
E.26
ghelix
ghelix
computes
allkindof
helixproperties.
First,
thepeptide
ischecked
tofind
thelongest
helicalpart.T
hisis
determined
byH
ydrogenbonds
andP
hi/Psiangles.
That
bitis
fittedto
anidealhelix
aroundthe
Z-axis
andcentered
aroundthe
origin.T
henthe
following
propertiesare
computed:
1.Helix
radius(file
radius.xvg).T
hisis
merely
theR
MS
deviationin
two
dimensions
forallC
alphaatom
s.itis
calcedas
sqrt((SU
Mi(x 2(i)+
y2(i)))/N
),where
Nis
thenum
berofbackbone
atoms.
For
anidealhelix
theradius
is0.23
nm2.
Twist
(filetw
ist.xvg).T
heaverage
helicalangle
perresidue
iscalculated.
For
alphahelix
itis
100degrees,for
3-10helices
itwillbe
smaller,for
5-helicesitw
illbelarger.
3.R
iseper
residue(file
rise.xvg).T
hehelicalrise
perresidue
isplotted
asthe
differencein
Z-coordinate
between
Ca
atoms.
For
anidealhelix
thisis
0.15nm
4.Totalhelixlength
(filelen-ahx.xvg).
The
totallengthofthe
helixin
nm.
This
issim
plythe
averagerise
(seeabove)
times
thenum
berofhelicalresidues
(seebelow
).5.N
umber
ofhelicalresidues(file
n-ahx.xvg).T
hetitle
saysitall.
6.Helix
Dipole,backbone
only(file
dip-ahx.xvg).7.R
MS
deviationfrom
idealhelix,calculatedfor
theC
alphaatom
sonly
(filerm
s-ahx.xvg).
19
8A
pp
en
dix
E.
Ma
nu
alP
age
s
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-d
strin
gZ
Take
the
norm
alon
the
mem
bran
ein
dire
ctio
nX
,Yor
Z.
-sl
int
0C
alcu
late
orde
rpa
ram
eter
asfu
nctio
nof
boxl
engt
h,di
vidi
ngth
ebo
xin
#nr
slic
es.
•T
hepr
ogra
mas
sign
sw
hole
wat
erm
olec
ules
toa
slic
e,ba
sed
onth
efir
stat
omof
thre
ein
the
inde
xfil
egr
oup.
Itas
sum
esan
orde
rO
,H,H
.Nam
eis
noti
mpo
rtan
t,bu
tthe
orde
ris
.If
this
dem
and
isno
tm
et,a
ssig
ning
mol
ecul
esto
slic
esis
diffe
rent
.
E.2
5g
hbon
d
ghb
ond
com
pute
san
dan
alyz
eshy
drog
enbo
nds.
Hyd
roge
nbo
nds
are
dete
rmin
edba
sed
oncu
toffs
for
the
angl
eD
onor
-H
ydro
gen
-A
ccep
tor
(zer
ois
exte
nded
)an
dth
edi
stan
ceH
ydro
gen
-A
ccep
tor.
OH
and
NH
grou
psar
ere
gard
edas
dono
rs,O
isan
acce
ptor
alw
ays,
Nis
anac
cept
orby
defa
ult,
butt
his
can
besw
itche
dus
ing-
nita
cc.
Dum
my
hydr
ogen
atom
sar
eas
sum
edto
beco
nnec
ted
toth
efir
stpr
eced
ing
non-
hydr
ogen
atom
.
You
need
tosp
ecify
two
grou
psfo
ran
alys
is,w
hich
mus
tbe
eith
erid
entic
alor
non-
over
lapp
ing.
All
hydr
o-ge
nbo
nds
betw
een
the
two
grou
psar
ean
alyz
ed.
Ifyo
use
t-sh
ell,
you
will
beas
ked
for
anad
ditio
nali
ndex
grou
pw
hich
shou
ldco
ntai
nex
actly
one
atom
.In
this
case
,onl
yhy
drog
enbo
nds
betw
een
atom
sw
ithin
the
shel
ldis
tanc
efr
omth
eon
eat
omar
eco
nsid
ered
.
Itis
also
poss
ible
toan
alys
esp
ecifi
chy
drog
enbo
nds
with
-se
l.
Thi
sin
dex
file
mus
tco
ntai
na
grou
pof
atom
trip
lets
Don
orH
ydro
gen
Acc
epto
r,in
the
follo
win
gw
ay:
[se
lect
ed
]2
02
12
42
52
62
91
36
Not
eth
atth
etr
iple
tsne
edno
tbe
onse
para
telin
es.
Eac
hat
omtr
iple
tsp
ecifi
esa
hydr
ogen
bond
tobe
anal
yzed
,not
eal
soth
atno
chec
kis
mad
efo
rth
ety
pes
ofat
oms.
-in
stu
rns
onco
mpu
ting
solv
enti
nser
tion
into
hydr
ogen
bond
s.In
this
case
anad
ditio
nalg
roup
mus
tbe
sele
cted
,spe
cify
ing
the
solv
entm
olec
ules
.
Out
put:
-nu
m:
num
ber
ofhy
drog
enbo
nds
asa
func
tion
oftim
e.-a
c:
aver
age
over
alla
utoc
orre
latio
nsof
the
exis
tenc
efu
nctio
ns(e
ither
0or
1)of
allh
ydro
gen
bond
s.-d
ist
:di
stan
cedi
strib
utio
nof
allh
ydro
gen
bond
s.-a
ng
:an
gle
dist
ribut
ion
ofal
lhyd
roge
nbo
nds.
-hx
:th
enu
mbe
rof
n-n+
ihyd
roge
nbo
nds
asa
func
tion
oftim
ew
here
nan
dn+
ista
ndfo
rre
sidu
enu
mbe
rsan
dir
ange
sfr
om0
to6.
Thi
sin
clud
esth
en-
n+3,
n-n+
4an
dn-
n+5
hydr
ogen
bond
sas
soci
ated
with
helic
esin
prot
eins
.-h
bn
:al
lsel
ecte
dgr
oups
,don
ors,
hydr
ogen
san
dac
cept
ors
fors
elec
ted
grou
ps,a
llhy
drog
enbo
nded
atom
sfr
omal
lgro
ups
and
alls
olve
ntat
oms
invo
lved
inin
sert
ion.
-hb
m:
exis
tenc
em
atrix
for
allh
ydro
gen
bond
sov
eral
lfra
mes
,th
isal
soco
ntai
nsin
form
atio
non
solv
ent
3.7
.S
imu
late
dA
nn
ea
ling
31
Thi
sco
rrec
tion
for
rota
tiona
lef
fect
sis
actu
ally
anite
rativ
epr
oces
s,bu
tdu
ring
MD
only
one
itera
tion
isap
plie
d.T
here
lativ
eco
nstr
aint
devi
atio
naf
ter
this
proc
edur
ew
illbe
less
than
0.00
01fo
rev
ery
cons
trai
nt.
Inen
ergy
min
imiz
atio
nth
ism
ight
notb
eac
cura
teen
ough
,so
the
num
ber
ofite
ratio
nsis
equa
lto
the
orde
rof
the
expa
nsio
n(s
eebe
low
).
Hal
foft
heC
PU
time
goes
toin
vert
ing
the
cons
trai
ntco
uplin
gm
atrix
BnM
−1B
T n,w
hich
has
tobe
done
ever
ytim
est
ep.
Thi
sK×K
mat
rixha
s1/m
i 1+
1/m
i 2on
the
diag
onal
.T
heof
f-di
agon
alel
emen
tsar
eon
lyno
n-ze
row
hen
two
bond
sar
eco
nnec
ted,
then
the
elem
ent
isco
sφ/m
c,
whe
rem
cis
the
mas
sof
the
atom
conn
ectin
gth
etw
obo
nds
and
φis
the
angl
ebe
twee
nth
ebo
nds.
The
mat
rixT
isin
vert
edth
roug
ha
pow
erex
pans
ion.
AK×K
mat
rixS
isin
trod
uced
whi
chis
the
inve
rse
squa
rero
otof
the
diag
onal
ofB
nM
−1B
T n.
Thi
sm
atrix
isus
edto
conv
ertt
hedi
agon
alel
emen
tsof
the
coup
ling
mat
rixto
one
(BnM
−1B
T n)−
1=
SS−
1(B
nM
−1B
T n)−
1S−
1S
=S
(SB
nM
−1B
T nS
)−1S
=S
(I−
An)−
1S
(3.5
7)
The
mat
rixA
nis
sym
met
rican
dsp
arse
and
has
zero
son
the
diag
onal
.T
hus
asi
mpl
etr
ick
can
beus
edto
calc
ulat
eth
ein
vers
e
(I−
An)−
1=
I+
An
+A
2 n+
A3 n
+...
(3.5
8)
Thi
sin
vers
ion
met
hod
ison
lyva
lidif
the
abso
lute
valu
esof
allt
heei
genv
alue
sof
An
are
smal
ler
than
one.
Inm
olec
ules
with
only
bond
cons
trai
nts
the
conn
ectiv
ityis
solo
wth
atth
isw
illal
way
sbe
true
,eve
nif
ring
stru
ctur
esar
epr
esen
t.P
robl
ems
can
aris
ein
angl
e-co
nstr
aine
dm
olec
ules
.B
yco
nstr
aini
ngan
gles
with
addi
tiona
ldis
tanc
eco
nstr
aint
sm
ultip
lesm
allr
ing
stru
ctur
esar
ein
tro-
duce
d.T
his
give
sa
high
conn
ectiv
ity,l
eadi
ngto
larg
eei
genv
alue
s.T
here
fore
LIN
CS
shou
ldN
OT
beus
edw
ithco
uple
dan
gle-
cons
trai
nts.
The
LIN
CS
Par
amet
ers
The
accu
racy
ofLI
NC
Sde
pend
son
the
num
ber
ofm
atric
esus
edin
the
expa
nsio
neq
n.3.
58.
For
MD
calc
ulat
ions
afo
urth
orde
rexp
ansi
onis
enou
gh.
For
Bro
wni
andy
nam
ics
with
larg
etim
est
eps
anei
ghth
orde
rex
pans
ion
may
bene
cess
ary.
The
orde
ris
apa
ram
eter
inth
ein
putfi
lefo
rm
dru
n.
The
impl
emen
tatio
nof
LIN
CS
isdo
nein
such
aw
ayth
atth
eal
gorit
hmw
illne
ver
cras
h.E
ven
whe
nit
isim
poss
ible
toto
rese
tthe
cons
trai
nts
LIN
CS
will
gene
rate
aco
nfor
mat
ion
whi
chfu
lfills
the
cons
trai
nts
asw
ella
spo
ssib
le.
How
ever
,LI
NC
Sw
illge
nera
tea
war
ning
whe
nin
one
step
abo
ndro
tate
sov
erm
ore
than
apr
edefi
ned
angl
e.T
his
angl
eis
set
byth
eus
erin
the
inpu
tfil
efo
rm
dru
n.
3.7
Sim
ulat
edA
nnea
ling
The
wel
lkno
wn
sim
ulat
edan
neal
ing
(SA
)pr
otoc
olis
impl
emen
ted
ina
sim
ple
way
into
GR
O-
MA
CS
.A
mod
ifica
tion
ofth
ete
mpe
ratu
reco
uplin
gsc
hem
eis
used
asa
very
basi
cim
plem
enta
-tio
nof
the
SA
algo
rithm
.T
hem
etho
dw
orks
asfo
llow
s:th
ere
fere
nce
tem
pera
ture
for
coup
ling
T0
(eqn
.3.2
2)is
notc
onst
antb
utca
nbe
varie
dlin
early
:
T0(s
tep)
=T
0∗
(λ0+
∆λ∗
step
)(3
.59)
32
Ch
ap
ter
3.
Alg
orith
ms
ifλ
0=
1and∆
λis
0this
isthe
plainM
Dalgorithm
.N
otethat
forstandard
SA
∆λ
must
benegative.
WhenT
0 (step)<0
itissetto
0,asnegative
temperatures
donothave
aphysicalm
eaning.T
his“feature”
allows
foran
annealingstrategy
inw
hichat
firstthe
temperature
isscaled
down
linearlyuntil0
K,and
when
more
stepsare
takenthe
simulation
proceedsat0
K.S
incethe
weak
couplingschem
edoes
notcouple
instantaneously,the
actualtemperature
willalw
aysbe
slightlyhigher
than0
K.
3.8S
tochasticD
ynamics
Stochastic
orvelocity
Langevindynam
icsadds
afriction
anda
noiseterm
toN
ewton’s
equationsofm
otion:
mi d
2ri
dt 2=−m
i ξi d
ri
dt
+F
i (r)+◦ri
(3.60)
where
ξi
isthe
frictionconstant[1/ps]
and◦ri (t)
isa
noiseprocess
with〈 ◦r
i (t)◦rj (t
+s)〉
=2m
i ξi k
BTδ(s)δ
ij .W
hen1/ξ
iis
largecom
paredto
thetim
escales
presentin
thesystem
,one
couldsee
stochasticdynam
icsas
molecular
dynamics
with
stochastictem
perature-coupling.T
headvantage
compared
toM
Dw
ithB
erendsentem
perature-couplingis
thatin
caseof
SD
thegen-
eratedensem
bleis
known.
For
vacuumsim
ulationsthere
isthe
additionaladvantagethatthere
isno
accumulation
oferrors
forthe
overalltranslationalandrotationaldegrees
offreedom
.W
hen1/ξ
iis
smallcom
paredto
thetim
escales
presentinthe
system,the
dynamics
willbe
completely
differentfromM
D,butthe
sampling
isstillcorrect.
GR
OM
AC
Suses
acom
plicatedthird-order
leap-frogalgorithm
[29]
tointegrate
equation(3.60).
When
constraintsare
presentinthe
system,tw
oconstraintsteps
areperform
edper
time
step.T
hekinetic
energyis
computed
atthew
holetim
estep,this
isdone
byaveraging
thevelocities
atminus
andplus
ahalftim
estep,w
itha
correctionfor
thefriction:
v(t)=
12 (v (
t−∆t2 )
+v (
t+∆t2 ))(
e −ξ∆
t+√
2 (1−e −
ξ∆
t ))(3.61)
Exactcontinuation
ofastochastic
dynamics
simulation
isnotpossible,since
apartfromthe
coor-dinates
andthe
velocitiesone
randomterm
oftheprevious
stepin
required,however,the
errorwill
bevery
small.
3.9B
rownian
Dynam
ics
Inthe
limitofhigh
frictionstochastic
dynamics
reducesto
Brow
niandynam
ics,also
calledposi-
tionLangevin
dynamics.
This
appliesto
over-damped
systems,
i.e.system
sin
which
theinertia
effectsare
negligible.T
heequation
is:
dri
dt=
1γi F
i (r)+◦ri
(3.62)
where
γi
isthe
frictioncoefficient[am
u/ps]and◦ri (t)
isa
noiseprocess
with〈 ◦r
i (t)◦rj (t+
s)〉=
2δ(s)δ
ij kBT/γ
i .In
GR
OM
AC
Sthe
equationsare
integratedw
itha
simple,explicitschem
e:
ri (t+
∆t)
=r
i (t)+
∆t
γiF
i (r(t))+ √
2kBT
∆t
γi
rGi
(3.63)
E.2
3.
gg
yrate
19
7
-nm
ol
int1
Num
berof
molecules
inyour
sample:
theenergies
aredivided
bythis
number
-nd
fint
3N
umber
ofdegrees
offreedom
perm
olecule.N
ecessaryfor
calculatingthe
heatcapacity-flu
cbool
no
Calculate
autocorrelationofenergy
fluctuationsrather
thanenergy
itself-a
cflen
int-1
Lengthofthe
AC
F,defaultishalfthe
number
offrames
-no
rma
lizebool
yes
Norm
alizeA
CF
-Penum
0O
rderofLegendre
polynomialfor
AC
F(0
indicatesnone):
0,1
,2or3
-fitfnenum
no
ne
Fitfunction:n
on
e,e
xp,a
exp
,exp
exp
orvac
-ncskip
int0
Skip
Npoints
inthe
outputfileofcorrelation
functions-b
eg
infit
real0
Tim
ew
hereto
beginthe
exponentialfitofthecorrelation
function-e
nd
fitreal
-1T
ime
where
toend
theexponentialfitofthe
correlationfunction,-1
istill
theend
E.23
ggyrate
ggyrate
computes
theradius
ofgyrationofa
groupofatom
sand
theradiiofgyration
aboutthex,y
andz
axes,asa
functionoftim
e.T
heatom
sare
explicitlym
assw
eighted.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-o
gyra
te.xvg
Output
xvgr/xmgr
file-n
ind
ex.n
dx
Input,Opt.
Indexfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-q
booln
oU
seabsolute
valueof
thecharge
ofan
atomas
weighting
factorinstead
ofmass
-pbool
no
Calculate
theradiiofgyration
abouttheprincipalaxes.
E.24
gh2order
Com
putethe
orientationofw
aterm
oleculesw
ithrespectto
thenorm
alofthebox.
The
programdeterm
inesthe
averagecosine
ofthe
anglebetw
eende
dipolem
oment
ofw
aterand
anaxis
ofthe
box.T
hebox
isdivided
inslices
andthe
averageorientation
perslice
isprinted.
Each
water
molecule
isassigned
toa
slice,per
time
frame,based
onthe
positionofthe
oxygen.W
hen-nm
isused
theangle
between
thew
aterdipole
andthe
axisfrom
thecenter
ofmass
tothe
oxygenis
calculatedinstead
oftheangle
between
thedipole
anda
boxaxis.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput
Indexfile
-nm
ind
ex.n
dx
Input,Opt.
Indexfile
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-oo
rde
r.xvgO
utputxvgr/xm
grfile
19
6A
pp
en
dix
E.
Ma
nu
alP
age
s
-lj
bool
yes
calc
ulat
eLe
nnar
d-Jo
nes
SR
ener
gies
-lj1
4bo
oln
oca
lcul
ate
Lenn
ard-
Jone
s1-
4en
ergi
es-b
ha
mbo
oln
oca
lcul
ate
Buc
king
ham
ener
gies
-fre
ebo
olye
sca
lcul
ate
free
ener
gy-t
em
pre
al3
00
refe
renc
ete
mpe
ratu
refo
rfr
eeen
ergy
calc
ulat
ion
E.2
2g
ener
gy
gen
ergy
extr
acts
ener
gyco
mpo
nent
sor
dist
ance
rest
rain
tdat
afr
oman
ener
gyfil
e.T
heus
eris
prom
pted
toin
tera
ctiv
ely
sele
ctth
een
ergy
term
ssh
ew
ants
.
Whe
nth
e-vi
ol
optio
nis
set,
the
time
aver
aged
viol
atio
nsar
epl
otte
dan
dth
eru
nnin
gtim
e-av
erag
edan
din
stan
tane
ous
sum
ofvi
olat
ions
are
reca
lcul
ated
.A
dditi
onal
lyru
nnin
gtim
e-av
erag
edan
din
stan
tane
ous
dist
ance
sbe
twee
nse
lect
edpa
irsca
nbe
plot
ted
with
the
-pa
irs
optio
n.
Ave
rage
and
RM
SD
are
calc
ulat
edw
ithfu
llpr
ecis
ion
from
the
sim
ulat
ion
(see
prin
ted
man
ual).
Drif
tis
calc
ulat
edby
perf
orm
ing
aLS
Qfit
ofth
eda
tato
ast
raig
htlin
e.To
tald
rifti
sdr
iftm
ultip
lied
byto
talt
ime.
With
-fe
ea
free
ener
gyes
timat
eis
calc
ulat
edus
ing
the
form
ula:
G=
-ln<
e(E
/kT
)>
*kT
,w
here
kis
Bol
tzm
ann’
sco
nsta
nt,T
isse
tby-fe
tem
pan
dth
eav
erag
eis
over
the
ense
mbl
e(o
rtim
ein
atr
ajec
tory
).N
ote
that
this
isin
prin
cipl
eon
lyco
rrec
twhe
nav
erag
ing
over
the
who
le(B
oltz
man
n)en
sem
ble
and
usin
gth
epo
tent
iale
nerg
y.T
his
also
allo
ws
for
anen
trop
yes
timat
eus
ing
G=
H-
TS
,w
here
His
the
enth
alpy
(H=
U+
pV
)an
dS
entr
opy.
Whe
na
seco
nden
ergy
file
issp
ecifi
ed(
-f2
),a
free
ener
gydi
ffere
nce
isca
lcul
ated
dF=
-kT
ln<
e-(
EB
-E
A)/
kT>
A,
whe
reE
Aan
dE
Bar
eth
een
ergi
esfr
omth
efir
stan
dse
cond
ener
gyfil
es,
and
the
aver
age
isov
erth
een
sem
ble
A.NO
TE
that
the
ener
gies
mus
tbot
hbe
calc
ulat
edfr
omth
esa
me
traj
ecto
ry.
File
s-f
en
er.
ed
rIn
put
Gen
eric
ener
gy:
edr
ene
-f2
en
er.
ed
rIn
put,
Opt
.G
ener
icen
ergy
:ed
ren
e-s
top
ol.t
pr
Inpu
t,O
pt.
Gen
eric
run
inpu
t:tp
rtp
btp
a-o
en
erg
y.xv
gO
utpu
txv
gr/x
mgr
file
-vio
lvi
ola
ver.
xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-pa
irs
pa
irs.
xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-co
rre
ne
corr
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-vis
visc
o.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-r
avg
run
avg
df.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-fe
ebo
oln
oD
oa
free
ener
gyes
timat
e-f
ete
mp
real
30
0R
efer
ence
tem
pera
ture
for
free
ener
gyca
lcul
atio
n-z
ero
real
0S
ubtr
acta
zero
-poi
nten
ergy
-su
mbo
oln
oS
umth
een
ergy
term
sse
lect
edra
ther
than
disp
lay
them
all
-dp
bool
no
Prin
tene
rgie
sin
high
prec
isio
n-m
uto
tbo
oln
oC
ompu
teth
eto
tald
ipol
em
omen
tfro
mth
eco
mpo
nent
s-s
kip
int
0S
kip
num
ber
offr
ames
betw
een
data
poin
ts-a
ver
bool
no
Prin
tals
oth
eX
1,ta
ndsi
gma1
,t,on
lyif
only
1en
ergy
isre
ques
ted
3.1
0.
En
erg
yM
inim
iza
tion
33
whe
rer
G iis
Gau
ssia
ndi
strib
uted
nois
ew
ithµ=
0,σ
=1.
The
fric
tion
coef
ficie
ntsγ
ica
nbe
chos
enth
esa
me
for
allp
artic
les
orasγ i
=m
i/ξ i
,whe
reth
efr
ictio
nco
nsta
ntsξ i
can
bedi
ffere
ntfo
rdi
ffere
ntgr
oups
ofat
oms.
Bec
ause
the
syst
emis
assu
med
tobe
over
dam
ped,
larg
etim
e-st
eps
can
beus
ed.
LIN
CS
shou
ldbe
used
for
the
cons
trai
nts
sinc
eS
HA
KE
will
notc
onve
rge
for
larg
eat
omic
disp
lace
men
ts.
BD
isan
optio
nof
the
md
run
prog
ram
.
3.10
Ene
rgy
Min
imiz
atio
n
Ene
rgy
min
imiz
atio
nin
GR
OM
AC
Sca
nbe
done
usin
ga
stee
pest
desc
ent
orco
njug
ate
grad
ient
met
hod.
EM
isju
stan
optio
nof
them
dru
npr
ogra
m.
3.10
.1S
teep
estD
esce
nt
Alth
ough
stee
pest
desc
ent
isce
rtai
nly
not
the
mos
tef
ficie
ntal
gorit
hmfo
rse
arch
ing,
itis
robu
stan
dea
syto
impl
emen
t.
We
defin
eth
eve
ctorr
asth
eve
ctor
ofal
l3Nco
ordi
nate
s.In
itial
lya
max
imum
disp
lace
men
th
0
(e.g
.0.0
1nm
)m
ustb
egi
ven.
Firs
tthe
forc
esF
and
pote
ntia
lene
rgy
are
calc
ulat
ed.
New
posi
tions
are
calc
ulat
edby
rn+
1=
rn
+F
n
max
(|Fn|)h
n(3
.64)
whe
reh
nis
the
max
imum
disp
lace
men
tandF
nis
the
forc
e,or
the
nega
tive
grad
ient
ofth
epo
ten-
tialV
.T
heno
tatio
nmax
(|Fn|)
mea
nsth
ela
rges
toft
heab
solu
teva
lues
ofth
efo
rce
com
pone
nts.
The
forc
esan
den
ergy
are
agai
nco
mpu
ted
for
the
new
posi
tions
If(V
n+
1<V
n)
the
new
posi
tions
are
acce
pted
and
hn+
1=
1.2h
n.
If(V
n+
1≥V
n)
the
new
posi
tions
are
reje
cted
and
hn
=0.
2hn.
The
algo
rithm
stop
sw
hen
eith
era
user
spec
ified
num
ber
offo
rce
eval
uatio
nsha
sbe
enpe
rfor
med
(e.g
.10
0),
orw
hen
the
max
imum
ofth
eab
solu
teva
lues
ofth
efo
rce
(gra
dien
t)co
mpo
nent
sis
smal
ler
than
asp
ecifi
edva
lueε.
Sin
cefo
rce
trun
catio
npr
oduc
esso
me
nois
ein
the
ener
gyev
alua
-tio
n,th
est
oppi
ngcr
iterio
nsh
ould
notb
em
ade
too
tight
toav
oid
endl
ess
itera
tions
.A
reas
onab
leva
lue
forε
can
bees
timat
edfr
omth
ero
otm
ean
squa
refo
rce
fa
harm
onic
osci
llato
rwou
ldex
hibi
tat
ate
mpe
ratu
reTT
his
valu
eis
f=
2πν√
2mkT
(3.6
5)
whe
reν
isth
eos
cilla
tor
freq
uenc
y,mth
e(r
educ
ed)
mas
s,an
dkB
oltz
man
n’s
cons
tant
.F
ora
wea
kos
cilla
tor
with
aw
ave
num
ber
of10
0cm−
1an
da
mas
sof
10at
omic
units
,ata
tem
pera
ture
of1
K,f
=7.
7kJ
mol−
1nm
−1.
Ava
lue
forε
betw
een
1an
d10
isac
cept
able
.
3.10
.2C
onju
gate
Gra
dien
t
Con
juga
tegr
adie
ntis
slow
erth
anst
eepe
stde
scen
tin
the
early
stag
esof
the
min
imiz
atio
n,bu
tbe
com
esm
ore
effic
ient
clos
erto
the
ener
gym
inim
um.
The
para
met
ers
and
stop
crite
rion
are
the
sam
eas
fors
teep
estd
esce
nt.
Con
juga
tegr
adie
ntca
nno
tbe
used
with
cons
trai
nts
orfr
eeze
grou
ps.
34
Ch
ap
ter
3.
Alg
orith
ms
3.11N
ormalM
odeA
nalysis
Norm
almode
analysis[30,31,32]can
beperform
edusing
GR
OM
AC
S,by
diagonalizationofthe
mass-w
eightedH
essian:M
−1/2H
M−
1/2Q
=ω
2Q(3.66)
where
Mcontains
theatom
icm
asses,Q
containseigenvectors,andωcontains
thecorresponding
eigenvalues(frequencies).
First,the
Hessian
matrix,w
hichis
a3N×
3Nm
atrixw
hereNis
thenum
berofatom
s,hasto
becalculated:
Hij
=∂
2V
∂x
i ∂x
j(3.67)
where
xi and
xj
denotethe
atomic
x,yor
zcoordinates.
Inpractice,these
equationshave
notbeendeveloped
analytically,buttheforce
isused
Fi
=∂V
∂x
i(3.68)
fromw
hichthe
Hessian
iscom
putednum
erically.Itshould
benoted
thatforausualN
ormalM
odecalculation,itis
necessaryto
completely
minim
izethe
energypriorto
computation
oftheH
essian.T
hisshould
bedone
with
conjugategradient
indouble
precision.A
number
ofG
RO
MA
CS
pro-gram
sare
involvedin
thesecalculations.
Firstn
mru
n,w
hichcom
putesthe
Hessian,and
secondlyg
nm
eig
which
doesthe
diagonalizationand
sortingofnorm
almodes
accordingto
frequencies.B
oththese
programs
shouldbe
runin
doubleprecision.
An
overviewofnorm
almode
analysisand
therelated
principalcomponentanalysis
(seesec.8.9)
canbe
foundin
[33].
3.12F
reeenergy
calculations
Free
energycalculations
canbe
performed
inG
RO
MA
CS
usingslow
-growth
methods.
An
exam-
pleproblem
might
be:calculate
thedifference
infree
energyof
bindingof
aninhibitor
Ito
anenzym
eEand
toa
mutated
enzymeE’.Itis
notfeasiblew
ithcom
putersim
ulationsto
performa
dockingcalculation
forsuch
alarge
complex,or
evenreleasing
theinhibitor
fromthe
enzyme
ina
reasonableam
ountof
computer
time
with
reasonableaccuracy.
How
ever,if
we
considerthe
freeenergy
cyclein
(Fig.3.9A
)w
ecan
write
∆G
1 −∆G
2=
∆G
3 −∆G
4(3.69)
Ifwe
areinterested
inthe
left-handterm
we
canequally
wellcom
putethe
right-handterm
.
Ifw
ew
antto
compute
thedifference
infree
energyof
bindingof
two
inhibitorsI
andI’
toan
enzymeE
(Fig.3.9B
)w
ecan
againuse
eqn.3.69
tocom
putethe
desiredproperty.
Free
energydifferences
between
two
molecular
speciescan
becalculated
inG
RO
MA
CS
usingthe
“slow-grow
th”m
ethod.In
fact,suchfree
energydifferences
between
differentmolecular
speciesare
physicallym
eaningless,but
theycan
beused
toobtain
meaningful
quantitiesem
ployinga
thermodynam
iccycle.
The
method
requiresa
simulation
duringw
hichthe
Ham
iltonianof
thesystem
changesslow
lyfrom
thatdescribing
onesystem
(A)
tothat
describingthe
othersystem
E.2
1.
ge
ne
ma
t1
95
Files
-fd
ynd
om
.pd
bInput
Protein
databank
file-o
rota
ted
.xtcO
utputG
enerictrajectory:
xtctrr
trjgrog96
pdb-n
do
ma
ins.n
dx
InputIndex
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int0
Setthe
nicelevel-firsta
ng
lereal
0A
ngleofrotation
aboutrotationvector
-lasta
ng
lereal
0A
ngleofrotation
aboutrotationvector
-nfra
me
int1
1N
umber
ofstepson
thepathw
ay-m
axa
ng
lereal
0D
ymD
omdterm
inedangle
ofrotationaboutrotation
vector-tra
ns
real0
Translation
(Aangstroem
)along
rotationvector
(seeD
ynDom
infofile)
-he
ad
vector0
00
Firstatom
ofthearrow
vector-ta
ilvector
00
0Lastatom
ofthearrow
vector
E.21
genem
at
genem
atextractsan
energym
atrixfrom
anenergy
file.W
ith-groups
afile
mustbe
suppliedw
ithon
eachline
agroup
tobe
used.F
orthese
groupsa
matrices
ofinteractionenergies
willbe
calculated.A
lsothe
totalinteraction
energyenergy
pergroup
iscalculated.
An
approximation
ofthe
freeenergy
iscalculated
using:E
(free)=
E0
+kT
log(<
exp((E-E
0)/kT)>
),w
here’<>
’standsfor
time-average.
Afile
with
referencefree
energiescan
besupplied
tocalculate
thefree
energydifference
with
some
referencestate.
Group
names
(e.g.residue
names
inthe
referencefile
shouldcorrespond
tothe
groupnam
esas
usedin
the-groups
file,but
aappended
number
(e.g.residue
number)in
the-groupsw
illbeignored
inthe
comparison.
Files
-fe
ne
r.ed
rInput,O
pt.G
enericenergy:
edrene
-gro
up
sg
rou
ps.d
at
InputG
enericdata
file-e
ref
ere
f.da
tInput,O
pt.G
enericdata
file-e
ma
te
ma
t.xpm
Output
XP
ixMap
compatible
matrix
file-e
tot
en
erg
y.xvgO
utputxvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-su
mbool
no
Sum
theenergy
terms
selectedrather
thandisplay
themall
-skipint
0S
kipnum
beroffram
esbetw
eendata
points-m
ea
nbool
yes
with
-groupscalculates
matrix
ofm
eanenergies
instead
ofm
atrixfor
eachtim
estep-n
leve
lsint
20
number
oflevelsfor
matrix
colors-m
ax
real1
e+
20
max
valuefor
energies-m
inreal
-1e
+2
0m
invalue
forenergies
-cou
lbool
yes
calculateC
oulomb
SR
energies-co
ulr
booln
ocalculate
Coulom
bLR
energies-co
ul1
4bool
no
calculateC
oulomb
1-4energies
19
4A
pp
en
dix
E.
Ma
nu
alP
age
s
-dm
drm
ax.
xvg
Out
put
xvgr
/xm
grfil
e-d
rre
str.
xvg
Out
put
xvgr
/xm
grfil
e-l
dis
res.
log
Out
put
Log
file
-nvi
ol.n
dx
Inpu
t,O
pt.
Inde
xfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-n
top
int
6N
umbe
rof
larg
evi
olat
ions
that
are
stor
edin
the
log
file
ever
yst
ep
E.1
9g
dist
gdi
stca
nca
lcul
ate
the
dist
ance
betw
een
the
cent
ers
ofm
ass
oftw
ogr
oups
ofat
oms
asa
func
tion
oftim
e.T
heto
tald
ista
nce
and
itsx,
yan
dz
com
pone
nts
are
plot
ted.
Or
whe
n-d
ist
isse
t,pr
inta
llth
eat
oms
ingr
oup
2th
atar
ecl
oser
than
ace
rtai
ndi
stan
ceto
the
cent
erof
mas
sof
grou
p1.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-od
ist.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-dis
tre
al0
Prin
tall
atom
sin
grou
p2
clos
erth
andi
stto
the
cent
erof
mas
sof
grou
p1
E.2
0g
dynd
om
gdy
ndom
read
sa
pdb
file
outp
utfr
omD
ynD
omht
tp://
md.
chem
.rug
.nl/
stev
e/D
ynD
om/d
yndo
m.h
ome.
htm
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ally
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tore
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rth
ese
cond
stru
ctur
eus
edfo
rge
nera
ting
the
Dyn
Dom
outp
ut.
Bec
ause
oflim
ited
num
eric
alac
cura
cyth
issh
ould
beve
rified
byco
mpu
ting
anal
l-ato
mR
MS
D(u
singg
con
frm
s)
rath
erth
anby
file
com
paris
on(u
sing
diff)
.
The
purp
ose
ofth
ispr
ogra
mis
toin
terp
olat
ean
dex
trap
olat
eth
ero
tatio
nas
foun
dby
Dyn
Dom
.A
sa
resu
ltun
phys
ical
stru
ctur
esw
ithlo
ngor
shor
tbon
ds,o
rov
erla
ppin
gat
oms
may
bepr
oduc
ed.
Vis
uali
nspe
ctio
n,an
den
ergy
min
imiz
atio
nm
aybe
nece
ssar
yto
valid
ate
the
stru
ctur
e.
3.1
2.
Fre
ee
ne
rgy
calc
ula
tion
s3
5
I E’
EI EE
’
G1
∆∆G
2
∆G4
∆G3
A
G1
∆∆G
2
∆G3
II’
EI
EI’
∆G4
B
Fig
ure
3.9:
Fre
een
ergy
cycl
es.A:
toca
lcul
ate∆G
12
orth
efr
eeen
ergy
diffe
renc
ebe
twee
nth
ebi
ndin
gof
inhi
bito
rIto
enzy
mes
Ere
spec
tivel
yE’.
B:t
oca
lcul
ate∆G
12
whi
chis
the
free
ener
gydi
ffere
nce
for
bind
ing
ofin
hibi
torsI
resp
ectiv
elyI
’to
enzy
meE
.
(B).
The
chan
gem
ustb
eso
slow
that
the
syst
emre
mai
nsin
equi
libriu
mdu
ring
the
proc
ess;
ifth
atre
quire
men
tis
fulfi
lled,
the
chan
geis
reve
rsib
lean
da
slow
-gro
wth
sim
ulat
ion
from
Bto
Aw
illyi
eld
the
sam
ere
sults
(but
with
adi
ffere
ntsi
gn)
asa
slow
-gro
wth
sim
ulat
ion
from
Ato
B.T
his
isa
usef
ulch
eck,
butt
heus
ersh
ould
beaw
are
ofth
eda
nger
that
equa
lity
offo
rwar
dan
dba
ckw
ard
grow
thre
sults
does
notg
uara
ntee
corr
ectn
ess
ofth
ere
sults
.
The
requ
ired
mod
ifica
tion
ofth
eH
amilt
onia
nHis
real
ized
bym
akin
gHa
func
tion
ofac
ou
plin
gp
ara
me
terλ
:H=H
(p,q
;λ)
insu
cha
way
thatλ
=0
desc
ribes
syst
emA
andλ=
1de
scrib
essy
stem
B:
H(p,q
;0)
=H
A(p,q
);H
(p,q
;1)
=H
B(p,q
).(3
.70)
InG
RO
MA
CS
,th
efu
nctio
nal
form
ofth
eλ-d
epen
denc
eis
diffe
rent
for
the
vario
usfo
rce-
field
cont
ribut
ions
and
isde
scrib
edin
sect
ion
sec.
4.3.
The
Hel
mho
ltzfr
eeen
ergyA
isre
late
dto
the
part
ition
func
tionQ
ofanN,V,T
ense
mbl
e,w
hich
isas
sum
edto
beth
eeq
uilib
rium
ense
mbl
ege
nera
ted
bya
MD
sim
ulat
ion
atco
nsta
ntvo
lum
ean
dte
mpe
ratu
re.
The
gene
rally
mor
eus
eful
Gib
bsfr
eeen
ergy
Gis
rela
ted
toth
epa
rtiti
onfu
nctio
n∆
ofanN,p,T
ense
mbl
e,w
hich
isas
sum
edto
beth
eeq
uilib
rium
ense
mbl
ege
nera
ted
bya
MD
sim
ulat
ion
atco
nsta
ntpr
essu
rean
dte
mpe
ratu
re:
A(λ
)=
−k
BT
lnQ
(3.7
1)
Q=
c
∫∫ex
p[−βH
(p,q
;λ)]dpdq
(3.7
2)
G(λ
)=
−k
BT
ln∆
(3.7
3)
∆=
c
∫∫∫ex
p[−βH
(p,q
;λ)−βpV
]dpdqdV
(3.7
4)
G=
A+pV,
(3.7
5)
whe
reβ
=1/
(kBT
)an
dc
=(N
!h3N
)−1.
The
sein
tegr
als
over
phas
esp
ace
cann
otbe
eval
uate
dfr
oma
sim
ulat
ion,
but
itis
poss
ible
toev
alua
teth
ede
rivat
ive
toth
epa
ram
eter
λas
anen
sem
ble
36
Ch
ap
ter
3.
Alg
orith
ms
average:dAdλ
= ∫∫(∂H/∂λ)exp[−
βH
(p,q;λ)]d
pdq
∫∫exp[−
βH
(p,q;λ)]d
pdq
= ⟨∂H∂λ ⟩
NV
T;λ,
(3.76)
with
asim
ilarrelation
fordG/dλ
inthe
N,p,T
ensemble.
The
differencein
freeenergy
between
Aand
Bcan
befound
byintegrating
thederivative
overλ
:
AB(V
,T)−
AA(V,T
)= ∫
1
0 ⟨∂H∂λ ⟩
NV
T;λdλ
(3.77)
GB(p
,T)−
GA(p,T
)= ∫
1
0 ⟨∂H∂λ ⟩
NpT
;λdλ.
(3.78)
Ifone
wishes
toevaluateG
B(p,T
)−G
A(p,T
),the
naturalchoiceis
aconstant-pressure
simu-
lation.H
owever,
thisquantity
canalso
beobtained
froma
slow-grow
thsim
ulationat
constantvolum
e,startingw
ithsystem
Aatpressure
pand
volumeV
andending
with
systemB
atpressurep
B,by
applyingthe
following
smallcorrection:
GB(p)−
GA(p)
=A
B(V)−
AA(V
)− ∫pB
p[V
B(p′)−
V]dp′
(3.79)
Here
we
omitted
theconstant
Tfrom
thenotation.
This
correctionis
roughlyequalto
−12 (p
B−
p)∆V
=(∆V
)2/(2κ
V),w
here∆V
isthe
volume
changeatpand
κis
theisotherm
alcompress-
ibility.T
hisis
usuallynegligible.
For
example,the
growth
ofaw
aterm
oleculefrom
nothingin
abath
of1000w
aterm
oleculesatconstantvolum
ew
ouldproduce
anadditionalpressure
of22bar
anda
correctionto
theH
elmholtz
freeenergy
of-20J/m
ol.
Incartesian
coordinates,thekinetic
energyterm
inthe
Ham
iltoniandepends
onlyon
them
omenta,
andcan
beseparately
integratedand
infact
removed
fromthe
equations.W
henm
assesdo
notchange,there
isno
contributionfrom
thekinetic
energyatall;otherw
isethe
integratedcontribution
tothe
freeenergy
is−32 k
BT
ln(mB/m
A).
This
isno
longertrue
inthe
presenceofconstraints.
GR
OM
AC
Soffers
thepossibility
tointegrate
eq.3.77
oreq.3.78
inone
simulation
overthe
fullrange
fromA
toB
.H
owever,
ifthe
changeis
largeand
sampling
insufficiencycan
beexpected,
theuser
may
preferto
determine
thevalue
of〈dG/dλ〉
accuratelyat
anum
berof
well-chosen
intermediate
valuesofλ.
This
canbe
easilydone
bysetting
thestepsize
deltalam
bdato
zero.E
achsim
ulationcan
beequilibrated
first,anda
propererrorestimate
canbe
made
foreachvalue
ofdG/dλ
fromthe
fluctuationof∂H/∂λ
.T
hetotalfree
energychange
isthen
determined
afterwards
byan
appropriatenum
ericalintegrationprocedure.
Theλ
-dependencefor
theforce-field
contributionsis
describedin
sectionsec.
4.3.
3.13E
ssentialDynam
icsS
ampling
The
resultsfrom
EssentialD
ynamics
(seesec.8.9)
ofaprotein
canbe
usedto
guideM
Dsim
ula-tions.
The
ideais
thatfrom
aninitialM
Dsim
ulation(or
fromother
sources)a
definitionof
thecollective
fluctuationsw
ithlargestam
plitudeis
obtained.T
heposition
alongone
orm
oreofthese
collectivem
odescan
beconstrained
ina
(second)M
Dsim
ulationin
anum
berofw
aysfor
severalpurposes.
Forexam
ple,theposition
alonga
certainm
odem
aybe
keptfixedto
monitorthe
average
E.1
8.
gd
isre1
93
-sto
po
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Output,O
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outputxvg,xpm,eps
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real5
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ulation,needed
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AR
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kipsteps
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Use
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atomof
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olecule(starting
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oleculesrather
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centerofcharge
(when
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Skip
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eg
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real0
Tim
ew
hereto
beginthe
exponentialfitofthecorrelation
function-e
nd
fitreal
-1T
ime
where
toend
theexponentialfitofthe
correlationfunction,-1
istill
theend
E.18
gdisre
gdisre
computes
violationsof
distancerestraints.
Ifnecessary
allprotons
canbe
addedto
aprotein
molecule.
The
programallw
ayscom
putesthe
instantaneousviolations
ratherthan
time-averaged,
becausethis
analysisis
donefrom
atrajectory
fileafterw
ardsitdoes
notmake
senseto
usetim
eaveraging.
An
indexfile
may
beused
toselectspecific
restraintsfor
printing.
Files
-sto
po
l.tpr
InputG
enericrun
input:tpr
tpbtpa
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
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Output
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ad
rave
r.xvgO
utputxvgr/xm
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drn
um
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utputxvgr/xm
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19
2A
pp
en
dix
E.
Ma
nu
alP
age
s
The
opth
erop
tion
isto
disc
retiz
eth
edi
hedr
alsp
ace
into
anu
mbe
rof
bins
,an
dgr
oup
each
conf
orm
atio
nin
dihe
dral
spac
ein
the
appr
opria
tebi
n.T
heou
tput
isth
engi
ven
asa
num
ber
ofdi
hedr
alco
nfor
mat
ions
sort
edac
cord
ing
tooc
cupa
ncy.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a-o
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llo.o
ut
Out
put
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eric
outp
utfil
e
Oth
erop
tions
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oln
oP
rinth
elp
info
and
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ein
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etth
eni
cele
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Firs
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Last
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e(p
s)to
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from
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ecto
ry-d
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Onl
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efr
ame
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ntM
OD
dt=
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oln
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iew
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uliti
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rdi
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alan
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(by
defa
ultr
ead
from
topo
logy
)
•sh
ould
nota
skfo
rnu
mbe
rof
fram
es
E.1
7g
dipo
les
gdi
pole
sco
mpu
tes
the
tota
ldip
ole
plus
fluct
uatio
nsof
asi
mul
atio
nsy
stem
.F
rom
this
you
can
com
pute
e.g.
the
diel
ectr
icco
nsta
ntfo
rlo
wdi
elec
tric
med
ia
The
file
dip.
xvg
cont
ains
the
tota
ldip
ole
mom
ent
ofa
fram
e,th
eco
mpo
nent
sas
wel
las
the
norm
ofth
eve
ctor
.T
hefil
eav
er.x
vgco
ntai
ns<or
Muo
r2>
and<
orM
uor>
2du
ring
the
sim
ulat
ion.
The
file
dip.
xvg
cont
ains
the
dist
ribut
ion
ofdi
pole
mom
ents
durin
gth
esi
mul
atio
nT
hem
um
axis
used
asth
ehi
ghes
tval
uein
the
dist
ribut
ion
grap
h.
Fur
ther
mor
eth
edi
pole
auto
corr
elat
ion
func
tion
will
beco
mpu
ted,
whe
nop
tion
-cis
used
.It
can
beav
er-
aged
over
allm
olec
ules
,or
(with
optio
n-a
verc
orr)
itca
nbe
com
pute
das
the
auto
corr
elat
ion
ofth
eto
tal
dipo
lem
omen
toft
hesi
mul
atio
nbo
x.
Att
hem
omen
tthe
diel
ectr
icco
nsta
ntis
calc
ulat
edon
lyco
rrec
tifa
rect
angu
lar
orcu
bic
sim
ulat
ion
box
isus
ed.
Opt
ion
-gpr
oduc
esa
plot
ofth
edi
stan
cede
pend
ent
Kirk
woo
dG
-fac
tor,
asw
ella
sth
eav
erag
eco
sine
ofth
ean
gle
betw
een
the
dipo
les
asa
func
tion
ofth
edi
stan
ce.
The
plot
also
incl
udes
gOO
and
hOO
acco
rdin
gto
Nym
and
&Li
nse,
JCP
112
(200
0)pp
6386
-639
5.
EX
AM
PLE
S
gdi
pole
s-P
1-n
mol
s-o
dips
qr-m
u2.
273
-mum
ax5.
0-n
offt
Thi
sw
illca
lcul
ate
the
auto
corr
elat
ion
func
tion
ofth
em
olec
ular
dipo
les
usin
ga
first
orde
rLe
gend
repo
ly-
nom
ialo
fth
ean
gle
ofth
edi
pole
vect
oran
dits
elf
atim
et
late
r.F
orth
isca
lcul
atio
n10
01fr
ames
will
beus
ed.
Fur
ther
the
diel
ectr
icco
nsta
ntw
illbe
calc
ulat
edus
ing
anep
silo
nRF
ofin
finity
(def
ault)
,te
mpe
ra-
ture
of30
0K
(def
ault)
and
anav
erag
edi
pole
mom
ento
fthe
mol
ecul
eof
2.27
3(S
PC
).F
orth
edi
strib
utio
nfu
nctio
na
max
imum
of5.
0w
illbe
used
.
File
s -en
xe
ne
r.e
dr
Inpu
t,O
pt.
Gen
eric
ener
gy:
edr
ene
-ftr
aj.x
tcIn
put
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b
3.1
4.
Pa
ralle
liza
tion
37
forc
e(f
ree-
ener
gygr
adie
nt)
onth
atco
ordi
nate
inth
atpo
sitio
n.A
noth
erap
plic
atio
nis
toen
hanc
esa
mpl
ing
effic
ienc
yw
ithre
spec
tto
usua
lM
D[
34,
35].
Inth
isca
se,
the
syst
emis
enco
urag
edto
sam
ple
itsav
aila
ble
confi
gura
tion
spac
em
ore
syst
emat
ical
lyth
anin
adi
ffusi
on-li
kepa
thth
atpr
otei
nsus
ually
take
.
All
avai
labl
eco
nstr
aint
type
sar
ede
scrib
edin
the
appr
opria
tech
apte
rof
the
WH
ATIF
[36
]man
-ua
l.
3.14
Par
alle
lizat
ion
The
purp
ose
ofth
isse
ctio
nis
todi
scus
sth
epa
ralle
lizat
ion
ofth
epr
inci
ple
MD
algo
rithm
and
nott
ode
scrib
eth
eal
gorit
hms
that
are
inpr
actic
alus
efo
rmol
ecul
arsy
stem
sw
ithth
eirc
ompl
exva
riety
ofat
oms
and
term
sin
the
forc
efie
ldde
scrip
tions
.W
esh
allt
here
fore
cons
ider
asan
exam
ple
asi
mpl
esy
stem
cons
istin
gon
lyof
asi
ngle
type
ofat
oms
with
asi
mpl
efo
rmof
the
inte
ract
ion
pote
ntia
l.T
heem
phas
isw
illbe
onth
esp
ecia
lpro
blem
sth
atar
ise
whe
nth
eal
gorit
hmis
impl
emen
ted
ona
para
llelc
ompu
ter.
The
sim
ple
mod
elpr
oble
mal
read
yco
ntai
nsth
ebo
ttlen
eck
ofal
lM
Dsi
mul
atio
ns:
the
com
pu-
tatio
nally
inte
nsiv
eev
alua
tion
ofth
enon
-bo
nd
edf
orce
sbe
twee
npa
irsof
atom
s,ba
sed
onth
edi
stan
cebe
twee
npa
rtic
les.
Com
plex
mol
ecul
arsy
stem
sw
illin
addi
tion
invo
lve
man
ydi
ffere
ntki
nds
ofb
on
de
dfor
ces
betw
een
desi
gnat
edat
oms.
Suc
hin
tera
ctio
nsad
dto
the
com
plex
ityof
the
algo
rithm
butd
ono
tmod
ifyth
eba
sic
cons
ider
atio
nsco
ncer
ning
para
lleliz
atio
n.
3.14
.1M
etho
dsof
para
lleliz
atio
n
The
rear
ea
num
ber
ofm
etho
dsto
para
lleliz
eth
eM
Dal
gorit
hm,
each
ofth
emw
ithth
eir
own
adva
ntag
esan
ddi
sadv
anta
ges.
The
met
hod
toch
oose
depe
nds
onth
eha
rdw
are
and
com
pile
rsav
aila
ble.
We
listt
hem
here
:
1M
ess
age
Pa
ssin
g.
Inth
ism
etho
d,w
hich
ism
ore
orle
ssth
etr
aditi
onal
way
ofpa
ralle
lpro
gram
min
g,al
lthe
para
llelis
mis
expl
icitl
ypr
ogra
mm
edby
the
user
.T
hedi
sadv
anta
geis
that
itta
kes
extr
aco
dean
def
fort
,th
ead
vant
age
isth
atth
epr
ogra
mm
erke
eps
full
cont
rolo
ver
the
data
flow
and
can
doop
timiz
atio
nsa
com
pile
rco
uld
notc
ome
upw
ith.
The
impl
emen
tatio
nis
typi
cally
done
byca
lling
ase
tof
libra
ryro
utin
esto
send
and
re-
ceiv
eda
tato
and
from
othe
rpr
oces
sors
.A
lmos
tal
lhar
dwar
eve
ndor
ssu
ppor
tth
isw
ayof
para
llelis
min
thei
rC
and
For
tran
com
pile
rs.
2D
ata
Pa
ralle
l.T
his
met
hod
lets
the
user
defin
ear
rays
onw
hich
toop
erat
ein
para
llel.
Pro
gram
min
gth
isw
ayis
muc
hlik
eve
ctor
izin
g:re
curr
ence
isno
tpar
alle
lized
(e.g
.fo
r(i=
1;
(i<
MA
X);
i++
)a
[i]=
a[i-
1]
+1
;do
esno
tvec
toriz
ean
dno
tpar
alle
lize,
beca
use
for
ever
yit
here
sult
from
the
prev
ious
step
isne
eded
).
The
adva
ntag
eof
data
para
llelis
mis
that
itis
easi
erfo
rth
eus
er;t
heco
mpi
ler
take
sca
reof
the
para
llelis
m.
The
disa
dvan
tage
isth
atit
issu
ppor
ted
bya
smal
l(th
ough
grow
ing)
num
ber
38
Ch
ap
ter
3.
Alg
orith
ms
ofhardw
arevendors,
andthat
itis
much
harderto
maintain
aprogram
thathas
torun
onboth
parallelandsequentialm
achines,because
theonly
standardlanguage
thatsupports
itis
Fortran-90
which
isnotavailable
onm
anyplatform
s.
Both
methods
allowfor
theM
Dalgorithm
tobe
implem
entedw
ithoutm
uchtrouble.
Message
passingM
Dalgorithm
shave
beenpublished
sincethe
mid
80’s([
37],[38])
anddevelopm
entis
stillcontinuing.D
ataparallelprogram
ming
isnew
er,butstartingfrom
aw
ellvectorizedprogram
itisnothard
todo.
Our
implem
entationof
MD
isa
message
passingone,
thereason
forw
hichis
partlyhistorical:
theproject
todevelop
aparallel
MD
programstarted
when
Fortran-90
was
stillin
them
aking,and
nocom
pilersw
ereexpected
tobe
available.A
tcurrent,we
stillbelievethatm
essagepassing
isthe
way
togo,
afterhaving
donesom
eexperim
entsw
ithdata
parallelprogramm
ingon
aC
on-nection
Machine
(CM
-5),because
ofportability
toother
hardware,
thepoor
performance
ofthe
codeproduced
bythe
compilers
andbecause
thisw
ayofprogram
ming
hasthe
same
drawback
asvectorization:
thepartofthe
programthatis
notvectorizedor
parallelizeddeterm
inesthe
runtime
oftheprogram
(Am
dahl’slaw
).
The
approachw
etook
toparallelism
was
am
inimalistone:
useas
littlenon-standard
elements
inthe
software
aspossible,
anduse
thesim
plestprocessortopology
thatdoesthe
job.W
etherefore
decidedto
usea
standardlanguage
(AN
SI-C
)w
ithas
littlenon-standard
routinesas
possible.W
eonly
use5
comm
unicationroutines
thatarenon-standard.
Itistherefore
veryeasy
toportour
codeto
otherm
achines.
For
anO
(N2)
problemlike
MD
,one
ofthe
bestschem
esfor
theinterprocessor
connectionsis
aring,so
oursoftw
aredem
andsthata
ringis
presentinthe
interprocessorconnections.
Aring
canessentially
always
bem
appedonto
anothernetw
orklike
ahypercube,
abus
interface(E
thernete.g.
usingM
essageP
assingInterface
MP
I)or
atree
(CM
-5).S
ome
hardware
vendorshave
veryluxurious
connectionschem
esthat
connectevery
processorto
everyother
processor,but
we
donot
reallyneed
itand
sodo
notuse
iteven
thoughit
might
come
inhandy
attim
es.T
headvan-
tagew
iththis
simplistic
scheme
isthatG
RO
MA
CS
performs
extremely
welleven
oninexpensive
workstation
clusters.
When
usinga
message
passingschem
eone
hasto
dividethe
particlesover
processors,which
canbe
donein
two
ways:
•S
pa
ceD
eco
mp
ositio
n.
An
element
ofspace
isallocated
toeach
processor,w
hendividing
acubic
boxw
ithedge
boverP
processorsthis
canbe
doneby
givingeach
processora
slabof
lengthb/P
.T
hism
ethodhas
theadvantage
thateachprocessor
hasaboutthe
same
number
ofinteractionsto
calculate(at
leastw
henthe
simulated
systemhas
ahom
ogeneousdensity,
likea
liquidor
agas).
The
disadvantageis
thata
lotof
bookkeepingis
necessaryfor
particlesthat
move
overprocessor
boundaries.W
henusing
more
complex
systems
likem
acromolecules
thereare
also3-and
4-atominteractions
thatwould
complicate
thebookkeeping
som
uchthatthis
method
isnotused
inour
program.
•P
article
De
com
po
sition
.E
veryprocessor
isallocated
anum
berof
particles.W
hendividing
Nparticles
overPprocessors
eachprocessor
will
getN/P
particles.T
heim
plementation
ofthis
method
isdescribed
inthe
nextsection.
E.1
5.
gd
iele
ctric1
91
E.15
gdielectric
dielectriccalculates
frequencydependentdielectric
constantsfrom
theautocorrelation
functionofthe
totaldipole
mom
entin
yoursim
ulation.T
hisA
CF
canbe
generatedby
gdipoles.
For
anestim
ateof
theerror
youcan
rungstatistics
onthe
AC
F,and
usethe
outputthus
generatedfor
thisprogram
.T
hefunctional
forms
oftheavailable
functionsare:
One
parmeter
:y
=E
xp[-a1x]Tw
oparm
eters:
y=
a2E
xp[-a1x]T
hreeparm
eter:y
=a2
Exp[-a1
x]+(1
-a2)
Exp[-a3
x]Startvalues
forthe
fitprocedurecan
begiven
onthe
comm
andline.Itis
alsopossible
tofix
parameters
attheirstartvalue,use
-fixw
iththe
number
oftheparam
eteryou
wantto
fix.
Three
outputfilesare
generated,thefirstcontains
theA
CF,an
exponentialfittoitw
ith1,2
or3
parameters,
andthe
numericalderivative
ofthe
combination
data/fit.T
hesecond
filecontains
therealand
imaginary
partsof
thefrequency-dependent
dielectricconstant,
thelast
givesa
plotknow
nas
theC
ole-Cole
plot,in
which
theim
aginarycom
ponentis
plottedas
afunction
ofthe
realcom
ponent.F
ora
pureexponential
relaxation(D
ebyerelaxation)
thelatter
plotshouldbe
onehalfofa
circle
Files
-fM
tot.xvg
Inputxvgr/xm
grfile
-dd
eriv.xvg
Output
xvgr/xmgr
file-o
ep
sw.xvg
Output
xvgr/xmgr
file-c
cole
.xvgO
utputxvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-fft
booln
ouse
fastfouriertransform
forcorrelation
function-x1
boolye
suse
firstcolumn
asX
axisrather
thanfirstdata
set-e
int
real5
Tim
ew
ereto
endthe
integrationofthe
dataand
starttouse
thefit
-bfit
real5
Begin
time
offit-e
fitreal
50
0E
ndtim
eoffit
-tail
real5
00
Lengthoffunction
includingdata
andtailfrom
fit-A
real0
.5S
tartvaluefor
fitparameter
A-ta
u1
real1
0S
tartvaluefor
fitparameter
tau1-ta
u2
real1
Startvalue
forfitparam
etertau2
-ep
s0real
80
Epsilon
0ofyour
liquid-e
psR
Freal
78
.5E
psilonofthe
reactionfield
usedin
yoursim
ulation.A
valueof0
means
infinity.-fix
int0
Fix
parameters
attheirstartvalues,A
(2),tau1(1),or
tau2(4)
-ffnenum
no
ne
Fitfunction:n
on
e,e
xp,a
exp
,exp
exp
orvac
-nsm
oo
thint
3N
umber
ofpointsfor
smoothing
E.16
gdih
gdih
cando
two
things.T
hedefaultis
toanalyze
dihedraltransitionsby
merely
computing
allthedihedral
anglesdefined
inyour
topologyfor
thew
holetrajectory.
When
adihedralflips
overto
anotherm
inimum
anangle/tim
eplotis
made.
19
0A
pp
en
dix
E.
Ma
nu
alP
age
s
-lco
var.
log
Out
put
Log
file
-xp
mco
var.
xpm
Out
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
-xp
ma
cova
ra.x
pm
Out
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-f
itbo
olye
sF
itto
are
fere
nce
stru
ctur
e-r
ef
bool
no
Use
the
devi
atio
nfr
omth
eco
nfor
mat
ion
inth
est
ruct
ure
file
inst
ead
offr
omth
eav
erag
e-m
wa
bool
no
Mas
s-w
eigh
ted
cova
rianc
ean
alys
is-la
stin
t-1
Last
eige
nvec
tor
tow
rite
away
(-1
istil
lthe
last
)
E.1
4g
dens
ity
Com
pute
part
iald
ensi
ties
acro
ssth
ebo
x,us
ing
anin
dex
file.
Den
sitie
sin
gram
/cub
icce
ntim
eter
,nu
mbe
rde
nsiti
esor
elec
tron
dens
ities
can
beca
lcul
ated
.F
orel
ectr
onde
nsiti
es,e
ach
atom
isw
eigh
edby
itsat
omic
part
ialc
harg
e.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-nin
de
x.n
dx
Inpu
t,O
pt.
Inde
xfil
e-s
top
ol.t
pr
Inpu
tG
ener
icru
nin
put:
tpr
tpb
tpa
-ei
ele
ctro
ns.
da
tO
utpu
tG
ener
icda
tafil
e-o
de
nsi
ty.x
vgO
utpu
txv
gr/x
mgr
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-d
strin
gZ
Take
the
norm
alon
the
mem
bran
ein
dire
ctio
nX
,Yor
Z.
-sl
int
10
Div
ide
the
box
in#n
rsl
ices
.-n
um
be
rbo
oln
oC
alcu
late
num
ber
dens
ityin
stea
dof
mas
sde
nsity
.H
ydro
gens
are
not
coun
ted!
-ed
bool
no
Cal
cula
teel
ectr
onde
nsity
inst
ead
ofm
ass
dens
ity-c
ou
nt
bool
no
Onl
yco
unta
tom
sin
slic
es,n
ode
nsiti
es.
Hyd
roge
nsar
eno
tcou
nted
•W
hen
calc
ulat
ing
elec
tron
dens
ities
,ato
mna
mes
are
used
inst
ead
ofty
pes.
Thi
sis
bad.
•W
hen
calc
ulat
ing
num
ber
dens
ities
,at
oms
with
nam
esth
atst
art
with
Har
eno
tco
unte
d.T
his
may
besu
rpris
ing
ifyo
uus
ehy
drog
ens
with
nam
eslik
eO
P3.
3.1
4.
Pa
ralle
liza
tion
39
3.14
.2M
Don
arin
gof
proc
esso
rs
Whe
na
neig
hbor
listi
sno
tuse
dth
eM
Dpr
oble
mis
inpr
inci
ple
anO
(N2)p
robl
emas
each
part
icle
can
inte
ract
with
ever
yot
her.
Thi
sca
nbe
sim
plifi
edus
ing
New
ton’
sth
irdla
w
Fij
=−F
ji(3
.80)
Thi
sim
plie
sth
atth
ere
isha
lfa
mat
rixof
inte
ract
ions
(with
outd
iago
nal,
apa
rtic
ledo
esno
tint
erac
tw
ithits
elf)
toco
nsid
er(F
ig.3.
10).
Whe
nw
ere
flect
the
uppe
rrig
httr
iang
leof
inte
ract
ions
toth
elo
wer
left
tria
ngle
ofth
em
atrix
,w
est
illco
ver
all
poss
ible
inte
ract
ions
,bu
tno
wev
ery
row
inth
em
atrix
has
alm
ost
the
sam
enu
mbe
rof
poin
tsor
poss
ible
inte
ract
ions
.W
eca
nno
was
sign
a(p
refe
rabl
yeq
ual)
num
ber
ofro
ws
toea
chpr
oces
sor
toco
mpu
teth
efo
rces
and
atth
esa
me
time
anu
mbe
rof
part
icle
sto
doth
eup
date
on,
the
ho
me
part
icle
s.T
henu
mbe
rof
inte
ract
ions
per
part
icle
isde
pend
ento
nth
etota
lnu
mb
erN
ofpa
rtic
les
(see
Fig
.3.11
)an
don
thep
art
icle
nu
mb
er
i.T
heex
actf
orm
ulae
are
give
nin
Tabl
e3.
2.
Aflo
wch
arto
fthe
algo
rithm
isgi
ven
inF
ig.3.12
.
Itis
the
sam
eas
the
sequ
entia
lalg
orith
m,e
xcep
tfor
two
com
mun
icat
ion
step
s.A
fter
the
part
icle
sha
vebe
enre
set
inth
ebo
x,ea
chpr
oces
sor
send
sits
coor
dina
tes
left
and
then
star
tsco
mpu
tatio
nof
the
forc
es.
Afte
rth
isst
epea
chpr
oces
sor
hold
sth
ep
art
ialf
orc
esf
orth
eav
aila
ble
part
icle
s,e.
g.pr
oces
sor
0ho
lds
forc
esac
ting
onho
me
part
icle
sfr
ompr
oces
sor
0,1,
2an
d3.
The
sefo
rces
mus
tbe
accu
mul
ated
and
sent
back
(rig
ht)
toth
eho
me
proc
esso
r.F
inal
lyth
eup
date
ofth
eve
loci
tyan
dco
ordi
nate
sis
done
onth
eho
me
proc
esso
r.
The
com
mu
nic
ate
rro
utin
eis
give
nbe
low
inth
efu
llC
-cod
e:
void
com
mu
nic
ate
_r(
int
np
rocs
,int
pid
,rve
cve
cs[]
,int
sta
rt[]
,int
ho
me
nr[
])/*
*n
pro
cs=
nu
mb
er
of
pro
cess
ors
*p
id=
pro
cess
or
id(0
..n
pro
cs-1
)*
vecs
=ve
cto
rs*
sta
rt=
sta
rtin
gin
de
xin
vecs
for
ea
chp
roce
sso
r*
ho
me
nr
=n
um
be
ro
fh
om
ep
art
icle
sfo
re
ach
pro
cess
or
*/{
int
i;/*
pro
cess
or
cou
nte
r*/
int
shift
;/*
the
am
ou
nt
of
pro
cess
ors
toco
mm
un
ica
tew
ith*/
int
cur;
/*cu
rre
nt
pro
cess
or
tose
nd
da
tafr
om
*/in
tn
ext
;/*
ne
xtp
roce
sso
ro
na
rin
g(u
sin
gm
od
ulo
)*/
cur
=p
id;
shift
=n
pro
cs/2
;
for
(i=
0;
(i<
shift
);i+
+)
{n
ext
=(c
ur+
1)
%n
pro
cs;
sen
d(le
ft,
vecs
[sta
rt[c
ur]
],h
om
en
r[cu
r]);
rece
ive
(rig
ht,
vecs
[sta
rt[n
ext
]],
ho
me
nr[
ne
xt])
;cu
r=n
ext
;}
} The
data
flow
arou
ndth
erin
gis
visu
aliz
edin
Fig
.3.
13.
Not
eth
atbe
caus
eof
the
ring
topo
logy
each
proc
esso
rau
tom
atic
ally
gets
the
prop
erpa
rtic
les
toin
tera
ctw
ith.
40
Ch
ap
ter
3.
Alg
orith
ms
012345678
012345678
01
23
45
67
80
12
34
56
78
jj
ii
Figure
3.10:T
heinteraction
matrix
(left)and
thesam
eusing
action=
−reaction
(right).
imod
2=
0im
od2
=0
imod
2=
1im
od2
=1
i<
N/2
i≥N
/2i<
N/2
i≥N
/2N
mod
2=
1N/2
N/2
N/2
N/2
Nm
od4
=2
N/2
N/2
N/2−
1N/2−
1N
mod
4=
0N/2
N/2−
1N/2−
1N/2
Table3.2:
The
number
ofinteractionsbetw
eenparticles.
The
number
ofj
particlesperi
particleis
afunction
ofthetotalnum
berofparticlesN
andparticle
numberi.
Note
thatherethe/
operatoris
usedfor
integerdivision,i.e.truncating
therem
inder.
j
i
j
i
j
i012345
01
23
45
01234567
01
23
45
67
0123456
01
23
45
6
N m
od 4 = 2N
mod 2 = 1
N m
od 4 = 0
Figure
3.11:Interaction
matrices
fordifferent
N.
The
number
ofj-particlesani-particle
interactsw
ithdepends
ontheto
talnum
berofparticles
andon
theparticle
nu
mb
er.
E.1
2.
gco
nfrm
s1
89
-see
dint
19
93
Random
number
seedfor
Monte
Carlo
clusteringalgorithm
-nite
rint
10
00
0N
umber
ofiterationsfor
MC
-kTreal
0.0
01
Boltzm
annw
eightingfactor
forM
onteC
arlooptim
ization(zero
turnsoff
uphillsteps)
E.12
gconfrm
s
gconfrm
scom
putesthe
rootmean
squaredeviation
(RM
SD
)oftw
ostructures
afterLS
Qfitting
thesecond
structureon
thefirstone.
The
two
structuresdo
NO
Tneed
tohave
thesam
enum
berofatom
s,onlythe
two
indexgroups
usedfor
thefitneed
tobe
identical.
The
superimposed
structuresare
written
tofile.
Ina
.pd
bfile
thetw
ostructures
willbe
written
asseparate
models
(userasm
ol
-nm
rpd
b).
Files-f1
con
f1.g
roInput
Structure+
mass(db):
tprtpb
tpagro
g96pdb
-f2co
nf2
.gro
InputG
enericstructure:
grog96
pdbtpr
tpbtpa
-ofit.p
db
Output
Generic
structure:gro
g96pdb
-n1
fit1.n
dx
Input,Opt.
Indexfile
-n2
fit2.n
dx
Input,Opt.
Indexfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-on
ebool
no
Only
write
thefitted
structureto
file-p
bc
booln
oT
ryto
make
molecules
whole
again
E.13
gcovar
gco
var
calculatesand
diagonalizesthe
(mass-w
eighted)covariance
matrix.
Allstructures
arefitted
tothe
structurein
thestructure
file.W
henthis
isnota
runinputfile
periodicityw
illnotbetaken
intoaccount.
When
thefit
andanalysis
groupsare
identicalandthe
analysisis
nonm
ass-weighted,
thefit
willalso
benon
mass-w
eighted.
The
eigenvectorsare
written
toa
trajectoryfile
(-v
).W
henthe
same
atoms
areused
forthe
fitand
thecovariance
analysis,the
referencestructure
forthe
fitis
written
firstw
itht=
-1.T
heaverage
(orreference
when
-ref
isused)structure
isw
rittenw
itht=
0,theeigenvectors
arew
rittenas
frames
with
theeigenvector
number
astim
estamp.
The
eigenvectorscan
beanalyzed
with
ga
na
eig
.
Option
-xpm
writes
thew
holecovariance
matrix
toan
xpmfile.
Option
-xpm
aw
ritesthe
atomic
covariancem
atrixto
anxpm
file,i.e.
foreach
atompair
thesum
ofthe
xx,yyand
zzcovariances
isw
ritten.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-oe
ige
nva
l.xvgO
utputxvgr/xm
grfile
-ve
ige
nve
c.trrO
utputF
ullprecisiontrajectory:
trrtrj
-av
ave
rag
e.p
db
Output
Generic
structure:gro
g96pdb
18
8A
pp
en
dix
E.
Ma
nu
alP
age
s
the
low
errig
htha
lf(d
epen
dson-
ma
xan
d-k
ee
pfr
ee
).-g
writ
esin
form
atio
non
the
optio
nsus
edan
da
deta
iled
listo
fall
clus
ters
and
thei
rm
embe
rs.
Add
ition
ally
,anu
mbe
rof
optio
nalo
utpu
tfile
sca
nbe
writ
ten:
-dis
tw
rites
the
RM
SD
dist
ribut
ion.
-ev
writ
esth
eei
genv
ecto
rsof
the
RM
SD
mat
rixdi
agon
aliz
atio
n.-s
zw
rites
the
clus
ter
size
s.-t
rw
rites
am
atrix
ofth
enu
mbe
rtr
ansi
tions
betw
een
clus
ter
pairs
.-n
trw
rites
the
tota
lnum
ber
oftr
ansi
tions
toor
from
each
clus
ter.
-clid
writ
esth
ecl
uste
rnu
mbe
ras
afu
nctio
nof
time.
-cl
writ
esav
erag
e(w
ithop
tion-a
v)
orce
ntra
lst
ruct
ure
ofea
chcl
uste
ror
writ
esnu
mbe
red
files
with
clus
ter
mem
bers
for
ase
lect
edse
tofc
lust
ers
(with
optio
n-w
cl,d
epen
dson
-nst
and
-rm
smin
).
File
s-f
tra
j.xtc
Inpu
t,O
pt.
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b-s
top
ol.t
pr
Inpu
t,O
pt.
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-dm
rmsd
.xp
mIn
put,
Opt
.X
Pix
Map
com
patib
lem
atrix
file
-orm
sd-c
lust
.xp
mO
utpu
tX
Pix
Map
com
patib
lem
atrix
file
-gcl
ust
er.
log
Out
put
Log
file
-dis
trm
sd-d
ist.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e-e
vrm
sd-e
ig.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-s
zcl
ust
-siz
e.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-t
rclu
st-t
ran
s.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e-n
trclu
st-t
ran
s.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e-c
lidcl
ust
-id
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-cl
clu
ste
rs.p
db
Out
put,
Opt
.G
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-dis
tabo
oln
oU
seR
MS
Dof
dist
ance
sin
stea
dof
RM
Sde
viat
ion
-nle
vels
int
40
Dis
cret
ize
RM
SD
mat
rixin
#le
vels
-ke
ep
fre
ein
t-4
if>
0#
leve
lsno
tto
use
whe
nco
lorin
gcl
uste
rs;i
f<
0nl
evel
s/-k
eepf
ree+
1le
vels
will
notb
eus
ed-c
uto
ffre
al0
.1R
MS
Dcu
t-of
f(nm
)fo
rtw
ost
ruct
ures
tobe
neig
hbor
-ma
xre
al-1
Max
imum
leve
lin
RM
SD
mat
rix-s
kip
int
1O
nly
anal
yze
ever
ynr
-th
fram
e-a
vbo
oln
oW
rite
aver
age
iso
mid
dle
stru
ctur
efo
rea
chcl
uste
r-w
clin
t0
Writ
eal
lstr
uctu
res
for
first
#cl
uste
rsto
num
bere
dfil
es-n
stin
t1
Onl
yw
rite
alls
truc
ture
sif
mor
eth
an#
per
clus
ter
-rm
smin
real
0m
inim
umrm
sdi
ffere
nce
with
rest
ofcl
uste
rfo
rw
ritin
gst
ruct
ures
-me
tho
den
umlin
kag
eM
etho
dfo
rcl
uste
rde
term
inat
ion:
linka
ge
,ja
rvis
-pa
tric
k,
mo
nte
-ca
rlo
,dia
go
na
liza
tion
org
rom
os
-bin
ary
bool
no
Tre
atth
eR
MS
Dm
atrix
asco
nsis
ting
of0
and
1,w
here
the
cut-
off
isgi
ven
by-c
utof
f-M
int
10
Num
ber
ofne
ares
tne
ighb
ors
cons
ider
edfo
rJa
rvis
-Pat
rick
algo
rithm
,0
isus
ecu
toff
-Pin
t3
Num
ber
ofid
entic
alne
ares
tnei
ghbo
rsre
quire
dto
form
acl
uste
r
3.1
4.
Pa
ralle
liza
tion
41
read
_dat
a
Don
e
NO
outp
ut_s
tep
upda
te_r
_and
_v
mor
e st
eps
?Y
ES
com
pute
_for
ces
* *
rese
t_r_
in_b
ox
com
mun
icat
e_r
com
mun
icat
e_an
d_su
m_f
Fig
ure
3.12
:T
heP
aral
lelM
Dal
gorit
hm.
Ifth
est
eps
mar
ked
*ar
ele
ftou
twe
have
the
sequ
entia
lal
gorit
hmag
ain.
42
Ch
ap
ter
3.
Alg
orith
ms
01
2
34
5
6
7Forces
Coordinates
Figure
3.13:D
ataflow
ina
ringofprocessors.
3.15P
arallelMolecular
Dynam
ics
Inthis
chapterw
edescribe
some
detailsof
theparallelM
Dalgorithm
usedin
GR
OM
AC
S.
This
alsoincludes
some
otherinform
ationon
neighborsearching
anda
sideexcursion
toparallelsort-
ing.P
leasenote
thefollow
ingw
hichw
euse
throughoutthischapter:
definition:N
:N
umber
ofparticles,Mnum
berofprocessors.
GR
OM
AC
Sem
ploystw
odifferentgrids:
theneighbor
searchinggrid
(NS
grid)and
thecom
binedcharge/potentialgrid
(FF
Tgrid),
asw
illbedescribed
below.
Tom
aximize
theconfusion,
thesetw
ogrids
arem
appedonto
agrid
ofprocessorsw
henG
RO
MA
CS
runson
aparallelcom
puter.
3.15.1D
omain
decomposition
Modern
dayparallelcom
puters,such
asan
IBM
SP
/2or
aC
rayT
3Econsist
ofrelatively
small
numbers
ofrelativelyfastscalar
processors(typically
8to
256).T
hecom
munication
channelsthat
areavailable
inhardw
areon
thesem
achineare
notdirectlyvisible
forthe
programm
er,asoftw
arelayer(usually
MP
I)hidesthis,and
makes
comm
unicationfrom
allprocessorsto
allotherspossible.
Incontrast,in
theG
RO
MA
CS
hardware
[1]only
comm
unicationin
aring
was
available,i.e.eachprocessor
couldcom
municate
with
itsdirectneighbors
only.
Itseem
slogicalto
map
thecom
putationalboxof
anM
Dsim
ulationsystem
toa
3Dgrid
ofpro-
cessors(e.g.4x4x4
fora
64processor
system).
This
ensuresthatm
ostinteractionsthatare
localinspace
canbe
computed
with
information
fromneighboring
processorsonly.
How
ever,thism
eansthat
therehave
tobe
comm
unicationchannels
in3
dimensions
too,w
hichis
notnecessarily
thecase.
Although
thism
aybe
overcome
insoftw
are,such
am
appingis
complicated
forthe
MD
software
asw
ell,withoutclear
benefitsin
terms
ofperformance
form
ostparallelcomputers.
Therefore
we
optfora
simple
one-dimensionaldivision
scheme
forthe
computationalbox.
Each
processorgets
aslab
ofthisbox
inthe
X-dim
ension.F
orthe
comm
unicationbetw
eenprocessors
thishas
two
main
advantages:
1.S
implicity
ofcoding.C
omm
unicationcan
onlybe
totw
oneighbors
(calledle
ftandrig
htin
GR
OM
AC
S).
E.1
1.
gclu
ster
18
7
-om
eg
abool
no
Outputfor
Om
egadihedrals
(peptidebonds)
-ram
abool
no
Generate
Phi/P
siandC
hi1/Chi2
ramachandran
plots-vio
lbool
no
Write
afile
thatgives0
or1
forviolated
Ram
achandranangles
-all
booln
oO
utputseparatefiles
forevery
dihedral.-sh
iftbool
no
Com
putechem
icalshiftsfrom
Phi/P
siangles-ru
nint
1perform
runningaverage
overndeg
degreesfor
histograms
-ma
xchi
enum0
calculatefirstndih
Chidihedrals:0,1
,2,3
,4,5
or6-n
orm
histo
boolye
sN
ormalize
histograms
-ram
om
eg
abool
no
compute
averageom
egaas
afunction
ofphi/psiandplotitin
anxpm
plot-b
fact
real-1
B-factor
valuefor
pdbfile
foratom
sw
ithno
calculateddihedral
orderparam
eter-b
ma
xreal
0M
aximum
B-factor
onany
oftheatom
sthatm
akeup
adihedral,
forthe
dihedralangleto
beconsidere
inthe
statistics.A
ppliesto
databasew
orkw
herea
number
ofX-R
aystructures
isanalyzed.
-bmax
<=
0m
eansno
limit.
-acfle
nint
-1Length
oftheA
CF,defaultis
halfthenum
beroffram
es-n
orm
alize
boolye
sN
ormalize
AC
F-P
enum0
Order
ofLegendrepolynom
ialforA
CF
(0indicates
none):0
,1,2
or3-fitfn
enumn
on
eF
itfunction:no
ne
,exp
,ae
xp,e
xpe
xporva
c-n
cskipint
0S
kipN
pointsin
theoutputfile
ofcorrelationfunctions
-be
gin
fitreal
0T
ime
where
tobegin
theexponentialfitofthe
correlationfunction
-en
dfit
real-1
Tim
ew
hereto
endthe
exponentialfitofthecorrelation
function,-1is
tillthe
end
•P
roducesM
AN
Youtputfiles
(upto
about4tim
esthe
number
ofresiduesin
theprotein,tw
icethatif
autocorrelationfunctions
arecalculated).
Typicallyseveralhundred
filesare
output.
E.11
gcluster
gcluster
cancluster
structuresw
ithseveraldifferent
methods.
Distances
between
structurescan
bedeter-
mined
froma
trajectoryor
readfrom
anX
PM
matrix
filew
iththe-d
moption.
RM
Sdeviation
afterfitting
orR
MS
deviationofatom
-pairdistances
canbe
usedto
definethe
distancebetw
eenstructures.
fulllinkage:add
astructure
toa
clusterw
henits
distanceto
anyelem
entofthecluster
isless
thancu
toff
.
JarvisP
atrick:add
astructure
toa
clusterw
henthis
structureand
astructure
inthe
clusterhave
eachother
asneighbors
andthey
havea
leastP
neighborsin
comm
on.T
heneighbors
ofastructure
arethe
Mclosest
structuresor
allstructuresw
ithincuto
ff.
Monte
Carlo:
reorderthe
RM
SD
matrix
usingM
onteC
arlo.
diagonalization:diagonalize
theR
MS
Dm
atrix.
gromos:
usealgorithm
asdescribed
inD
aurae
tal.(A
ngew
.C
he
m.
Int.
Ed
.1999,38,pp
236-240).C
ountnum
berofneighbors
usingcut-off,take
structurew
ithlargestnum
berofneighbors
with
allitsneighbors
ascluster
andelem
inateitfrom
thepoolofclusters.
Repeatfor
remaining
structuresin
pool.
When
theclustering
algorithmassigns
eachstructure
toexactly
onecluster
(fulllinkage,JarvisP
atrickand
gromos)
anda
trajectoryfile
issupplied,
thestructure
with
thesm
allestaverage
distanceto
theothers
orthe
averagestructure
orallstructures
foreach
clusterw
illbew
rittento
atrajectory
file.W
henw
ritingall
structures,separatenum
beredfiles
arem
adefor
eachcluster.
Two
outputfilesare
always
written:
-ow
ritesthe
RM
SD
valuesin
theupper
lefthalfofthem
atrixand
agraphicaldepiction
oftheclusters
in
18
6A
pp
en
dix
E.
Ma
nu
alP
age
s
-otr
bu
ntil
tr.x
vgO
utpu
txv
gr/x
mgr
file
-otl
bu
ntil
tl.xv
gO
utpu
txv
gr/x
mgr
file
-ok
bu
nki
nk.
xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-okr
bu
nki
nkr
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-okl
bu
nki
nkl
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-oa
axe
s.p
db
Out
put,
Opt
.P
rote
inda
taba
nkfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-n
ain
t0
Num
ber
ofax
es-z
bool
no
Use
the
Z-a
xis
asre
fere
nce
iso
the
aver
age
axis
E.1
0g
chi
gch
icom
pute
sph
i,ps
i,om
ega
and
chid
ihed
rals
for
ally
our
amin
oac
idba
ckbo
nean
dsi
dech
ains
.It
can
com
pute
dihe
dral
angl
eas
afu
nctio
nof
time,
and
ashi
stog
ram
dist
ribut
ions
.O
utpu
tis
info
rmof
xvgr
files
,as
wel
las
aLa
TeX
tabl
eof
the
num
ber
oftr
ansi
tions
per
nano
seco
nd.
Ord
erpa
ram
eter
sS
2fo
rea
chof
the
dihe
dral
sar
eca
lcul
ated
and
outp
utas
xvgr
file
and
optio
nally
asa
pdb
file
with
the
S2
valu
esas
B-f
acto
r.
Ifop
tion
-cis
give
n,th
epr
ogra
mw
illca
lcul
ate
dihe
dral
auto
corr
elat
ion
func
tions
.T
hefu
nctio
nus
edis
C(t
)=<
cos(
chi(t
au))
cos(
chi(t
au+
t))>.
The
use
ofco
sine
sra
ther
than
angl
esth
emse
lves
,re
solv
esth
epr
oble
mof
perio
dici
ty.
(Van
der
Spo
el&
Ber
ends
en(1
997)
,B
ioph
ys.
J.72
,203
2-20
41).
The
optio
n-r
gene
rate
sa
cont
our
plot
ofth
eav
erag
eom
ega
angl
eas
afu
nctio
nof
the
phia
ndps
iang
les,
that
is,i
na
Ram
acha
ndra
npl
otth
eav
erag
eom
ega
angl
eis
plot
ted
usin
gco
lor
codi
ng.
File
s-c
con
f.g
roIn
put
Gen
eric
stru
ctur
e:gr
og9
6pd
btp
rtp
btp
a-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-oo
rde
r.xv
gO
utpu
txv
gr/x
mgr
file
-po
rde
r.p
db
Out
put,
Opt
.P
rote
inda
taba
nkfil
e-s
sss
du
mp
.da
tIn
put,
Opt
.G
ener
icda
tafil
e-jc
Jco
up
ling
.xvg
Out
put
xvgr
/xm
grfil
e-c
orr
dih
corr
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-gch
i.lo
gO
utpu
tLo
gfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-r
0in
t1
star
ting
resi
due
-ph
ibo
oln
oO
utpu
tfor
Phi
dihe
dral
angl
es-p
sibo
oln
oO
utpu
tfor
Psi
dihe
dral
angl
es
3.1
5.
Pa
ralle
lMo
lecu
lar
Dyn
am
ics
43
X Y Z0
12
N-1
01
23
45
CPU
num
ber
atom
num
ber
inde
x
coor
d.
Fig
ure
3.14
:In
dex
inth
eco
ordi
nate
arra
y.T
hedi
visi
onin
slab
sis
indi
cate
dby
dash
edlin
es.
2.C
omm
unic
atio
nca
nus
ually
bedo
nein
larg
ech
unks
,whi
chm
akes
itm
ore
effic
ient
onm
ost
hard
war
epl
atfo
rms.
Mos
tint
erac
tions
inm
olec
ular
dyna
mic
sha
vein
prin
cipl
ea
shor
tran
ged
char
acte
r.B
onds
,ang
les
and
dihe
dral
sar
egu
aran
teed
toha
veth
eco
rres
pond
ing
part
icle
scl
ose
insp
ace.
3.15
.2D
omai
nde
com
posi
tion
for
non-
bond
edfo
rces
For
larg
epa
ralle
lco
mpu
ters
,do
mai
nde
com
posi
tion
ispr
efer
able
over
part
icle
deco
mpo
sitio
n,si
nce
itis
easi
erto
dolo
adba
lanc
ing.
With
out
load
bala
ncin
gth
esc
alin
gof
the
code
isra
ther
poor
...F
orth
ispu
rpos
e,th
eco
mpu
tatio
nalb
oxis
divi
ded
inM
slab
s,w
hereM
iseq
ualt
oth
enu
mbe
rof
proc
esso
rs.
The
rear
em
ultip
lew
ays
ofdi
vidi
ngth
ebo
xov
erpr
oces
sors
,but
sinc
eth
eG
RO
MA
CS
code
assu
mes
arin
gto
polo
gyfo
rthe
proc
esso
rs,i
tis
logi
calt
ocu
tthe
syst
emin
slab
sin
just
one
dim
ensi
on,t
heX
dim
ensi
on.
The
algo
rithm
for
neig
hbor
sear
chin
gth
enbe
com
es:
1.M
ake
alis
tof
char
gegr
oup
indi
ces
sort
edon
(incr
easi
ng)
Xco
ordi
nate
(Fig
.3.
14).
Not
eth
atca
rem
ustb
eta
ken
topa
ralle
lize
the
sort
ing
algo
rithm
asw
ell.
See
sec.
3.15
.4.
2.D
ivid
eth
islis
tint
osl
abs,
such
that
each
slab
has
the
sam
enu
mbe
rof
char
gegr
oups
3.P
utth
epa
rtic
les
corr
espo
ndin
gto
the
loca
lsla
bon
a3D
NS
grid
asde
scrib
edin
sec.
3.4.
2.
4.C
omm
unic
ate
the
NS
grid
tone
ighb
orin
gpr
oces
sors
(not
nece
ssar
ilyto
allp
roce
ssor
s).
The
amou
ntof
neig
hbor
ing
NS
grid
cells
(N gx)
toco
mm
unic
ate
isde
term
ined
byth
ecu
t-of
fle
ngthr c
acco
rdin
gto
Ngx
=r cM l x
(3.8
1)
whe
rel x
isth
ebo
xle
ngth
inth
esl
abbi
ngdi
rect
ion.
5.O
nea
chpr
oces
sor
com
pute
the
neig
hbor
list
for
all
char
gegr
oups
inits
slab
usin
gth
eno
rmal
grid
neig
hbor
-sea
rchi
ng.
For
hom
ogen
eous
syst
em,
this
iscl
ose
toan
optim
allo
adba
lanc
ing,
with
out
actu
ally
doin
glo
adba
lanc
ing.
For
inho
mog
eneo
ussy
stem
,suc
has
mem
bran
es,o
rin
terf
aces
,the
dim
ensi
onfo
rsl
ab-
bing
mus
tbe
chos
ensu
chth
atit
ispe
rpen
dicu
lart
oth
ein
terf
ace;
inth
isfa
shio
nea
chpr
oces
sorh
as
44
Ch
ap
ter
3.
Alg
orith
ms
“alittle
bitofeverything”.T
heG
RO
MA
CS
utilityprograme
ditco
nf
hasan
optionto
rotatea
whole
computationalbox.
The
following
observationsare
importanthere:
•P
articlesm
aydiffuse
fromone
slabto
theother,therefore
eachprocessor
musthold
coordi-nates
forallparticles
allthetim
e,anddistribute
forcesback
toallprocessors
asw
ell.
•Velocities
arekepton
the“hom
eprocessor”
foreach
particle,where
theintegration
ofNew
-ton’s
equationsis
done.
•F
ixedinteraction
lists(bonds,
anglesetc.)
arekept
eachon
asingle
processor.S
inceall
processorshave
allcoordinates,it
doesnot
matter
where
interactionsare
calculated.T
hedivision
isactually
doneby
theG
RO
MA
CS
preprocessorg
rom
pp
andcare
istaken
that,asfar
aspossible,every
processorgets
thesam
enum
berofbonded
interactions.
Inall,
thism
akesfor
am
ixedparticle
decomposition/dom
aindecom
positionschem
efor
paral-lelization
ofthe
MD
code.T
hecom
munication
costsare
fourtim
eshigher
thanfor
thesim
pleparticle
decomposition
method
describedin
sec.3.14
(thew
holecoordinate
andforce
arrayare
comm
unicatedacross
thew
holering,
ratherthan
halfthe
arrayover
halfthe
ring).H
owever,
forlarge
numbers
ofprocessorsthe
improved
loadbalancing
compensates
thiseasily.
3.15.3P
arallelPP
PM
Afurther
reasonfor
domain
decomposition
isthe
PP
PM
algorithm.
This
algorithmw
orksw
itha
3DF
astF
ourierT
ransform.
Item
ploysa
discretegrid
ofdim
ensions(
nx ,n
y ,nz ),
theF
FT
grid.T
healgorithm
consistoffivesteps,each
ofwhich
haveto
beparallelized:
1.S
preadingcharges
onthe
FF
Tgrid
toobtain
thecharge
distributionρ(r).
This
bitinvolvesthe
following
sub-steps:
a.putparticle
inthe
box
b.find
theF
FT
gridcellin
which
theparticle
resides
c.add
thecharge
ofthe
particletim
esthe
appropriatew
eightfactor
(seesec.
4.6.3)to
eachofthe
27grid
points(3
x3
x3).
Inthe
parallelcase,theF
FT
gridm
ustbefilled
oneach
processorw
ithits
shareofthe
par-ticles,
andsubsequently
theF
FT
gridsof
allprocessorsm
ustbe
summ
edto
findthe
totalcharge
distribution.It
may
beclear
thatthis
inducesa
largeam
ountof
unnecessaryw
ork,unless
we
usedom
aindecom
position.If
eachprocessor
onlyhas
particlesin
acertain
re-gion
ofspace,itonlyhas
tocalculate
thecharge
distributionfor
thatregionofspace.
Since
GR
OM
AC
Sw
orksw
ithslabs,this
means
thateachprocessor
fillsthe
FF
Tgrid
cellscorre-
spondingto
it’sslab
inspace
andaddition
ofFF
Tgrids
needonly
bedone
forneighboring
slabs.To
bem
oreprecise,the
slabxforprocessori
isdefined
as:
ilxM
≤x<
(i+1)lxM
(3.82)
E.8
.g
bo
nd
18
5
E.8
gbond
gbond
makes
adistribution
ofbond
lengths.If
allisw
ellagaussian
distributionshould
bem
adew
henusing
aharm
onicpotential.
bondsare
readfrom
asingle
groupin
theindex
filein
orderi1-j1
i2-j2thru
in-jn.
-tol
givesthe
half-width
ofthe
distributionas
afraction
ofthe
bondlength(
-ble
n).
That
means,
fora
bondof0.2
atolof0.1
givesa
distributionfrom
0.18to
0.22
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-nin
de
x.nd
xInput
Indexfile
-ob
on
ds.xvg
Output
xvgr/xmgr
file-l
bo
nd
s.log
Output,O
pt.Log
file
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-btim
e-1
Firstfram
e(ps)
toread
fromtrajectory
-etim
e-1
Lastframe
(ps)to
readfrom
trajectory-d
ttim
e-1
Only
usefram
ew
hentM
OD
dt=firsttim
e(ps)
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-b
len
real-1
Bond
length.B
ydefaultlength
offirstbond-to
lreal
0.1
Halfw
idthofdistribution
asfraction
ofblen-a
ver
boolye
sS
umup
distributions
•Itshould
bepossible
togetbond
information
fromthe
topology.
E.9
gbundle
gbundle
analyzesbundles
ofaxes.T
heaxes
canbe
forinstance
helixaxes.
The
programreads
two
indexgroups
anddivides
bothofthem
in-naparts.
The
centersofm
assofthese
partsdefine
thetops
andbottom
sof
theaxes.
Severalquantities
arew
rittento
file:the
axislength,
thedistance
andthe
z-shiftof
theaxis
mid-points
with
respecttothe
averagecenter
ofallaxes,thetotaltilt,the
radialtiltandthe
lateraltiltwith
respecttothe
averageaxis.
With
options-ok
,-okr
and-o
klthe
total,radialandlateralkinks
oftheaxes
areplotted.
An
extraindex
groupofkink
atoms
isrequired,w
hichis
alsodivided
into-n
aparts.
The
kinkangle
isdefined
asthe
anglebetw
eenthe
kink-topand
thebottom
-kinkvectors.
With
option-o
athe
top,m
id(or
kinkw
hen-ok
isset)
andbottom
pointsof
eachaxis
arew
rittento
apdb
fileeach
frame.
The
residuenum
berscorrespond
tothe
axisnum
bers.W
henview
ingthis
filew
ithra
smo
l,
usethe
comm
andline
option-nm
rpd
b,
andtypese
ta
xistru
eto
displaythe
referenceaxis.
Files
-ftra
j.xtcInput
Generic
trajectory:xtc
trrtrjgro
g96pdb
-sto
po
l.tpr
InputS
tructure+m
ass(db):tpr
tpbtpa
grog96
pdb-n
ind
ex.n
dx
Input,Opt.
Indexfile
-ol
bu
nle
n.xvg
Output
xvgr/xmgr
file-o
db
un
dist.xvg
Output
xvgr/xmgr
file-o
zb
un
z.xvgO
utputxvgr/xm
grfile
-ot
bu
ntilt.xvg
Output
xvgr/xmgr
file
18
4A
pp
en
dix
E.
Ma
nu
alP
age
s
E.7
gan
gle
gan
gle
com
pute
sth
ean
gle
dist
ribut
ion
for
anu
mbe
rof
angl
esor
dihe
dral
s.T
his
way
you
can
chec
kw
heth
eryo
ursi
mul
atio
nis
corr
ect.
With
optio
n-o
vyo
uca
npl
otth
eav
erag
ean
gle
ofa
grou
pof
angl
esas
afu
nctio
nof
time.
With
the
-all
optio
nth
efir
stgr
aph
isth
eav
erag
e,th
ere
star
eth
ein
divi
dual
angl
es.
With
the
-ofo
ptio
nga
ngle
also
calc
ulat
esth
efr
actio
nof
tran
sdi
hedr
als
(onl
yfo
rdi
hedr
als)
asfu
nctio
nof
time,
butt
his
ispr
obab
lyon
lyfu
nfo
ra
sele
cted
few
.
With
optio
n-o
ca
dihe
dral
corr
elat
ion
func
tion
isca
lcul
ated
.
Itsh
ould
beno
ted
that
the
inde
xfile
shou
ldco
ntai
nat
om-t
riple
sfo
rang
les
orat
om-q
uadr
uple
tsfo
rdih
edra
ls.
Ifth
isis
nott
heca
se,t
hepr
ogra
mw
illcr
ash.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Gen
eric
run
inpu
t:tp
rtp
btp
a-n
an
gle
.nd
xIn
put
Inde
xfil
e-o
da
ng
dis
t.xv
gO
utpu
txv
gr/x
mgr
file
-ov
an
ga
ver.
xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-of
dih
fra
c.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e-o
td
ihtr
an
s.xv
gO
utpu
t,O
pt.
xvgr
/xm
grfil
e-o
htr
his
to.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-o
cd
ihco
rr.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-wbo
oln
oV
iew
outp
utxv
g,xp
m,e
psan
dpd
bfil
es-t
ype
enum
an
gle
Type
ofan
gle
toan
alys
e:a
ng
le,
dih
ed
ral
,im
pro
pe
ror
ryck
ae
rt-b
elle
ma
ns
-all
bool
no
Plo
tall
angl
esse
para
tely
inth
eav
erag
esfil
e,in
the
orde
rof
appe
aran
cein
the
inde
xfil
e.-b
inw
idth
real
1bi
nwid
th(d
egre
es)
for
calc
ulat
ing
the
dist
ribut
ion
-ch
an
dle
rbo
oln
oU
seC
hand
ler
corr
elat
ion
func
tion
(N[tr
ans]
=1,
N[g
auch
e]=
0)ra
ther
than
cosi
neco
rrel
atio
nfu
nctio
n.T
rans
isde
fined
asph
i<
-60
orph
i>60
.-a
verc
orr
bool
no
Ave
rage
the
corr
elat
ion
func
tions
for
the
indi
vidu
alan
gles
/dih
edra
ls-a
cfle
nin
t-1
Leng
thof
the
AC
F,de
faul
tis
half
the
num
ber
offr
ames
-no
rma
lize
bool
yes
Nor
mal
ize
AC
F-P
enum
0O
rder
ofLe
gend
repo
lyno
mia
lfor
AC
F(0
indi
cate
sno
ne):
0,1
,2or
3-f
itfn
enum
no
ne
Fit
func
tion:
no
ne
,exp
,ae
xp,e
xpe
xpor
vac
-ncs
kip
int
0S
kip
Npo
ints
inth
eou
tput
file
ofco
rrel
atio
nfu
nctio
ns-b
eg
infit
real
0T
ime
whe
reto
begi
nth
eex
pone
ntia
lfito
fthe
corr
elat
ion
func
tion
-en
dfit
real
-1T
ime
whe
reto
end
the
expo
nent
ialfi
toft
heco
rrel
atio
nfu
nctio
n,-1
istil
lth
een
d
•C
ount
ing
tran
sitio
nson
lyw
orks
for
dihe
dral
sw
ithm
ultip
licity
3
3.1
5.
Pa
ralle
lMo
lecu
lar
Dyn
am
ics
45
Par
ticle
with
thisx
coor
dina
tera
nge
will
add
toth
ech
arge
dist
ribut
ion
onth
efo
llow
ing
rang
eof
ofF
FT
grid
slab
sin
thex
dire
ctio
n:
trun
c( il xn
x
M
) −1≤i x≤
trun
c( (i
+1)l xn
x
M
) +2
(3.8
3)
whe
retr
unc
indi
cate
sth
etr
unca
tion
ofa
real
num
ber
toth
ela
rges
tin
tege
rsm
alle
rth
anor
equa
lto
that
real
num
ber.
2.D
oing
the
Fou
rier
tran
sfor
mof
the
char
gedi
strib
utio
nρ(r
)in
para
llelt
oob
tainρ
(k).
Thi
sis
done
usin
gth
eF
FT
Wlib
rary
(seew
ww
.fftw
.org
)w
hich
empl
oys
the
MP
Ilib
rary
for
mes
sage
pass
ing
prog
ram
s(n
ote
that
ther
ear
eal
sosh
ared
mem
ory
vers
ions
ofth
eF
FT
Wco
de).
Thi
sF
FT
algo
rithm
actu
ally
use
slab
sas
wel
l(go
odth
inki
ng!)
.E
ach
proc
esso
rdo
es2D
FF
TS
onits
slab
,and
then
the
who
leF
FT
grid
istr
ansp
osed
inp
lace
(i.e.
with
outu
sing
extr
am
emor
y).
Thi
sm
eans
that
afte
rthe
FF
Tth
eX
and
Yco
mpo
nent
sar
esw
appe
d.To
com
plet
eth
eF
FT,
this
swap
ping
shou
ldbe
undo
nein
prin
cipl
e(b
ytr
ansp
osin
gba
ck).
Hap
pily
the
FF
TW
code
has
anop
tion
toom
itth
is,w
hich
we
use
inth
ene
xtst
ep.
3.C
onvo
luteρ(k
)w
ithth
eF
ourie
rtr
ansf
orm
ofth
ech
arge
spre
adfu
nctio
ng(k
)(w
hich
we
have
tabu
late
dbe
fore
)to
obta
inth
epo
tent
ial
φ(k
).A
san
optim
izat
ion,
we
stor
eth
eg(k)
intr
ansp
osed
form
asw
ell,
mat
chin
gth
etr
ansp
osed
form
ofρ(k
)w
hich
we
get
from
the
FF
TW
rout
ine.
Afte
rth
isst
epw
eha
veth
epo
tent
ial
φ(k
)in
Fou
rier
spac
e,bu
tst
illon
the
tran
spos
edF
FT
grid
.
4.D
oan
inve
rse
tran
sfor
mofφ
(k)
toob
tainφ(r
).S
ince
the
algo
rithm
mus
tdo
atr
ansp
ose
ofth
eda
tath
isst
epac
tual
lyyi
elds
the
wan
ted
resu
lt:th
eun
-tra
nspo
sed
pote
ntia
lin
real
spac
e.
5.In
terp
olat
eth
epo
tent
ialφ(r
)in
real
spac
eat
the
part
icle
posi
tions
toob
tain
forc
esan
den
ergy
.F
orth
isbi
tth
esa
me
cons
ider
atio
nsto
war
dspa
ralle
lism
hold
asfo
rth
ech
arge
spre
adin
g.H
owev
erin
this
case
mor
ene
ighb
orin
ggr
idce
llsar
ene
eded
,suc
hth
atw
ene
edth
efo
llow
ing
seto
fFF
Tgr
idsl
abs
inth
exdi
rect
ion:
trun
c( il xn
x
M
) −3≤i x≤
trun
c( (i
+1)l xn
x
M
) +4
(3.8
4)
The
algo
rithm
assk
etch
edab
ove
requ
ires
com
mun
icat
ion
fors
prea
ding
the
char
ges,
fort
heF
FT
Wfo
rwar
dan
dba
ckw
ard,
and
for
inte
rpol
atin
gth
efo
rces
.T
heG
RO
MA
CS
bits
ofth
epr
ogra
mus
eon
lyle
ftan
drig
htco
mm
unic
atio
n,i.e
.us
ing
two
com
mun
icat
ion
chan
nels
.T
heF
FT
Wro
utin
esac
tual
lyus
eot
herf
orm
sof
com
mun
icat
ion
asw
ell,
and
thes
ero
utin
esar
eco
ded
with
MP
Irou
tines
for
mes
sage
pass
ing.
Thi
sim
plie
sth
atG
RO
MA
CS
can
only
perf
orm
the
PP
PM
algo
rithm
onpa
ralle
lcom
pute
rsco
mpu
ters
that
supp
ort
MP
I.H
owev
er,
mos
tsh
ared
mem
ory
com
pute
rs,
such
asth
eS
GIO
rigin
also
supp
ortM
PIu
sing
the
shar
edm
emor
yfo
rco
mm
unic
atio
n.
3.15
.4P
aral
lels
ortin
g
For
the
dom
ain
deco
mpo
sitio
nbi
tofG
RO
MA
CS
itis
nece
ssar
yto
sort
the
coor
dina
tes
(or
rath
erth
ein
dex
toco
ordi
nate
s)ev
ery
time
ane
ighb
orlis
tis
mad
e.If
we
use
brut
efo
rce,
and
sort
all
46
Ch
ap
ter
3.
Alg
orith
ms
coordinateson
eachprocessor
(which
istechnically
possiblesince
we
haveallthe
coordinates),then
thissorting
procedurew
illtakea
constanttime
(proportionaltoN
2logN
,independentofthenum
berof
processors.W
ecan
however
doa
littlebetter,
ifw
eassum
ethat
particlesdiffuse
onlyslow
ly.A
parallelsortingalgorithm
canbe
conceivedas
follows:
Atthe
firststepofthe
simulation
1.D
oa
fullsortofallindicesusing
e.g.thequick-sortalgorithm
thatisbuilt-in
inthe
standardC
-library
2.D
ividethe
sortedarray
intoslabs
(asdescribed
abovesee
Fig.
3.14).
Atsubsequentsteps
ofthesim
ulation:
1.S
endthe
indicesfor
eachprocessor
tothe
precedingprocessor
(ifnot
processor0)
andto
thenext
processor(if
notM-1).
The
comm
unicationassociated
with
thisoperation
isproportionalto
2N/M
.
2.S
ortthecom
binedindices
ofthethree
(ortw
o)processors.
Note
thattheC
PU
time
associ-ated
with
sortingis
now(3N
/M) 2log
(3N/M
).
3.O
neach
processor,the
indicesbelonging
toit’s
slabcan
bedeterm
inedfrom
theorder
ofthe
array(F
ig.3.14).
E.6
.g
an
alyze
18
3
This
isusefulfor
principalcomponents
obtainedfrom
covarianceanalysis,since
theprincipalcom
ponentsofrandom
diffusionare
purecosines.
Option
-msd
producesthe
mean
squaredisplacem
ent(s).
Option
-dist
producesdistribution
plot(s).
Option
-av
producesthe
averageover
thesets.
Error
barscan
beadded
with
theoption
-errb
ar
.T
heerrorbars
canrepresentthe
standarddeviation,the
error(assuming
thepoints
areindependent)orthe
intervalcontaining
90%ofthe
points,bydiscarding
5%ofthe
pointsatthe
topand
thebottom
.
Option
-ee
produceserror
estimates
usingblock
averaging.A
setis
dividedin
anum
berof
blocksand
averagesare
calculatedfor
eachblock.
The
errorfor
thetotal
averageis
calculatedfrom
thevariance
between
averagesofthe
mblocks
Biasfollow
s:error 2
=S
um(B
i-<
B>
) 2/(m
*(m-1)).
These
errorsare
plottedas
afunction
oftheblock
size.A
lsoan
analyticalblockaverage
curveis
plotted,assuming
thattheautocorrelation
isa
sumoftw
oexponentials.
The
analyticalcurvefor
theblock
averageB
Ais:
BA
(t)=
sigma
sqrt(2/T(
a(tau1
((exp(-t/tau1)-
1)tau1/t+
1))+
(1-a)(tau2
((exp(-t/tau2)-
1)tau2/t+
1)))),w
hereT
isthe
totaltime.
a,tau1
andtau2
areobtained
byfitting
BA
(t)to
thecalculated
blockaverage.
When
theactualblock
averageis
veryclose
tothe
analyticalcurve,the
erroris
sigma*sqrt(2/T
(atau1
+(1-a)
tau2)).
Option
-po
we
rfits
thedata
tob
ta,which
isaccom
plishedby
fittingto
at+
bon
log-logscale.
Allpoints
afterthe
firstzeroor
negativevalue
areignored.
Files
-fg
rap
h.xvg
Inputxvgr/xm
grfile
-ac
au
toco
rr.xvgO
utput,Opt.
xvgr/xmgr
file-m
sdm
sd.xvg
Output,O
pt.xvgr/xm
grfile
-ccco
scon
t.xvgO
utput,Opt.
xvgr/xmgr
file-d
istd
istr.xvgO
utput,Opt.
xvgr/xmgr
file-a
va
vera
ge
.xvgO
utput,Opt.
xvgr/xmgr
file-e
ee
rrest.xvg
Output,O
pt.xvgr/xm
grfile
Other
options-h
booln
oP
rinthelpinfo
andquit
-nice
int1
9S
etthenicelevel
-wbool
no
View
outputxvg,xpm,eps
andpdb
files-tim
ebool
yes
Expecta
time
inthe
input-b
real-1
Firsttim
eto
readfrom
set-e
real-1
Lasttime
toread
fromset
-nint
1R
ead#
setsseperated
by&
-dbool
no
Use
thederivative
-bw
real0
.1B
inwidth
forthe
distribution-e
rrba
renum
no
ne
Error
barsfor
-av:no
ne
,stdd
ev
,erro
ror9
0-p
ow
er
booln
oF
itdatato:
bta
-sub
av
boolye
sS
ubtracttheaverage
beforeautocorrelating
-on
ea
cfbool
no
Calculate
oneA
CF
overallsets
-acfle
nint
-1Length
oftheA
CF,defaultis
halfthenum
beroffram
es-n
orm
alize
boolye
sN
ormalize
AC
F-P
enum0
Order
ofLegendrepolynom
ialforA
CF
(0indicates
none):0
,1,2
or3-fitfn
enumn
on
eF
itfunction:no
ne
,exp
,ae
xp,e
xpe
xporva
c-n
cskipint
0S
kipN
pointsin
theoutputfile
ofcorrelationfunctions
-be
gin
fitreal
0T
ime
where
tobegin
theexponentialfitofthe
correlationfunction
-en
dfit
real-1
Tim
ew
hereto
endthe
exponentialfitofthecorrelation
function,-1is
tillthe
end
18
2A
pp
en
dix
E.
Ma
nu
alP
age
s
whe
reM
1an
dM
2ar
eth
etw
oco
varia
nce
mat
rices
and
tris
the
trac
eof
am
atrix
.T
henu
mbe
rsar
epr
o-po
rtio
nalt
oth
eov
erla
pof
the
squa
rero
otof
the
fluct
uatio
ns.
The
norm
aliz
edov
erla
pis
the
mos
tus
eful
num
ber,
itis
1fo
rid
entic
alm
atric
esan
d0
whe
nth
esa
mpl
edsu
bspa
ces
are
orth
ogon
al.
File
s-v
eig
en
vec.
trr
Inpu
tF
ullp
reci
sion
traj
ecto
ry:
trr
trj
-v2
eig
en
vec2
.trr
Inpu
t,O
pt.
Ful
lpre
cisi
ontr
ajec
tory
:tr
rtr
j-f
tra
j.xtc
Inpu
t,O
pt.
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b-s
top
ol.t
pr
Inpu
t,O
pt.
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-eig
1e
ige
nva
l1.x
vgIn
put,
Opt
.xv
gr/x
mgr
file
-eig
2e
ige
nva
l2.x
vgIn
put,
Opt
.xv
gr/x
mgr
file
-dis
pe
igd
isp
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
-pro
jp
roj.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-2
d2
dp
roj.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-3
d3
dp
roj.p
db
Out
put,
Opt
.G
ener
icst
ruct
ure:
gro
g96
pdb
-filt
filte
red
.xtc
Out
put,
Opt
.G
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-ext
re
xtre
me
.pd
bO
utpu
t,O
pt.
Gen
eric
traj
ecto
ry:
xtc
trr
trjg
rog9
6pd
b-o
ver
ove
rla
p.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-in
pr
inp
rod
.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-first
int
1F
irste
igen
vect
orfo
ran
alys
is(-
1is
sele
ct)
-la
stin
t8
Last
eige
nvec
tor
for
anal
ysis
(-1
istil
lthe
last
)-s
kip
int
1O
nly
anal
yse
ever
ynr
-th
fram
e-m
ax
real
0M
axim
umfo
rpr
ojec
tion
ofth
eei
genv
ecto
ron
the
aver
age
stru
ctur
e,m
ax=
0gi
ves
the
extr
emes
-nfr
am
es
int
2N
umbe
rof
fram
esfo
rth
eex
trem
esou
tput
-sp
litbo
oln
oS
plit
eige
nvec
tor
proj
ectio
nsw
here
time
isze
ro
E.6
gan
alyz
e
gan
alyz
ere
ads
anas
ciifi
lean
dan
alyz
esda
tase
ts.
Alin
ein
the
inpu
tfile
may
star
twith
atim
e(s
eeop
tion
-tim
e)
and
any
num
ber
ofy
valu
esm
ayfo
llow
.M
ultip
lese
tsca
nal
sobe
read
whe
nth
eyar
ese
pera
ted
by&
(opt
ion
-n),
inth
isca
seon
lyon
ey
valu
eis
read
from
each
line.
All
lines
star
ting
with
#an
d@
are
skip
ped.
All
anal
yses
can
also
bedo
nefo
rth
ede
rivat
ive
ofa
set(
optio
n-d
).
All
optio
ns,e
xcep
tfor
-av
and
-po
we
ras
sum
eth
atth
epo
ints
are
equi
dist
anti
ntim
e.
gan
alyz
eal
way
ssh
ows
the
aver
age
and
stan
dard
devi
atio
nof
each
set.
For
each
set
ital
sosh
ows
the
rela
tive
devi
atio
nof
the
third
and
fort
hcu
mul
ant
from
thos
eof
aG
auss
ian
dist
ribut
ion
with
the
sam
est
anda
rdde
viat
ion.
Opt
ion
-ac
prod
uces
the
auto
corr
elat
ion
func
tion(
s).
Opt
ion
-cc
plot
sth
ere
sem
blan
ceof
seti
with
aco
sine
ofi/2
perio
ds.
The
form
ula
is:
2(in
t0-T
y(t)
cos(
pit/i
)dt
)2/i
nt0-
Ty(
t)y(
t)dt
Cha
pter
4
For
cefie
lds
Afo
rce
field
isbu
iltup
from
two
dist
inct
com
pone
nts:
•T
hese
tofe
quat
ions
(cal
led
thepo
ten
tialf
un
ctio
ns)us
edto
gene
rate
the
pote
ntia
lene
rgie
san
dth
eir
deriv
ativ
es,t
hefo
rces
.
•T
hepa
ram
eter
sus
edin
this
seto
fequ
atio
ns
With
inon
ese
tof
equa
tions
vario
usse
tsof
para
met
ers
can
beus
ed.
Car
em
ust
beta
ken
that
the
com
bina
tion
ofeq
uatio
nsan
dpa
ram
eter
sfo
rma
cons
iste
ntse
t.It
isin
gene
rald
ange
rous
tom
ake
ad
ho
ccha
nges
ina
subs
etof
para
met
ers,
beca
use
the
vario
usco
ntrib
utio
nsto
the
tota
lfor
cear
eus
ually
inte
rdep
ende
nt.
InG
RO
MA
CS
3.0
the
forc
efie
ldis
base
don
GR
OM
OS
-87
[39
],w
itha
smal
lmod
ifica
tion
con-
cern
ing
the
inte
ract
ion
betw
een
wat
er-o
xyge
nsan
dca
rbon
atom
s[
40,4
1],a
sw
ella
s10
extr
aat
omty
pes
[42,
43,4
0,41
,44]
.H
owev
er,t
heus
eris
free
tom
ake
hero
wn
mod
ifica
tions
(bew
are!
).T
his
will
beex
plai
ned
inde
tails
inch
apte
r5,w
hich
deal
sw
ithth
eTop
olog
y.To
acco
mm
odat
eth
epo
tent
ial
func
tions
used
inso
me
popu
lar
forc
efie
lds,
GR
OM
AC
Sof
fers
ach
oice
offu
nctio
ns,
both
for
non-
bond
edin
tera
ctio
nan
dfo
rdi
hedr
alin
tera
ctio
ns.
The
yar
ede
scrib
edin
the
appr
opria
tesu
bsec
tions
.
The
pote
ntia
lfun
ctio
nsca
nbe
subd
ivid
edin
toth
ree
part
s
1.N
on
-bo
nd
ed:
Lenn
ard-
Jone
sor
Buc
king
ham
,and
Cou
lom
bor
mod
ified
Cou
lom
b.T
heno
n-bo
nded
inte
ract
ions
are
com
pute
don
the
basi
sof
ane
ighb
orlis
t(a
listo
fnon
-bon
ded
atom
sw
ithin
ace
rtai
nra
dius
),in
whi
chex
clus
ions
are
alre
ady
rem
oved
.
2.B
on
de
d:co
vale
ntbo
nd-s
tret
chin
g,an
gle-
bend
ing,
impr
oper
dihe
dral
s,an
dpr
oper
dihe
dral
s.T
hese
are
com
pute
don
the
basi
sof
fixed
lists
.
3.S
pe
cia
l:po
sitio
nre
stra
ints
and
dist
ance
rest
rain
ts,b
ased
onfix
edlis
ts.
48
Ch
ap
ter
4.
Force
field
s
0.40.5
0.60.7
0.8r (nm
)
–0.2
0.0
0.2
0.4
V (kJ mole–1
)Figure
4.1:T
heLennard-Jones
interaction.
4.1N
on-bondedinteractions
Non-bonded
interactionsin
GR
OM
AC
Sare
pair-additiveand
centro-symm
etric:
V(r
1 ,...rN
)= ∑i<
j
Vij (r
ij );(4.1)
Fi =
− ∑j
dV
ij (rij )
drij
rij
rij
=−
Fj
(4.2)
The
non-bondedinteractions
containa
repulsionterm
,a
dispersionterm
,and
aC
oulomb
term.
The
repulsionand
dispersionterm
arecom
binedin
eitherthe
Lennard-Jones(or
6-12interaction),
orthe
Buckingham
(orexp-6
potential).In
addition,(partially)
chargedatom
sact
throughthe
Coulom
bterm
.
4.1.1T
heLennard-Jones
interaction
The
Lennard-Jonespotential
VL
Jbetw
eentw
oatom
sequals
VL
J (rij )
=C
(12)
ij
r12
ij
−C
(6)
ij
r6ij
(4.3)
seealso
Fig.4.1
The
parametersC
(12)
ijand
C(6
)ij
dependon
pairsofato
mtyp
es;consequently
theyare
takenfrom
am
atrixofLJ-param
eters.
The
forcederived
fromthis
potentialis:
Fi (r
ij )=
12C
(12)
ij
r12
ij
−6C
(6)
ij
r6ij
rij
rij
(4.4)
E.5
.g
an
ae
ig1
81
-nice
int1
9S
etthenicelevel
-breal
-1F
irsttime
touse
-ereal
-1Lasttim
eto
use-d
treal
0O
nlyw
riteoutfram
ew
hentM
OD
dt=offset
-offse
treal
0T
ime
offsetfor-dtoption
-settim
ebool
no
Change
startingtim
einteractively
-sort
boolye
sS
ortenergyfiles
(notframes)
-scale
fac
real1
Multiply
energycom
ponentbythis
factor-e
rror
boolye
sS
topon
errorsin
thefile
•W
hencom
biningtrajectories
thesigm
aand
E2
(necessaryfor
statistics)are
notupdated
correctly.O
nlythe
actualenergyis
correct.O
nethus
hasto
compute
statisticsin
anotherw
ay.
E.5
ganaeig
ga
na
eig
analyzeseigenvectors.
The
eigenvectorscan
beof
acovariance
matrix
(g
cova
r)
orof
aN
ormalM
odesanaysis
(g
nm
eig
).
When
atrajectory
isprojected
oneigenvectors,
allstructuresare
fittedto
thestructure
inthe
eigenvectorfile,ifpresent,otherw
iseto
thestructure
inthe
structurefile.
When
norun
inputfileis
supplied,periodicityw
illnotbetaken
intoaccount.
Mostanalyses
areperform
edon
eigenvectors-first
to-la
st,butw
hen-first
issetto
-1you
willbe
prompted
fora
selection.
-disp
:plotallatom
displacements
ofeigenvectors-first
to-la
st.
-pro
j:
calculateprojections
ofa
trajectoryon
eigenvectors-first
to-la
st.
The
projectionsof
atrajectory
onthe
eigenvectorsof
itscovariance
matrix
arecalled
principalcomponents
(pc’s).It
isoften
usefultocheck
thecosine
contentthepc’s,since
thepc’s
ofrandomdiffusion
arecosines
with
thenum
berof
periodsequalto
halfthe
pcindex.
The
cosinecontent
ofthe
pc’scan
becalculated
with
theprogram
ga
na
lyze.
-2d
:calculate
a2d
projectionofa
trajectoryon
eigenvectors-first
and-la
st.
-3d
:calculate
a3d
projectionofa
trajectoryon
thefirstthree
selectedeigenvectors.
-filt:
filterthe
trajectoryto
showonly
them
otionalong
eigenvectors-first
to-la
st.
-extr
:calculate
thetw
oextrem
eprojections
alonga
trajectoryon
theaverage
structureand
interpolate-n
fram
es
frames
between
them,or
setyourow
nextrem
esw
ith-m
ax
.T
heeigenvector-first
willbe
written
unless-firstand
-last
havebeen
setexplicitly,inw
hichcase
alleigenvectorsw
illbew
rittento
separatefiles.
Chain
identifiersw
illbeadded
when
writing
a.p
db
filew
ithtw
oor
threestructures
(youcan
userasm
ol
-nm
rpd
bto
viewsuch
apdb
file).
Overlap
calculationsbetw
eencovariance
analysis:N
OT
E:the
analysisshould
usethe
same
fittingstructure
-ove
r:
calculatethe
subspaceoverlap
oftheeigenvectors
infile
-v2w
itheigenvectors-first
to-la
stin
file-v
.
-inp
r:
calculatea
matrix
ofinner-products
between
eigenvectorsin
files-v
and-v2
.A
lleigenvectorsofboth
filesw
illbeused
unless-firstand
-last
havebeen
setexplicitly.
When
-v,
-eig
1,
-v2and
-eig
2are
given,a
singlenum
berfor
theoverlap
between
thecovariance
matrices
isgenerated.
The
formulas
are:difference
=sqrt(tr((sqrt(M
1)-
sqrt(M2)) 2))
normalized
overlap=
1-
difference/sqrt(tr(M1)
+tr(M
2))shape
overlap=
1-
sqrt(tr((sqrt(M1/tr(M
1))-
sqrt(M2/tr(M
2)))2))
18
0A
pp
en
dix
E.
Ma
nu
alP
age
s
-fco
nf.g
roIn
put
Gen
eric
stru
ctur
e:gr
og9
6pd
btp
rtp
btp
a-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-oo
ut.g
roO
utpu
tG
ener
icst
ruct
ure:
gro
g96
pdb
-bf
bfa
ct.d
at
Inpu
t,O
pt.
Gen
eric
data
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t0
Set
the
nice
leve
l-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-nd
ef
bool
no
Cho
ose
outp
utfr
omde
faul
tind
exgr
oups
-bt
enum
tric
Box
type
for
-box
and
-d:
tric
,cu
bic
,d
od
eca
he
dro
nor
oct
ah
ed
ron
-bo
xve
ctor
00
0B
oxve
ctor
leng
ths
(a,b
,c)
-an
gle
sve
ctor9
09
09
0A
ngle
sbe
twee
nth
ebo
xve
ctor
s(b
c,ac
,ab)
-dre
al0
Dis
tanc
ebe
twee
nth
eso
lute
and
the
box
-cbo
oln
oC
ente
rm
olec
ule
inbo
x(im
plie
dby
-box
and
-d)
-ce
nte
rve
ctor
00
0C
oord
inat
esof
geom
etric
alce
nter
-ro
tate
vect
or0
00
Rot
atio
nar
ound
the
X,Y
and
Zax
esin
degr
ees
-prin
cbo
oln
oO
rient
mol
ecul
e(s)
alon
gth
eir
prin
cipa
laxe
s-s
cale
vect
or1
11
Sca
ling
fact
or-d
en
sity
real
10
00
Den
sity
(g/l)
ofth
eou
tput
box
achi
eved
bysc
alin
g-p
bc
bool
no
Rem
ove
the
perio
dici
ty(m
ake
mol
ecul
ew
hole
agai
n)-m
ea
dbo
oln
oS
tore
the
char
geof
the
atom
inth
eoc
cupa
ncy
field
and
the
radi
usof
the
atom
inth
eB
-fac
tor
field
-gra
spbo
oln
oS
tore
the
char
geof
the
atom
inth
eB
-fac
tor
field
and
the
radi
usof
the
atom
inth
eoc
cupa
ncy
field
-rvd
wre
al0
.12
Def
ault
Van
der
Waa
lsra
dius
ifon
eca
nno
tbe
foun
din
the
data
base
-ato
mbo
oln
oF
orce
B-f
acto
rat
tach
men
tper
atom
-le
ge
nd
bool
no
Mak
eB
-fac
tor
lege
nd-la
be
lst
ring
AA
ddch
ain
labe
lfor
allr
esid
ues
•F
orco
mpl
exm
olec
ules
,th
epe
riodi
city
rem
oval
rout
ine
may
brea
kdo
wn,
inth
atca
seyo
uca
nus
etr
jcon
v
E.4
enec
onv
Whe
n-f
isn
ots
peci
fied:
Con
cate
nate
sse
vera
lene
rgy
files
inso
rted
orde
r.In
case
ofdo
uble
time
fram
esth
eon
ein
the
late
rfil
eis
used
.B
ysp
ecify
ing-s
ettim
eyo
uw
illbe
aske
dfo
rth
est
artt
ime
ofea
chfil
e.T
hein
putfi
les
are
take
nfr
omth
eco
mm
and
line,
such
that
the
com
man
de
ne
con
v-o
fixe
d.e
dr
*.e
dr
shou
lddo
the
tric
k.
With
-fsp
ecifi
ed:
Rea
dson
een
ergy
file
and
writ
esan
othe
r,ap
plyi
ngth
e-d
t,-
offse
t,-
t0an
d-s
ettim
eop
tions
and
conv
ertin
gto
adi
ffere
ntfo
rmat
ifne
cess
ary
(indi
cate
dby
file
exte
ntio
ns).
-se
ttim
eis
appl
ied
first
,the
n-dt
/-o
ffse
tfo
llow
edby
-ban
d-e
tose
lect
whi
chfr
ames
tow
rite.
File
s-f
en
er.
ed
rIn
put
Gen
eric
ener
gy:
edr
ene
-ofix
ed
.ed
rO
utpu
t,O
pt.
Gen
eric
ener
gy:
edr
ene
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
4.1
.N
on
-bo
nd
ed
inte
ract
ion
s4
9
0.2
0.3
0.4
0.5
0.6
0.7
0.8
r (n
m)
–0.5
0.0
0.5
1.0
1.5
V (kJ mole–1
) Fig
ure
4.2:
The
Buc
king
ham
inte
ract
ion.
The
LJpo
tent
ialm
ayal
sobe
writ
ten
inth
efo
llow
ing
form
:
VL
J(r
ij)
=4ε
ij
( σ ij r ij
) 12−( σ ij r i
j
) 6 (4
.5)
Inco
nstr
uctin
gth
epa
ram
eter
mat
rixfo
rth
eno
n-bo
nded
LJ-p
aram
eter
s,tw
oty
pes
ofco
mbi
natio
nru
les
can
beus
edw
ithin
GR
OM
AC
S:
C(6
)ij
=( C
(6)
ii∗C
(6)
jj
) 1/2C
(12)
ij=
( C(1
2)
ii∗C
(12)
jj
) 1/2(4
.6)
or,a
ltern
ativ
ely,
σij
=1 2(σ
ii+σ
jj)
ε ij
=(ε
iiε j
j)1
/2
(4.7
)
4.1.
2B
ucki
ngha
mpo
tent
ial
The
Buc
king
ham
pote
ntia
lhas
am
ore
flexi
ble
and
real
istic
repu
lsio
nte
rmth
anth
eLe
nnar
d-Jo
nes
inte
ract
ion,
buti
sal
som
ore
expe
nsiv
eto
com
pute
.T
hepo
tent
ialf
orm
is:
Vbh
(rij)
=A
ijex
p(−B
ijr i
j)−C
ij
r6 ij
(4.8
)
see
also
Fig
.4.2,
the
forc
ede
rived
from
this
is:
Fi(r i
j)
=
[ −A
ijB
ijr i
jex
p(−B
ijr i
j)−
6C
ij
r6 ij
] rij
r ij
(4.9
)
50
Ch
ap
ter
4.
Force
field
s
0.00.2
0.40.6
0.81.0
r (nm)
0
500
1000
1500
V (kJ mol� −1)
Coulom
bW
ith RF
�RF
− C
Figure
4.3:T
heC
oulomb
interaction(for
particlesw
ithequal
signedcharge)
with
andw
ithoutreaction
field.In
thelatter
caseεrf
was
78,andrc
was
0.9nm
.T
hedot-dashed
lineis
thesam
eas
thedashed
line,exceptfora
constant.
4.1.3C
oulomb
interaction
The
Coulom
binteraction
between
two
chargeparticles
isgiven
by:
Vc (r
ij )=fqi q
j
εr r
ij(4.10)
seealso
Fig.4.3,w
heref=
14πε0
=138.935
485(see
chapter2)
The
forcederived
fromthis
potentialis:
Fi (r
ij )=fqi q
j
εr r
2ij
rij
rij
(4.11)
InG
RO
MA
CS
therelative
dielectricconstant
εr
may
besetin
thein
theinputforgro
mp
p.
4.1.4C
oulomb
interactionw
ithreaction
field
The
coulomb
interactioncan
bem
odifiedfor
homogeneous
systems,
byassum
inga
constantdi-
electricenvironm
entbeyond
thecut-off
rc
with
adielectric
constantofεr
f .T
heinteraction
thenreads:
Vcr
f=
fqi q
j
rij [1
+εrf−
12ε
rf
+1r3ij
r3c ]
−fqi q
j
rc
3εrf
2εrf
+1
(4.12)
inw
hichthe
constantexpression
onthe
rightm
akesthe
potentialzeroat
thecut-offrc .
We
canrew
ritethis
forsim
plicityas
Vcr
f=
fqi q
j [1rij
+k
rfr2ij −
crf ]
(4.13)
E.3
.e
ditco
nf
17
9
E.3
editconf
editconfconvertsgeneric
structureform
atto.g
ro,.g
96
or.pd
b.
The
boxcan
bem
odifiedw
ithoptions-bo
x,-d
and-a
ng
les
.B
oth-b
ox
and-d
willcenter
thesystem
inthe
box.
Option
-bt
determines
thebox
type:tricis
atriclinic
box,cub
icis
acubic
box,do
de
cah
ed
ron
isa
rhombic
dodecahedronandocta
he
dro
nis
atruncated
octahedron.T
helast
two
arespecialcases
ofa
triclinicbox.
The
lengthof
thethree
boxvectors
ofthe
truncatedoctahedron
isthe
shortestdistance
between
two
oppositehexagons.
The
volume
ofadodecahedron
is0.71
andthatofa
truncatedoctahedron
is0.77
ofthatofacubic
boxw
iththe
same
periodicim
agedistance.
Option
-bo
xrequires
onlyone
valuefor
acubic
box,dodecahedronand
atruncated
octahedron.W
ith-d
andtric
thesize
ofthesystem
inthe
x,yand
zdirections
isused.
With
-dand
cub
ic,d
od
eca
he
dro
noro
ctah
ed
ron
thediam
eterofthe
systemis
used,which
isthe
largestdistancebetw
eentw
oatom
s.
Option
-an
gle
sis
onlym
eaningfulwith
option-bo
xand
atriclinic
boxand
cannotbe
usedw
ithoption
-d.
When
-nor
-nd
ef
isset,a
groupcan
beselected
forcalculating
thesize
andthe
geometric
center,other-w
isethe
whole
systemis
used.
-rota
terotates
thecoordinates
andvelocities.
-prin
caligns
theprincipalaxes
ofthe
systemalong
thecoordinate
axes,this
may
allowyou
todecrease
thebox
volume,
butbew
arethat
molecules
canrotate
significantlyin
ananosecond.
Scaling
isapplied
beforeany
ofthe
otheroperations
areperform
ed.B
oxescan
bescaled
togive
acertain
density(option-d
en
sity).
Aspecialfeature
ofthe
scalingoption,
when
thefactor
-1is
givenin
onedim
ension,oneobtains
am
irrorim
age,mirrored
inone
oftheplains,w
henone
uses-1
inthree
dimensions
apoint-m
irrorim
ageis
obtained.
Groups
areselected
afteralloperations
havebeen
applied.
Periodicity
canbe
removed
ina
crudem
anner.Itis
importantthatthe
boxsizes
atthebottom
ofyourinput
fileare
correctwhen
theperiodicity
isto
berem
oved.
The
programcan
optionallyrotate
thesolute
molecule
toalign
them
oleculealong
itsprincipal
axes(-ro
tate
)
When
writing
.pd
bfiles,B
-factorscan
beadded
with
the-bfoption.
B-factors
areread
froma
filew
ithw
ithfollow
ingform
at:firstline
statesnum
berofentries
inthe
file,nextlinesstate
anindex
followed
bya
B-factor.
The
B-factors
willbe
attachedper
residueunless
anindex
islarger
thanthe
number
ofresidues
orunless
the-ato
moption
isset.
Obviously,any
typeofnum
ericdata
canbe
addedinstead
ofB-factors.
-leg
en
dw
illproduce
arow
ofC
Aatom
sw
ithB
-factorsranging
fromthe
minim
umto
them
aximum
valuefound,effectively
making
alegend
forview
ing.
With
theoption
-mead
aspecialpdb
filefor
theM
EA
Delectrostatics
program(P
oisson-Boltzm
annsolver)
canbe
made.
Afurther
prerequisiteis
thattheinputfile
isa
runinputfile.
The
B-factor
fieldis
thenfilled
with
theVan
derW
aalsradius
oftheatom
sw
hilethe
occupancyfield
willhold
thecharge.
The
option-grasp
issim
ilar,butitputsthe
chargesin
theB
-factorand
theradius
inthe
occupancy.
Finally
with
option-la
be
leditconf
canadd
achain
identifierto
apdb
file,w
hichcan
beuseful
foranalysis
with
e.g.rasm
ol.
Toconverta
truncatedoctrahedron
fileproduced
bya
packagew
hichuses
acubic
boxw
iththe
cornerscut
off(suchas
Grom
os)use:
ed
itcon
f-f
<in>
-rota
te0
-45
-35
.26
4-b
to
-bo
x<
vecle
n>
-o<
ou
t>
whereve
clen
isthe
sizeofthe
cubicbox
times
sqrt(3)/2.F
iles
17
8A
pp
en
dix
E.
Ma
nu
alP
age
s
•M
ost
GR
OM
AC
Spr
ogra
ms
can
proc
ess
atr
ajec
tory
with
less
atom
sth
anth
eru
nin
put
orst
ruct
ure
file,
buto
nly
ifth
etr
ajec
tory
cons
ists
ofth
efir
stn
atom
sof
the
run
inpu
tor
stru
ctur
efil
e.
•M
any
GR
OM
AC
Spr
ogra
ms
will
acce
ptth
e-tu
optio
nto
set
the
time
units
tous
ein
outp
utfil
es(e
.g.
forx
mg
rgr
aphs
orxp
mm
atric
es)
and
inal
ltim
eop
tions
.
E.2
dods
sp
dods
spre
ads
atr
ajec
tory
file
and
com
pute
sth
ese
cond
ary
stru
ctur
efo
rea
chtim
efr
ame
calli
ngth
eds
sppr
ogra
m.
Ifyo
udo
not
have
the
dssp
prog
ram
,ge
tit.
dodssp
assu
mes
that
the
dssp
exec
utab
leis
in/h
ome/
mdg
roup
/dss
p/ds
sp.
Ifth
atis
nott
heca
se,t
hen
you
shou
ldse
tan
envi
ronm
entv
aria
ble
DS
SP
poin
t-in
gto
the
dssp
exec
utab
leas
in:
sete
nv
DS
SP
/usr
/loca
l/bin
/dss
p
The
stru
ctur
eas
sign
men
tfo
rea
chre
sidu
ean
dtim
eis
writ
ten
toan
.xp
mm
atrix
file.
Thi
sfil
eca
nbe
visu
aliz
edw
ithfo
rin
stan
cexv
and
can
beco
nver
ted
topo
stsc
riptw
ithxpm
2p
s.
The
num
ber
ofre
sidu
esw
ithea
chse
cond
ary
stru
ctur
ety
pean
dth
eto
tals
econ
dary
stru
ctur
e(
-sss
)co
unta
sa
func
tion
oftim
ear
eal
sow
ritte
nto
file
(-sc
).
Sol
vent
acce
ssib
lesu
rfac
e(S
AS
)per
resi
due
can
beca
lcul
ated
,bot
hin
abso
lute
valu
es(A
2)a
ndin
frac
tions
ofth
em
axim
alac
cess
ible
surf
ace
ofa
resi
due.
The
max
imal
acce
ssib
lesu
rfac
eis
defin
edas
the
acce
ssib
lesu
rfac
eof
are
sidu
ein
ach
ain
ofgl
ycin
es.
Not
eth
atth
epr
ogra
mgsa
sca
nal
soco
mpu
teS
AS
and
that
ism
ore
effic
ient
.
Fin
ally
,th
ispr
ogra
mca
ndu
mp
the
seco
ndar
yst
ruct
ure
ina
spec
ial
file
ssd
um
p.d
at
for
usag
ein
the
prog
ram
gch
i.
Toge
ther
thes
etw
opr
ogra
ms
can
beus
edto
anal
yze
dihe
dral
prop
ertie
sas
afu
nctio
nof
seco
ndar
yst
ruct
ure
type
.
File
s-f
tra
j.xtc
Inpu
tG
ener
ictr
ajec
tory
:xt
ctr
rtr
jgro
g96
pdb
-sto
po
l.tp
rIn
put
Str
uctu
re+
mas
s(db
):tp
rtp
btp
agr
og9
6pd
b-n
ind
ex.
nd
xIn
put,
Opt
.In
dex
file
-ssd
um
pss
du
mp
.da
tO
utpu
t,O
pt.
Gen
eric
data
file
-ma
pss
.ma
pIn
put,
Lib.
File
that
map
sm
atrix
data
toco
lors
-oss
.xp
mO
utpu
tX
Pix
Map
com
patib
lem
atrix
file
-sc
sco
un
t.xv
gO
utpu
txv
gr/x
mgr
file
-aa
rea
.xp
mO
utpu
t,O
pt.
XP
ixM
apco
mpa
tible
mat
rixfil
e-t
ato
tare
a.x
vgO
utpu
t,O
pt.
xvgr
/xm
grfil
e-a
aa
vera
rea
.xvg
Out
put,
Opt
.xv
gr/x
mgr
file
Oth
erop
tions
-hbo
oln
oP
rinth
elp
info
and
quit
-nic
ein
t1
9S
etth
eni
cele
vel
-btim
e-1
Firs
tfra
me
(ps)
tore
adfr
omtr
ajec
tory
-etim
e-1
Last
fram
e(p
s)to
read
from
traj
ecto
ry-d
ttim
e-1
Onl
yus
efr
ame
whe
ntM
OD
dt=
first
time
(ps)
-tu
enum
ps
Tim
eun
it:p
s,f
s,n
s,u
s,m
s,s
,mor
h-w
bool
no
Vie
wou
tput
xvg,
xpm
,eps
and
pdb
files
-sss
strin
gH
EB
TS
econ
dary
stru
ctur
esfo
rst
ruct
ure
coun
t
•T
hepr
ogra
mis
very
slow
4.1
.N
on
-bo
nd
ed
inte
ract
ion
s5
1
with
krf
=1 r3 c
ε rf−
1(2ε r
f+
1)(4
.14)
c rf
=1 r c
+k
rfr2 c
=1 r c
3εrf
(2ε r
f+
1)(4
.15)
for
larg
eε r
fth
ek
rf
goes
to0.
5r−
3c
,w
hile
forε r
f=
1th
eco
rrec
tion
vani
shes
.T
his
mak
esit
poss
ible
tous
eth
esa
me
expr
essi
onw
ithan
dw
ithou
trea
ctio
nfie
ld,a
lbei
tats
ome
com
puta
tiona
lco
st.
InF
ig.4
.3th
em
odifi
edin
tera
ctio
nis
plot
ted,
and
itis
clea
rth
atth
ede
rivat
ive
with
resp
ect
tor i
j(=
-for
ce)
goes
toze
roat
the
cut-
offd
ista
nce.
The
forc
ede
rived
from
this
pote
ntia
lrea
ds:
Fi(
rij)
=fq iq j
[ 1 r2 ij
−2k
rfr i
j
] rij
r ij
(4.1
6)
Tiro
nie
tal.
have
intr
oduc
eda
gene
raliz
edre
actio
nfie
ldin
whi
chth
edi
elec
tric
cont
inuu
mbe
yond
the
cut-
offr
cal
soha
san
ioni
cst
reng
thI[4
5].
Inth
isca
sew
eca
nre
writ
eth
eco
nsta
nts
krf
and
c rf
usin
gth
ein
vers
eD
ebye
scre
enin
gle
ngth
κ:
κ=
2IF
2
ε 0ε r
fRT
=F
2
ε 0ε r
fRT
K ∑ i=1
c iz i
(4.1
7)
krf
=1 r3 c
(εrf−
1)(1
+κr c
)+ε r
f(κr c
)2
(2ε r
f+
1)(1
+κr c
)+
2εrf(κr c
)2(4
.18)
c rf
=1 r c
3εrf(1
+κr c
+(κr c
)2)
(2ε r
f+
1)(1
+κr c
)+
2εrf(κr c
)2(4
.19)
whe
reF
isF
arad
ay’s
cons
tant
,Ris
the
idea
lga
sco
nsta
nt,T
the
abso
lute
tem
pera
ture
,c i
the
mol
arco
ncen
trat
ion
fors
peci
esian
dzith
ech
arge
num
bero
fspe
ciesiw
here
we
haveK
diffe
rent
spec
ies.
Inth
elim
itof
zero
ioni
cst
reng
th(
κ=
0)eq
ns.4
.18
and
4.19
redu
ceto
the
sim
ple
form
sof
eqns
.4.1
4an
d4.
15re
spec
tivel
y.
4.1.
5M
odifi
edno
n-bo
nded
inte
ract
ions
Inth
eG
RO
MA
CS
forc
efie
ldth
eno
n-bo
nded
pote
ntia
lsca
nbe
mod
ified
bya
shift
func
tion.
The
purp
ose
ofth
isis
tore
plac
eth
etr
unca
ted
forc
esby
forc
esth
atar
eco
ntin
uous
and
have
cont
inuo
usde
rivat
ives
atth
ecu
t-of
frad
ius.
With
such
forc
esth
etim
e-st
epin
tegr
atio
npr
oduc
esm
uch
smal
ler
erro
rsan
dth
ere
are
nosu
chco
mpl
icat
ions
ascr
eatin
gch
arge
sfr
omdi
pole
sby
the
trun
catio
npr
oced
ure.
Infa
ct,b
yus
ing
shift
edfo
rces
ther
eis
none
edfo
rch
arge
grou
psin
the
cons
truc
tion
ofne
ighb
orlis
ts.
How
ever
,th
esh
iftfu
nctio
npr
oduc
esa
cons
ider
able
mod
ifica
tion
ofth
eC
oulo
mb
pote
ntia
l.U
nles
sth
e’m
issi
ng’l
ong-
rang
epo
tent
iali
spr
oper
lyca
lcul
ated
and
adde
d(t
hrou
ghth
eus
eof
PP
PM
,Ew
ald,
orP
ME
),th
eef
fect
ofsu
chm
odifi
catio
nsm
ustb
eca
refu
llyev
alua
ted.
The
mod
ifica
tion
ofth
eLe
nnar
d-Jo
nes
disp
ersi
onan
dre
puls
ion
ison
lym
inor
,but
itdo
esre
mov
eth
eno
ise
caus
edby
cut-
offe
ffect
s.
The
reis
no
fund
amen
tald
iffer
ence
betw
een
asw
itch
func
tion
(whi
chm
ultip
lies
the
pote
ntia
lwith
afu
nctio
n)an
da
shift
func
tion
(whi
chad
dsa
func
tion
toth
efo
rce
orpo
tent
ial).
The
switc
h
52
Ch
ap
ter
4.
Force
field
s
functionis
aspecialcase
oftheshiftfunction,w
hichw
eapply
tothe
force
fun
ctionF
(r),relatedto
theelectrostatic
orVan
derW
aalsforce
actingon
particlei
byparticle
jas
Fi =
cF(r
ij ) rij
rij
(4.20)
For
pureC
oulomb
orLennard-Jones
interactionsF
(r)=F
α (r)=r −
(α+
1).
The
shiftedforce
Fs (r)
cangenerally
bew
rittenas:
Fs (r)
=F
α (r)r<r1
Fs (r)
=F
α (r)+S
(r)r1≤r<rc
Fs (r)
=0
rc ≤
r
(4.21)
When
r1
=0
thisis
atraditional
shiftfunction,
otherwise
itacts
asa
switch
function.T
hecorresponding
shiftedcoulom
bpotentialthen
reads:
Vs (r
ij )=fΦ
s (rij )q
i qj
(4.22)
whereΦ
(r)is
thepotentialfunctionΦ
s (r)= ∫
∞rF
s (x)dx
(4.23)
The
GR
OM
AC
Sshiftfunction
shouldbe
smooth
attheboundaries,therefore
thefollow
ingbound-
aryconditions
areim
posedon
theshiftfunction:
S(r
1 )=
0S′(r
1 )=
0S
(rc )
=−F
α (rc )
S′(r
c )=
−F′α (r
c )
(4.24)
A3
rd
degreepolynom
ialoftheform
S(r)
=A
(r−r1 )
2+B
(r−r1 )
3(4.25)
fulfillsthese
requirements.
The
constantsA
andB
aregiven
bythe
boundarycondition
atrc :
A=
−(α
+4)r
c−
(α+
1)r1
rα+
2c
(rc −
r1 )
2
B=
(α+
3)rc−
(α+
1)r1
rα+
2c
(rc −
r1 )
3
(4.26)
Thus
thetotalforce
functionis
Fs (r)
=1
rα+
1+A
(r−r1 )
2+B
(r−r1 )
3(4.27)
andthe
potentialfunctionreads
Φ(r)
=1rα−A3
(r−r1 )
3−B4
(r−r1 )
4−C
(4.28)
Appendix
E
ManualP
ages
E.1
options
AllG
RO
MA
CS
programs
have6
standardoptions,ofw
hichsom
eare
hiddenby
default:
Other
options-h
booln
oP
rinthelpinfo
andquit
-Xbool
no
Use
dialogbox
GU
Itoeditcom
mand
lineoptions
-nice
int0
Setthe
nicelevel
•Ifthe
configurationscriptfound
Motifor
Lesstifonyour
system,you
canuse
thegraphicalinterface
(ifnot,youw
illgetanerror):
-Xbooln
oU
sedialog
boxG
UIto
editcomm
andline
options
•W
hencom
piledon
anS
GI-IR
IXsystem
,allGR
OM
AC
Sprogram
shave
anadditionaloption:
-np
riint
0S
etnonblocking
priority(try
128)
•O
ptionalfilesare
notusedunless
theoption
isset,in
contrasttonon
optionalfiles,where
thedefault
filenam
eis
usedw
henthe
optionis
notset.
•A
llGR
OM
AC
Sprogram
sw
illacceptfileoptions
withouta
fileextension
orfilename
beingspecified.
Insuch
casesthe
defaultfilenam
esw
illbe
used.W
ithm
ultipleinput
filetypes,
suchas
genericstructure
format,
thedirectory
will
besearched
forfiles
ofeach
typew
iththe
suppliedor
defaultnam
e.W
henno
suchfile
isfound,or
with
outputfilesthe
firstfiletype
willbe
used.
•A
llGR
OM
AC
Sprogram
sw
iththe
exceptionofmd
run
,n
mru
nand
en
eco
nv
checkif
thecom
-m
andline
optionsare
valid.Ifthis
isnotthe
case,theprogram
willbe
halted.
•E
numerated
options(enum
)shouldbe
usedw
ithone
oftheargum
entslisted
inthe
optiondescription,
theargum
entmay
beabbreviated.
The
firstmatch
tothe
shortestargumentin
thelistw
illbeselected.
•Vector
optionscan
beused
with
1or
3param
eters.W
henonly
oneparam
eteris
suppliedthe
two
othersare
alsosetto
thisvalue.
•F
orm
anyG
RO
MA
CS
programs,the
time
optionscan
besupplied
indifferenttim
eunits,depending
onthe
settingofthe-tu
option.
•A
llGR
OM
AC
Sprogram
scan
readcom
pressedor
g-zippedfiles.
There
might
bea
problemw
ithreading
compressed.xtc
,.trrand
.trjfiles,butthese
willnotcom
pressvery
wellanyw
ay.
17
6A
pp
en
dix
D.
Ave
rage
sa
nd
fluct
ua
tion
s4
.1.
No
n-b
on
de
din
tera
ctio
ns
53
0.0
1.0
2.0
3.0
4.0
5.0
r�
−0.
5
0.0
0.5
1.0
1.5
f(r)
Nor
mal
For
ceS
hifte
d F
orce
Shi
ft F
unct
ion
Fig
ure
4.4:
The
Cou
lom
bF
orce
,Shi
fted
For
cean
dS
hift
Fun
ctio
nS
(r),
usin
gr 1
=2
and
r c=
4.
whe
re
C=
1 rα c
−A 3
(rc−r 1
)3−B 4
(rc−r 1
)4(4
.29)
Whe
nr 1
=0,
the
mod
ified
Cou
lom
bfo
rce
func
tion
is
Fs(r
)=
1 r2−
5r2
r4 c
+4r
3
r5 c
(4.3
0)
iden
tical
toth
epa
rab
olic
forc
efu
nctio
nre
com
men
ded
tobe
used
asa
shor
t-ra
nge
func
tion
inco
njun
ctio
nw
itha
Poi
sson
solv
erfo
rth
elo
ng-r
ange
part
[13
].T
hem
odifi
edC
oulo
mb
pote
ntia
lfu
nctio
nis
Φ(r
)=
1 r−
5 3rc
+5r
3
3r4 c
−r4 r5 c
(4.3
1)
see
also
Fig
.4.4.
4.1.
6M
odifi
edsh
ort-
rang
ein
tera
ctio
nsw
ithE
wal
dsu
mm
atio
n
Whe
nE
wal
dsu
mm
atio
nor
part
icle
-mes
hE
wal
dis
used
toca
lcul
ate
the
long
-ran
gein
tera
ctio
ns,
the
shor
t-ra
nge
coul
omb
pote
ntia
lmus
tals
obe
mod
ified
,sim
ilar
toth
esw
itch
func
tion
abov
e.In
this
case
the
shor
tran
gepo
tent
iali
sgi
ven
by
V(r
)=f
erfc(βr i
j)
r ij
q iq j,
(4.3
2)
whe
reβ
isa
para
met
erth
atde
term
ines
the
rela
tive
wei
ght
betw
een
the
dire
ctsp
ace
sum
and
the
reci
proc
alsp
ace
sum
and
erfc(x)
isth
eco
mpl
emen
tary
erro
rfu
nctio
n.F
orfu
rthe
rde
tails
onlo
ng-
rang
eel
ectr
osta
tics,
see
sec.
4.6.
54
Ch
ap
ter
4.
Force
field
s
b0
0.080.09
0.100.11
r (nm)
0 50
100
150
200
V (kJ mole–1
)F
igure4.5:
Principle
ofbondstretching
(left),andthe
bondstretching
potential(right).
4.2B
ondedinteractions
Bonded
interactionsare
basedon
afixed
listof
atoms.
They
arenot
exclusivelypair
interac-tions,
butinclude
3-and
4-bodyinteractions
asw
ell.T
hereare
bo
nd
stretch
ing(2-body),b
on
da
ng
le(3-body),
anddih
ed
rala
ng
le(4-body)interactions.
Aspecialtype
ofdihedralinteraction
(calledim
pro
pe
rd
ihe
dra
l)isused
toforce
atoms
torem
ainin
aplane
orto
preventtransitionto
aconfiguration
ofoppositechirality
(am
irrorim
age).
4.2.1B
ondstretching
Harm
onicpotential
The
bondstretching
between
two
covalentlybonded
atoms
iand
jis
representedby
aharm
onicpotential
Vb(r
ij )=
12k
bij (rij −
bij )
2(4.33)
seealso
Fig.4.5,w
iththe
force
Fi (r
ij )=k
bij (rij −
bij ) r
ij
rij
(4.34)
Fourth
power
potential
Inthe
GR
OM
OS
-96force
field[46]
thecovalent
bondpotentialis
written
forreasons
ofcom
pu-tationalefficiency
as:
Vb(r
ij )=
14k
bij (r2ij −
b2ij )
2(4.35)
thecorresponding
forceis:
Fi (r
ij )=k
bij (r2ij −
b2ij )
rij
(4.36)
D.2
.Im
ple
me
nta
tion
17
5
which
we
canexpand
to:
n∑i=
m S∑s=
1 (xsi )
2+ (
XSm
,n
m−n
+1 )
2−2
XSm
,n
m−n
+1
S∑s=
1
xsi+
S∑s=
1
S∑s ′=
s+1
xsi x
s ′i −
S∑s=
1
n∑i=
m [(xsi )
2−2
Xsm
,n
m−n
+1x
si+ (
Xsm
,n
m−n
+1 )
2 ]=
∆σ
(D.31)
theterm
sw
ith(xsi )
2cancel,so
thatwe
cansim
plifyto:
(X
Sm,n )
2
m−n
+1−
2X
Sm,n
m−n
+1
n∑i=
m
S∑s=
1
xsi −
2n∑i=
m
S∑s=
1
S∑s ′=
s+1
xsi x
s ′i−
S∑s=
1
n∑i=
m [−2
Xsm
,n
m−n
+1x
si+ (
Xsm
,n
m−n
+1 )
2 ]=
∆σ
(D.32)
or
− (X
Sm,n )
2
m−n
+1−
2n∑i=
m
S∑s=
1
S∑s ′=
s+1
xsi x
s ′i+
S∑s=
1 (X
sm,n )
2
m−n
+1
=∆σ
(D.33)
Ifwe
nowexpand
thefirstterm
usingeqn.
D.28
we
obtain:
− (∑Ss=
1X
sm,n )
2
m−n
+1
−2
n∑i=
m
S∑s=
1
S∑s ′=
s+1
xsi x
s ′i+
S∑s=
1 (X
sm,n )
2
m−n
+1
=∆σ
(D.34)
which
we
canreform
ulateto:
−2
S∑s=
1
S∑s ′=
s+1
Xsm
,nX
s ′m
,n+
n∑i=
m
S∑s=
1
S∑s ′=
s+1
xsi x
s ′i =
∆σ
(D.35)
or
−2
S∑s=
1
Xsm
,n
S∑s ′=
s+1
Xs ′m
,n+
S∑s=
1
n∑i=
m
xsi
S∑s ′=
s+1
xs ′i
=∆σ
(D.36)
which
gives
−2
S∑s=
1 X
sm,n
S∑s ′=
s+1
n∑i=
m
xs ′i
+n∑i=
m
xsi
S∑s ′=
s+1
xs ′i
=∆σ
(D.37)
Since
we
needalldata
pointsitoevaluate
this,ingeneralthis
isnotpossible.
We
canthen
make
anestim
ateofσ
Sm,n
usingonly
thedata
pointsthatare
availableusing
thelefthand
sideofeqn.D
.30.W
hilethe
averagecan
becom
putedusing
alltim
esteps
inthe
simulation,
theaccuracy
ofthe
fluctuationsis
thuslim
itedby
thefrequency
with
which
energiesare
saved.S
incethis
canbe
easilydone
with
aprogram
suchas
xmgr
thisis
notbuilt-inin
GR
OM
AC
S.
17
4A
pp
en
dix
D.
Ave
rage
sa
nd
fluct
ua
tion
s
and
thus n+
m ∑ i=1
[ xA
Bi
−X
AB
1,n
+m
n+m
] 2 =n ∑ i=1
[ xA i−X
A 1,n
n
] 2 +m ∑ i=
1
[ xB i−X
B 1,m
m
] 2 +∆σ
(D.2
4)
or
n+
m ∑ i=1
(xAB
i)2−
2xA
Bi
XA
B1,n
+m
n+m
+
( XA
B1,n
+m
n+m
) 2 −n ∑ i=1
(xA i)2−
2xA i
XA 1,n
n+
( XA 1,n
n
) 2 −m ∑ i=
1
(xB i)2−
2xB i
XB 1,m
m+
( XB 1,m
m
) 2 =∆σ
(D.2
5)
allt
hex
2 ite
rms
drop
out,
and
the
term
sin
depe
nden
toft
hesu
mm
atio
nco
unte
ri
can
besi
mpl
ified
:( X
AB
1,n
+m
) 2n
+m
−
( XA 1,n
) 2n
−
( XB 1,m
) 2m
−
2X
AB
1,n
+m
n+m
n+
m ∑ i=1
xA
Bi
+2X
A 1,n
n
n ∑ i=1
xA i
+2X
B 1,m
m
m ∑ i=1
xB i
=∆σ
(D.2
6)
we
reco
gniz
eth
eth
ree
part
ials
ums
onth
ese
cond
line
and
use
eqn.
D.2
1to
obta
in:
∆σ
=
( mX
A 1,n−nX
B 1,m
) 2nm
(n+m
)(D
.27)
ifw
ech
eck
this
byin
sert
ingm
=1
we
getb
ack
eqn.D
.11
D.2
.3S
umm
ing
ener
gyte
rms
The
gen
ergy
prog
ram
can
also
sum
ener
gyte
rms
into
one,
e.g.
pote
ntia
l+ki
netic
=to
tal.
For
the
part
iala
vera
ges
this
isag
ain
easy
ifw
eha
veS
ener
gyco
mpo
nent
ss:
XS m
,n=
n ∑ i=m
S ∑ s=1
xs i
=S ∑ s=
1
n ∑ i=m
xs i
=S ∑ s=
1
Xs m
,n(D
.28)
For
the
fluct
uatio
nsit
isle
sstr
ivia
laga
in,c
onsi
derin
gfo
rex
ampl
eth
atth
eflu
ctua
tion
inpo
tent
ial
and
kine
ticen
ergy
shou
ldca
ncel
.N
ever
thel
ess
we
can
try
the
sam
eap
proa
chas
befo
reby
writ
ing:
σS m
,n=
S ∑ s=1
σs m
,n+
∆σ
(D.2
9)
ifw
efil
lin
eqn.
D.6
:
n ∑ i=m
[( S ∑ s=1
xs i
) −X
S m,n
m−n
+1
] 2 =S ∑ s=
1
n ∑ i=m
[ (xs i)−
Xs m
,n
m−n
+1
] 2 +∆σ
(D.3
0)
4.2
.B
on
de
din
tera
ctio
ns
55
The
forc
eco
nsta
nts
for
this
form
ofth
epo
tent
iali
sre
late
dto
the
usua
lhar
mon
icfo
rce
cons
tant
kb,
harm
(sec
.4.2
.1)
as2k
bb2 ij
=k
b,harm
(4.3
7)
The
forc
eco
nsta
nts
are
mos
tlyde
rived
from
the
harm
onic
ones
used
inG
RO
MO
S-8
7[
39].
Al-
thou
ghth
isfo
rmis
com
puta
tiona
llym
ore
effic
ient
(bec
ause
nosq
uare
root
has
tobe
eval
uate
d),i
tis
conc
eptu
ally
mor
eco
mpl
ex.
One
part
icul
ardi
sadv
anta
geis
that
sinc
eth
efo
rmis
noth
arm
onic
,th
eav
erag
een
ergy
ofa
sing
lebo
ndis
note
qual
to1 2kT
asit
isfo
rth
eno
rmal
harm
onic
pote
ntia
l.
4.2.
2M
orse
pote
ntia
lbon
dst
retc
hing
For
som
esy
stem
sth
atre
quire
anan
harm
onic
bond
stre
tchi
ngpo
tent
ial,
the
Mor
sepo
tent
ial[
47]
betw
een
two
atom
sian
dj
isav
aila
ble
inG
RO
MA
CS
.T
his
pote
ntia
ldiff
ers
from
the
harm
onic
pote
ntia
lin
havi
ngan
asym
met
ricpo
tent
ialw
ella
nda
zero
forc
eat
infin
itedi
stan
ceT
hefu
nctio
nal
form
is:
Vm
orse
(rij
)=D
ij[1−
exp(−β
ij(r
ij−b i
j))
]2,
(4.3
8)
see
also
Fig
.4.6,
and
the
corr
espo
ndin
gfo
rce
is:
Fm
orse
(rij)
=2D
ijβ
ijr i
jex
p(−β
ij(r
ij−b i
j))∗
[1−
exp(−β
ij(r
ij−b i
j))
]r ij
r ij,
(4.3
9)
whe
reD
ijis
the
dept
hof
the
wel
lin
kJ/m
ol,βij
defin
esth
est
eepn
ess
ofth
ew
ell(
innm−1),
and
b ij
isth
eeq
uilib
rium
dist
ance
innm
.T
hest
eepn
ess
para
met
erβ
ijca
nbe
expr
esse
din
term
sof
the
redu
ced
mas
sof
the
atom
sia
ndj,
the
fund
amen
talv
ibra
tion
freq
uenc
yω
ijan
dth
ew
elld
epth
Dij
:
βij
=ω
ij
√ µij
2Dij
(4.4
0)
and
beca
useω
=√ k
/µ,o
neca
nre
writ
eβij
inte
rms
ofth
eha
rmon
icfo
rce
cons
tantk ij
βij
=
√ kij
2Dij
(4.4
1)
For
smal
ldev
iatio
ns(r
ij−b i
j),
one
can
expa
ndth
eexp-
term
tofir
st-o
rder
inth
eTa
ylor
expa
nsio
n:
exp(−x)≈
1−x
(4.4
2)
Sub
stitu
ting
this
inth
efu
nctio
nalf
rom
;
Vm
orse
(rij)
=D
ij[1−
exp(−β
ij(r
ij−b i
j))
]2
=D
ij[1−
(1−√ k
ij
2D
ij(r
ij−b i
j))
]2
=1 2k
ij(r
ij−b i
j))
2,
(4.4
3)
one
reco
vers
the
harm
onic
bond
stre
tchi
ngpo
tent
ial.
56
Ch
ap
ter
4.
Force
field
s
0.10.2
0.30.4
0.50.6
rij (nm)
0
100
200
300
400
Vij (kJ / mol)
Figure
4.6:T
heM
orsepotentialw
ell,with
bondlength
0.15nm
.
4.2.3C
ubicbond
stretchingpotential
Another
anharmonic
bondstretching
potentialthat
isslightly
simpler
thanthe
Morse
potentialadds
acubic
termin
thedistance
tothe
simple
harmonic
form:
Vb(r
ij )=k
bij (rij −
bij )
2+k
bij kcu
bij
(rij −
bij )
3(4.44)
Aflexible
water
model(based
onthe
SP
Cw
aterm
odel[48])
includinga
cubicbond
stretchingpotential
forthe
O-H
bondw
asdeveloped
byF
erguson[
49].T
hism
odelw
asfound
toyield
areasonable
Infraredspectrum
.T
heF
ergusonw
aterm
odelisavailable
inthe
GR
OM
AC
Slibrary.
Itshould
benoted
thatthe
potentialisasym
etric,overstretching
leadsto
infinitelylow
energies.T
heintegration
timestep
istherefore
limited
to1
fs.
The
forcecorresponding
tothis
potentialis:
Fi (r
ij )=
2k
bij (rij −
bij )
rij
rij
+3k
bij kcu
bij
(rij −
bij )
2r
ij
rij
(4.45)
4.2.4H
armonic
anglepotential
The
bondangle
vibrationbetw
eena
tripletof
atoms
i-j
-k
isalso
representedby
aharm
onicpotentialon
theangleθ
ijk
Va (θ
ijk )=
12k
θijk (θijk
−θ0ijk )
2(4.46)
As
thebond-angle
vibrationis
representedby
aharm
onicpotentialthe
formis
thesam
eas
thebond
stretching(F
ig.4.5).
The
forceequations
aregiven
bythe
chainrule:
Fi
=−dV
a (θijk )
dr
i
Fk
=−dV
a (θijk )
dr
kF
j=
−F
i −F
k
where
θijk
=arccos
(rij ·r
kj )
rij r
kj
(4.47)
D.2
.Im
ple
me
nta
tion
17
3
D.2.1
Partofa
Sim
ulation
Itis
notuncom
mon
toperform
asim
ulationw
herethe
firstpart,
e.g.100
ps,is
takenas
equili-bration.
How
ever,the
averagesand
fluctuationsas
printedin
thelog
fileare
computed
overthe
whole
simulation.
The
equilibrationtim
e,which
isnow
partofthesim
ulation,may
insuch
acase
invalidatethe
averagesand
fluctuations,because
thesenum
bersare
nowdom
inatedby
theinitial
drifttowards
equilibrium.
Using
eqns.D.7
andD
.8the
averageand
standarddeviation
overpart
ofthe
trajectorycan
becom
putedas:X
m+
1,m
+k
=X
1,m
+k−X
1,m
(D.15)
σm
+1,m
+k
=σ
1,m
+k−σ
1,m− [
X1,m
m−X
1,m
+k
m+k ]
2m
(m+k)
k(D
.16)
or,more
generally(w
ithp≥
1and
q≥p):
Xp,q
=X
1,q −
X1,p−
1(D
.17)
σp,q
=σ
1,q −
σ1,p−
1 − [X
1,p−
1
p−
1−X
1,q
q ]2
(p−
1)qq−p
+1
(D.18)
Note
thatim
plementation
ofthis
isnot
entirelytrivial,
sinceenergies
arenot
storedevery
time
stepofthe
simulation.
We
thereforehave
toconstruct
X1,p−
1and
σ1,p−
1from
theinform
ationat
timep
usingeqns.D
.11and
D.12:
X1,p−
1=
X1,p −
xp
(D.19)
σ1,p−
1=
σ1,p −
[X
1,p−
1 −(p−
1)xp
] 2
(p−
1)p(D
.20)
D.2.2
Com
biningtw
osim
ulations
Another
frequentlyoccurring
problemis,
thatthe
fluctuationsof
two
simulations
must
becom
-bined.
Consider
thefollow
ingexam
ple:w
ehave
two
simulations
(A)
ofn
and(B
)ofm
steps,inw
hichthe
secondsim
ulationis
acontinuation
ofthe
first.H
owever,
thesecond
simulation
startsnum
beringfrom
1instead
offromn
+1.
For
thepartialsum
thisis
noproblem
,w
ehave
toadd
XA1,n
fromrun
A:
XA
B1,n
+m
=X
A1,n
+X
B1,m
(D.21)
When
we
want
tocom
putethe
partialvariance
fromthe
two
components
we
haveto
make
acorrection∆
σ:
σA
B1,n
+m
=σ
A1,n
+σ
B1,m
+∆σ
(D.22)
ifwe
definex
AB
ias
thecom
binedand
renumbered
setofdatapoints
we
canw
rite:
σA
B1,n
+m
=n+
m∑i=
1 [x
AB
i−X
AB
1,n
+m
n+m ]
2
(D.23)
17
2A
pp
en
dix
D.
Ave
rage
sa
nd
fluct
ua
tion
s
and
the
part
ialv
aria
nce
σn,m
=m ∑ i=
n
[ xi−
Xn,m
m−n
+1
] 2(D
.6)
Itca
nbe
show
nth
atX
n,m
+k
=X
n,m
+X
m+
1,m
+k
(D.7
)
and
σn,m
+k
=σ
n,m
+σ
m+
1,m
+k
+[
Xn,m
m−n
+1−
Xn,m
+k
m+k−n
+1
] 2 ∗
(m−n
+1)
(m+k−n
+1)
k(D
.8)
Forn
=1
one
finds
σ1,m
+k
=σ
1,m
+σ
m+
1,m
+k
+[ X 1
,m
m−X
1,m
+k
m+k
] 2 m(m
+k)
k(D
.9)
and
forn
=1
andk
=1
(eqn
.D.8
)be
com
es
σ1,m
+1
=σ
1,m
+[ X 1
,m
m−X
1,m
+1
m+
1
] 2 m(m
+1)
(D.1
0)
=σ
1,m
+[X
1,m−mx
m+
1]2
m(m
+1)
(D.1
1)
whe
rew
eha
veus
edth
ere
latio
n X1,m
+1
=X
1,m
+x
m+
1(D
.12)
Usi
ngfo
rmul
ae(e
qn.D.1
1)an
d(e
qn.D
.12)
the
aver
age
〈x〉
=X
1,N
x
Nx
(D.1
3)
and
the
fluct
uatio
n⟨ (∆
x)2⟩1 2
=[ σ 1,
Nx
Nx
]1 2
(D.1
4)
can
beob
tain
edby
one
swee
pth
roug
hth
eda
ta.
D.2
Impl
emen
tatio
n
InG
RO
MA
CS
the
inst
anta
neou
sen
ergi
esE(m
)are
stor
edin
the
ener
gyfil
e,al
ong
with
the
valu
esofσ
1,m
andX
1,m
.A
lthou
ghth
est
eps
are
coun
ted
from
0,fo
rthe
ener
gyan
dflu
ctua
tions
step
sar
eco
unte
dfr
om1.
Thi
sm
eans
that
the
equa
tions
pres
ente
dhe
rear
eth
eon
esth
atar
eim
plem
ente
d.W
egi
veso
mew
hatl
engt
hyde
rivat
ions
inth
isse
ctio
nto
sim
plify
chec
king
ofco
dean
deq
uatio
nsla
ter
on.
4.2
.B
on
de
din
tera
ctio
ns
57
θ 0
100.
0
�
110.
0
�
120.
0
�
130.
0
�
140.
0
�
θ
0.0
10.0
20.0
30.0
40.0
50.0
Va (kJ mole �
–1)
Fig
ure
4.7:
Prin
cipl
eof
angl
evi
brat
ion
(left)
and
the
bond
angl
epo
tent
ial(
right
).
The
num
berin
gi,j,k
isin
sequ
ence
ofco
vale
ntly
bond
edat
oms,
withjde
notin
gth
em
iddl
eat
om(s
eeF
ig.4
.7).
4.2.
5C
osin
eba
sed
angl
epo
tent
ial
Inth
eG
RO
MO
S-9
6fo
rce
field
asi
mpl
ified
func
tion
isus
edto
repr
esen
tang
levi
brat
ions
:
Va(θ
ijk)
=1 2k
θ ijk
( cos(θ i
jk)−
cos(θ0 ij
k)) 2
(4.4
8)
whe
reco
s(θ i
jk)
=r
ij·r
kj
r ijr k
j(4
.49)
The
corr
espo
ndin
gfo
rce
can
bede
rived
bypa
rtia
ldiff
eren
tiatio
nw
ithre
spec
tto
the
atom
icpo
si-
tions
.T
hefo
rce
cons
tant
sin
this
func
tion
are
rela
ted
toth
efo
rce
cons
tant
sin
the
harm
onic
form
kθ,h
arm
(sec
.4.2
.4)
by:
kθsi
n2(θ
0 ijk)
=k
θ,h
arm
(4.5
0)
4.2.
6Im
prop
erdi
hedr
als
Impr
oper
dihe
dral
sar
em
eant
toke
eppl
anar
grou
pspl
anar
(e.g
.ar
omat
icrin
gs)
orto
prev
ent
mol
ecul
esfr
omfli
ppin
gov
erto
thei
rm
irror
imag
es,s
eeF
ig.
4.8.
Vid
(ξij
kl)
=k
ξ(ξ
ijkl−ξ 0
)2(4
.51)
Thi
sis
also
aha
rmon
icpo
tent
ial,
itis
plot
ted
inF
ig.
4.9.
Not
eth
at,s
ince
itis
harm
onic
,per
iodi
city
isno
tta
ken
into
acco
unt,
soit
isbe
stto
defin
eim
prop
erdi
hedr
als
toha
vea
ξ 0as
far
away
from
±18
0◦as
you
can
man
age.
4.2.
7P
rope
rdi
hedr
als
For
the
norm
aldi
hedr
alin
tera
ctio
nth
ere
isa
choi
ceof
eith
erth
eG
RO
MO
Spe
riodi
cfu
nctio
nor
afu
nctio
nba
sed
onex
pans
ion
inpo
wer
sofcosφ
(the
so-c
alle
dR
ycka
ert-
Bel
lem
ans
pote
ntia
l).T
his
58
Ch
ap
ter
4.
Force
field
s
k
li
j
i
kj
l
k
i
j
l
Figure
4.8:P
rincipleof
improper
dihedralangles.
Out
ofplane
bendingfor
rings(left),
sub-stituents
ofrings
(middle),
outoftetrahedral(right).T
heim
properdihedralangle
ξis
definedas
theangle
between
planes(i,j,k)
and(j,k,l)
inallcases.
–20.0–10.0
0.010.0 �
20.0 �
ξ
0.0
10.0
20.0
30.0
Vi (kJ mole�–1
)
Figure
4.9:Im
properdihedralpotential.
Appendix
D
Averages
andfluctuations
D.1
Form
ulaefor
averaging
Note:this
sectionw
astaken
fromref[
77].
When
analyzinga
MD
trajectoryaverages
〈x〉and
fluctuations
⟨(∆x)
2 ⟩12
= ⟨[x−〈x〉] 2 ⟩
12(D
.1)
ofaquantityx
areto
becom
puted.T
hevariance
σx
ofaseries
ofNxvalues,{x
i },canbe
computed
from
σx
=N
x∑i=
1
x2i−
1Nx (
Nx
∑i=1
xi )
2
(D.2)
Unfortunately
thisform
ulais
numerically
notveryaccurate,especially
whenσ
12xis
smallcom
paredto
thevalues
ofxi .
The
following
(equivalent)expression
isnum
ericallym
oreaccurate
σx
=N
x∑i=
1 [xi −
〈x〉] 2(D
.3)
with
〈x〉=
1Nx
Nx
∑i=1
xi
(D.4)
Using
eqns.D.2
andD
.4one
hasto
gothrough
theseries
ofx
ivalues
twice,
onceto
determine
〈x〉and
againto
computeσ
x ,w
hereaseqn.D.1
requiresonly
onesequential
scanof
theseries
{xi }.
How
ever,onem
aycasteqn.
D.2
inanother
form,containing
partialsums,w
hichallow
sfor
asequentialupdate
algorithm.
Define
thepartialsum
Xn,m
=m∑i=
n
xi
(D.5)
17
0A
pp
en
dix
C.
Lo
ng
ran
geco
rre
ctio
ns
4.2
.B
on
de
din
tera
ctio
ns
59
j
k
l
i
0.0
90.0�
180.
0
�
270.
0
�
360.
0
�
φ
0.0
20.0
40.0
60.0
80.0
Vd (kJ mole �
–1)
Fig
ure
4.10
:P
rinci
ple
ofpr
oper
dihe
dral
angl
e(le
ft,intra
nsf
orm
)and
the
dihe
dral
angl
epo
tent
ial
(rig
ht).
C0
9.28
C2
-13.
12C
426
.24
C1
12.1
6C
3-3
.06
C5
-31.
5
Tabl
e4.
1:C
onst
ants
for
Ryc
kaer
t-B
elle
man
spo
tent
ial(
kJm
ol−
1).
choi
ceha
sco
nseq
uenc
esfo
rth
ein
clus
ion
ofsp
ecia
lint
erac
tions
betw
een
the
first
and
the
four
that
omof
the
dihe
dral
quad
rupl
e.W
ithth
epe
riodi
cG
RO
MO
Spo
tent
iala
spec
ial1
-4LJ
-inte
ract
ion
mus
tbe
incl
uded
;w
ithth
eR
ycka
ert-
Bel
lem
ans
pote
ntia
lthe
1-4
inte
ract
ions
mus
tbe
excl
uded
from
the
non-
bond
edlis
t.
Pro
per
dihe
dral
s:pe
riodi
cty
pe
Pro
per
dihe
dral
angl
esar
ede
fined
acco
rdin
gto
the
IUP
AC
/IUB
conv
entio
n,w
here
φis
the
angl
ebe
twee
nth
eijk
and
thejkl
plan
es,
with
zero
corr
espo
ndin
gto
theci
sco
nfigu
ratio
n(i
andl
onth
esa
me
side
).
Vd(φ
ijkl)
=k
φ(1
+co
s(nφ−φ
0))
(4.5
2)
Pro
per
dihe
dral
s:R
ycka
ert-
Bel
lem
ans
func
tion
For
alka
nes,
the
follo
win
gpr
oper
dihe
dral
pote
ntia
lis
ofte
nus
ed(s
eeF
ig.
4.11
)
Vrb(φ
ijkl)
=5 ∑ n=
0
Cn(c
os(ψ
))n,
(4.5
3)
whe
reψ
=φ−
180◦
.N
ote:
Aco
nver
sion
from
one
conv
entio
nto
anot
her
can
beac
hiev
edby
mul
tiply
ing
ever
yco
effi-
cien
tCn
by(−
1)n.
An
exam
ple
ofco
nsta
nts
forC
isgi
ven
inTa
ble4
.1.
60
Ch
ap
ter
4.
Force
field
s
0.090.0 �
180.0 �
270.0 �
360.0 �
φ
0.0
10.0
20.0
30.0
40.0
50.0
Vd (kJ mole�–1
)
Figure
4.11:R
yckaert-Bellem
ansdihedralpotential.
(Note:T
heuse
ofthispotentialim
pliesexclusions
ofLJ-interactionsbetw
eenthe
firstandthe
lastatom
ofthedihedral,andψ
isdefined
accordingto
the’polym
erconvention’(
ψtr
ans
=0).)
The
RB
dihedralfunctioncan
alsobe
usedto
includethe
OP
LSdihedralpotential[
50].T
heO
PLS
potentialfunctionis
givenas
thefirstfour
terms
ofaF
ourierseries:
Vrb (φ
ijkl )
=V
0+
12(V
1 (1+
cos(ψ))
+V
2 (1−
cos(2ψ))
+V
3 (1+
cos(3ψ))),
(4.54)
with
ψ=
φ(protein
convention).B
ecauseof
theequalities
cos(2φ)=
2(cos(φ))2−
1and
cos(3φ)=
4(cos(φ))3−
3cos(φ),one
cantranslate
theO
PLS
parameters
toR
yckaert-Bellem
ansparam
etersas
follows:
C0
=V
0+V
2+
12 (V1+V
3 )C
1=
12 (3V3 −
V1 )
C2
=−V
2
C3
=−
2V
3
C4
=0
C5
=0
(4.55)
with
OP
LSparam
etersin
proteinconvention
andR
Bparam
etersin
polymer
convention.N
ote:Mind
theconversion
fromkcalm
ol −
1forO
PLS
andR
Bparam
etersin
literatureto
kJm
ol −
1
inG
RO
MA
CS
.
4.2.8S
pecialinteractions
Special
potentialsare
usedfor
imposing
restraintson
them
otionof
thesystem
,either
toavoid
disastrousdeviations,or
toinclude
knowledge
fromexperim
entaldata.In
eithercase
theyare
notreally
partof
theforce
fieldand
thereliability
ofthe
parameters
isnot
important.
The
potentialform
s,asim
plemented
inG
RO
MA
CS
,arem
entionedjustfor
thesake
ofcompleteness.
C.1
.D
ispe
rsion
16
9
For
homogeneous
mixtures
we
canagain
usethe
averagedispersion
constant〈C
6 〉(eqn.C
.6):
Plr
=−
43π〈C
6 〉ρ2r −
3c
(C.12)
For
inhomogeneous
systems
eqn.C
.12can
beapplied
underthe
same
restrictionas
holdsfor
theenergy
(seesec.C.1.1).
16
8A
pp
en
dix
C.
Lo
ng
ran
geco
rre
ctio
ns
Ifw
eco
nsid
erfo
rex
ampl
ea
box
ofpu
rew
ater
,si
mul
ated
with
acu
t-of
fof0
.9nm
and
ade
nsity
of1
gcm
−3
this
corr
ectio
nis
-0.2
5kJ
mol−1.
For
aho
mog
eneo
usm
ixtu
reofM
com
pone
ntsj
with
Nj
part
icle
sea
ch,
we
can
writ
eth
elo
ngra
nge
cont
ribut
ion
toth
een
ergy
as:
Vlr
=M ∑ i6=
j
−2N
iNj
3VπC
6(ij)r−
3c
(C.5
)
Thi
sca
nbe
rew
ritte
nif
we
defin
eana
vera
ged
isp
ers
ion
con
sta
nt〈C6〉:
〈C6〉
=∑ i6=
j
NiN
j
N2C
6(ij)
(C.6
)
Vlr
=−
2 3Nρπ〈C
6〉r
−3
c(C
.7)
Asp
ecia
lfor
mof
ano
n-ho
mog
eneo
ussy
stem
inth
isre
spec
t,is
apu
reliq
uid
inw
hich
the
atom
sha
vedi
ffere
ntC
6va
lues
.In
prac
tice
this
defin
ition
enco
mpa
sses
alm
ost
ever
ym
olec
ule,
exce
ptm
ono-
atom
icm
olec
ules
and
sym
met
ricm
olec
ules
like
N2
orO
2.
The
refo
rew
eal
way
sha
veto
dete
rmin
eth
eav
erag
edi
sper
sion
cons
tant
〈C6〉i
nsi
mul
atio
ns.
Inth
eca
seof
inho
mog
eneo
ussi
mul
atio
nsy
stem
s,e.
g.a
syst
emw
itha
lipid
inte
rfac
e,th
een
ergy
corr
ectio
nca
nbe
appl
ied
if〈C6〉f
orbo
thco
mpo
nent
sis
com
para
ble.
C.1
.2V
irial
and
pres
sure
The
scal
arvi
rialo
fth
esy
stem
due
toth
edi
sper
sion
inte
ract
ion
betw
een
two
part
icle
si
andj
isgi
ven
by:
Ξ=
−r
ij·F
ij=
6C6r−
6ij
(C.8
)
The
pres
sure
isgi
ven
by:
P=
2 3V
(Ekin−
Ξ)
(C.9
)
We
can
agai
nin
tegr
ate
the
long
rang
eco
ntrib
utio
nto
the
viria
l[65
]:
Ξlr
=1 2Nρ
∫ ∞ r c4πr2
Ξdr
=12NπρC
6
∫ ∞ r cr−
4ij
dr
=4πC
6Nρr−
3c
(C.1
0)
The
corr
espo
ndin
gco
rrec
tion
toth
epr
essu
reis
Plr
=−
4 3πC
6ρ2r−
3c
(C.1
1)
Usi
ngth
esa
me
exam
ple
ofa
wat
erbo
x,th
eco
rrec
tion
toth
evi
riali
s3
kJm
ol−
1th
eco
rres
pond
ing
corr
ectio
nto
the
pres
sure
for
SP
Cw
ater
atliq
uid
dens
ityis
appr
ox.
-280
bar.
4.2
.B
on
de
din
tera
ctio
ns
61
0.00�
0.02�
0.04�
0.06�
0.08�
0.10�
r-R
(nm
)�
0.0
2.0
4.0
6.0
8.0
10.0
Vposre (kJ mole–1
)
Fig
ure
4.12
:P
ositi
onre
stra
intp
oten
tial.
4.2.
9P
ositi
onre
stra
ints
The
sear
eus
edto
rest
rain
part
icle
sto
fixed
refe
renc
epo
sitio
nsR
i.T
hey
can
beus
eddu
ring
equi
libra
tion
inor
dert
oav
oid
too
dras
ticre
arra
ngem
ents
ofcr
itica
lpar
ts(e
.g.t
ore
stra
inm
otio
nin
apr
otei
nth
atis
subj
ecte
dto
larg
eso
lven
tfor
ces
whe
nth
eso
lven
tis
noty
eteq
uilib
rate
d).
Ano
ther
appl
icat
ion
isth
ere
stra
inin
gof
part
icle
sin
ash
ella
roun
da
regi
onth
atis
sim
ulat
edin
deta
il,w
hile
the
shel
lis
only
appr
oxim
ated
beca
use
itla
cks
prop
erin
tera
ctio
nfr
omm
issi
ngpa
rtic
les
outs
ide
the
shel
l.R
estr
aini
ngw
illth
enm
aint
ain
the
inte
grity
ofth
ein
ner
part
.F
orsp
heric
alsh
ells
itis
aw
ise
proc
edur
eto
mak
eth
efo
rce
cons
tant
depe
ndon
the
radi
us,i
ncre
asin
gfr
omze
roat
the
inne
rbo
unda
ryto
ala
rge
valu
eat
the
oute
rbo
unda
ry.
Thi
sap
plic
atio
nha
sno
tbe
enim
plem
ente
din
GR
OM
AC
Sho
wev
er.
The
follo
win
gfo
rmis
used
:
Vpr(r
i)=
1 2k
pr|r
i−
Ri|2
(4.5
6)
The
pote
ntia
lis
plot
ted
inF
ig.4.12
.
The
pote
ntia
lfor
mca
nbe
rew
ritte
nw
ithou
tlos
sof
gene
ralit
yas
:
Vpr(r
i)=
1 2
[ kx pr(x
i−X
i)2x
+k
y pr(y
i−Y
i)2y
+k
z pr(z
i−Z
i)2z]
(4.5
7)
Now
the
forc
esar
e:F
x i=
−k
x pr
(xi−X
i)F
y i=
−k
y pr
(yi−Y
i)F
z i=
−k
z pr
(zi−Z
i)(4
.58)
Usi
ngth
ree
diffe
rent
forc
eco
nsta
nts
the
posi
tion
rest
rain
tsca
nbe
turn
edon
orof
fin
each
spat
ial
dim
ensi
on;
this
mea
nsth
atat
oms
can
beha
rmon
ical
lyre
stra
ined
toa
plan
eor
alin
e.P
ositi
onre
stra
ints
are
appl
ied
toa
spec
ial
fixed
list
ofat
oms.
Suc
ha
list
isus
ually
gene
rate
dby
the
pdb2
gmx
prog
ram
.
62
Ch
ap
ter
4.
Force
field
s
4.2.10A
nglerestraints
These
areused
torestrain
theangle
between
two
pairsofparticles
orbetw
eenone
pairofparticles
andthe
Z-axis.
The
functionalformis
similar
tothatofa
properdihedral.
For
two
pairsofatom
s:
Var (r
i ,rj ,r
k ,rl )
=k
ar (1
−cos(n(θ
−θ0 ))),
where
θ=
arccos (r
j −r
i
‖r
j −r
i ‖·
rl −
rk
‖r
l −r
k ‖ )(4.59)F
orone
pairofatom
sand
theZ
-axis:
Var (r
i ,rj )
=k
ar (1
−cos(n(θ
−θ0 ))),
where
θ=
arccos r
j −r
i
‖r
j −r
i ‖·
001 (4.60)
Am
ultiplicity(n
)of
2is
usefulwhen
youdo
notw
antto
distinguishbetw
eenparalleland
anti-parallelvectors.
4.2.11D
istancerestraints
Distance
restraintsadd
apenalty
tothe
potentialw
henthe
distancebetw
eenspecified
pairsof
atoms
exceedsa
thresholdvalue.
They
arenorm
allyused
toim
poseexperim
entalrestraints,as
fromexperim
entsin
nuclearm
agneticresonance
(NM
R),on
them
otionofthe
system.
Thus
MD
canbe
usedfor
structurerefinem
entusing
NM
Rdata.
The
potentialform
isquadratic
belowa
specifiedlow
erbound
andbetw
eentw
ospecified
upperbounds
andlinear
beyondthe
largestbound
(seeF
ig.4.13).
Vdr (r
ij )=
12 kdr (r
ij −r0 )
2for
rij
<r0
0for
r0
≤rij
<r1
12 kdr (r
ij −r1 )
2for
r1
≤rij
<r2
12 kdr (r
2 −r1 )(2r
ij −r2 −
r1 )
forr2
≤rij
(4.61)
The
forcesare
Fi
=
−k
dr (r
ij −r0 ) r
ij
rij
forrij
<r0
0for
r0
≤rij
<r1
−k
dr (r
ij −r1 ) r
ij
rij
forr1
≤rij
<r2
−k
dr (r
2 −r1 ) r
ij
rij
forr2
≤rij
(4.62)
Tim
eaveraging
Distance
restraintsbased
oninstantaneous
distancescan
potentiallyreduce
thefluctuations
ina
molecule
significantly.T
hisproblem
canbe
overcome
byrestraining
toa
time
ave
rageddis-
Appendix
C
Longrange
corrections
C.1
Dispersion
Inthis
sectionw
ederive
longrange
correctionsdue
tothe
useof
acut-off
forLennard
Jonesinteractions.
We
assume
thatthecut-offis
solong
thattherepulsion
termcan
safelybe
neglected,and
thereforeonly
thedispersion
termis
takeninto
account.D
ueto
thenature
ofthe
dispersioninteraction,
energyand
pressurecorrections
bothare
negative.W
hilethe
energycorrection
isusually
small,itm
aybe
importantforfree
energycalculations.
The
pressurecorrection
incontrast
isvery
largeand
cannotbe
neglected.A
lthoughitis
inprinciple
possibleto
parameterize
aforce
fieldsuch
thatthe
pressureis
closeto
1bar
evenw
ithoutcorrection,
sucha
method
makes
theparam
eterizationdependent
onthe
cut-offand
istherefore
undesirable.P
leasenote
thatit
isnot
consistentto
usethe
longrange
correctionto
thedispersion
without
usingeither
areaction
fieldm
ethodor
aproper
longrange
electrostaticsm
ethodsuch
asE
wald
summ
ationor
PP
PM
.
C.1.1
Energy
The
longrange
contributionofthe
dispersioninteraction
tothe
virialcanbe
derivedanalytically,if
we
assume
ahom
ogeneoussystem
beyondthe
cut-offdistancerc .
The
dispersionenergy
between
two
particlesis
written
as:V
(rij )
=−C
6 r −6
ij(C
.1)
andthe
correspondingforce
isF
ij=
−6C
6 r −8
ijr
ij(C
.2)
The
longrange
contributionto
thedispersion
energyin
asystem
with
Nparticles
andparticle
densityρ=N/V
,whereV
isthe
volume,is
[65]:
Vlr
=12Nρ ∫
∞rc
4πr2g(r)V
(r)dr
(C.3)
which
we
canintegrate
assuming
thattheradialdistribution
functiong(r)
is1
beyondthe
cut-offrc
Vlr
=−
23NρπC
6 r −3
c(C
.4)
16
6A
pp
en
dix
B.
So
me
imp
lem
en
tatio
nd
eta
ils
elec
tros
tatic
,dis
pers
ion
and
repu
lsio
nin
tera
ctio
ns,b
utfo
rth
esa
keof
cach
ing
perf
orm
ance
thes
eha
vebe
enco
mbi
ned
into
asi
ngle
arra
y.T
hecu
bic
splin
ein
terp
olat
ion
look
slik
eth
is:
y(x
)=
ηy i
+εy
i+1+h
2 6
[ (η3−η)y
′′ i+
(ε3−ε)y′′ i+
1
](B
.58)
whe
reε
=1-η,a
ndy i
andy′′ i
are
the
tabu
late
dva
lues
ofa
func
tiony(x
)an
dits
seco
ndde
rivat
ive
resp
ectiv
ely.
Fur
ther
mor
e,
h=
xi+
1−x
i(B
.59)
ε=
(x−x
i)/h
(B.6
0)
soth
at0≤ε<
1.eq
n.B
.58
can
bere
writ
ten
as
y(x
)=
y i+ε
( y i+
1−y i−h
2 6
( 2y′′ i
+y′′ i+
1
)) +ε2( h2 2
y′′ i
) +ε3h
2 6
( y′′ i+
1−y′′ i
) (B.6
1)
Not
eth
atth
ex-
depe
nden
ceis
com
plet
ely
inε.
Thi
sca
nab
brev
iate
dto
y(x
)=
y i+εF
i+ε2G
i+ε3H
i(B
.62)
Fro
mth
isw
eca
nca
lcul
ate
the
deriv
ativ
ein
orde
rto
dete
rmin
eth
efo
rces
:
dy(x
)dx
=dy
(x)
dεdε dx
=(F
i+
2εG
i+
3ε2H
i)/h
(B.6
3)
Ifw
est
ore
inth
eta
bley
i,F
i,G
ian
dH
iw
ene
eda
tabl
eof
leng
th4n
.T
henu
mbe
rof
poin
tspe
rna
nom
eter
shou
ldbe
onth
eor
der
of50
0to
1000
,fo
rac
cura
tere
pres
enta
tion
(rel
ativ
eer
ror
<10−
4w
hen
n=
500
poin
ts/n
m).
The
forc
ero
utin
esge
tasc
alin
gfa
ctor
sas
apa
ram
eter
that
iseq
ualt
oth
enu
mbe
rof
poin
tspe
rnm
.(N
ote
thath
iss−
1).
The
algo
rithm
goes
alit
tleso
met
hing
like
this
:
1.C
alcu
late
dist
ance
vect
or(
rij
)an
ddi
stan
cer ij
2.M
ultip
lyr i
jbys
and
trun
cate
toan
inte
ger
valu
en
0to
geta
tabl
ein
dex
3.C
alcu
late
frac
tiona
lcom
pone
nt(
ε=sr
ij−n
0)
andε2
4.D
oth
ein
terp
olat
ion
toca
lcul
ate
the
pote
ntia
lV
and
the
the
scal
arfo
rcef
5.C
alcu
late
the
vect
orfo
rceF
bym
ultip
lyin
gf
with
rij
The
tabl
esar
est
ored
inte
rnal
lyas
yi,
F i,
Gi,
Hi
inth
eor
der
coul
omb,
disp
ersi
on,
repu
lsio
n.In
tota
lthe
rear
e12
valu
esin
each
tabl
een
try.
Not
eth
atta
ble
look
upis
sign
ifica
ntly
slo
we
rtha
nco
mpu
tatio
nof
the
mos
tsi
mpl
eLe
nnar
d-Jo
nes
and
Cou
lom
bin
tera
ctio
n.H
owev
er,
itis
muc
hfa
ster
than
the
shift
edco
ulom
bfu
nctio
nus
edin
conj
unct
ion
with
the
PP
PM
met
hod.
Fin
ally
itis
muc
hea
sier
tom
odify
ata
ble
for
the
pote
ntia
l(an
dge
ta
grap
hica
lrep
rese
ntat
ion
ofit)
than
tom
odify
the
inne
rlo
ops
ofth
eM
Dpr
ogra
m.
4.2
.B
on
de
din
tera
ctio
ns
63
0�
0.1
0.2
0.3
0.4
0.5
r (n
m)
051015
Vdisre (kJ mol−1
)
r 0r 1
r 2
Fig
ure
4.13
:D
ista
nce
Res
trai
ntpo
tent
ial.
tanc
e[51
].T
hefo
rces
with
time
aver
agin
gar
e:
Fi
=
−k
dr(r
ij−r 0
)rij
r ij
for
r ij
<r 0
0fo
rr 0
≤r i
j<
r 1
−k
dr(r
ij−r 1
)rij
r ij
forr 1
≤r i
j<
r 2
−k
dr(r
2−r 1
)rij
r ij
forr 2
≤r i
j
(4.6
3)
whe
rer i
jis
give
nby
:
r ij
=<r−
3ij
>−
1/3
(4.6
4)
Bec
ause
ofth
etim
eav
erag
ing
we
can
nolo
nger
spea
kof
adi
stan
cere
stra
intp
oten
tial.
Thi
sw
ayan
atom
can
satis
fytw
oin
com
patib
ledi
stan
cere
stra
ints
on
ave
rage
bym
ovin
gbe
twee
ntw
opo
sitio
ns.
An
exam
ple
wou
ldbe
anam
ino-
acid
side
-cha
inw
hich
isro
tatin
gar
ound
itsχ
dihe
dral
angl
e,th
ereb
yco
min
gcl
ose
tova
rious
othe
rgr
oups
.S
uch
am
obile
side
chai
nm
aygi
veris
eto
mul
tiple
NO
Es,
whi
chca
nno
tbe
fulfi
lled
ina
sing
lest
ruct
ure.
The
com
puta
tion
ofth
etim
eav
erag
eddi
stan
cein
the
md
run
prog
ram
isdo
nein
the
follo
win
gfa
shio
n:
r−3ij(0
)=
r ij(0
)−3
r−3ij(t
)=
r−3ij(t−
∆t)
exp( −
∆t
τ
) +r i
j(t
)−3[ 1−
exp( −
∆t
τ
)](4
.65)
Whe
na
pair
isw
ithin
the
boun
dsit
can
still
feel
afo
rce,
beca
use
the
time
aver
aged
dist
ance
can
still
bebe
yond
abo
und.
Topr
even
tth
epr
oton
sfr
ombe
ing
pulle
dto
ocl
ose
toge
ther
am
ixed
appr
oach
can
beus
ed.
Inth
isap
proa
chth
epe
nalty
isze
row
hen
the
inst
anta
neou
sdi
stan
ceis
with
inth
ebo
unds
,ot
herw
ise
the
viol
atio
nis
the
squa
rero
otof
the
prod
uct
ofth
ein
stan
tane
ous
viol
atio
nan
dth
etim
eav
erag
edvi
olat
ion.
64
Ch
ap
ter
4.
Force
field
s
Averaging
overm
ultiplepairs
Som
etimes
itis
unclearfrom
experimentaldata
which
atompair
givesrise
toa
singleN
OE
,in
otheroccasions
itcan
beobvious
thatm
orethan
onepair
contributesdue
tothe
symm
etryof
thesystem
,e.g.
am
ethylgroupw
iththree
protons.F
orsuch
agroup
itis
notpossible
todistinguish
between
theprotons,therefore
theyshould
allbetaken
intoaccountw
hencalculating
thedistance
between
thism
ethylgroupand
anotherproton
(orgroup
ofprotons).D
ueto
thephysicalnature
ofm
agneticresonance,the
intensityofthe
NO
Esignalis
proportionaltothe
distancebetw
eenatom
sto
thepow
erof
-6.T
hus,w
hencom
biningatom
pairs,a
fixedlist
ofN
restraintsm
aybe
takentogether,w
herethe
apparent“distance”is
givenby:
rN
(t)= [
N∑n=
1
rn (t) −
6 ]−
1/6
(4.66)
where
we
userij
oreqn.4.64
forthe
rn .
TherN
oftheinstantaneous
andtim
e-averageddistances
canbe
combined
todo
am
ixedrestraining
asindicated
above.A
sm
orepairs
ofprotonscontribute
tothe
same
NO
Esignal,
theintensity
willincrease,
andthe
summ
ed“distance”
willbe
shorterthan
anyofits
components
dueto
thereciprocalsum
mation.
There
aretw
ooptions
fordistributing
theforces
overthe
atompairs.
Inthe
conservativeoption
theforce
isdefined
asthe
derivateof
therestraint
potentialwith
respectto
thecoordinates.
This
resultsin
aconservative
potentialwhen
notim
eaveraging
isused.
The
forcedistribution
overthe
pairsis
proportionaltor −6.
This
means
thata
closepair
feelsa
much
largerforce
thana
distantpair,
which
might
leadto
a’too
rigid’molecule.
The
otheroption
isan
equalforcedistribution.
Inthis
caseeach
pairfeels1/N
ofthederivative
oftherestraintpotentialw
ithrespectto
rN
.T
headvantage
ofthism
ethodis
thatmore
conformations
mightbe
sampled,butthe
non-conservativenature
oftheforces
canlead
tolocalheating
oftheprotons.
Itis
alsopossible
touseen
sem
ble
ave
ragin
gusingm
ultiple(protein)
molecules.
Inthis
casethe
boundsshould
below
eredas
in:
r1
=r1 ∗
M−
1/6
r2
=r2 ∗
M−
1/6
(4.67)
where
Mis
thenum
berof
molecules.
The
GR
OM
AC
Spreprocessor
gro
mp
pcan
dothis
auto-m
aticallyw
henthe
appropriateoption
isgiven.
The
resulting“distance”
isthen
usedto
calculatethe
scalarforce
accordingto:
Fi
=0
rN<r1
=−k
dr (r
N−r1 ) r
ij
rij
r1≤rN<r2
=−k
dr (r
2 −r1 ) r
ij
rij
rN≥r2
(4.68)
where
iand
jdenote
theatom
sofallthe
pairsthatcontribute
tothe
NO
Esignal.
Using
distancerestraints
Alist
ofdistance
restrainsbased
onN
OE
datacan
beadded
toa
molecule
definitionin
yourtopology
file,likein
thefollow
ingexam
ple:
B.4
.Ta
bula
ted
fun
ction
s1
65
For(127
−E
)=odd
equation(eqn.B.45)
canbe
rewritten
as
y(x)=
(2127−
E−
12
)( 1.F2) −
1/2
(B.52)
thus
E′=
126−E
2+
127(B
.53)
which
alsocan
becalculated
exactlyin
integerarithm
etic.N
otethatthe
fractionis
automatically
correctedfor
itsrange
earlierm
entioned,sothe
exponentdoesnotneed
anextra
correction.
The
conclusionsfrom
thisare:
•T
hefraction
andexponent
lookuptable
areindependent.
The
fractionlookup
tableexists
oftwo
tables(odd
andeven
exponent)so
theodd/even
information
oftheexponent(lsb
bit)has
tobe
usedto
selecttherighttable.
•T
heexponenttable
isan
256x
8bittable,initialized
forodd
andeven
.
B.3.6
Implem
entation
The
lookuptables
canbe
generatedby
asm
allC
program,
which
usesfloating
pointnum
bersand
operationsw
ithIE
EE
32bit
singleprecision
format.
Note
thatbecause
ofthe
odd/ev
eninform
ationthatis
needed,thefraction
tableis
twice
thesize
earlierspecified
(13biti.s.o.
12bit).
The
functionaccording
toequation
(eqn.B
.29)has
tobe
implem
ented.A
ppliedto
the1/ √x
function,equation(eqn.B.28)
leadsto
f=a−
1y2
(B.54)
andso
f′=
2y3
(B.55)
so
yn+
1=y
n−a−
1y2n
2y3n
(B.56)
ory
n+
1=y
n2(3−ay
2n )(B
.57)
Where
y0
canbe
foundin
thelookup
tables,andy1
givesthe
resulttothe
maxim
umaccuracy.
Itis
clearthatonly
oneiteration
extra(in
doubleprecision)
isneeded
fora
doubleprecision
result.
B.4
Tabulatedfunctions
Insom
eofthe
innerloops
ofGR
OM
AC
Slookup
tablesare
usedfor
computation
ofpotentialandforces.
The
tablesare
interpolatedusing
acubic
splinealgorithm
.T
hereare
separatetables
for
16
4A
pp
en
dix
B.
So
me
imp
lem
en
tatio
nd
eta
ils
B.3
.5S
epar
ate
expo
nent
and
frac
tion
com
puta
tion
The
used
IEE
E32
bits
ingl
epr
ecis
ion
float
ing
poin
tfor
mat
spec
ifies
that
anu
mbe
ris
repr
esen
ted
bya
expo
nent
and
afr
actio
n.T
hepr
evio
usse
ctio
nsp
ecifi
esfo
rev
ery
poss
ible
float
ing
poin
tnu
mbe
rth
elo
okup
tabl
ele
ngth
and
wid
th.
Onl
yth
esi
zeof
the
frac
tion
ofa
float
ing
poin
tnum
ber
defin
esth
eac
cura
cy.
The
conc
lusi
onfr
omth
isca
nbe
that
the
size
ofth
elo
okup
tabl
eis
leng
thof
look
upta
ble,
earli
ersp
ecifi
ed,
times
the
size
ofth
eex
pone
nt(
21228,1Mb)
.T
he1/√x
func
tion
has
the
prop
erty
that
the
expo
nent
isin
depe
nden
toft
hefr
actio
n.T
his
beco
mes
clea
rift
heflo
atin
gpo
intr
epre
sent
atio
nis
used
.D
efine x≡
(−1)
S(2
E−
127)(
1.F
)(B
.42)
see
Fig
.B.1
whe
re0≤S≤
1,0≤E≤
255,
1≤
1.F<
2an
dS
,E,F
inte
ger
(nor
mal
izat
ion
cond
ition
s).
The
sign
bit(S
)ca
nbe
omitt
edbe
caus
e1/√x
ison
lyde
fined
forx>
0.T
he1/√x
func
tion
appl
ied
tox
resu
ltsin
y(x
)=
1 √x
(B.4
3)
or
y(x
)=
1√ (2
E−
127)(
1.F
)(B
.44)
this
can
bere
writ
ten
asy(x
)=
(2E−
127)−
1/2(1.F
)−1/2
(B.4
5)
Defi
ne(2
E′ −
127)≡
(2E−
127)−
1/2
(B.4
6)
1.F′≡
(1.F
)−1/2
(B.4
7)
then
1 √2<
1.F′≤
1ho
lds,
soth
eco
nditi
on1≤
1.F′<
2w
hich
ises
sent
ialf
orno
rmal
ized
real
repr
esen
tatio
nis
not
valid
anym
ore.
By
intr
oduc
ing
anex
tra
term
this
can
beco
rrec
ted.
Rew
rite
the1/√x
func
tion
appl
ied
toflo
atin
gpo
intn
umbe
rs,e
quat
ion
(eqn
.B
.45)
as
y(x
)=
(2127−
E2
−1)(
2(1.F
)−1/2)
(B.4
8)
and
(2E′ −
127)≡
(2127−
E2
−1)
(B.4
9)
1.F′≡
2(1.F
)−1/2
(B.5
0)
then√
2<
1.F≤
2ho
lds.
Thi
sis
not
the
exac
tva
lidra
nge
asde
fined
for
norm
aliz
edflo
atin
gpo
int
num
bers
ineq
uatio
n(e
qn.
B.4
2).
The
valu
e2ca
uses
the
prob
lem
.B
ym
appi
ngth
isva
lue
onth
ene
ares
tre
pres
enta
tion<
2th
isca
nbe
solv
ed.
The
smal
lerr
orth
atis
intr
oduc
edby
this
appr
oxim
atio
nis
with
inth
eal
low
able
rang
e.
The
inte
gerr
epre
sent
atio
nof
the
expo
nent
isth
ene
xtpr
oble
m.
Cal
cula
ting
(2127−
E2
−1)
intr
oduc
esa
frac
tiona
lre
sult
if(12
7−E
)=odd.
Thi
sis
agai
nea
sily
acco
unte
dfo
rby
split
ting
upth
eca
lcul
atio
nin
toan
odd
and
anev
enpa
rt.
For(127−E
)=even
E′in
equa
tion
(eqn
.B.4
9)ca
nbe
exac
tlyca
lcul
ated
inin
tege
rar
ithm
etic
asa
func
tion
ofE
.
E′=
127−E
2+
126
(B.5
1)
4.2
.B
on
de
din
tera
ctio
ns
65
[d
ista
nce
_re
stra
ints
];
ai
aj
typ
ein
de
xty
pe
’lo
wu
p1
up
2fa
c1
01
61
01
0.0
0.3
0.4
1.0
10
28
11
10
.00
.30
.41
.01
04
61
11
0.0
0.3
0.4
1.0
16
22
12
10
.00
.30
.42
.51
63
41
31
0.0
0.5
0.6
1.0
Inth
isex
ampl
ea
num
ber
offe
atur
esca
nbe
foun
d.In
colu
mns
ai
and
aj
you
find
the
atom
num
bers
ofth
epa
rtic
les
tobe
rest
rain
ed.
Thetyp
eco
lum
nsh
ould
alw
ays
be1.
As
expl
aine
din
sec.
4.2.
11,m
ultip
ledi
stan
ces
can
cont
ribut
eto
asi
ngle
NO
Esi
gnal
.In
the
topo
logy
this
can
bese
tus
ing
thein
de
xco
lum
n.In
our
exam
ple,
the
rest
rain
ts10
-28
and
10-4
6bo
thha
vein
dex
1,th
eref
ore
they
are
trea
ted
sim
ulta
neou
sly.
An
extr
are
quire
men
tfor
trea
ting
rest
rain
tsto
geth
er,
isth
atth
ere
stra
ints
shou
ldbe
onsu
cces
sive
lines
,w
ithou
tan
yot
her
inte
rven
ing
rest
rain
t.T
hety
pe
’co
lum
nw
illus
ually
be1,
butc
anbe
sett
o2
toob
tain
adi
stan
cere
stra
intw
hich
will
neve
rbe
time
and
ense
mbl
eav
erag
ed,
this
can
beus
eful
for
rest
rain
ing
hydr
ogen
bond
s.T
heco
lum
nslo
w,u
p1
and
up
2ho
ldth
eva
lues
ofr0,r
1an
dr 2
from
eqn.
4.61
.In
som
eca
ses
itca
nbe
usef
ulto
have
diffe
rent
forc
eco
nsta
nts
for
som
ere
stra
ints
,th
isis
cont
rolle
dby
the
colu
mn
fac
.T
hefo
rce
cons
tant
inth
epa
ram
eter
file
ism
ultip
lied
byth
eva
lue
inth
eco
lum
nfa
cfo
rea
chre
stra
int.
Som
epa
ram
eter
sfo
rN
MR
refin
emen
tcan
besp
ecifi
edin
the
gro
mp
p.m
dp
file:
dis
re:
type
ofdi
stan
cere
stra
inin
g.T
hed
isre
varia
ble
sets
the
type
ofdi
stan
cere
stra
in-
ing.
no
/sim
ple
turn
sth
edi
stan
cere
stra
inin
gof
f/on.
Whe
nm
ultip
lepr
otei
nsor
pep-
tides
are
used
inth
esi
mul
atio
nen
sem
ble
aver
agin
gca
nbe
turn
edon
byse
tting
dis
re=
en
sem
ble
.
dis
rew
eig
htin
g:
forc
e-w
eigh
ting
inre
stra
ints
with
mul
tiple
pairs
.B
yde
faul
t,th
efo
rce
due
toth
edi
stan
cere
stra
inti
sdi
strib
uted
equa
llyov
eral
lthe
pairs
invo
lved
inth
ere
stra
int.
Thi
sca
nal
sobe
expl
icitl
yse
lect
edw
ithdis
rew
eig
htin
g=
eq
ua
l.
Ifyo
uin
stea
dse
tth
isop
tion
tod
isre
we
igh
ting
=co
nse
rva
tive
you
get
cons
erva
tive
forc
esw
hen
dis
reta
u=
0.
dis
rem
ixe
d:
how
toca
lcul
ate
the
viol
atio
ns.d
isre
mix
ed
=n
ogi
ves
norm
altim
eav
-er
aged
viol
atio
ns.
Whe
ndisr
em
ixe
d=
yes
the
squa
rero
otof
the
prod
ucto
fthe
time
aver
aged
and
the
inst
anta
neou
svi
olat
ions
isus
ed.
dis
refc
:fo
rce
cons
tantk
dr
for
dist
ance
rest
rain
ts.k
dr
(eqn
.4.6
1)ca
nbe
set
asva
riabl
ed
isre
fc=
10
00
for
afo
rce
cons
tant
of10
00kJ
mol−1
nm−
2.
Thi
sva
lue
ism
ulti-
plie
dby
the
valu
ein
thefa
cco
lum
nin
the
dist
ance
rest
rain
tent
ries
inth
eto
polo
gyfil
e.
dis
reta
u:
time
cons
tant
for
rest
rain
ts.τ
(eqn
.4.6
5)ca
nbe
set
asva
riabl
edisr
eta
u=
10
for
atim
eco
nsta
ntof
10ps
.T
ime
aver
agin
gca
nbe
turn
edof
fby
setti
ngd
isre
tau
to0.
nst
dis
reo
ut
:pa
irdi
stan
ceou
tput
freq
uenc
y.D
eter
min
esho
wof
ten
the
time
aver
aged
and
inst
anta
neou
sdi
stan
ces
ofal
lat
ompa
irsin
volv
edin
dist
ance
rest
rain
tsar
ew
ritte
nto
the
ener
gyfil
e.
66
Ch
ap
ter
4.
Force
field
s
4.3F
reeenergy
interactions
This
sectiondescribes
theλ-dependenceof
thepotentials
usedfor
freeenergy
calculations(see
sec.3.12).A
llcomm
ontypes
ofpotentialsand
constraintscan
beinterpolated
smoothly
fromstate
A(λ
=0)
tostate
B(λ
=1)
andvice
versa.A
llbondedinteractions
areinterpolated
bylinear
interpolationof
theinteraction
parameters.
Non-bonded
interactionscan
beinterpolated
linearlyor
viasoft-core
interactions.
Harm
onicpotentials
The
example
givenhere
isfor
thebond
potentialw
hichis
harmonic
inG
RO
MA
CS
.H
owever,
theseequations
applyto
theangle
potentialandthe
improper
dihedralpotentialasw
ell.
Vb
=12((1
−λ)k
Ab+λk
Bb)(b−
(1−λ)b
A0−λbB0
)2
(4.69)
∂V
b
∂λ
=12(k
Bb−k
Ab) [b−
(1−λ)b
A0+λbB0
)2+
(bA0−bB0
)(b−(1−λ)b
A0−λbB0
) ](4.70)
GR
OM
OS
-96bonds
andangles
Fourth
power
bondstretching
andcosine
basedangle
potentialsare
interpolatedby
linearinterpo-
lationofthe
forceconstantand
theequilibrium
position.F
ormulas
arenotgiven
here.
Proper
dihedrals
For
theproper
dihedrals,theequations
aresom
ewhatm
orecom
plicated:
Vd
=((1
−λ)k
Ad+λk
Bd)(1
+cos(n
φφ−
((1−λ)φ
A0+λφ
B0))
(4.71)∂V
d
∂λ
=(k
Bd−k
Ad) [1
+cos(n
φφ−
[(1−λ)φ
A0+λφ
B0])−
((1−λ)k
Ad+λk
Bd)(φ
A0−φ
B0)sin(n
φφ−
[(1−λ)φ
A0+λφ
B0] ]
(4.72)
Note:
thatthem
ultiplicitynφ
cannotbe
parameterized
becausethe
functionshould
remain
peri-odic
onthe
interval[0,2π].
Coulom
binteraction
The
Coulom
binteraction
between
two
particlesofw
hichthe
chargevaries
with
λis:
Vc
=f
εrf r
ij [((1−λ)q
Ai+λqBi
)·((1−λ)q
Aj+λqBi
) ](4.73)
∂V
c
∂λ
=f
εrf r
ij [(qBj−qAj)((1
−λ)q
Ai+λqBi
)+
(qBi−qAi)((1
−λ)q
Aj+λqBj
) ](4.74)
where
f=
14πε0
=138.935
485(see
chapter2)
B.3
.C
om
pu
tatio
no
fthe
1.0
/sqrtfu
nctio
n.
16
3
B.3.4
Specification
ofthelookup
table
Tocalculate
thefunction1/ √
xusing
thepreviously
mentioned
iterationschem
e,itisclearthatthe
firstestim
ationof
thesolution
must
beaccurate
enoughto
getprecise
results.T
herequirem
entsfor
thecalculation
are
•M
aximum
possibleaccuracy
with
theused
IEE
Eform
at
•U
seonly
oneiteration
stepfor
maxim
umspeed
The
firstrequirem
entstates
thatthe
resultof
1/ √
xm
ayhave
arelative
errorεrequal
tothe
εr
ofa
IEE
E32
bitsingle
precisionfloating
pointnum
ber.F
romthis
the1/ √
xof
theinitial
approximation
canbe
derived,rew
ritingthe
definitionof
therelative
errorfor
succeedingsteps,
equation(eqn.B.34)
εny
= √εrn+
1
2f′
yf′′
(B.35)
So
forthe
lookuptable
theneeded
accuracyis
∆YY
= √232−
24
(B.36)
which
definesthe
width
ofthetable
thatmustbe≥
13bit.
Atthis
pointtherelative
errorεrn
ofthelookup
tableis
known.
From
thisthe
maxim
umrelative
errorin
theargum
entcanbe
calculatedas
follows.
The
absoluteerror
∆x
isdefined
as
∆x≡
∆Y
Y′
(B.37)
andthus
∆x
Y=
∆YY
(Y′) −
1(B
.38)
andthus
∆x
=con
stantYY′
(B.39)
forthe
1/ √
xfunction
Y/Y′∼
xholds,
so∆x/x
=con
stant.
This
isa
propertyof
theused
floatingpoint
representationas
earlierm
entioned.T
heneeded
accuracyof
theargum
entof
thelookup
tablefollow
sfrom
∆xx
=−
2∆YY
(B.40)
so,usingthe
floatingpointaccuracy,equation
(eqn.B
.36)
∆xx
=−
2 √232−
24
(B.41)
This
definesthe
lengthofthe
lookuptable
which
shouldbe
≥12
bit.
16
2A
pp
en
dix
B.
So
me
imp
lem
en
tatio
nd
eta
ils
︸︷︷
︸︸
︷︷︸
?F
ES
023
31
Value
=(−
1)S(2
E−
127)(
1.F
)
023
31
Value
=(−
1)S(2
E−
127)(
1.F
)
Fig
ure
B.1
:IE
EE
sing
lepr
ecis
ion
float
ing
poin
tfor
mat
can
now
beso
lved
usin
gN
ewto
n-R
aphs
on.
An
itera
tion
ispe
rfor
med
byca
lcul
atin
g
y n+
1=y n−f(y
n)
f′ (y n
)(B
.29)
The
abso
lute
erro
rε,in
this
appr
oxim
atio
nis
defin
edby
ε≡y n−q
(B.3
0)
usin
gTa
ylor
serie
sex
pans
ion
toes
timat
eth
eer
ror
resu
ltsin
ε n+
1=−ε2 n 2f′′ (y n
)f′ (y n
)(B
.31)
acco
rdin
gto
[76]e
quat
ion
(3.2
).T
his
isan
estim
atio
nof
the
abso
lute
erro
r.
B.3
.3A
pplie
dto
float
ing
poin
tnum
bers
Flo
atin
gpo
intn
umbe
rsin
IEE
E32
bits
ingl
epr
ecis
ion
form
atha
vea
near
lyco
nsta
ntre
lativ
eer
ror
of∆x/x
=2−
24.
As
seen
earli
erin
the
Tayl
orse
ries
expa
nsio
neq
uatio
n(e
qn.
B.3
1),t
heer
ror
inev
ery
itera
tion
step
isab
solu
tean
din
gene
rald
epen
dent
ofy.
Ifth
eer
ror
isex
pres
sed
asa
rela
tive
erro
rεr
the
follo
win
gho
lds
ε rn+
1≡ε n
+1
y(B
.32)
and
so
ε rn+
1=−
(εn y)2yf′′
2f′
(B.3
3)
for
the
func
tionf
(y)
=y−
2th
ete
rmyf′′ /
2f′ i
sco
nsta
nt(e
qual
to−3/
2)so
the
rela
tive
erro
rε rn
isin
depe
nden
tofy.
ε rn+
1=
3 2(ε
r n)2
(B.3
4)
The
conc
lusi
onof
this
isth
atth
efu
nctio
n1/√x
can
beca
lcul
ated
with
asp
ecifi
edac
cura
cy.
4.3
.F
ree
en
erg
yin
tera
ctio
ns
67
Cou
lom
bin
tera
ctio
nw
ithR
eact
ion
Fie
ld
The
coul
omb
inte
ract
ion
incl
udin
ga
reac
tion
field
,be
twee
ntw
opa
rtic
les
ofw
hich
the
char
geva
ries
withλ
is:
Vc
=f
[ 1 r ij
+k
rfr2 ij
−c r
f
] [ ((1−λ)q
A i+λqB i
)·(
(1−λ)q
A j+λqB i
)](4
.75)
∂V
c
∂λ
=f
[ 1 r ij
+k
rfr2 ij
−c r
f
] ·[ (q
B j−qA j
)((1−λ)q
A i+λqB i
)+
(qB i−qA i
)((1−λ)q
A j+λqB j
)](4
.76)
Not
eth
atth
eco
nsta
ntsk r
fan
dc r
far
ede
fined
usin
gth
edi
elec
tric
cons
tantε rf
ofth
em
ediu
m(s
eese
c.4.1
.4).
Lenn
ard-
Jone
sin
tera
ctio
n
For
the
Lenn
ard-
Jone
sin
tera
ctio
nbe
twee
ntw
opa
rtic
les
ofw
hich
the
ato
mty
pev
arie
sw
ithλ
we
can
writ
e:
VL
J=
((1−λ)C
A 12+λC
B 12)
r12
ij
−(1−λ)C
A 6+λC
B 6
r6 ij
(4.7
7)
∂V
LJ
∂λ
=C
B 12−C
A 12
r12
ij
−C
B 6−C
A 6
r6 ij
(4.7
8)
Itsh
ould
beno
ted
that
itis
also
poss
ible
toex
pres
sa
path
way
from
stat
eA
tost
ate
Bus
ing
σan
dε
(see
eqn.4
.5).
Itm
ayse
emto
mak
ese
nse
phys
ical
ly,
tova
ryth
efo
rcefi
eld
para
met
ers
σan
dε
rath
erth
anth
ede
rived
para
met
ers
C12
andC
6.
How
ever
,the
diffe
renc
ebe
twee
nth
epa
thw
ays
inpa
ram
eter
spac
eis
notl
arge
,and
the
free
ener
gyits
elfd
oes
notd
epen
don
the
path
way
,the
refo
rew
eus
eth
esi
mpl
efo
rmul
atio
npr
esen
ted
abov
e.
Kin
etic
Ene
rgy
Whe
nth
em
ass
ofa
part
icle
chan
ges
ther
eis
also
aco
ntrib
utio
nof
the
kine
ticen
ergy
toth
efr
eeen
ergy
(not
eth
atw
eca
nno
tw
rite
the
mom
entu
mp
asmv
sinc
eth
atw
ould
resu
ltin
the
sign
of∂E
k∂λ
bein
gin
corr
ect[5
2]):
Ek
=1 2
p2
(1−λ)m
A+λm
B(4
.79)
∂Ek
∂λ
=−
1 2p
2(m
B−m
A)
((1−λ)m
A+λm
B)2
(4.8
0)
afte
rta
king
the
deriv
ativ
e,w
ecan
inse
rtp
=m
v,s
uch
that
:
∂Ek
∂λ
=−
1 2v
2(m
B−m
A)
(4.8
1)
68
Ch
ap
ter
4.
Force
field
s
0 �
0.51�
1.52 �
2.53 �
r�
−1 0 1 2 3 4 5
Vsc�
LJ, α=
0LJ, α
=1.5
LJ, α=
23/r,
�
α=
03/r,
�
α=
1.53/r,
�
α=
2
Figure
4.14:S
oft-coreinteractions
atλ
=0.5,w
ithC
A6=C
A12
=C
B6=C
B12
=1.
Constraints
The
constraintsare
formally
partoftheH
amiltonian,and
thereforethey
givea
contributionto
thefree
energy.In
GR
OM
AC
Sthis
canbe
calculatedusing
theLIN
CS
orthe
SH
AK
Ealgorithm
.If
we
havea
number
ofconstraintequationsgk :
gk
=rk−d
k(4.82)
where
rk
isthe
distancevector
between
two
particlesandd
kis
theconstraint
distancebetw
eenthe
two
particlesw
ecan
write
thisusing
aλ
dependentdistanceas
gk
=rk− ((1
−λ)d
Ak+λd
Bk )(4.83)
thecontributionC
λto
theH
amiltonian
usingLagrange
multipliers
λ:
Cλ
= ∑k
λk g
k(4.84)
∂C
λ
∂λ
= ∑k
λk (d
Bk−d
Ak )(4.85)
4.3.1S
oft-coreinteractions
The
linearinterpolation
oftheLennard-Jones
andC
oulomb
potentialsgives
problems
when
grow-
ingparticles
outofnothingor
when
making
particlesdisappear
(λ
closeto
0or
1).To
circumvent
theseproblem
s,thesingularities
inthe
potentialsneed
tobe
removed.
This
isdone
with
soft-corepotentials.
InG
RO
MA
CS
thesoft-core
potentialV
scis:
Vsc (r)
=(1−λ)V
A(r
A)+λV
B(r
B)
(4.86)
rA
= (ασ
6Aλ
2+r6 )
16(4.87)
B.3
.C
om
pu
tatio
no
fthe
1.0
/sqrtfu
nctio
n.
16
1
Note
thatthis
loopprovides
much
lessoptim
izationthan
thew
aterloop,
butit
isslightly
betterthan
thedefaultroutine.
The
gainof
theseim
plementations
isthat
thereare
more
floatingpoint
operationsin
asingle
loop,w
hichim
pliesthat
some
compilers
canschedule
thecode
better.H
owever,
itturns
outthat
evensom
eofthe
mostadvanced
compilers
haveproblem
sw
ithscheduling,im
plyingthatm
anualtw
eakingis
necessaryto
getoptim
umperform
ance.T
hism
ayinclude
comm
on-subexpressionelim
ination,orm
ovingcode
around.
B.2.2
Fortran
Code
Unfortunately,F
ortrancom
pilersare
stillbetterthan
C-com
pilers,form
ostmachines
anyway.
For
some
machines
(e.g.SG
IPow
erC
hallenge)the
differencem
aybe
upto
afactor
of3,in
thecase
ofvectorcom
putersthis
may
beeven
larger.T
herefore,some
oftheroutines
thattakeup
alotof
computer
time
havebeen
translatedinto
Fortran
andeven
assembly
codefor
IntelandA
MD
x86processors.
Inm
ostcases,the
Fortran
orassem
blyloops
shouldbe
selectedautom
aticallyby
theconfigure
scriptwhen
appropriate,butyoucan
alsotw
eakthis
bysetting
optionsto
theconfigure
script.
B.3
Com
putationofthe
1.0/sqrtfunction.
B.3.1
Introduction.
The
GR
OM
AC
Sprojectstarted
with
thedevelopm
entofa1/ √
xprocessor
which
calculates
Y(x)
=1√x
(B.25)
As
theprojectcontinued,the
Inteli860
processorw
asused
toim
plementG
RO
MA
CS
,which
nowturned
intoalm
ostafullsoftw
areproject.
The1/ √
xprocessor
was
implem
entedusing
aN
ewton-
Raphson
iterationschem
efor
onestep.
For
thisit
neededlookup
tablesto
providethe
initialapproxim
ation.T
he1/ √x
functionm
akesitpossible
touse
two
almostindependenttables
forthe
exponentseedand
thefraction
seedw
iththe
IEE
Efloating
pointrepresentation.
B.3.2
General
According
to[76]
the1/ √
xcan
becalculated
usingthe
New
ton-Raphson
iterationschem
e.T
heinverse
functionis
X(y)
=1y2
(B.26)
So
insteadofcalculating
Y(a)
=q
(B.27)
theequation
X(q)−
a=
0(B
.28)
16
0A
pp
en
dix
B.
So
me
imp
lem
en
tatio
nd
eta
ils
B.1
.5V
irial
from
Sha
ke.
An
impo
rtan
tcon
trib
utio
nto
the
viria
lcom
esfr
omsh
ake.
Sat
isfy
ing
the
cons
trai
nts
afo
rce
Gis
exer
ted
onth
epa
rtic
les
shak
en.
Ifth
isfo
rce
does
not
com
eou
tof
the
algo
rithm
(as
inst
anda
rdsh
ake)
itca
nbe
calc
ulat
edaf
terw
ards
(whe
nus
ing
lea
p-f
rog)
by:
∆r
i=
ri(t+
∆t)−
[ri(t)
+v
i(t−
∆t 2)∆t+
Fi
mi∆t2
](B
.22)
Gi
=m
i∆r
i
∆t2
(B.2
3)
but
this
does
not
help
usin
the
gene
ralc
ase.
Onl
yw
hen
nope
riodi
city
isne
eded
(like
inrig
idw
ater
)th
isca
nbe
used
,oth
erw
ise
we
mus
tadd
the
viria
lcal
cula
tion
inth
ein
ner
loop
ofsh
ake.
Whe
nit
isap
plic
able
the
viria
lcan
beca
lcul
ated
inth
esi
ngle
sum
way
:
Ξ=
−1 2
Nc ∑ i
ri⊗
Fi
(B.2
4)
whe
reN
cis
the
num
ber
ofco
nstr
aine
dat
oms.
B.2
Opt
imiz
atio
ns
Her
ew
ede
scrib
eso
me
ofth
eal
gorit
hmic
optim
izat
ions
used
inG
RO
MA
CS
,ap
art
from
par-
alle
lism
.O
neof
thes
e,th
eim
plem
enta
tion
ofth
e1.
0/sq
rt(x
)fu
nctio
nis
trea
ted
sepa
rate
lyin
sec.
B.3
.T
hem
osti
mpo
rtan
toth
erop
timiz
atio
nsar
ede
scrib
edbe
low
.
B.2
.1In
ner
Loop
sfo
rW
ater
GR
OM
AC
Sus
ers
spec
iali
nner
loop
toca
lcul
ate
non-
bond
edin
tera
ctio
nsfo
rwat
erm
olec
ules
with
othe
rat
oms,
and
yeta
noth
erse
tofl
oops
for
inte
ract
ions
betw
een
pairs
ofw
ater
mol
ecul
es.
Thi
sve
ryop
timiz
edlo
opas
sum
esa
wat
erm
odel
sim
ilar
toS
PC
[48
],i.e
.:
1.T
here
are
thre
eat
oms
inth
em
olec
ule.
2.T
hefir
stat
omha
sLe
nnar
d-Jo
nes
(sec
.4.
1.1)
and
coul
omb
(sec
.4.1.
3)in
tera
ctio
ns.
3.A
tom
stw
oan
dth
ree
have
only
coul
omb
inte
ract
ions
,and
equa
lcha
rges
.
The
loop
also
wor
ksfo
rth
eS
PC
/E[
75]
and
TIP
3P[42
]w
ater
mod
els.
For
mor
eco
mpl
icat
edm
olec
ules
ther
eis
age
nera
lsol
vent
loop
assu
min
g(n
ote
the
orde
r):
1.A
tth
ebe
ginn
ing
ofth
em
olec
ule
topo
logy
ther
eis
anar
bitr
ary
num
ber
ofat
oms
with
Lenn
ard-
Jone
san
dco
ulom
bin
tera
ctio
ns.
2.T
hen
we
have
anar
bitr
ary
num
ber
ofat
oms
with
coul
omb
inte
ract
ions
only
.
3.A
ndfin
ally
ther
eca
nbe
anar
bitr
ary
num
bero
fato
ms
with
Lenn
ard-
Jone
sin
tera
ctio
nson
ly.
4.4
.M
eth
od
s6
9
i+1
i+3
ii+
2i+
4
Fig
ure
4.15
:A
tom
sal
ong
anal
kane
chai
n.
r B=( ασ
6 B(1−λ)2
+r6)1 6
(4.8
8)
whe
reV
Aan
dV
Bar
eth
eno
rmal
’har
dco
re’V
ande
rW
aals
orE
lect
rost
atic
pote
ntia
lsin
stat
eA
(λ=
0)an
dst
ate
B(λ
=1)
resp
ectiv
ely,α
isth
eso
ft-co
repa
ram
eter
,whi
chm
ainl
yco
ntro
lsth
ehe
ight
ofth
epo
tent
iala
roun
dr=
0,σ
isth
era
dius
ofth
ein
tera
ctio
n,w
hich
is(C12/C
6)1
/6
ora
pred
efine
dva
lue
whe
nC6
orC
12
isze
ro.
For
inte
rmed
iateλ
,r A
andr B
alte
rth
ein
tera
ctio
nsve
rylit
tlew
henr>α
1/6σ
and
they
quic
kly
switc
hth
eso
ft-co
rein
tera
ctio
nto
anal
mos
tcon
stan
tva
lue
whe
nrbe
com
essm
alle
r(F
ig.4.14
).T
hefo
rce
is:
Fsc
(r)
=−∂V
sc(r
)∂r
=(1−λ)F
A(r
A)( r r A
) 5 +λF
B(r
B)( r r B
) 5(4
.89)
whe
reF
Aan
dF
Bar
eth
e’h
ard
core
’for
ces.
The
cont
ribut
ion
toth
ede
rivat
ive
ofth
efr
eeen
ergy
is: ∂V
sc(r
)∂λ
=−V
A(r
A)+V
B(r
B)+
1 3αλ(1−λ)( −
FA(r
A)σ
6 Ar−
5A
+F
B(r
B)σ
6 Br−
5B
) (4.9
0)
4.4
Met
hods
4.4.
1E
xclu
sion
san
d1-
4In
tera
ctio
ns.
Ato
ms
with
ina
mol
ecul
eth
atar
ecl
ose
byin
the
chai
n,i.e
.at
oms
that
are
cova
lent
lybo
nded
,or
linke
dby
one
resp
ectiv
ely
two
atom
sar
eso
-cal
led
first
ne
igh
bo
rs,
seco
nd
ne
igh
bo
rsand
third
ne
igh
bo
rs,(s
eeF
ig.4
.15)
.S
ince
the
inte
ract
ions
ofat
omiw
ithi+
1
and
the
inte
ract
ion
ofat
omi
with
atom
i+2
are
mai
nly
quan
tum
mec
hani
cal,
they
can
not
bem
odel
edby
aLe
nnar
d-Jo
nes
pote
ntia
l.In
stea
dit
isas
sum
edth
atth
ese
inte
ract
ions
are
adeq
uate
lym
odel
edby
aha
rmon
icbo
ndte
rmor
cons
trai
nt(
i,i+
1)an
da
harm
onic
angl
ete
rm(
i,i+
2).
The
first
and
seco
ndne
ighb
ors
(ato
ms
i+1a
ndi+
2)ar
eth
eref
oree
xclu
de
dfro
mth
eLe
nnar
d-Jo
nes
inte
ract
ion
listo
fato
mi;a
tom
si+
1an
di+
2ar
eca
llede
xclu
sio
nso
fato
mi.
For
third
neig
hbor
sth
eno
rmal
Lenn
ard-
Jone
sre
puls
ion
isso
met
imes
still
too
stro
ng,w
hich
mea
nsth
atw
hen
appl
ied
toa
mol
ecul
eth
em
olec
ule
wou
ldde
form
orbr
eak
due
toth
ein
tern
alst
rain
.T
his
ises
peci
ally
the
case
for
Car
bon-
Car
bon
inte
ract
ions
ina
cis-
conf
orm
atio
n(e
.g.ci
s-bu
tane
).T
here
fore
for
som
eof
thes
ein
tera
ctio
nsth
eLe
nnar
d-Jo
nes
repu
lsio
nha
sbe
enre
duce
din
the
GR
OM
OS
forc
efie
ld,w
hich
isim
plem
ente
dby
keep
ing
ase
para
telis
tof1
-4an
dno
rmal
Lenn
ard-
Jone
spa
ram
eter
s.In
othe
rfor
cefie
lds,
such
asO
PLS
[50
],th
est
anda
rdLe
nnar
d-Jo
nes
para
met
ers
are
redu
ced
bya
fact
orof
two,
buti
nth
atca
seal
soth
edi
sper
sion
(r−
6)a
ndth
eco
ulom
bin
tera
ctio
nar
esc
aled
.G
RO
MA
CS
can
use
eith
erof
thes
em
etho
ds.
70
Ch
ap
ter
4.
Force
field
s
4.4.2C
hargeG
roups.
Inprinciple
theforce
calculationin
MD
isanO
(N2)
problem.
Therefore
we
applya
cut-offfor
non-bondedforce
(NB
F)
calculations:only
theparticles
within
acertain
distanceof
eachother
areinteracting.
This
reducesthe
costtoO
(N)
(typically100
Nto
200N
)of
theN
BF.
Italso
introducesan
error,which
is,inm
ostcases,acceptable,exceptwhen
applyingthe
cut-offimplies
thecreation
ofcharges,inw
hichcase
youshould
considerusing
thelattice
summ
ethodsprovided
byG
RO
MA
CS
.
Consider
aw
aterm
oleculeinteracting
with
anotheratom
.W
henw
ew
ouldapply
thecut-offon
anatom
-atombasis
we
might
includethe
atom-O
xygeninteraction
(with
acharge
of-0.82)
without
thecom
pensatingcharge
oftheH
ydrogensand
soinduce
alarge
dipolem
omentover
thesystem
.T
hereforew
ehave
tokeep
groupsof
atoms
with
totalcharge
0together,
theso-called
cha
rgeg
rou
ps.
4.4.3Treatm
entofcut-offs
GR
OM
AC
Sis
quiteflexible
intreating
cut-offs,w
hichim
pliesthere
canbe
quitea
number
ofparam
etersto
set.T
heseparam
etersare
setin
theinput
filefor
grompp.
There
aretw
osort
ofparam
etersthat
affectthe
cut-offinteractions;
youcan
selectw
hichtype
ofinteraction
touse
ineach
case,andw
hichcut-offs
shouldbe
usedin
theneighborsearching.
For
bothC
oulomb
andvan
derW
aalsinteractions
thereare
interactiontype
selectors(term
edvd
wtyp
eand
cou
lom
btyp
e)
andtw
oparam
eters,for
atotal
ofsix
nonbondedinteraction
parameters.
See
sec.7.3.1
fora
complete
descriptionofthese
parameters.
The
neighborsearching
(NS
)can
beperform
edusing
asingle-range,
ora
twin-range
approach.S
incethe
former
ism
erelya
specialcaseofthe
latterw
ew
illdiscussthe
more
generaltwin-range.
Inthis
caseN
Sis
describedby
two
radiirlist
andm
ax(rcou
lom
b,rvd
w).
Usually
onebuilds
theneighbor
listevery10
time
stepsor
every20
fs(param
etern
stlist).
Inthe
neighborlistall
interactionpairs
thatfallw
ithinrlistare
stored.F
urthermore,
theinteractions
between
pairsthatdo
notfallwithinrlist
butdofallw
ithinand
max(rco
ulo
mb
,rvdw
)arecom
putedduring
NS
,andthe
forcesand
energyare
storedseparately,and
addedto
short-rangeforces
ateverytim
estep
between
successiveN
S.Ifrlist
=m
ax(rcou
lom
b,rvd
w)
noforces
areevaluated
duringneighbor
listgeneration.T
hevirialis
calculatedfrom
thesum
oftheshort-
andlong-range
forces.T
hism
eansthat
thevirialcan
beslightly
asymm
etricalatnon-N
Ssteps.
Insingle
precisionthe
virialisalm
ostalways
asymm
etrical,becausethe
off-diagonalelements
areaboutas
largeas
eachelem
entin
thesum
.In
most
casesthis
isnot
reallya
problem,
sincethe
fluctuationsin
devirial
canbe
2orders
ofmagnitude
largerthan
theaverage.
Except
forthe
plaincut-off,
allof
theinteraction
functionsin
Table4.2
requirethat
neighborsearching
isdone
with
alarger
radiusthan
therc
specifiedfor
thefunctionalform
,becauseofthe
useof
chargegroups.
The
extraradius
istypically
ofthe
orderof
0.25nm
(roughlythe
largestdistance
between
two
atoms
ina
chargegroup
plusthe
distancea
chargegroup
candiffuse
within
neighborlistupdates).
B.1
.S
ing
leS
um
Viria
linG
RO
MA
CS
.1
59
The
algorithmto
generatesuch
alistcan
bederived
fromgraph
theory,consideringeach
particlein
am
oleculeas
abead
ina
graph,thebonds
asedges.
1representthe
bondsand
atoms
asbidirectionalgraph
2m
akeallatom
sw
hite
3m
akeone
ofthew
hiteatom
sblack
(atomi)andputitin
thecentralbox
4m
akeallofthe
neighborsofithatare
currentlyw
hite,grey
5pick
oneofthe
greyatom
s(atomj),give
itthecorrectperiodicity
with
respecttoany
ofitsblack
neighborsand
make
itblack
6m
akeallofthe
neighborsofjthatare
currentlyw
hite,grey
7ifany
greyatom
remains,goto
[5]
8ifany
white
atomrem
ains,goto[3]
Using
thisalgorithm
we
can
•optim
izethe
bondedforce
calculationas
wellas
shake
•calculate
thevirialfrom
thebonded
forcesin
thesingle
sumw
ayagain
Find
arepresentation
ofthebonds
asa
bidirectionalgraph.
B.1.4
Virialfrom
CovalentB
onds.
The
covalentbondforce
givesa
contributionto
thevirial,w
ehave
b=
‖r
nij ‖(B
.15)
Vb
=12k
b (b−b0 )
2(B
.16)
Fi
=−∇V
b(B
.17)
=k
b (b−b0 ) r
nij
b(B
.18)
Fj
=−
Fi
(B.19)
The
virialcontributionfrom
thebonds
thenis
Ξb
=−
12(r
ni⊗
Fi
+r
j ⊗F
j )(B
.20)
=−
12r
nij ⊗F
i(B
.21)
15
8A
pp
en
dix
B.
So
me
imp
lem
en
tatio
nd
eta
ils
Ina
tric
linic
syst
emth
ere
are
27po
ssib
leim
ages
ofi,
whe
ntr
unca
ted
octa
hedr
onis
used
ther
ear
e15
poss
ible
imag
es.
B.1
.2V
irial
from
non-
bond
edfo
rces
.
Her
eth
ede
rivat
ion
for
the
sing
lesu
mvi
riali
nth
en
on
-bo
nd
ed
forc
erout
ine
isgi
ven.i6=j
inal
lfo
rmul
aebe
low
.
Ξ=
−1 2
N ∑ i<j
rn ij⊗
Fij
(B.5
)
=−
1 4
N ∑ i=1
N ∑ j=1
(ri+δ i−
rj)⊗
Fij
(B.6
)
=−
1 4
N ∑ i=1
N ∑ j=1
(ri+δ i
)⊗
Fij−
rj⊗
Fij
(B.7
)
=−
1 4
N ∑ i=1
N ∑ j=1
(ri+δ i
)⊗
Fij−
N ∑ i=1
N ∑ j=1
rj⊗
Fij
(B
.8)
=−
1 4
N ∑ i=1
(ri+δ i
)⊗
N ∑ j=1
Fij−
N ∑ j=1
rj⊗
N ∑ i=1
Fij
(B
.9)
=−
1 4
N ∑ i=1
(ri+δ i
)⊗
Fi
+N ∑ j=
1
rj⊗
Fj
(B
.10)
=−
1 4
( 2N ∑ i=
1
ri⊗
Fi+
N ∑ i=1
δ i⊗
Fi)
(B.1
1)
Inth
ese
form
ulae
we
intr
oduc
ed
Fi
=N ∑ j=
1
Fij
(B.1
2)
Fj
=N ∑ i=
1
Fji
(B.1
3)
whi
chis
the
tota
lfor
ceoni
resp
.j.
Bec
ause
we
use
New
ton’
sth
irdla
w
Fij
=−
Fji
(B.1
4)
we
mus
tin
the
impl
emen
tatio
ndo
uble
the
term
cont
aini
ngth
esh
iftδ i
.
B.1
.3T
hein
tram
olec
ular
shift
(mol
-shi
ft).
For
the
bond
ed-f
orce
san
dsh
ake
itis
poss
ible
tom
ake
am
ol-sh
iftlis
t,in
whi
chth
epe
riodi
city
isst
ored
.W
esi
mpl
eha
vean
arra
ym
shift
inw
hich
for
each
atom
anin
dex
inth
eshift
vec
arra
yis
stor
ed.
4.5
.D
um
my
ato
ms.
71
Type
Par
amet
ers
Cou
lom
bP
lain
cut-
off
r c,ε
r
Rea
ctio
nfie
ldr c
,εrf
Shi
ftfu
nctio
nr 1
,rc,ε
r
Sw
itch
func
tion
r 1,r
c,ε
r
VdW
Pla
incu
t-of
fr c
Shi
ftfu
nctio
nr 1
,rc
Sw
itch
func
tion
r 1,r
c
Tabl
e4.
2:P
aram
eter
sfo
rth
edi
ffere
ntfu
nctio
nalf
orm
sof
the
non-
bond
edin
tera
ctio
ns.
4.5
Dum
my
atom
s.
Dum
my
atom
sca
nbe
used
inG
RO
MA
CS
ina
num
ber
ofw
ays.
We
writ
eth
epo
sitio
nof
the
dum
my
part
icle
rd
asa
func
tion
ofth
epo
sitio
nsof
othe
rpa
rtic
les
ri:
rd
=f(r
1..r
n).
The
dum
my,
whi
chm
ayca
rry
char
ge,o
rca
nbe
invo
lved
inot
her
inte
ract
ions
can
now
beus
edin
the
forc
eca
lcul
atio
n.T
hefo
rce
actin
gon
the
dum
my
part
icle
mus
tbe
redi
strib
uted
over
the
atom
sin
aco
nsis
tent
way
.A
good
way
todo
this
can
befo
und
inre
f.[
53].
We
can
writ
eth
epo
tent
ial
ener
gyas
V=V
(rd,r
1..r
n)
=V∗ (
r1..r
n)
(4.9
1)
The
forc
eon
the
part
iclei
isth
en
Fi=−∂V∗
∂r
i=−∂V
∂r
i−∂r
d
∂r
i
∂V
∂r
d=
Fdir
ect
i+
F′ i
(4.9
2)
the
first
term
ofw
hich
isth
eno
rmal
forc
e.T
hese
cond
term
isth
efo
rce
onpa
rtic
lei
due
toth
edu
mm
ypa
rtic
le,w
hich
can
bew
ritte
nin
tens
orno
tatio
n:
F′ i=
∂x
d
∂x
i
∂y d∂x
i
∂z d∂x
i∂x
d
∂y i
∂y d∂y i
∂z d∂y i
∂x
d
∂z i
∂y d∂z i
∂z d∂z i
Fd
(4.9
3)
whe
reF
dis
the
forc
eon
the
dum
my
part
icle
andx
d,y
dan
dz d
are
the
coor
dina
tes
ofth
edu
mm
ypa
rtic
le.
Inth
isw
ayth
eto
talf
orce
and
the
tota
ltor
que
are
cons
erve
d[
53].
As
afu
rthe
rno
te,t
heco
mpu
tatio
nof
the
viria
l(eq
n.3.18
)vi
riali
sno
n-tr
ivia
lwhe
ndu
mm
yat
oms
are
used
.S
ince
the
viria
linv
olve
sa
sum
mat
ion
over
allt
heat
oms
(rat
hert
han
virt
ualp
artic
les)
the
forc
esm
ostb
ere
dist
ribut
edfr
omth
edu
mm
ies
toth
eat
oms
(usi
ngeq
n.4.
93)
be
fore
com
puta
tion
ofth
evi
rial.
Inso
me
spec
ial
case
sw
here
the
forc
eson
the
atom
sca
nbe
writ
ten
asa
linea
rco
mbi
natio
nof
the
forc
eson
the
dum
mie
s(t
ypes
2an
d3
belo
w)
ther
eis
nodi
ffere
nce
betw
een
com
putin
gth
evi
rial
befo
rean
daf
ter
the
redi
strib
utio
nof
forc
es.
How
ever
,in
the
gene
ralc
ase
redi
strib
utio
nsh
ould
bedo
nefir
st.
The
rear
esi
xw
ays
toco
nstr
uctd
umm
ies
from
surr
ound
ing
atom
sin
GR
OM
AC
S,
whi
chw
eca
t-eg
oriz
eba
sed
onth
enu
mbe
rof
cons
truc
ting
atom
s.N
ote
that
alld
umm
ies
type
sm
entio
ned
can
72
Ch
ap
ter
4.
Force
field
s
����� ���������� �������������������������� ���������� ����� | |
3fd
| || |
1-aab
a
1-a
a
��������������
����������
������
����
23fad
3ou
t4fd c
b
3
��������������
����������
θ
d
� � � �
����������
������������������� �����
������������������� �����
������������������� �����
��������������
����������
����������
����������
����������
����������
��������������
����������
����������
����������
Figure
4.16:T
hesix
differenttypesofdum
my
atomconstruction
inG
RO
MA
CS
,theconstructing
atoms
areshow
nas
blackcircles,the
dumm
yatom
sin
grey.
beconstructed
fromtypes
3fd(norm
alized,in-plane)
and3out
(non-normalized,
outof
plane).H
owever,
theam
ountof
computation
involvedincreases
sharplyalong
thislist,
soit
isstrongly
recomm
endedto
always
usethe
firstdumm
ytype
thatwillbe
sufficientfora
certainpurpose.
An
overviewofthe
dumm
yconstructions
isgiven
inF
ig.4.16.
2.A
sa
linearcom
binationoftw
oatom
s(F
ig.4.16
2):
rd
=r
i +ar
ij(4.94)
inthis
casethe
dumm
yis
onthe
linethrough
atoms
iand
j.T
heforce
onparticlesi
andj
dueto
theforce
onthe
dumm
ycan
becom
putedas:
F′i
=(1−a)F
d
F′j
=a
Fd
(4.95)
3.A
sa
linearcom
binationofthree
atoms
(Fig.4.16
3):
rd
=r
i +ar
ij+br
ik(4.96)
inthis
casethe
dumm
yis
inthe
planeofthe
otherthree
particles.T
heforce
onparticlesi,j
andk
dueto
theforce
onthe
dumm
ycan
becom
putedas:
F′i
=(1−a−b)F
d
F′j
=a
Fd
F′k
=bF
d
(4.97)
3fd.In
theplane
ofthreeatom
s,with
afixed
distance(F
ig.4.16
3fd):
rd
=r
i +b
rij
+ar
jk
|rij
+ar
jk |(4.98)
inthis
casethe
dumm
yis
inthe
planeofthe
otherthree
particlesata
distanceof
|b|fromi.
The
forceon
particlesi,j
andk
dueto
theforce
onthe
dumm
ycan
becom
putedas:
F′i
=F
d −γ(F
d −p)
F′j
=(1−a)γ(F
d −p)
F′k
=aγ(F
d −p)
where
γ=
b
|rij
+ar
jk |
p=
rid ·F
d
rid ·r
idr
id
(4.99)
Appendix
B
Som
eim
plementation
details
Inthis
chapterw
ew
illpresentsom
eim
plementation
details.T
hisis
farfrom
complete,
butw
edeem
editnecessary
toclarify
some
thingsthatw
ouldotherw
isebe
hardto
understand.
B.1
Single
Sum
Virialin
GR
OM
AC
S.
The
virialΞcan
bew
rittenin
fulltensorform
as:
Ξ=
−12
N∑i<j
rij ⊗
Fij
(B.1)
where⊗
denotesthed
irect
pro
du
ctoftw
ovectors 1.
When
thisis
computed
inthe
innerloop
ofan
MD
program9
multiplications
and9
additionsare
needed2.
Here
itisshow
nhow
itispossible
toextractthe
virialcalculationfrom
theinner
loop[
74].
B.1.1
Virial.
Ina
systemw
ithP
eriodicB
oundaryC
onditions,theperiodicity
mustbe
takeninto
accountforthe
virial:
Ξ=
−12
N∑i<j
rnij ⊗
Fij
(B.2)
wherer
nijdenotes
thedistance
vectorofthen
ea
restim
ageofatomi
fromatom
j.In
thisdefinition
we
addash
iftvecto
rδi
tothe
positionvectorr
iofatom
i.T
hedifference
vectorrnij
isthus
equalto:
rnij
=r
i +δi −
rj
(B.3)
orin
shorthand:r
nij=
rni−
rj
(B.4)
1(u⊗
v)α
β=
uαv
β2T
hecalculation
ofLennard-Jonesand
Coulom
bforces
isabout50
floatingpointoperations.
15
6A
pp
en
dix
A.
Tech
nic
alD
eta
ils
2.IA
MC
OO
L,if
this
isex
plic
itly
sett
oN
Oyo
urG
RO
MA
CS
life
will
bedu
llan
dbo
ring.
(i.e.
,no
cool
quot
es).
3.W
HE
RE,w
hen
setp
rintd
ebug
ging
info
onlin
enu
mbe
rs.
4.L
OG
BU
FS,
the
size
ofth
ebu
ffer
for
file
I/O.W
hen
sett
o0,
allfi
leI/O
will
beun
buffe
red
and
ther
efor
eve
rysl
ow.
Thi
sca
nbe
hand
yfo
rde
bugg
ing
purp
oses
,bec
ause
iten
sure
sth
atal
lfile
sar
eal
way
sto
tally
up-t
o-da
te.
5.G
MX
NP
RI,f
orS
GIs
yste
ms
only
.W
hen
set,
give
sth
ede
faul
tnon
-deg
radi
ngpr
iorit
y(n
pri)
form
dru
n,n
mru
n,g
cova
ran
dgn
me
ig,e
.g.s
ettin
gse
ten
vG
MX
NP
RI
25
0ca
uses
allr
uns
tobe
perf
orm
edat
near
-low
estp
riorit
yby
defa
ult.
6.G
MXV
IEW
XP
M,G
MXV
IEW
XV
G,G
MXV
IEW
EP
San
dGM
XV
IEW
PD
B,co
mm
ands
used
toau
tom
atic
ally
view
resp
..xvg
,.xp
m,.
ep
san
d.p
db
file
type
s.D
efau
lttox
v,x
mg
r,g
ho
stvi
ew
and
rasm
ol
.S
etto
empt
yto
disa
ble
auto
mat
icvi
ewin
gof
apa
rtic
ular
file
type
.T
heco
mm
and
will
befo
rked
offa
ndru
nin
the
back
grou
ndat
the
sam
epr
iorit
yas
the
GR
OM
AC
Sto
ol(w
hich
mig
htno
tbe
wha
tyo
uw
ant)
.B
eca
refu
lnot
tous
ea
com
man
dw
hich
bloc
ksth
ete
rmin
al(e
.g.vi
),si
nce
mul
tiple
inst
ance
sm
ight
beru
n.
Som
eot
her
envi
ronm
entv
aria
bles
are
spec
ific
toon
epr
ogra
m,s
uch
asT
OTA
Lfo
rth
ed
osh
iftpr
ogra
m,a
ndD
SP
Pfo
rth
edod
ssp
prog
ram
.
4.5
.D
um
my
ato
ms.
73
3fad
.In
the
plan
eof
thre
eat
oms,
with
afix
edan
gle
and
dist
ance
(Fig
.4.
163f
ad):
rd
=r
i+d
cosθ
rij
|rij|+
dsi
nθ
r⊥
|r⊥|
whe
rer⊥
=r
jk−
rij·r
jk
rij·r
ijr
ij(4
.100
)
inth
isca
seth
edu
mm
yis
inth
epl
ane
ofth
eot
her
thre
epa
rtic
les
ata
dist
ance
of|d|f
romi
atan
angl
eofα
with
rij
.A
tomk
defin
esth
epl
ane
and
the
dire
ctio
nof
the
angl
e.N
ote
that
inth
isca
seb
andα
mus
tbe
spec
ified
inst
ead
ofaan
db
(see
also
sec.5
.2.2
).T
hefo
rce
onpa
rtic
lesi
,jan
dk
due
toth
efo
rce
onth
edu
mm
yca
nbe
com
pute
das
(with
r⊥
asde
fined
ineq
n.4.
100)
:
F′ i
=F
d−
dco
sθ|r
ij|
F1
+d
sinθ
|r⊥|
( rij·r
jk
rij·r
ijF
2+
F3
)
F′ j
=d
cosθ
|rij|
F1
−d
sinθ
|r⊥|
( F2+
rij·r
jk
rij·r
ijF
2+
F3
)
F′ k
=d
sinθ
|r⊥|
F2
whe
reF
1=
Fd−
rij·F
d
rij·r
ijr
ij,
F2
=F
1−
r⊥·F
d
r⊥·r
⊥r⊥
and
F3
=r
ij·F
d
rij·r
ijr⊥ (4.1
01)
3out
.A
sa
non-
linea
rco
mbi
natio
nof
thre
eat
oms,
outo
fpla
ne(F
ig.
4.16
3out
):
rd
=r
i+ar
ij+br
ik+c(
rij×
rik
)(4
.102
)
this
enab
les
the
cons
truc
tion
ofdu
mm
ies
outo
fthe
plan
eof
the
othe
rat
oms.
The
forc
eon
part
icle
si,j
andk
due
toth
efo
rce
onth
edu
mm
yca
nbe
com
pute
das
:
F′ j
=
a
−cz i
kcy i
k
cz i
ka
−cx
ik
−cy i
kcx
ika
F d
F′ k
=
b
cz i
j−cy i
j
−cz i
jb
cx
ij
cy i
j−cx
ijb
F dF′ i
=F
d−
F′ j−
F′ k
(4.1
03)
4fd.
Fro
mfo
urat
oms,
with
afix
eddi
stan
ce(F
ig.
4.16
4fd)
:
rd
=r
i+c
rij
+ar
jk+br
jl
|rij
+ar
jk+br
jl|
(4.1
04)
inth
isca
seth
edu
mm
yis
ata
dist
ance
of|c|f
romi.
The
forc
eon
part
icle
si,j,k
andl
due
toth
efo
rce
onth
edu
mm
yca
nbe
com
pute
das
:
F′ i
=F
d−γ(F
d−
p)
F′ j
=(1−a−b)γ(F
d−
p)
F′ k
=aγ(F
d−
p)
F′ l
=bγ
(Fd−
p)
whe
re
γ=
c
|rij
+ar
jk+br
jl|
p=
rid·F
d
rid·r
idr
id
(4.1
05)
74
Ch
ap
ter
4.
Force
field
s
4.6Long
Range
Electrostatics
4.6.1E
wald
summ
ation
The
totalelectrostaticenergy
ofN
particlesand
theperiodic
images
aregiven
by
V=f2 ∑n
x ∑ny ∑n
z ∗
N∑i
N∑j
qi q
j
rij,n
.(4.106)
(nx ,n
y ,nz )
=n
isthe
boxindex
vector,and
thestar
indicatesthat
terms
with
i=j
shouldbe
omitted
when(n
x ,ny ,n
z )=
(0,0,0).
The
distancerij,n
isthe
realdistancebetw
eenthe
chargesand
notthem
inimum
-image.
This
sumis
conditionallyconvergent,butvery
slow.
Ew
aldsum
mation
was
firstintroduced
asa
method
tocalculate
long-rangeinteractions
ofthe
periodicim
agesin
crystals[
54].T
heidea
isto
convertthesingle
slowly
convergingsum
eqn.4.106
intotw
ofastconverging
terms
anda
constantterm:
V=
Vdir
+V
rec +
V0
(4.107)
Vdir
=f2
N∑i,j ∑nx ∑n
y ∑nz ∗qi q
j erfc(βrij,n )
rij,n
(4.108)
Vrec
=f
2πV
N∑i,j
qi q
j ∑mx ∑m
y ∑mz ∗
exp (−(π
m/β
)2+
2πim
·(ri −
rj ) )
m2
(4.109)
V0
=−fβ
√π
N∑i
q2i ,
(4.110)
where
βis
aparam
eterthat
determines
therelative
weight
ofthe
directand
reciprocalsums
andm
=(m
x ,my ,m
z ).In
thisw
ayw
ecan
usea
shortcut-off
(ofthe
orderof
1nm
)in
thedirect
spacesum
anda
shortcut-offinthe
reciprocalspacesum
(e.g.10w
avevectors
ineach
direction).U
nfortunately,the
computationalcostofthe
reciprocalpartofthesum
increasesas
N2
(orN
3/2
with
aslightly
betteralgorithm
)and
itistherefore
notrealisticto
usefor
anylarge
systems.
Using
Ew
ald
Don’tuse
Ew
aldunless
youare
absolutelysure
thisis
whatyou
want-foralm
ostallcasesthe
PM
Em
ethodbelow
willperform
much
better.If
youstillw
antto
employ
classicalEw
aldsum
mation
enterthis
inyour.m
dp
file,iftheside
ofyourbox
isabout3nm
:
cou
lom
btyp
e=
Ew
ald
rvdw
=0
.9rlist
=0
.9rco
ulo
mb
=0
.9fo
urie
rspa
cing
=0
.6e
wa
ld_
rtol
=1
e-5
A.4
.E
nviron
me
ntV
aria
ble
s1
55
A.3.1
Multi-processor
Optim
ization
Ifyou
want
to,you
couldw
riteyour
own
optimized
comm
unication(perhaps
usingspecific
li-braries
foryour
hardware)
insteadof
MP
I.T
hisshould
neverbe
necessaryfor
normal
use(w
ehaven’theard
ofam
oderncom
puterwhere
itisn’tpossibleto
runM
PI),butifyou
absolutelyw
antto
doit,here
aresom
eclues.
The
interfacebetw
eenthe
comm
unicationroutines
andthe
restof
theG
RO
MA
CS
systemis
de-scribed
inthe
file$G
MX
HO
ME
/src/inclu
de
/ne
two
rk.hW
ew
illgivea
shortdescriptionof
thedifferentroutines
below.
externvoid
gmx
tx(intpid,void*buf,intbufsize);
This
routine,w
hencalled
with
thedestination
processornum
ber,a
pointerto
a(byte
ori-ented)transferbuffer,and
thesize
ofthebufferw
illsendthe
buffertothe
indicatedprocessor
(inour
casealw
aysthe
neighboringprocessor).
The
routinedoesnotw
aituntilthetransfer
isfinished.
externvoid
gmx
txw
ait(intpid);T
hisroutine
waits
untiltheprevious,or
theongoing
transmission
isfinished.
externvoid
gmx
txs(intpid,void*buf,intbufsize);
This
routineim
plements
asynchronous
sendby
callingthe
a-synchronousroutine
andthen
thew
ait.Itm
ightcome
inhandy
tocode
thisdifferently.
externvoid
gmx
rx(intpid,void*buf,intbufsize);
externvoid
gmx
rxw
ait(intpid);
externvoid
gmx
rxs(intpid,void*buf,intbufsize);
The
verysam
eroutines
forreceiving
abuffer
andw
aitinguntilthe
receptionis
finished.
externvoid
gmx
init(intpid,intnprocs);T
hisroutine
initializesthe
differentdevicesneeded
todo
thecom
munication.
Ingeneralit
setsup
thecom
munication
hardware
(ifitisaccessible)ordoes
aninitialize
calltothe
lower
levelcomm
unicationsubsystem
.
externvoid
gmx
stat(FILE
*fp,char*m
sg);W
iththis
routinew
ecan
diagnosethe
ongoingcom
munication.
Inthe
currentim
plemen-
tationit
printsthe
variouscontents
ofthe
hardware
comm
unicationregisters
ofthe
(Inteli860)
multiprocessor
boardsto
afile.
A.4
Environm
entVariables
GR
OM
AC
Sprogram
sm
aybe
influencedby
theuse
ofenvironmentvariables.
Firstofall,the
vari-ables
setinthe
GM
XR
Cfile
areessentialfor
runningand
compiling
GR
OM
AC
S.O
thervariables
are:1.D
UM
PNL,dum
pneighbor
list.Ifsetto
apositive
number
thee
ntire
neighborlistis
printedin
thelog
file(m
aybe
many
megabytes).
Mainly
fordebugging
purposes,butm
ayalso
behandy
forporting
toother
platforms.
15
4A
pp
en
dix
A.
Tech
nic
alD
eta
ils
The
ener
gies
insi
ngle
prec
isio
nar
eac
cura
teup
toth
ela
stde
cim
al,t
hela
ston
eor
two
deci
mal
sof
the
forc
esar
eno
n-si
gnifi
cant
.T
hevi
riali
sle
ssac
cura
teth
anth
efo
rces
,sin
ceth
evi
riali
son
lyon
eor
dero
fmag
nitu
dela
rger
than
the
size
ofea
chel
emen
tin
the
sum
over
alla
tom
s(s
ec.
B.1
).In
mos
tca
ses
this
isno
trea
llya
prob
lem
,si
nce
the
fluct
uatio
nsin
devi
rialc
anbe
2or
ders
ofm
agni
tude
larg
erth
anth
eav
erag
e.In
perio
dic
char
ged
syst
ems
thes
eer
rors
are
ofte
nne
glig
ible
.E
spec
ially
cut-
off’s
for
the
Cou
lom
bin
tera
ctio
nsca
use
larg
eer
rors
inth
een
ergi
es,
forc
esan
dvi
rial.
Eve
nw
hen
usin
ga
reac
tion-
field
orla
ttice
sum
met
hod
the
erro
rsar
ela
rger
than
orco
mpa
rabl
eto
the
erro
rsdu
eto
the
sing
lepr
ecis
ion.
Sin
ceM
Dis
chao
tic,
traj
ecto
ries
with
very
sim
ilar
star
ting
cond
ition
sw
illdi
verg
era
pidl
y,th
edi
verg
ence
isfa
ster
insi
ngle
prec
isio
nth
anin
doub
lepr
ecis
ion.
For
mos
tsi
mul
atio
nssi
ngle
prec
isio
nis
accu
rate
enou
gh.
Inso
me
case
sdo
uble
prec
isio
nis
re-
quire
dto
getr
easo
nabl
ere
sults
:
•no
rmal
mod
ean
alys
is,
for
the
conj
ugat
egr
adie
ntm
inim
izat
ion
and
the
calc
ulat
ion
and
di-
agon
aliz
atio
nof
the
Hes
sian
•ca
lcul
atio
nof
the
cons
trai
ntfo
rce
betw
een
two
larg
egr
oups
ofat
oms
•en
ergy
cons
erva
tion
(thi
sca
non
lybe
done
with
out
tem
pera
ture
coup
ling
and
with
out
cut-
off’s
)
A.3
Por
ting
GR
OM
AC
S
The
GR
OM
AC
Ssy
stem
isde
sign
edw
ithpo
rtab
ility
asa
maj
orde
sign
goal
.H
owev
erth
ere
are
anu
mbe
rof
thin
gsw
eas
sum
eto
bepr
esen
ton
the
syst
emG
RO
MA
CS
isbe
ing
port
edon
.W
eas
sum
eth
efo
llow
ing
feat
ures
:
1.A
UN
IX-li
keop
erat
ing
syst
em(B
SD
4.x
orS
YS
TE
MV
rev.
3or
high
er)
orU
NIX
-like
libra
ries
runn
ing
unde
re.
g.C
ygW
in
2.an
AN
SIC
com
pile
r
3.op
tiona
llya
For
tran
-77
com
pile
ror
For
tran
-90
com
pile
rfo
rfa
ster
(on
som
eco
mpu
ters
)in
ner
loop
rout
ines
4.op
tiona
llyth
eN
asm
asse
mbl
erto
use
the
asse
mbl
yin
nerlo
ops
onx8
6pr
oces
sors
.
The
rear
eso
me
addi
tiona
lfea
ture
sin
the
pack
age
that
requ
ireex
tra
stuf
fto
bepr
esen
t,bu
tit
isch
ecke
dfo
rin
the
confi
gura
tion
scrip
tand
you
will
bew
arne
dif
anyt
hing
impo
rtan
tis
mis
sing
.
Tha
t’sth
ere
quire
men
tsfo
ra
sing
lepr
oces
sor
syst
em.
Ifyo
uw
ant
toco
mpi
leG
RO
MA
CS
for
am
ultip
lepr
oces
sor
envi
ronm
ent
you
also
need
aM
PI
libra
ry(M
essa
ge-P
assi
ngIn
terf
ace)
tope
rfor
mth
epa
ralle
lcom
mun
icat
ion.
Thi
sis
alw
ays
ship
ped
with
supe
rcom
pute
rs,a
ndfo
rw
ork-
stat
ions
you
can
find
links
tofr
eeM
PI
impl
emen
tatio
nsth
roug
hth
eG
RO
MA
CS
hom
epag
eat
ww
w.g
rom
acs.
org.
4.6
.L
on
gR
an
geE
lect
rost
atic
s7
5
The
fou
rie
rsp
aci
ng
para
met
ertim
esth
ebo
xdi
men
sion
sde
term
ines
the
high
est
mag
nitu
deof
wav
eve
ctor
smx,m
y,m
zto
use
inea
chdi
rect
ion.
With
a3
nmcu
bic
box
this
exam
ple
wou
ldus
e11
wav
eve
ctor
s(f
rom−
5to
5)in
each
dire
ctio
n.T
hee
wa
ldrt
ol
para
met
eris
the
rela
tive
stre
ngth
ofth
eel
ectr
osta
ticin
tera
ctio
nat
the
cut-
off.
Dec
reas
ing
this
give
syo
ua
mor
eac
cura
tedi
rect
sum
,but
ale
ssac
cura
tere
cipr
ocal
sum
.
4.6.
2P
ME
Par
ticle
-mes
hE
wal
dis
am
etho
dpr
opos
edby
Tom
Dar
den
[55
,56]
toim
prov
eth
epe
rfor
man
ceof
the
reci
proc
alsu
m.
Inst
ead
ofdi
rect
lysu
mm
ing
wav
eve
ctor
s,th
ech
arge
sar
eas
sign
edto
agr
idus
ing
card
inal
B-s
plin
ein
terp
olat
ion.
Thi
sgr
idis
then
Fou
rier
tran
sfor
med
with
a3D
FF
Tal
gorit
hman
dth
ere
cipr
ocal
ener
gyte
rmob
tain
edby
asi
ngle
sum
over
the
grid
ink-
spac
e.
The
pote
ntia
lat
the
grid
poin
tsis
calc
ulat
edby
inve
rse
tran
sfor
mat
ion,
and
byus
ing
the
inte
rpo-
latio
nfa
ctor
sw
ege
tthe
forc
eson
each
atom
.
The
PM
Eal
gorit
hmsc
ales
asNlo
g(N
),an
dis
subs
tant
ially
fast
erth
anor
dina
ryE
wal
dsu
mm
a-tio
non
med
ium
tola
rge
syst
ems.
On
very
smal
lsys
tem
sit
mig
htst
illbe
bette
rto
use
Ew
ald
toav
oid
the
over
head
inse
tting
upgr
ids
and
tran
sfor
ms.
Usi
ngP
ME
Tous
eP
artic
le-m
esh
Ew
ald
sum
mat
ion
inG
RO
MA
CS
,spe
cify
the
follo
win
glin
esin
your
.md
pfil
e:
cou
lom
bty
pe
=P
ME
rvd
w=
0.9
rlis
t=
0.9
rco
ulo
mb
=0
.9fo
urie
rsp
aci
ng
=0
.12
pm
e_
ord
er
=4
ew
ald
_rt
ol
=1
e-5
Inth
isca
seth
efou
rie
rsp
aci
ng
para
met
erde
term
ines
the
max
imum
spac
ing
fort
heF
FT
grid
and
pm
eo
rde
rco
ntro
lsth
ein
terp
olat
ion
orde
r.U
sing
4th
orde
r(c
ubic
)in
terp
olat
ion
and
this
spac
ing
shou
ldgi
veel
ectr
osta
ticen
ergi
esac
cura
teto
abou
t5·1
0−3.
Sin
ceth
eLe
nnar
d-Jo
nes
ener
gies
are
nott
his
accu
rate
itm
ight
even
bepo
ssib
leto
incr
ease
this
spac
ing
slig
htly
.
Pre
ssur
esc
alin
gw
orks
with
PM
E,b
utbe
awar
eof
the
fact
that
anis
otro
pic
scal
ing
can
intr
oduc
ear
tifici
alor
derin
gin
som
esy
stem
s.
4.6.
3P
PP
M
The
Par
ticle
-Par
ticle
Par
ticle
-Mes
hm
etho
dsof
Hoc
kney
&E
astw
ood
can
also
beap
plie
din
GR
O-
MA
CS
for
the
trea
tmen
tofl
ong
rang
eel
ectr
osta
ticin
tera
ctio
ns[
57,5
5,58
].W
ithth
isal
gorit
hmth
ech
arge
sof
all
part
icle
sar
esp
read
over
agr
idof
dim
ensi
ons
(n
x,n
y,n
z)
usin
ga
wei
ghtin
g
76
Ch
ap
ter
4.
Force
field
s
functioncalled
thetriangle-shaped
chargeddistribution:
W(r)
=W
(x)W
(y)W
(z)
W(ξ)
= 34− (
ξh )2
|ξ|≤h2
12 (32−
|ξ|h )2
h2<|ξ|
<3h2
03h2≤|ξ|
(4.111)
where
ξ(is
x,y
orz)
isthe
distanceto
agrid
pointin
thecorresponding
dimension.
Only
the27
closestgridpoints
needto
betaken
intoaccountfor
eachcharge.
Then,
thischarge
distributionis
Fourier
transformed
usinga
3Dinverse
FF
Troutine.
InF
ourierspace
aconvolution
with
functionGis
performed:
G(k)
=g(k)ε0 k
2(4.112)
where
gis
theF
ouriertransform
ofthe
chargespread
functiong(r).
This
yieldthe
longrange
potentialφ(k)on
them
esh,w
hichcan
betransform
edusing
aforw
ardF
FT
routineinto
thereal
spacepotential.
Finally
thepotentialand
forcesare
retrievedusing
interpolation[
58].Itis
noteasyto
calculatethe
fulllong-rangevirialtensor
with
PP
PM
,butitispossible
toobtain
thetrace.
This
means
thatthesum
ofthepressure
components
iscorrect(and
thereforethe
isotropicpressure)but
notnecessarilythe
individualpressurecom
ponents!
Using
PP
PM
Touse
theP
PP
Malgorithm
inG
RO
MA
CS
,specifythe
following
linesin
your.m
dp
file:
cou
lom
btyp
e=
PP
PM
rlist=
1.0
rcou
lom
b=
0.8
5rco
ulo
mb
_sw
itch=
0.0
rvdw
=1
.0fo
urie
rspa
cing
=0
.07
5
For
detailson
thesw
itchparam
eterssee
thesection
onm
odifiedlong-range
interactionsin
thism
anual.W
henusing
PP
PM
we
recomm
endto
takeatm
ost0.075nm
pergridpoint(e.g.20
grid-points
for1.5
nm).
PP
PM
doesnot
providethe
same
accuracyas
PM
Ebut
canbe
slightlyfaster
insom
ecases.
Due
tothe
problemw
iththe
pressuretensor
youshouldn’t
useit
with
pressurecoupling.
We’re
somew
hatambivalentaboutP
PP
M,so
ifyouuse
itpleasecontactus
-otherw
iseitm
ightberem
ovedfrom
futurerelases
sow
ecan
concentrateour
effortson
PM
E.
4.6.4O
ptimizing
Fourier
transforms
Togetthe
bestpossibleperform
anceyou
shouldtry
toavoid
largeprim
enum
bersfor
griddim
en-sions.
The
FF
Tcode
usedin
GR
OM
AC
Sis
optimized
forgrid
sizesofthe
form2
a3b5
c7d11
e13f,
Appendix
A
TechnicalDetails
A.1
Installation
The
entireG
RO
MA
CS
packageis
Free
Softw
are,licensedunderthe
GN
UG
eneralPublic
License.T
hem
aindistribution
siteis
ourW
WW
serveratw
ww
.gromacs.org.
The
packageis
mainly
distributedas
sourcecode,
butwe
alsoprovide
RP
Mpackages
forLinux.
On
thehom
epage
youw
illfindallthe
information
youneed
toinstallthe
package,m
ailinglists
with
archives,andseveraladditionalonline
resourceslike
contributedtopologies,etc.
The
defaultinstallation
actionis
simply
tounpack
thesource
codeand
theissue
./con
figu
rem
ake
ma
kein
stall
The
configurationscript
shouldautom
aticallydeterm
inethe
bestoptions
foryour
platform,
andit
will
tellyou
ifanything
ism
issingon
yoursystem
.You
will
alsofind
detailedstep-by-step
installationinstructions
onthe
website.
A.2
Single
orD
oubleprecision
GR
OM
AC
Scan
becom
piledin
eithersingle
ordouble
precision.T
hedefault
choiceis
singleprecision,butitis
easyto
turnon
doubleprecision
byselecting
the--e
na
ble
-do
ub
leoption
tothe
configurationscript.
Double
precisionw
illbe0
to50%
slowerthan
singleprecision
dependingon
thearchitecture
youare
runningon.
Double
precisionw
illusesom
ewhat
more
mem
oryand
runinput,
energyand
full-precisiontrajectory
filesw
illbealm
osttw
iceas
large.N
otethat
theassem
blyloops
areonly
availablein
singleprecision;
Although
theIntel
SS
E2
instructionset
(availableon
Pentium
IVand
later)supports
doubleprecision
instructionsthe
performance
ism
uchlow
erthan
singleprecision.
Itwould
alsom
eanvery
much
extraw
orkfor
afeature
thatveryfew
peopleuse,
sow
ew
illprobably
notprovide
doubleprecision
assembly
loopsin
thefuture
either.
15
2C
ha
pte
r8
.A
na
lysi
s4
.7.
All-
hyd
roge
nfo
rce
field
77
whe
ree+f
is0
or1
and
the
othe
rex
pone
nts
arbi
trar
y.(S
eefu
rthe
rth
edo
cum
enta
tion
ofth
eF
FT
algo
rithm
sat
ww
w.ff
tw.o
rg.
Itis
also
poss
ible
toop
timiz
eth
etr
ansf
orm
sfo
rth
ecu
rren
tpro
blem
bype
rfor
min
gso
me
calc
ula-
tions
atth
est
arto
fthe
run.
Thi
sis
notd
one
per
defa
ults
ince
itta
kes
aco
uple
ofm
inut
es,b
utfo
rla
rge
runs
itw
illsa
vetim
e.T
urn
iton
bysp
ecify
ing
op
timiz
e_
fft
=ye
s
inyo
ur.m
dp
file.
Whe
nru
nnin
gin
para
llelt
hegr
idm
ust
beco
mm
unic
ated
seve
ralt
imes
and
thus
hurt
ing
scal
ing
perf
orm
ance
.W
ithP
ME
you
can
impr
ove
this
byin
crea
sing
grid
spac
ing
whi
lesi
mul
tane
ousl
yin
crea
sing
the
inte
rpol
atio
nto
e.g.
6th
orde
r.S
ince
the
inte
rpol
atio
nis
entir
ely
loca
lath
isw
illim
prov
eth
esc
alin
gin
mos
tcas
es.
4.7
All-
hydr
ogen
forc
efiel
d
The
GR
OM
AC
Sal
l-hyd
roge
nfo
rcefi
eld
isal
mos
tide
ntic
alto
the
norm
alG
RO
MA
CS
forc
efiel
d,si
nce
the
extr
ahy
drog
ens
have
noLe
nnar
d-Jo
nes
inte
ract
ion
and
zero
char
ge.
The
only
diffe
renc
esar
ein
the
bond
angl
ean
dim
prop
erdi
hedr
alan
gle
term
s.T
his
forc
efiel
dis
only
usef
ulw
hen
you
need
the
exac
thy
drog
enpo
sitio
ns,
for
inst
ance
for
dist
ance
rest
rain
tsde
rived
from
NM
Rm
easu
rem
ents
.
4.8
GR
OM
OS
-96
note
s
4.8.
1T
heG
RO
MO
S-9
6fo
rce
field
GR
OM
AC
Ssu
ppor
tsth
eG
RO
MO
S-9
6fo
rce
field
s[
46].
All
para
met
ers
for
the
43a1
,43
a2(d
e-ve
lopm
ent,
impr
oved
alka
nedi
hedr
als)
and
43b1
(vac
uum
)fo
rce
field
sar
ein
clud
ed.
All
stan
-da
rdbu
ildin
gbl
ocks
are
incl
uded
and
topo
logi
esca
nbe
build
auto
mat
ical
lyby
pd
b2
gm
x.
The
GR
OM
OS
-96
forc
efie
ldis
afu
rthe
rde
velo
pmen
tof
the
GR
OM
OS
-87
forc
efie
ldon
whi
chth
eG
RO
MA
CS
forc
efiel
dis
base
d.T
heG
RO
MO
S-9
6fo
rce
field
has
impr
ovem
ents
over
the
GR
O-
MA
CS
forc
efie
ldfo
rpr
otei
nsan
dsm
allm
olec
ules
.It
is,
how
ever
,no
tre
com
men
ded
tobe
used
for
long
alka
nes
and
lipid
s.T
heG
RO
MO
S-9
6fo
rce
field
diffe
rsfr
omth
eG
RO
MA
CS
forc
efie
ldin
afe
was
pect
s:
•th
efo
rce
field
para
met
ers
•th
epa
ram
eter
sfo
rth
ebo
nded
inte
ract
ions
are
notl
inke
dto
atom
type
s
•a
four
thpo
wer
bond
stre
tchi
ngpo
tent
ial(
sec.
4.2.
1)
•an
angl
epo
tent
ialb
ased
onth
eco
sine
ofth
ean
gle
(sec
.4.
2.4)
The
rear
etw
odi
ffere
nces
inim
plem
enta
tion
betw
een
GR
OM
AC
San
dG
RO
MO
S-9
6w
hich
can
lead
tosl
ight
lydi
ffere
ntre
sults
whe
nsi
mul
atin
gth
esa
me
syst
emw
ithbo
thpa
ckag
es:
78
Ch
ap
ter
4.
Force
field
s
•in
GR
OM
OS
-96neighborsearching
forsolventsis
performed
onthe
firstatomofthe
solventm
olecule,this
isnot
implem
entedin
GR
OM
AC
S,
butthe
differencew
ithsearching
with
centersofcharge
groupsis
verysm
all
•the
virialinG
RO
MO
S-96
ism
oleculebased,this
isnotim
plemented
inG
RO
MA
CS
,which
usesatom
icvirials
The
GR
OM
OS
-96force
fieldw
asparam
eterizedw
itha
Lennard-Jonescut-offof1.4
nm,so
besure
touse
aLennard-Jones
cut-offof
atleast
1.4.A
largercut-off
ispossible,
becausethe
Lennard-Jones
potentialandforces
arealm
ostzerobeyond
1.4nm
.
4.8.2G
RO
MO
S-96
files
GR
OM
AC
Scan
readand
write
GR
OM
OS
-96coordinate
andtrajectory
files.T
hesefiles
shouldhave
theextension.g
96
.S
ucha
filecan
bea
GR
OM
OS
-96initial/finalconfiguration
fileor
acoordinate
trajectoryfile
ora
combination
ofboth.T
hefile
isfixed
format,allfloats
arew
rittenas
15.9(files
cangethuge).
GR
OM
AC
Ssupports
thefollow
ingdata
blocksin
thegiven
order:
•H
eaderblock:
TIT
LE
(ma
nd
ato
ry)
•F
rame
blocks:
TIM
ES
TE
P(o
ptio
na
l)P
OS
ITIO
N/P
OS
ITIO
NR
ED
(ma
nd
ato
ry)V
EL
OC
ITY
/VE
LO
CIT
YR
ED
(op
tion
al)
BO
X(o
ptio
na
l)
See
theG
RO
MO
S-96
manual[
46]for
acom
pletedescription
ofthe
blocks.N
otethat
allGR
O-
MA
CS
programs
canread
compressed
orgzip:ed
files.
8.1
3.
Ch
em
icalsh
ifts1
51
thedouble
integralofthecharge
density(
ρ(z)):
ψ(z)−
ψ(−∞
)=− ∫
z
−∞dz′ ∫
z′
−∞ρ(z
′′)dz′′/ε0
(8.38)
where
thepositionz
=−∞
isfar
enoughin
thebulk
phasethat
thefield
iszero.
With
thism
ethod,itispossible
to“split”
thetotalpotentialinto
separatecontributions
fromlipid
andw
aterm
olecules.T
heprogramg
po
ten
tial
dividesthe
boxin
slicesand
sums
allcharges
ofthe
atoms
ineach
slice.Itthen
integratesthis
chargedensity,giving
theelectric
field,andthe
electricfield,giving
thepotential.
Charge
density,fieldand
potentialarew
rittento
xvgr-
inputfiles.
The
programg
coo
rdis
avery
simple
analysisprogram
.A
llitdoes
isprint
thecoordinates
ofselected
atoms
tothree
files,containing
respectivelythe
x-,y-and
z-coordinatesof
thoseatom
s.Itcan
alsocalculate
thecenter
ofmass
ofoneor
more
molecules
andprintthe
coordinatesofthe
centerof
mass
tothree
files.B
yitself,
thisis
probablynot
avery
usefulanalysis,but
havingthe
coordinatesof
selectedm
oleculesor
atoms
canbe
veryhandy
forfurther
analysis,not
onlyin
interfacesystem
s.
The
programg
pvd
calculatesa
lotofproperties,among
which
thedensity
ofagroup
inparticles
perunitofvolum
e,butnota
densitythattakes
them
assofthe
atoms
intoaccount.
The
programg
de
nsity
alsocalculates
thedensity
ofagroup,buttakes
them
assesinto
accountandgives
aplot
ofthe
densityagainst
abox
axis.T
hisis
usefulforlooking
atthe
distributionof
groupsor
atoms
acrossthe
interface.
8.13C
hemicalshifts
tota
ld
o_
shift
Youcan
compute
theN
MR
chemicalshifts
ofprotons
with
theprogram
do
shift
.T
hisis
justan
GR
OM
AC
Sinterface
tothe
publicdom
ainprogram
tota
l[73].
For
furtherinform
ation,readthe
article.
15
0C
ha
pte
r8
.A
na
lysi
s
HP
r-A
HIS
-15+
THR-16
AR
G-17+
PRO-18
ALA-1
9
ALA-20
GLN-21
PH
E-2
2
VAL-23
LYS
-24+
GLU-25-
ALA
-26
LYS-27+
GLY-28
Fig
ure
8.13
:H
elic
alw
heel
proj
ectio
nof
the
N-t
erm
inal
helix
ofH
Pr.
8.12
Inte
rfac
ere
late
dite
ms
g_
ord
er
g_
de
nsi
tyg
_p
ote
ntia
lg
_co
ord
Whe
nsi
mul
atin
gm
olec
ules
with
long
carb
onta
ils,i
tcan
bein
tere
stin
gto
calc
ulat
eth
eir
aver
age
orie
ntat
ion.
The
rear
ese
vera
lflav
ors
ofor
der
para
met
ers,
mos
tofw
hich
are
rela
ted.
The
prog
ram
go
rde
rca
nca
lcul
ate
orde
rpa
ram
eter
sus
ing
the
equa
tion
Sz
=3 2〈c
os2θ z〉−
1 2(8
.37)
whe
reθ z
isth
ean
gle
betw
een
thez-
axis
ofth
esi
mul
atio
nbo
xan
dth
em
olec
ular
axis
unde
rco
nsid
erat
ion.
The
latte
ris
defin
edas
the
vect
orfr
omC
n−
1to
Cn+
1.
The
para
met
ersSx
andS
yar
ede
fined
inth
esa
me
way
.T
hebr
acke
tsim
ply
aver
agin
gov
ertim
ean
dm
olec
ules
.O
rder
para
met
ers
can
vary
betw
een
1(f
ullo
rder
alon
gth
ein
terf
ace
norm
al)
and
−1/
2(f
ullo
rder
perp
endi
cula
rto
the
norm
al),
with
ava
lue
ofze
roin
the
case
ofis
otro
pic
orie
ntat
ion.
The
prog
ram
can
dotw
oth
ings
fory
ou.
Itca
nca
lcul
ate
the
orde
rpar
amet
erfo
reac
hC
H2
segm
ent
sepa
rate
ly,f
oran
yof
thre
eax
es,o
rit
can
divi
deth
ebo
xin
slic
esan
dca
lcul
ate
the
aver
age
valu
eof
the
orde
rpa
ram
eter
per
segm
enti
non
esl
ice.
The
first
met
hod
give
san
idea
ofth
eor
derin
gof
am
olec
ule
from
head
tota
il,th
ese
cond
met
hod
give
san
idea
ofth
eor
derin
gas
func
tion
ofth
ebo
xle
ngth
.
The
elec
tros
tatic
pote
ntia
l(ψ)a
cros
sth
ein
terf
ace
can
beco
mpu
ted
from
atr
ajec
tory
byev
alua
ting
Cha
pter
5
Topo
logi
es
5.1
Intro
duct
ion
GR
OM
AC
Sm
ust
know
onw
hich
atom
san
dco
mbi
natio
nsof
atom
sth
eva
rious
cont
ribut
ions
toth
epo
tent
ial
func
tions
(see
chap
ter
4)m
ust
act.
Itm
ust
also
know
wha
tpa
ram
eter
sm
ust
beap
plie
dto
the
vario
usfu
nctio
ns.
All
this
isde
scrib
edin
the
top
olo
gyfi
le*.
top
,w
hich
lists
the
con
sta
nt
attribu
teso
fea
chat
om.
The
rear
em
any
mor
eat
omty
pes
than
elem
ents
,bu
ton
lyat
omty
pes
pres
enti
nbi
olog
ical
syst
ems
are
para
met
eriz
edin
the
forc
efie
ld,p
lus
som
em
etal
s,io
nsan
dsi
licon
.T
hebo
nded
and
spec
iali
nter
actio
nsar
ede
term
ined
byfix
edlis
tsth
atar
ein
clud
edin
the
topo
logy
file.
Cer
tain
non-
bond
edin
tera
ctio
nsm
ust
beex
clud
ed(fi
rst
and
seco
ndne
ighb
ors)
,as
thes
ear
eal
read
ytr
eate
din
bond
edin
tera
ctio
ns.
Inad
ditio
nth
ere
are
dyn
am
ica
ttribu
teso
fato
ms:
thei
rpo
sitio
ns,v
eloc
ities
and
forc
es,b
utth
ese
dono
tstr
ictly
belo
ngto
the
mol
ecul
arto
polo
gy.
Thi
sC
hapt
erde
scrib
esth
ese
tup
ofth
eto
polo
gyfil
e,th
e*.
top
file:
wha
tthe
para
met
ers
stan
dfo
ran
dho
w/w
here
toch
ange
them
ifne
eded
.
Not
e:if
you
cons
truc
tyo
urow
nto
polo
gies
,w
een
cour
age
you
toup
load
them
toou
rto
polo
gyar
chiv
eat
ww
w.g
rom
acs.
org!
Just
imag
ine
how
than
kful
you’
dha
vebe
enif
your
topo
logy
had
been
avai
labl
eth
ere
befo
reyo
ust
arte
d.T
hesa
me
goes
for
new
forc
efie
ldor
mod
ified
vers
ions
ofth
est
anda
rdfo
rce
field
s-
cont
ribut
eth
emto
the
forc
efie
ldar
chiv
e!
The
files
are
grou
ped
per
forc
efie
ldty
pe(n
amed
e.g.
gm
xfo
rth
eG
RO
MA
CS
forc
efie
ldor
G4
3a
1fo
rth
eG
RO
MO
S96
forc
efie
ld).
All
files
for
one
forc
efie
ldha
vena
mes
begi
nnin
gw
ithff?
??
whe
re?
??
stan
dsfo
rth
efo
rce
field
nam
e.
5.2
Par
ticle
type
InG
RO
MA
CS
ther
ear
e5
type
sof
part
icle
s,se
eTa
ble
5.1.
Onl
yre
gula
rat
oms
and
dum
my
part
icle
sar
eus
edin
GR
OM
AC
S,n
ucle
i,sh
ells
and
bond
shel
lsar
ene
cess
ary
for
pola
rizab
lefo
rce
field
s,w
hich
we
don’
tyet
have
.
80
Ch
ap
ter
5.
Top
olog
ies
Particle
Sym
bolatom
sA
nucleussN
shellsS
bondshells
Bdum
mys
D
Table5.1:
Particle
typesin
GR
OM
AC
S
5.2.1A
tomtypes
GR
OM
AC
Suses
47different
atomtypes,
aslisted
below,
with
theircorresponding
masses
(ina.m
.u.).T
hisis
thesam
elisting
asin
thefileff?
??
.atp
(.atp=
atomtype
parameter
file),therefore
inthis
fileyou
canchange
and/oradd
anatom
type.
O1
5.9
99
40
;ca
rbo
nyl
oxyg
en
(C=
O)
OM
15
.99
94
0;
carb
oxyl
oxyg
en
(CO
-)O
A1
5.9
99
40
;h
ydro
xylo
xyge
n(O
H)
OW
15
.99
94
0;
wa
ter
oxyg
en
N1
4.0
06
70
;p
ep
tide
nitro
ge
n(N
or
NH
)N
T1
4.0
06
70
;te
rmin
al
nitro
ge
n(N
H2
)N
L1
4.0
06
70
;te
rmin
al
nitro
ge
n(N
H3
)N
R5
14
.00
67
0;
aro
ma
ticN
(5-rin
g,2
bo
nd
s)N
R5
*1
4.0
06
70
;a
rom
atic
N(5
-ring
,3b
on
ds)
NP
14
.00
67
0;
po
rphyrin
nitro
ge
nC
12
.01
10
0;
ba
reca
rbo
n(p
ep
tide
,C=
O,C
-N)
CH
11
3.0
19
00
;a
liph
atic
CH
-gro
up
CH
21
4.0
27
00
;a
liph
atic
CH
2-g
rou
pC
H3
15
.03
50
0;
alip
hatic
CH
3-g
rou
pC
R5
11
3.0
19
00
;a
rom
atic
CH
-gro
up
(5-rin
g),
un
ited
CR
61
13
.01
90
0;
aro
ma
ticC
H-g
rou
p(6
-ring
),u
nite
dC
B1
2.0
11
00
;b
are
carb
on
(5-,6
-ring
)H
1.0
08
00
;h
ydro
ge
nb
on
de
dto
nitro
ge
nH
O1
.00
80
0;
hyd
roxyl
hyd
rog
en
HW
1.0
08
00
;w
ate
rh
ydro
ge
nH
S1
.00
80
0;
hyd
rog
en
bo
nd
ed
tosu
lfur
S3
2.0
60
00
;su
lfur
FE
55
.84
70
0;
iron
ZN
65
.37
00
0;
zinc
NZ
14
.00
67
0;
arg
NH
(NH
2)
NE
14
.00
67
0;
arg
NE
(NH
)P
30
.97
38
0;
ph
osp
ho
rO
S1
5.9
99
40
;su
ga
ro
re
ster
oxyg
en
CS
11
3.0
19
00
;su
ga
rC
H-g
rou
pN
R6
14
.00
67
0;
aro
ma
ticN
(6-rin
g,2
bo
nd
s)N
R6
*1
4.0
06
70
;a
rom
atic
N(6
-ring
,3b
on
ds)
CS
21
4.0
27
00
;su
ga
rC
H2
-gro
up
SI
28
.08
00
0;
silicon
NA
22
.98
98
0;
sod
ium
(1+
)C
L3
5.4
53
00
;ch
lorin
e(1
-)
8.1
1.
Pro
tein
rela
ted
item
s1
49
0100
200300
400500
600700
800900
1000
1 5 10 15
Residue
Tim
e (ps)C
oilB
endT
urnA
-Helix
B-B
ridge
Figure
8.10:A
nalysisofthe
secondarystructure
elements
ofapeptide
intim
e.
C
O
N
CH
R
C
Oα
N
H
H
ψφ
Figure
8.11:D
efinitionofthe
dihedralanglesφ
andψ
oftheprotein
backbone.
–180.0
�
–120.0
�
–60.00.0
60.0 �
120.0 �
180.0 �
Phi
–180.0
�
–120.0
�
–60.0
�
0.0
60.0
120.0
180.0
Psi
Ram
achandran Plot
Figure
8.12:R
amachandran
plotofasm
allprotein.
14
8C
ha
pte
r8
.A
na
lysi
s
•T
helif
etim
eof
the
H-b
onds
isca
lcul
ated
from
the
aver
age
over
alla
utoc
orre
latio
nfu
nctio
nsof
the
exis
tenc
efu
nctio
ns(e
ither
0or
1)of
allH
-bon
ds:
C(τ
)=
〈si(t)s i
(t+τ)〉
(8.3
5)
with
s i(t
)={0,1}
for
H-b
ondi
attim
et.
The
inte
gral
ofC
(τ)
give
sa
roug
hes
timat
eof
the
aver
age
H-b
ond
lifet
imeτ H
B: τ H
B=
∫ ∞ 0C
(τ)dτ
(8.3
6)
Bot
hth
ein
tegr
alan
dth
eco
mpl
ete
auto
corr
elat
ion
func
tion
C(τ
)w
illbe
outp
ut,
soth
atm
ore
soph
istic
ated
anal
ysis
(e.g
.usi
ngm
ulti-
expo
nent
ialfi
ts)
can
beus
edto
getb
ette
res
ti-m
ates
forτ
HB
.
•A
nH
-bon
dex
iste
nce
map
can
bege
nera
ted
ofdi
men
sion
s#
H-b
on
ds×
#fr
am
es.
•In
dex
grou
psar
eou
tput
cont
aini
ngth
ean
alyz
edgr
oups
,al
ldo
nor-
hydr
ogen
atom
pairs
and
acce
ptor
atom
sin
thes
egr
oups
,don
or-h
ydro
gen-
acce
ptor
trip
lets
invo
lved
inhy
drog
enbo
nds
betw
een
the
anal
yzed
grou
psan
dal
lsol
vent
atom
sin
volv
edin
inse
rtio
n.
•S
olve
ntin
sert
ion
into
H-b
onds
can
bean
alyz
ed,s
eeF
ig.
8.9.
Inth
isca
sean
addi
tiona
lgro
upid
entif
ying
the
solv
ent
mus
tbe
sele
cted
.T
heoc
curr
ence
ofin
sert
ion
will
bein
dica
ted
inth
eex
iste
nce
map
.N
ote
that
inse
rtio
nin
toan
dex
iste
nce
ofa
spec
ific
H-b
ond
can
occu
rsi
mul
tane
ousl
yan
dw
illal
sobe
indi
cate
das
such
inth
eex
iste
nce
map
.
8.11
Pro
tein
rela
ted
item
s
do
_d
ssp
g_
ram
axr
am
aw
he
el
Toan
alyz
est
ruct
ural
chan
ges
ofa
prot
ein,
you
can
calc
ulat
eth
era
dius
ofgy
ratio
nor
the
min
imum
resi
due
dist
ance
sdu
ring
time
(see
sec.
8.7)
,or
calc
ulat
eth
eR
MS
D(s
ec.8.8)
.
You
can
also
look
atth
ech
angi
ngofse
con
da
ryst
ruct
ure
ele
me
ntsdu
ring
your
run.
For
this
you
can
use
the
prog
ramd
od
ssp
,whi
chis
anin
terf
ace
for
the
com
mer
cial
prog
ramdssp
[72]
.F
orfu
rthe
rinf
orm
atio
n,se
eth
edssp
-man
ual.
Aty
pica
lout
putp
loto
fdod
ssp
isgi
ven
inF
ig.8
.10.
One
othe
rim
port
anta
naly
sis
ofpr
otei
nsis
the
soca
lled
Ra
ma
cha
nd
ran
plo
t.T
his
isth
epr
ojec
tion
ofth
est
ruct
ure
onth
etw
odi
hedr
alan
glesφ
andψ
ofth
epr
otei
nba
ckbo
ne,s
eeF
ig.
8.11
.
Toev
alua
teth
isR
amac
hand
ran
plot
you
can
use
the
prog
ram
gra
ma
.A
typi
calo
utpu
tis
give
nin
Fig
.8.1
2.
Itis
also
poss
ible
toge
nera
tean
anim
atio
nof
the
Ram
acha
ndra
npl
otin
time.
Thi
sca
nbe
ofhe
lpfo
ran
alyz
ing
cert
ain
dihe
dral
tran
sitio
nsin
your
prot
ein.
You
can
use
the
prog
ram
xra
ma
for
this
.
Whe
nst
udyi
ngα
-hel
ices
itis
usef
ulto
have
ahelic
al
wh
ee
lpro
ject
ion
ofyo
urpe
ptid
e,to
see
whe
ther
ape
ptid
eis
amph
ipat
ic.
Thi
sca
nbe
done
usin
gth
ew
he
el
prog
ram
.Tw
oex
ampl
esar
epl
otte
din
Fig
.8.1
3.
5.2
.P
art
icle
typ
e8
1
CA
40
.08
00
0;
calc
ium
(2+
)M
G2
4.3
05
00
;m
ag
ne
sium
(2+
)F
18
.99
84
0;
fluo
rine
(co
v.b
ou
nd
)C
P2
14
.02
70
0;
alip
ha
ticC
H2
-gro
up
usi
ng
Ryc
kae
rt-B
ell.
CP
31
5.0
35
00
;a
liph
atic
CH
3-g
rou
pu
sin
gR
ycka
ert
-Be
ll.C
R5
12
.01
10
0;
aro
ma
ticC
H-g
rou
p(5
-rin
g)+
HC
R6
12
.01
10
0;
aro
ma
ticC
-b
on
de
dto
H(6
-rin
g)+
HH
CR
1.0
08
00
;H
atta
che
dto
aro
ma
ticC
(5o
r6
riO
WT
31
5.9
99
40
;T
IP3
Pw
ate
ro
xyg
en
SD
32
.06
00
0;
DM
SO
Su
lph
ur
OD
15
.99
94
0;
DM
SO
Oxy
ge
nC
D1
5.0
35
00
;D
MS
OC
arb
on
Ato
mic
deta
ilis
used
exce
ptfo
rhy
drog
enat
oms
boun
dto
(alip
hatic
)ca
rbon
atom
s,w
hich
are
trea
ted
asu
nite
da
tom
s.N
osp
ecia
lhyd
roge
n-bo
ndte
rmis
incl
uded
.
The
last
10at
omty
pes
are
extr
aat
omty
pes
with
resp
ectt
oth
eG
RO
MO
S-8
7fo
rce
field
[39
]:
•F
was
take
nfr
omre
f.[43
],
•C
P2
and
CP
3fr
omre
f.[40]a
ndre
fere
nces
cite
dth
erei
n,
•C
R5,
CR
6an
dH
CR
from
ref.
[59]
•O
WT
3fr
omre
f.[4
2]
•S
D,O
Dan
dC
Dfr
omre
f.[44
]
The
refo
re,i
fyou
use
the
GR
OM
AC
Sfo
rce
field
asit
is,m
ake
sure
you
use
the
refe
renc
esin
your
publ
icat
ions
asm
entio
ned
abov
e.
Not
e:G
RO
MA
CS
mak
esus
eof
the
atom
type
sas
ana
me,
no
tas
anu
mbe
r(a
se.
g.in
GR
OM
OS
).
5.2.
2D
umm
yat
oms
Som
efo
rce
field
sus
edu
mm
yat
oms
(virt
uals
ites
that
are
cons
truc
ted
from
real
atom
s)on
whi
chce
rtai
nin
tera
ctio
nsar
elo
cate
d(e
.g.o
nbe
nzen
erin
gs,t
ore
prod
uce
the
corr
ectq
uadr
upol
e).
Thi
sis
desc
ribed
inse
c.4.5
.
Tom
ake
dum
my
atom
sin
your
syst
em,
you
shou
ldin
clud
ea
sect
ion
[d
um
mie
s?]
inyo
urto
polo
gyfil
e,w
here
the
‘?’
stan
dsfo
rth
enu
mbe
rco
nstr
uctin
gat
oms
for
the
dum
my
atom
.T
his
will
be‘2
’for
type
2,‘3
’for
type
s3,
3fd,
3fad
and
3out
and
‘4
’for
type
4fd
(the
diffe
rent
type
sar
eex
plai
ned
inse
c.4.5
).
Par
amet
ers
for
type
2sh
ould
look
like
this
:
[d
um
mie
s2]
;D
um
my
fro
mfu
nct
a5
12
10
.74
39
75
6
for
type
3lik
eth
is:
82
Ch
ap
ter
5.
Top
olog
ies
[d
um
mie
s3]
;D
um
my
from
fun
cta
b5
12
31
0.7
43
97
56
0.1
28
01
2
fortype
3fdlike
this:
[d
um
mie
s3]
;D
um
my
from
fun
cta
d5
12
32
0.5
-0.1
05
fortype
3fadlike
this:
[d
um
mie
s3]
;D
um
my
from
fun
ctth
eta
d5
12
33
12
00
.5
fortype
3outlikethis:
[d
um
mie
s3]
;D
um
my
from
fun
cta
bc
51
23
4-0
.4-0
.46
.92
81
fortype
4fdlike
this:
[d
um
mie
s4]
;D
um
my
from
fun
cta
bd
51
23
41
0.3
33
33
0.3
33
33
-0.1
05
This
willresultin
theconstruction
ofadum
my
‘atom’,num
ber5(firstcolum
n‘
Du
mm
y’),basedon
thepositions
of1and
2or
1,2and
3or
1,2,3and
4(nexttw
o,threeor
fourcolum
ns‘
from
’)fol-
lowing
therules
determined
bythe
functionnum
ber(nextcolum
n‘
fun
ct’)
with
theparam
etersspecified
(lastone,two
orthree
columns
‘a
b.
.’).
Note
thatany
bondsdefined
between
dumm
yatom
sand/or
normal
atoms
will
berem
ovedby
gro
mp
pafter
theexclusions
havebeen
generated.T
hisw
ay,exclusionsw
illnotbeaffected
byan
atombeing
definedas
dumm
yatom
ornot,butby
thebonding
configurationofthe
atom.
5.3P
arameter
files
5.3.1A
toms
Anum
berofsta
ticproperties
areassigned
tothe
atomtypes
inthe
GR
OM
AC
Sforce
field:Type,
Mass,
Charge,εand
σ(see
Table5.2T
hem
assis
listedinff?
??
.atp
(see5.2.1),w
hereasthe
chargeis
listedinff?
??
.rtp(.rtp
=residuetopologyparam
eterfile,
see5.5.1).T
hisim
pliesthat
thecharges
areonly
definedin
thebuilding
blocksof
amino
acidsor
userdefined
buildingblocks.
When
generatinga
topology(
*.top
)using
thepd
b2
gm
xprogram
theinform
ationfrom
thesefiles
iscom
bined.
The
following
dyn
am
icquantitiesare
associatedw
ithan
atom
8.1
0.
Hyd
rogen
bo
nd
s1
47
D
H
α
A
r
Figure
8.8:G
eometricalH
ydrogenbond
criterion.
O
DA
H
H
H
(1)(2)
(2)
Figure
8.9:Insertion
ofw
aterinto
anH
-bond.(1)
Norm
alH
-bondbetw
eentw
oresidues.
(2)H
-bondingbridge
viaa
water
molecule.
8.10H
ydrogenbonds
g_
hb
on
d
The
programg
hb
on
danalyses
thehyd
rogen
bo
nd
s(H-bonds)betw
eenallpossible
donorsD
andacceptors
A.To
determine
ifanH
-bondexists,a
geometricalcriterion
isused,see
alsoF
ig.8.8:
r≤
rH
B=
0.35nm
α≤
αH
B=
60o
(8.34)
The
valueofr
HB
=0.35
nmcorresponds
tothe
firstminim
umofthe
rdfofSP
C-w
ater(see
alsoF
ig.8.3).
The
programg
hb
on
danalyses
allhydrogenbonds
existingbetw
eentw
ogroups
ofatoms
(which
mustbe
eitheridenticalor
non-overlapping)or
inspecified
Donor
Hydrogen
Acceptor
triplets,inthe
following
ways:
•D
onor-Acceptor
distance(r)
distributionofallH
-bonds
•H
ydrogen-Donor-A
cceptorangle
(α
)distribution
ofallH-bonds
•T
hetotalnum
berofH
-bondsin
eachtim
efram
e
•T
henum
berof
H-bonds
intim
ebetw
eenresidues,
dividedinto
groupsn
-n+i
where
nand
n+i
standfor
residuenum
bersandigoes
from0
to6.
The
groupfori=
6also
includesallH
-bondsfori
>6.
These
groupsinclude
then-n+3,
n-n
+4and
n-n
+5H
-bondsw
hichprovide
am
easurefor
theform
ationofα
-helicesorβ
-turnsor
strands.
14
6C
ha
pte
r8
.A
na
lysi
s
beca
lcul
ated
from
the
eige
nval
ues
λi
and
the
eige
nvec
tors
,whi
char
eth
eco
lum
nsof
the
rota
tion
mat
rixR
.F
ora
sym
met
rican
ddi
agon
ally
-dom
inan
tm
atrixA
ofsi
ze3N
×3N
the
squa
rero
otca
nbe
calc
ulat
edas
:
A1 2
=R
diag
(λ1 2 1,λ
1 2 2,...,λ
1 2 3N
)RT
(8.2
7)
Itca
nbe
verifi
edea
sily
that
the
prod
uct
ofth
ism
atrix
with
itsel
fgi
ves
A.
Now
we
can
defin
ea
diffe
renc
edbe
twee
nco
varia
nce
mat
ricesA
andB
asfo
llow
s:
d(A,B
)=
√ tr( ( A
1 2−B
1 2
) 2)(8
.28)
=√ tr
( A+B−
2A1 2B
1 2
)(8
.29)
=
N ∑ i=1
( λA i
+λ
B i
) −2
N ∑ i=1
N ∑ j=1
√ λA iλ
B j
( RA i·R
B j
) 2 1 2
(8.3
0)
whe
retr
isth
etr
ace
ofa
mat
rix.
We
can
now
defin
eth
eov
erla
ps
as:
s(A,B
)=
1−
d(A,B
)√
trA
+trB
(8.3
1)
The
over
lap
is1
ifan
don
lyif
mat
ricesA
andB
are
iden
tical
.It
is0
whe
nth
esa
mpl
edsu
bspa
ces
are
com
plet
ely
orth
ogon
al.
Aco
mm
only
used
mea
sure
isth
esu
bspa
ceov
erla
pof
the
first
few
eige
nvec
tors
ofco
varia
nce
mat
rices
.T
heov
erla
pof
the
subs
pace
span
ned
bym
orth
onor
mal
vect
orsw
1,...,w
mw
itha
refe
renc
esu
bspa
cesp
anne
dbynor
thon
orm
alve
ctor
sv1,...,v
nca
nbe
quan
tified
asfo
llow
s:
over
lap(v,w
)=
1 n
n ∑ i=1
m ∑ j=1
(vi·w
j)2
(8.3
2)
The
over
lap
will
incr
ease
with
incr
easi
ngman
dw
illbe
1w
hen
setv
isa
subs
pace
ofse
tw.
The
disa
dvan
tage
ofth
ism
etho
dis
that
itdo
esno
ttak
eth
eei
genv
alue
sin
toac
coun
t.A
llei
genv
ecto
rsar
ew
eigh
ted
equa
llyan
dw
hen
dege
nera
tesu
bspa
ces
are
pres
ent(
equa
leig
enva
lues
)the
calc
ulat
edov
erla
pw
illbe
too
low
.
Ano
ther
usef
ulch
eck
isth
eco
sine
cont
ent.
Itha
sbe
enpr
oven
the
the
prin
cipa
lcom
pone
nts
ofra
ndom
diffu
sion
are
cosi
nes
with
the
num
ber
ofpe
riods
equa
lto
half
the
prin
cipa
lcom
pone
ntin
dex[
71].
The
eige
nval
ues
are
prop
ortio
nalt
oth
ein
dex
toth
epo
wer
−2.
The
cosi
neco
nten
tis
defin
edas
:2 T
( ∫ T 0co
s(kπt)p
i(t)
dt
) 2(∫ T 0
p2 i(t
)dt) −1
(8.3
3)
Whe
nth
eco
sine
cont
ento
fthe
first
few
prin
cipa
lcom
pone
nts
iscl
ose
to1,
the
larg
estfl
uctu
atio
nsar
eno
tcon
nect
edw
ithth
epo
tent
ial,
butw
ithra
ndom
diffu
sion
.
The
cova
rianc
em
atrix
isbu
iltan
ddi
agon
aliz
edbyg
cova
r.
The
prin
cipa
lco
mpo
nent
san
dov
erla
p(a
nym
any
mor
eth
ings
)ca
nbe
plot
ted
and
anal
yzed
with
ga
na
eig
.T
heco
sine
cont
ent
can
beca
lcul
ated
withg
an
aly
ze.
5.3
.P
ara
me
ter
file
s8
3
Pro
pert
yS
ymbo
lU
nit
Type
--
Mas
sm
a.m
.u.
Cha
rge
qel
ectr
onep
silo
nε
kJ/m
olsi
gma
σnm
Tabl
e5.
2:S
tatic
atom
type
prop
ertie
sin
GR
OM
AC
S
•P
ositi
onx
•Ve
loci
tyv
The
sequ
antit
ies
are
liste
din
the
coor
dina
tefil
e,*.
gro
(see
sect
ion
File
form
at,5.6.
6).
5.3.
2B
onde
dpa
ram
eter
s
The
bond
edpa
ram
eter
s(i.
e.bo
nds,
bond
angl
es,
impr
oper
and
prop
erdi
hedr
als)
are
liste
din
ff?
??
bo
n.it
p.
The
term
fun
cis
1fo
rha
rmon
ican
d2
for
GR
OM
OS
-96
bond
and
angl
epo
tent
ials
.F
orth
edi
hedr
al,t
his
isex
plai
ned
afte
rth
islis
ting.
[b
on
dty
pe
s]
;i
jfu
nc
b0
kbC
O1
0.1
23
00
50
20
80
.C
OM
10
.12
50
04
18
40
0.
......
[a
ng
lety
pe
s]
;i
jk
fun
cth
0ct
hH
OO
AC
11
09
.50
03
97
.48
0H
OO
AC
H1
11
09
.50
03
97
.48
0......
[d
ihe
dra
ltyp
es
];
il
fun
cq
0cq
NR
5*
NR
52
0.0
00
16
7.3
60
NR
5*
NR
5*
20
.00
01
67
.36
0......
[d
ihe
dra
ltyp
es
];
jk
fun
cp
hi0
cpm
ult
CO
A1
18
0.0
00
16
.73
62
CN
11
80
.00
03
3.4
72
2......
[d
ihe
dra
ltyp
es
]; ;
Ryc
kae
rt-B
elle
ma
ns
Dih
ed
rals
;
84
Ch
ap
ter
5.
Top
olog
ies
;a
ja
kfu
nct
CP
2C
P2
39.2
78
91
2.1
56
-13
.12
0-3
.05
97
26
.24
0-3
1.4
95
Also
inthis
fileare
theR
yckaert-Bellem
ans[
60]parameters
forthe
CP
2-CP
2dihedrals
inalkanes
oralkane
tailsw
iththe
following
constants:
(kJ/mol)
C0
=9.28
C2
=−
13.12C
4=
26.24C
1=
12.16C
3=
−3.06
C5
=−
31.5
(Note:T
heuse
ofthispotentialim
pliesexclusions
ofLJ-interactionsbetw
eenthe
firstandthe
lastatom
ofthedihedral,andψ
isdefined
accordingto
the’polym
erconvention’(
ψtr
ans
=0)).
So
thereare
threetypes
ofdihedralsin
theG
RO
MA
CS
forcefield:
•proper
dihedral:funct=
1,with
mult=
multiplicity,so
thenum
berofpossible
angles
•im
properdihedral:
funct=2
•R
yckaert-Bellem
ansdihedral:
funct=3
Inthe
fileff?
??
bo
n.itp
youcan
addbonded
parameters.
Ifyou
want
toinclude
parameters
fornew
atomtypes,m
akesure
youdefine
thisnew
atomtype
inff?
??
.atp
asw
ell.
5.3.3N
on-bondedparam
eters
The
non-bondedparam
etersconsistofthe
Vander
Waals
parameters
Aand
C,as
listedin
thefile
ff??
?n
b.itp
,wherep
type
isthe
particletype
(seeTable5.1):
[a
tom
type
s]
;na
me
ma
ssch
arg
ep
type
c6c1
2O
15
.99
94
00
.00
0A
0.2
26
17
E-0
20
.74
15
8E
-06
OM
15
.99
94
00
.00
0A
0.2
26
17
E-0
20
.74
15
8E
-06
.....
[n
on
bo
nd
_p
ara
ms
];
ij
fun
cc6
c12
OO
10
.22
61
7E
-02
0.7
41
58
E-0
6O
OA
10
.22
61
7E
-02
0.1
38
07
E-0
5.....
[p
airtyp
es
];
ij
fun
ccs6
cs12
;T
HE
SE
AR
E1
-4IN
TE
RA
CT
ION
SO
O1
0.2
26
17
E-0
20.7
41
58
E-0
6O
OM
10
.22
61
7E
-02
0.7
41
58
E-0
6.....
With
Aand
Cbeing
definedas
Aii =
4εi σ
12
i(5.1)
8.9
.C
ovaria
nce
an
alysis
14
5
Instead
ofcomparing
thestructures
tothe
initialstructureattim
et=
0(so
forexam
plea
crystalstructure),one
canalso
calculateeqn.8.20
usinga
time
shiftτ:
RMSD
(t;τ)= [
1N
N∑i=1 ‖r
i (t)−ri (t−
τ)‖2 ]
12
(8.22)
socom
paringto
aleast-square
structureat
t−τ.
This
givessom
einsight
inthe
mobility
asa
functionofτ.
Use
theprogramg
run
rms
.
8.9C
ovarianceanalysis
Covariance
analysis,alsocalled
principalcomponentanalysis
oressentialdynam
ics[
70],canfind
correlatedm
otions.Ituses
thecovariance
matrixC
oftheatom
iccoordinates:
Cij
= ⟨M
12ii (xi −
〈xi 〉)M
12jj (xj −
〈xj 〉) ⟩
(8.23)
where
Mis
adiagonal
matrix
containingthe
masses
ofthe
atoms
(mass-w
eightedanalysis)
orthe
unitm
atrix(non-m
assw
eightedanalysis).
Cis
asym
metric3
N×
3Nm
atrix,w
hichcan
bediagonalized
with
anorthonorm
altransformation
matrixR
:
RTCR
=diag(λ
1 ,λ2 ,...,λ
3N
)w
hereλ
1≥λ
2≥...≥
λ3N
(8.24)
The
columns
ofRare
theeigenvectors,
alsocalled
principalor
essentialm
odes.R
definesa
transformation
toa
newcoordinate
system.
The
trajectorycan
beprojected
onthe
principalmodes
togive
theprincipalcom
ponentspi (t):
p(t)
=R
TM
12(x(t)−〈x〉)
(8.25)
The
eigenvalueλi is
them
eansquare
fluctuationofprincipalcom
ponenti.
The
firstfewprincipal
modes
oftendescribe
collective,globalmotions
inthe
system.
The
trajectorycan
befiltered
alongone
(orm
ore)principalm
odes.F
orone
principalmodei
thisgoes
asfollow
s:
xf(t)
=〈x〉
+M
−12R
∗i p
i (t)(8.26)
When
theanalysis
isperform
edon
am
acromolecule,one
oftenw
antsto
remove
theoverallrota-
tionand
translationto
lookatthe
internalmotion
only.T
hiscan
beachieved
byleastsquare
fittingto
areference
structure.C
arehas
tobe
takenthat
thereference
structureis
representativefor
theensem
ble,since
thechoice
ofreference
structureinfluences
thecovariance
matrix.
One
shouldalw
ayscheck
ifthe
principalmodes
arew
elldefined.If
thefirst
principalcomponent
resembles
ahalf
cosineand
thesecond
resembles
afullcosine,
youm
ightbe
filteringnoise.
Agood
way
tocheck
therelevance
ofthefirstfew
principalmodes
isto
calculatethe
overlapofthe
sampling
between
thefirstand
secondhalfofthe
simulation.
Note
thatthiscan
onlybe
donew
henthe
same
referencestructure
isused
forthe
two
halves.
The
elements
ofthe
covariancem
atrixare
proportionaltothe
squareof
thedisplacem
ent,so
we
needto
takethe
squarerootofthe
matrix
toexam
inethe
extentofsampling.
The
squarerootcan
14
4C
ha
pte
r8
.A
na
lysi
s
2130
4050
6070
8090
2130405060708090 t=0 ps
Res
idue
Num
ber
0D
ista
nce
(nm
)1.
2
Fig
ure
8.7:
Am
inim
umdi
stan
cem
atrix
for
ape
ptid
e[
3].
8.8
Roo
tmea
nsq
uare
devi
atio
nsin
stru
ctur
e
g_
rms
g_
rmsd
ist
The
roo
tme
an
squ
are
dev
iatio
n(RMSD
)of
cert
ain
atom
sin
am
olec
ule
with
resp
ectt
oa
refe
r-en
cest
ruct
ure
can
beca
lcul
ated
with
the
prog
ram
grm
sby
leas
t-sq
uare
fittin
gth
est
ruct
ure
toth
ere
fere
nce
stru
ctur
e(
t 2=
0)an
dsu
bseq
uent
lyca
lcul
atin
gth
eRMSD
(eqn
.8.2
0).
RMSD
(t1,t
2)
=
[ 1 N
N ∑ i=1
‖ri(t 1
)−
r i(t
2)‖
2
]1 2
(8.2
0)
whe
rer i
(t)
isth
epo
sitio
nof
atomi
attim
et.
NO
TE
that
fittin
gdo
esno
tha
veto
use
the
sam
eat
oms
asth
eca
lcul
atio
nof
theRMSD
;e.
g.:
apr
otei
nis
usua
llyfit
ted
onth
eba
ckbo
neat
oms
(N,C
α,C
),bu
ttheRMSD
can
beco
mpu
ted
ofth
eba
ckbo
neor
ofth
ew
hole
prot
ein.
Inst
ead
ofco
mpa
ring
the
stru
ctur
esto
the
initi
alst
ruct
ure
attim
et
=0
(so
for
exam
ple
acr
ysta
lst
ruct
ure)
,one
can
also
calc
ulat
eeq
n.8.
20w
itha
stru
ctur
eat
timet 2
=t 1−τ.
Thi
sgi
ves
som
ein
sigh
tin
the
mob
ility
asa
func
tion
ofτ.
Als
oa
mat
rixca
nbe
mad
ew
ithth
eRMSD
asa
func
tion
oft 1
andt 2
,thi
sgi
ves
ani
cegr
aphi
cali
mpr
essi
onof
atr
ajec
tory
.If
ther
ear
etr
ansi
tions
ina
traj
ecto
ry,t
hey
will
clea
rlysh
owup
insu
cha
mat
rix.
Alte
rnat
ivel
yth
eRMSD
can
beco
mpu
ted
usin
ga
fit-f
ree
met
hod
with
the
prog
ram
grm
sdis
t:
RMSD
(t)
=
1 N2
N ∑ i=1
N ∑ j=1
‖rij(t
)−
r ij(0
)‖2
1 2
(8.2
1)
whe
reth
edis
tan
cer i
jbe
twee
nat
oms
attim
etis
com
pare
dw
ithth
edi
stan
cebe
twee
nth
esa
me
atom
sat
time0
.
5.4
.C
on
stra
ints
85
Cii
=4ε
iσ6 i
(5.2
)
and
com
pute
dac
cord
ing
toth
eco
mbi
natio
nru
les
:
Aij
=(A
iiA
jj)1 2
(5.3
)
Cij
=(C
iiC
jj)1 2
(5.4
)
Itis
also
poss
ible
tous
eth
eco
mbi
natio
nru
les
whe
reth
eσ
’sar
eav
erag
ed:
σij
=1 2(σ
ii+σ
jj)
(5.5
)
ε ij
=√ε i
iεjj
(5.6
)
5.3.
41-
4in
tera
ctio
ns
The
1-4
inte
ract
ions
for
the
atom
type
sinff?
??
nb
.itp
are
liste
din
the[
pa
irty
pe
s]
sect
ion.
The
GR
OM
AC
San
dG
RO
MO
Sfo
rce
field
slis
tsal
lthe
sein
tera
ctio
nsex
plic
itly,
butt
his
sect
ion
mig
htbe
empt
yfo
rfo
rce
field
slik
eO
PLS
that
calc
ulat
eth
e1-
4in
tera
ctio
nsby
scal
ing.
5.3.
5E
xclu
sion
s
The
excl
usio
nsfo
rbo
nded
part
icle
sar
ege
nera
ted
byg
rom
pp
for
neig
hbor
ing
atom
sup
toa
cert
ain
num
ber
ofbo
nds
away
,as
defin
edin
the
[m
ole
cule
typ
e]
sect
ion
inth
eto
polo
gyfil
e(s
ee5.
6.1)
.P
artic
les
are
cons
ider
edbo
nded
whe
nth
eyar
eco
nnec
ted
bybo
nds
([
bo
nd
s]
type
s1
to5)
orco
nstr
aint
s(
[co
nst
rain
ts]
type
1).
[b
on
ds
]ty
pe5
can
beus
edto
crea
tea
conn
ectio
nbe
twee
ntw
oat
oms
with
out
crea
ting
anin
tera
ctio
n.T
here
isa
harm
onic
inte
ract
ion
([b
on
ds
]ty
pe6)
whi
chdo
esno
tco
nnec
tth
eat
oms
bya
chem
ical
bond
.T
here
isal
soa
seco
ndco
nstr
aint
type
([
con
stra
ints
]ty
pe2)
whi
chfix
esth
edi
stan
ce,b
utdo
esno
tcon
nect
the
atom
sby
ach
emic
albo
nd.
Ext
raex
clus
ions
with
ina
mol
ecul
eca
nbe
adde
dm
anua
llyin
a[
exc
lusi
on
s]
sect
ion.
Eac
hlin
esh
ould
star
tw
ithon
eat
omin
dex,
follo
wed
byon
eor
mor
eat
omin
dice
s.A
llno
n-bo
nded
inte
ract
ions
betw
een
the
first
atom
and
the
othe
rat
oms
will
beex
clud
ed.
Whe
nal
lnon
-bon
ded
inte
ract
ions
with
inor
betw
een
grou
psof
atom
sne
edto
beex
clud
ed,
isit
mor
eco
nven
ient
and
muc
hm
ore
effic
ient
tous
een
ergy
mon
itor
grou
pex
clus
ions
(see
sec.
3.3)
.
5.4
Con
stra
ints
Con
stra
ints
are
defin
edin
the[co
nst
rain
ts]
sect
ion.
The
form
atis
two
atom
num
bers
fol-
low
edby
the
func
tion
type
,w
hich
can
be1
or2
and
the
cons
trai
ntdi
stan
ce.
The
only
diffe
renc
ebe
twee
nth
etw
oty
pes
isth
atty
pe1
isus
edfo
rge
nera
ting
excl
usio
nsan
dw
hile
type
2is
not(
see
5.3.
5).
The
dist
ance
sar
eco
nstr
aine
dus
ing
the
LIN
CS
orth
eS
HA
KE
algo
rithm
,whi
chca
nbe
se-
lect
edin
the*
.md
pfil
e.B
oth
type
sof
cons
trai
nts
can
bepe
rtur
bed
infr
ee-e
nerg
yca
lcul
atio
nsby
addi
nga
seco
ndco
nstr
aint
dist
ance
(see
5.6.
5).
Sev
eral
type
sof
bond
san
dan
gles
(see
Tabl
e5.
4)
86
Ch
ap
ter
5.
Top
olog
ies
canbe
convertedautom
aticallyto
constraintsby
gro
mp
p.
There
areseveraloptions
forthis
inthe
*.md
pfile.
We
havealso
implem
entedthe
SE
TT
LEalgorithm
[27]w
hichis
ananalyticalsolution
ofSH
AK
Especifically
forw
ater.S
ET
TLE
canbe
selectedin
thetopology
file.C
heckfor
instancethe
SP
Cm
oleculedefinition:
[m
ole
cule
type
];
mo
lna
me
nre
xclS
OL
1
[a
tom
s]
;n
ra
ttyp
ere
sn
rre
nn
ma
tn
mcg
nr
cha
rge
1O
W1
SO
LO
W1
1-0
.82
2H
W1
SO
LH
W2
10
.41
3H
W1
SO
LH
W3
10
.41
[se
ttles
];
OW
fun
ctd
oh
dh
h1
10
.10
.16
33
3
[e
xclusio
ns
]1
23
21
33
12
The
section[se
ttles
]defines
thefirstatom
ofthew
aterym
olecule,thesettle
functisalw
aysone,and
thedistance
between
Oand
H,and
distancebetw
eenboth
Hatom
sm
ustbegiven.
Note
thatthe
algorithmcan
alsobe
usedfor
TIP
3Pand
TIP
4P[
42].T
IP3P
justhas
anothergeom
etry.T
IP4P
hasa
dumm
yatom
,butsincethatis
generateditdoes
notneedto
beshaken
(norstirred).
5.5D
atabases
5.5.1R
esiduedatabase
The
fileholding
theresidue
databaseis
ff??
?.rtp
.O
riginallythis
filecontained
buildingblocks
(amino
acids)forproteins,andis
theG
RO
MA
CS
interpretationofthert3
7c4
.da
tfile
ofGR
O-
MO
S.S
othe
residuefile
containsinform
ation(bonds,
charge,charge
groupsand
improper
dihe-drals)
fora
frequentlyused
buildingblock.
Itisbetter
no
ttochange
thisfile
becauseitis
standardinput
forpd
b2
gm
x,
butif
changesare
neededm
akethem
inthe
*.top
file(see
sectionTopol-
ogyfile,5.6.1).
How
ever,in
theff??
?.rtp
filethe
usercan
definea
newbuilding
blockor
molecule:
seefor
example
2,2,2-trifluoroethanol(T
FE
)or
n-decane(C
10).B
utw
hendefining
newm
olecules(non-protein)
itis
preferableto
createa
*.itpfile.
This
willbe
discussedin
anextsection
(section5.6.2).
The
fileff?
??
.rtpis
onlyused
bypd
b2
gm
x.
As
mentioned
before,theonly
extrainform
ationthis
programneeds
fromff??
?.rtp
isbonds,
chargesof
atoms,
chargegroups
andim
proper
8.7
.R
ad
ius
ofg
yratio
na
nd
dista
nce
s1
43
For
planesituses
thenorm
alvectorperpendicular
tothe
plane.Itcan
alsocalculate
thed
istan
cedbetw
eenthe
geometricalcenter
oftwo
planes(see
Fig.
8.6D),and
thedistancesd1
andd
2betw
een2
atoms
(ofa
vector)and
thecenter
ofa
planedefined
by3
atoms
(seeF
ig.8.6D
).It
furthercalculates
thedistancedbetw
eenthe
centerofthe
planeand
them
iddleofthis
vector.D
ependingon
theinput
groups(i.e.
groupsof
2or
3atom
numbers),
theprogram
decidesw
hatangles
anddistances
tocalculate.
For
example,the
index-filecould
looklike
this:
[a
_p
lan
e]
12
3[
a_
vecto
r]
34
5
8.7R
adiusofgyration
anddistances
g_
gyra
teg
_sg
an
gle
g_
min
dist
g_
md
ma
txp
m2
ps
Tohave
arough
measure
forthe
compactness
ofastructure,you
cancalculate
thera
diu
so
fgyra
-tio
nw
iththe
programg
gyra
teas
follows:
Rg
= (∑i ‖r
i ‖2m
i∑
i mi )
12
(8.19)
where
mi
isthe
mass
ofatomiandr
ithe
positionofatomi
with
respecttothe
centerofm
assof
them
olecule.Itis
especiallyusefulto
characterizepolym
ersolutions
andproteins.
Som
etimes
itis
interestingto
plotthedista
ncebetw
eentw
oatom
s,or
themin
imu
mdistance
be-tw
eentw
ogroups
ofatoms
(e.g.:protein
side-chainsin
asaltbridge).
Tocalculate
thesedistances
between
certaingroups
thereare
severalpossibilities:
•T
hed
istan
ceb
etw
ee
nth
ege
om
etrica
lcen
ters
oftwo
groupscan
becalculated
with
theprogram
gsg
an
gle
,asexplained
insec.8.6.
•T
hem
inim
um
dista
ncebetw
eentw
ogroups
ofatom
sduring
time
canbe
calculatedw
iththe
programg
min
dist
.Italso
calculatesthenu
mb
ero
fcon
tactsbetw
eenthese
groupsw
ithina
certainradiusr
max .
•To
monitorthem
inim
um
dista
nce
sb
etw
ee
nre
sidu
es
(seechapter5)w
ithina
(protein)molecule,
youcan
usethe
programgm
dm
at.
This
minim
umdistance
between
two
residuesA
iand
Aj
isdefined
asthe
smallestdistance
between
anypairofatom
s(i
∈A
i ,j∈A
j ).T
heoutput
isa
symm
etricalmatrix
ofsmallestdistances
between
allresidues.To
visualizethis
matrix,
youcan
usea
programsuch
asxv
.Ifyou
wantto
viewthe
axesand
legendor
ifyouw
antto
printthem
atrix,youcan
convertitwithxp
m2
ps
intoa
Postscriptpicture,see
Fig.8.7.
Plotting
thesem
atricesfor
differenttime-fram
es,one
cananalyze
changesin
thestructure,
ande.g.form
ingofsaltbridges.
14
2C
ha
pte
r8
.A
na
lysi
s
φ =
0φ
= 0
AB
Fig
ure
8.5:
Dih
edra
lcon
vent
ions
:A
.“B
ioch
emic
alco
nven
tion”
.B
.“P
olym
erco
nven
tion”
.
bb
a
φ
2
C
D
d
d
E
φ
d
φ
AB
n
1d
n
n
Fig
ure
8.6:
Opt
ions
ofgsg
an
gle
:A
.Ang
lebe
twee
n2
vect
ors.
B.A
ngle
betw
een
ave
ctor
and
the
norm
alof
apl
ane.
C.A
ngle
betw
een
two
plan
es.
D.D
ista
nce
betw
een
the
geom
etric
alce
nter
sof
2pl
anes
.E
.Dis
tanc
esbe
twee
na
vect
oran
dth
ece
nter
ofa
plan
e.
5.5
.D
ata
ba
ses
87
dihe
dral
s,be
caus
eth
ere
stis
read
from
the
coor
dina
tein
put
file
(inth
eca
seof
pd
b2
gm
x,
apd
bfo
rmat
file)
.S
ome
prot
eins
cont
ain
resi
dues
that
are
nots
tand
ard,
buta
relis
ted
inth
eco
ordi
nate
file.
You
have
toco
nstr
ucta
build
ing
bloc
kfo
rthi
s“s
tran
ge”r
esid
ue,o
ther
wis
eyo
uw
illno
tobt
ain
a*.
top
file.
Thi
sal
soho
lds
for
mol
ecul
esin
the
coor
dina
tefil
elik
eph
osph
ate
orsu
lpha
teio
ns.
The
resi
due
data
base
isco
nstr
ucte
din
the
follo
win
gw
ay:
[b
on
de
dty
pe
s]
;m
an
dato
ry;
bo
nd
sa
ng
les
dih
ed
rals
imp
rop
ers
11
12
;m
an
da
tory
[G
LY
];
ma
nd
ato
ry
[a
tom
s]
;m
an
da
tory
;n
am
ety
pe
cha
rge
cha
rge
gro
up
NN
-0.2
80
0H
H0
.28
00
CA
CH
20
.00
01
CC
0.3
80
2O
O-0
.38
02
[b
on
ds
];
op
tion
al
;ato
m1
ato
m2
b0
kbN
HN
CA
CA
CC
O-C
N
[e
xclu
sio
ns
];
op
tion
al
;ato
m1
ato
m2
[a
ng
les
];
op
tion
al
;ato
m1
ato
m2
ato
m3
th0
cth
[d
ihe
dra
ls]
;o
ptio
na
l;a
tom
1a
tom
2a
tom
3a
tom
4p
hi0
cpm
ult
[im
pro
pe
rs]
;o
ptio
na
l;a
tom
1a
tom
2a
tom
3a
tom
4q
0cq
N-C
CA
H-C
-CA
N-O
[Z
N]
[a
tom
s]
ZN
ZN
2.0
00
0
The
file
isfr
eefo
rmat
,th
eon
lyre
stric
tion
isth
atth
ere
can
beat
mos
ton
een
try
ona
line.
The
first
field
inth
efil
eis
the[
bo
nd
ed
typ
es
]fie
ld,
whi
chis
follo
wed
byfo
urnu
mbe
rs,
that
indi
cate
the
inte
ract
ion
type
for
bond
s,an
gles
,dih
edra
lsan
dim
prop
erdi
hedr
als.
The
file
cont
ains
resi
due
entr
ies,
whi
chco
nsis
tofa
tom
san
dop
tiona
llybo
nds,
angl
esdi
hedr
als
and
impr
oper
s.T
hech
arge
grou
pco
des
deno
teth
ech
arge
grou
pnu
mbe
rs.
Ato
ms
inth
esa
me
char
gegr
oup
shou
ld
88
Ch
ap
ter
5.
Top
olog
ies
always
bebelow
eachother.
When
usingthe
hydrogendatabase
with
pd
b2
gm
xforadding
missing
hydrogens,the
atomnam
esdefined
inthe.rtp
entryshould
correspondexactly
tothe
naming
conventionused
inthe
hydrogendatabase,
see5.5.2.
The
atomnam
esin
thebonded
interactioncan
bepreceded
bya
minus
ora
plus,indicating
thatthe
atomis
inthe
precedingor
following
residuerespectively.
Param
eterscan
beadded
tobonds,
angles,dihedrals
andim
propers,these
parameters
overridethe
standardparam
etersin
the.itp
files.T
hisshould
onlybe
usedin
specialcases.
Insteadof
parameters,
astring
canbe
addedfor
eachbonded
interaction,this
isused
inG
RO
MO
S96.rtp
files.T
hesestrings
arecopied
tothe
topologyfile
andcan
bereplaced
byforce
fieldparam
etersby
theC
-preprocessorin
gro
mp
pusing
#d
efin
estatem
ents.
pd
b2
gm
xautom
aticallygenerates
allangles,this
means
thatfor
theG
RO
MA
CS
forcefield
the[
an
gle
s]
fieldis
onlyusefulfor
overriding.itpparam
eters.F
orthe
GR
OM
OS
-96force
fieldthe
interactionnum
beroffallangles
needto
bespecified.
pd
b2
gm
xautom
aticallygenerates
oneproper
dihedralfor
everyrotatable
bond,preferably
onheavy
atoms.
When
the[d
ihe
dra
ls]
fieldis
used,noother
dihedralsw
illbegenerated
forthe
bondscorresponding
tothe
specifieddihedrals.
Itispossible
toputm
orethan
onedihedralon
arotatable
bond.
pd
b2
gm
xsets
thenum
berexclusions
to3,
which
means
thatinteractions
between
atoms
con-nected
byat
most
3bonds
areexcluded.
Pair
interactionsare
generatedfor
allpairs
ofatom
sw
hichare
seperatedby
3bonds
(exceptpairs
ofhydrogens).
When
more
interactionsneed
tobe
excluded,orsom
epair
interactionsshould
notbegenerated,an
[e
xclusio
ns
]field
canbe
added,follow
edby
pairsof
atomnam
eson
seperatelines.
Allnon-bonded
andpair
interactionsbetw
eenthese
atoms
willbe
excluded.
5.5.2H
ydrogendatabase
The
hydrogendatabase
isstored
inff?
??
.hd
b.
Itcontainsinform
ationfor
thepd
b2
gm
xpro-
gramon
howto
connecthydrogenatom
sto
existingatom
s.H
ydrogenatom
sare
named
afterthe
atomthey
areconnected
to:the
firstletteroftheatom
name
isreplaced
byan
’H’.Ifm
orethen
onehydrogen
atomis
connectedto
thesam
eatom
,anum
berw
illbeadded
tothe
endofthe
hydrogenatom
name.
For
example,adding
two
hydrogenatom
sto
ND
2(in
asparagine),thehydrogen
atoms
willbe
namedH
D2
1and
HD
22.
This
isim
portantsinceatom
naming
inthe.rtp
file(see5.5.1)
mustbe
thesam
e.T
heform
atofthehydrogen
databaseis
asfollow
s:
;re
s#
ad
ditio
ns
#H
ad
dtyp
ei
jk
AL
A11
1N
-CC
AA
RG
412
NC
AC
11
NE
CD
CZ
23
NH
1C
ZN
E2
3N
H2
CZ
NE
On
thefirstline
we
seethe
residuenam
e(A
LAor
AR
G)
andthe
number
ofadditions.A
fterthat
follows
oneline
foreach
addition,onw
hichw
esee:
•T
henum
berofH
atoms
added
8.6
.B
on
ds,a
ng
les
an
dd
ihe
dra
ls1
41
0.050.0 �
100.0 �
150.0 �
Tim
e (ps)
�
0.0
1000.0
2000.0
3000.0
4000.0
MSD (10-5 cm
2 s
-1)
Mean S
quare Displacem
entD
= 3.5027 (10
-5 cm2 s
-1)
Figure
8.4:M
eanS
quareD
isplacementofS
PC
-water.
Tom
onitorspecificb
on
dsin
yourm
oleculesduring
time,
theprogramg
bo
nd
calculatesthe
distributionof
thebond
lengthin
time.
The
indexfile
consistsof
pairsof
atomnum
bers,for
example
[b
on
ds_
1]
12
34
91
0[
bo
nd
s_2
]1
21
3
The
programg
an
gle
calculatesthe
distributionofan
gle
sandd
ihe
dra
lsintim
e.It
alsogives
theaverage
angleor
dihedral.T
heindex
fileconsists
oftripletsor
quadruplesofatom
numbers:
[a
ng
les
]1
23
23
43
45
[d
ihe
dra
ls]
12
34
23
55
For
thedihedralangles
youcan
useeither
the“biochem
icalconvention”(
φ=
0≡cis)
or“poly-
mer
convention”(φ
=0≡tra
ns),see
Fig.8.5.
Tofollow
specifican
gle
sintim
ebetw
eentw
ovectors,a
vectorand
aplane
ortw
oplanes
(definedby
2,resp.3
atoms
insideyour
molecule,see
Fig.
8.6A,B
,C),use
theprogramg
sga
ng
le.
14
0C
ha
pte
r8
.A
na
lysi
s
The
self
diffu
sion
coef
ficie
ntca
nbe
calc
ulat
edus
ing
the
Gre
en-K
ubo
rela
tion
[65
]
DA
=1 3
∫ ∞ 0〈v
i(t)·v
i(0)〉 i∈
Adt
(8.1
6)
whi
chis
just
the
inte
gral
ofth
eve
loci
tyau
toco
rrel
atio
nfu
nctio
n.T
here
isa
wid
ely
held
belie
fth
atth
eve
loci
tyA
CF
conv
erge
sfa
ster
than
the
mea
nsq
uare
disp
lace
men
t(se
c.8.
5.5)
,whi
chca
nal
sobe
used
for
the
com
puta
tion
ofdi
ffusi
onco
nsta
nts.
How
ever
,Alle
n&
Tild
esly
[65
]war
nus
that
the
long
time
cont
ribut
ion
toth
eve
loci
tyA
CF
can
notb
eig
nore
d,so
care
mus
tbe
take
n.
Ano
ther
impo
rtan
tqu
antit
yis
the
dipo
leco
rrel
atio
ntim
e.T
hedip
ole
corr
ela
tion
fun
ctio
nfor
part
icle
sAis
calc
ulat
edas
follo
ws
bygd
ipo
les
:
Cµ(τ
)=
〈µi(τ)·µ
i(0)〉 i∈
A(8
.17)
with
µi
=∑ j∈
ir jq j
.T
hedi
pole
corr
elat
ion
time
can
beco
mpu
ted
usin
geq
n.8.
8.F
orso
me
appl
icat
ions
see
[67].
The
visc
osity
ofa
liqui
dca
nbe
rela
ted
toth
eco
rrel
atio
ntim
eof
the
Pre
ssur
ete
nsor
P[6
8,69
].g
en
erg
yca
nco
mpu
teth
evi
scos
ity,b
utin
our
expe
rienc
eth
isis
notv
ery
accu
rate
(act
ually
the
valu
esdo
notc
onve
rge.
..).
8.5.
5M
ean
Squ
are
Dis
plac
emen
t
Tode
term
ine
the
self
diffu
sion
coef
ficie
ntDA
ofpa
rtic
lesA
one
can
use
the
Ein
stei
nre
latio
n[
65]
lim t→∞〈‖
r i(t
)−
r i(0
)‖2〉 i∈
A=
6DAt
(8.1
8)
Thi
sM
ea
nS
qu
are
Dis
pla
cem
en
tan
dD
Aar
eca
lcul
ated
byth
epr
ogra
mgm
sd.
For
mol
ecul
esco
nsis
ting
ofm
ore
than
one
atom
,r i
isth
ece
nter
ofm
ass
posi
tions
.In
that
case
you
shou
ldus
ean
inde
xfil
ew
ithm
olec
ule
num
bers
!T
hepr
ogra
mca
nal
sobe
used
for
calc
ulat
ing
diffu
sion
inon
eor
two
dim
ensi
ons.
Thi
sis
usef
ulfo
rst
udyi
ngla
tera
ldiff
usio
non
inte
rfac
es.
An
exam
ple
ofth
em
ean
squa
redi
spla
cem
ento
fSP
C-w
ater
isgi
ven
inF
ig.
8.4.
8.6
Bon
ds,a
ngle
san
ddi
hedr
als
g_
bo
nd
g_
an
gle
g_
sga
ng
le
5.5
.D
ata
ba
ses
89
•T
hew
ayof
addi
ngH
atom
s,ca
nbe
any
of
1o
ne
pla
na
rh
ydro
gen
,e.g
.rin
gs
or
pe
ptid
eb
on
don
ehy
drog
enat
om(n
)is
gene
rate
d,ly
ing
inth
epl
ane
ofat
oms
(i,j,k
)on
the
line
bise
ctin
gan
gle
(j-i-k
)at
adi
stan
ceof
0.1
nmfr
omat
omi,
such
that
the
angl
es(n
-i-j)
and
(n-i-
k)ar
e>90
degr
ees
2o
ne
sin
gle
hyd
roge
n,e
.g.h
ydro
xyl
one
hydr
ogen
atom
(n)i
sge
nera
ted
ata
dist
ance
of0.
1nm
from
atom
i,su
chth
atan
gle
(n-i-
j)=10
9.5
degr
ees
and
dihe
dral
(n-i-
j-k)=
tran
s
3tw
op
lan
ar
hyd
roge
ns,
e.g.
-NH 2
two
hydr
ogen
s(n
1,n2
)ar
ege
nera
ted
ata
dist
ance
of0.
1nm
from
atom
i,su
chth
atan
gle
(n1-
i-j)=
(n2-
i-j)=
120
degr
ees
and
dihe
dral
(n1-
i-j-k
)=ci
san
d(n
2-i-j
-k)=
tran
s,su
chth
atna
mes
are
acco
rdin
gto
IUP
AC
stan
dard
s[
61]
4tw
oo
rth
ree
tetr
ah
ed
ralh
ydro
gen
s,e.
g.-C
H3
thre
e(n
1,n2
,n3)
ortw
o(n
1,n2
)hy
drog
ens
are
gene
rate
dat
adi
stan
ceof
0.1
nmfr
omat
omi,
such
that
angl
e(n
1-i-j
)=(n
2-i-j
)=(n
3-i-j
)=10
9.5,
dihe
dral
(n1-
i-j-k
)=tr
ans,
(n2-
i-j-k
)=tr
ans+
120
and
(n3-
i-j-k
)=tr
ans+
240
degr
ees
5o
ne
tetr
ah
ed
ralh
ydro
gen
,e.g
.C 3CH
one
hydr
ogen
atom
(n1)
isge
nera
ted
ata
dist
ance
of0.
1nm
from
atom
iin
tetr
ahed
ral
conf
orm
atio
nsu
chth
atan
gle
(n1-
i-j)=
(n1-
i-k)=
(n1-
i-l)=
109.
5de
gree
s
6tw
ote
tra
he
dra
lhyd
roge
ns,
e.g.
C-C
H2-C
two
hydr
ogen
atom
s(n
1,n2
)ar
ege
nera
ted
ata
dist
ance
of0.
1nm
from
atom
iin
tetr
ahed
ralc
onfo
rmat
ion
onth
epl
ane
biss
ectin
gan
gle
i-j-k
with
angl
e(n
1-i-n
2)=
(n1-
i-j)=
(n1-
i-k)=
109.
5
7tw
ow
ate
rh
ydro
gen
stw
ohy
drog
ens
are
gene
rate
dar
ound
atom
iac
cord
ing
toS
PC
[48
]w
ater
geom
etry
.T
hesy
mm
etry
axis
will
alte
rnat
ebe
twee
nth
ree
coor
dina
teax
esin
both
dire
ctio
ns
•T
hree
orfo
urco
ntro
lato
ms
(i,j,k
,l),w
here
the
first
alw
ays
isth
eat
omto
whi
chth
eH
atom
sar
eco
nnec
ted.
The
othe
rtw
oor
thre
ede
pend
onth
eco
dese
lect
ed.
5.5.
3Te
rmin
idat
abas
e
The
term
inid
atab
ases
are
stor
edin
ff?
??
-n.td
ban
dff?
??
-c.td
bfo
rthe
N-a
ndC
-ter
min
ire
spec
tivel
y.T
hey
cont
ain
info
rmat
ion
fort
hepdb
2g
mx
prog
ram
onho
wto
conn
ectn
ewat
oms
toex
istin
gon
es,w
hich
atom
ssh
ould
bere
mov
edor
chan
ged
and
whi
chbo
nded
inte
ract
ions
shou
ldbe
adde
d.T
hefo
rmat
ofth
eis
asfo
llow
s(t
his
isan
exam
ple
from
the
ffg
mx-
c.td
b):
[N
on
e]
[C
OO
-]
[re
pla
ce]
CC
C1
2.0
11
0.2
7[
ad
d]
28
CC
AN
OO
M1
5.9
99
4-0
.63
5
90
Ch
ap
ter
5.
Top
olog
ies
[d
ele
te]
O[im
pro
pe
rs]
CO
1O
2C
A
The
fileis
organizedin
blocks,each
with
aheader
specifyingthe
name
ofthe
block.T
heseblocks
correspondto
differenttypes
ofterm
inithat
canbe
addedto
am
olecule.In
thisexam
-ple
[N
on
e]
isthe
firstblock,
correspondingto
aterm
inusthat
leavesthe
molecule
asit
is;[
CO
O-
]is
thesecond
terminus
type,correspondingto
changingthe
terminalcarbon
atominto
adeprotonated
carboxylgroup.B
locknam
escannot
beany
ofthe
following:
rep
lace
,a
dd
,d
ele
te,
bo
nd
s,
an
gle
s,
dih
ed
rals
,im
pro
pe
rs;
thisw
ouldinterfere
with
theparam
e-ters
oftheblock,and
would
probablyalso
bevery
confusingto
human
readers.
Per
blockthe
following
optionsare
present:
•[
rep
lace
]replace
anexisting
atomby
onew
itha
differentatomtype,atom
name,charge
and/orm
ass.F
oreach
atomto
bereplaced
online
shouldbe
enteredw
iththe
following
fields:
–nam
eofthe
atomto
bereplaced
–new
atomnam
e
–new
atomtype
–new
mass
–new
charge
•[
ad
d]
addnew
atoms.
For
each(group
of)added
atom(s),
atw
o-lineentry
isnecessary.
The
firstline
containsthe
same
fieldsas
anentry
inthe
hydrogendatabase
(number
ofatoms,type
ofaddition,
controlatoms,
see5.5.1),but
thepossible
typesof
additionare
extendedby
two
more,specifically
forC
-terminaladditions:
8tw
oca
rbo
xyloxyge
ns,-C
OO −
two
oxygens(n1,n2)
aregenerated
accordingto
rule3,ata
distanceof0.136
nmfrom
atomiand
anangle
(n1-i-j)=(n2-i-j)=
117degrees
9ca
rbo
xyloxyge
ns
an
dh
ydroge
n,-C
OO
Htw
ooxygens
(n1,n2)are
generatedaccording
torule
3,at
distancesof
0.123nm
and0.125
nmfrom
atomifor
n1and
n2resp.
andangles
(n1-i-j)=121
and(n2-i-j)=
115degrees.
One
hydrogen(n’)
isgenerated
aroundn2
accordingto
rule2,
where
n-i-jand
n-i-j-kshould
beread
asn’-n2-iand
n’-n2-i-jresp.
After
thisline
anotherline
follows
which
specifiesthe
detailsof
theadded
atom(s),
inthe
same
way
asfor
replacingatom
s,i.e.:
–atom
name
–atom
type
–m
ass
–charge
8.5
.C
orre
latio
nfu
nctio
ns
13
9
intervals(j<<M
),butitmakes
iteasierto
interprettheresults.
Another
aspectthatmay
notbeneglected
when
computing
AC
Fs
fromsim
ulation,isthatusually
thetim
eoriginsξ
(eqn.8.6)are
notstatisticallyindependent,w
hichm
ayintroduce
abias
inthe
results.T
hiscan
betested
usinga
block-averagingprocedure,w
hereonly
time
originsw
itha
spacingatleastthe
lengthofthe
time
lagare
included,e.g.usingktime
originsw
ithspacing
ofM∆t
(where
kM
≤N
):
Cf (j∆
t)=
1k
k−1
∑i=0
f(iM∆t)f((iM
+j)∆
t)(8.11)
How
ever,oneneeds
verylong
simulations
togetgood
accuracythis
way,because
thereare
many
fewer
pointsthatcontribute
tothe
AC
F.
8.5.2U
singF
FT
forcom
putationofthe
AC
F
The
computationalcostfor
calculatingan
AC
Faccording
toeqn.8.9
isproportionaltoN
2,which
isconsiderable.
How
ever,thiscan
beim
provedby
usingfastF
ouriertransform
sto
dothe
convo-lution
[65].
8.5.3S
pecialforms
oftheA
CF
There
aresom
eim
portantvarietieson
theA
CF,e.g.the
AC
Fofa
vectorp
:
Cp(t)
= ∫∞0P
n (cos6
(p(t),p(t+ξ))d
ξ(8.12)
where
Pn (x)
isthe
nth
orderLegendre
polynomial 1.
Such
correlationtim
escan
actuallybe
ob-tained
experimentally
usinge.g.N
MR
orother
relaxationexperim
ents.G
RO
MA
CS
cancom
putecorrelations
usingthe
1stand
2 nd
orderLegendre
polynomial(eqn.
8.12).T
hiscan
a.o.be
usedfor
rotationalautocorrelation(gro
tacf
),dipoleautocorrelation
(gd
ipo
les
).
Inorder
tostudy
torsionangle
dynamics
we
definea
dihedralautocorrelationfunction
as[
66]:
C(t)
=〈cos(θ(τ)−
θ(τ+t))〉
τ(8.13)
Note
thatthisis
notaproductoftw
ofunctions
asis
generallyused
forcorrelation
functions,butitm
aybe
rewritten
asthe
sumoftw
oproducts:
C(t)
=〈cos(θ(τ))cos(θ(τ
+t))
+sin(θ(τ))sin(θ(τ
+t))〉
τ(8.14)
8.5.4S
ome
Applications
The
programg
vela
cccalculates
thisVe
locity
Au
toC
orre
latio
nF
un
ction.
Cv(τ)
=〈v
i (τ)·v
i (0)〉i∈
A(8.15)
1P0 (x
)=
1,P1 (x
)=
x,P
2 (x)
=(3
x2−
1)/
2
13
8C
ha
pte
r8
.A
na
lysi
s
0.0
0.5
1.0
1.5
2.0
r (n
m)
0.0
1.0
2.0
3.0
g(r) �
Gro
mac
s R
DF
OW
1-O
W1
Fig
ure
8.3:g O
O(r
)fo
rO
xyge
n-O
xyge
nof
SP
C-w
ater
.
whe
reth
eno
tatio
non
the
right
hand
side
mea
nsav
erag
ing
over
ξ,i.e
.ove
rtim
eor
igin
s.It
isal
sopo
ssib
leto
com
pute
cros
s-co
rrel
atio
nfu
nctio
nfr
omtw
opr
oper
ties
f(t
)an
dg(t
):
Cfg(t
)=
〈f(ξ
)g(ξ
+t)〉 ξ
(8.7
)
how
ever
,in
GR
OM
AC
Sth
ere
isno
stan
dard
mec
hani
smto
doth
is(
note
:yo
uca
nus
eth
exmg
rpr
ogra
mto
com
pute
cros
sco
rrel
atio
ns).
The
inte
gral
ofth
eco
rrel
atio
nfu
nctio
nov
ertim
eis
the
corr
elat
ion
timeτ
f:
τ f=
∫ ∞ 0C
f(t
)dt
(8.8
)
Inpr
actic
eco
rrel
atio
nfu
nctio
nsar
eca
lcul
ated
base
don
data
poin
tsw
ithdi
scre
tetim
ein
terv
als
∆t,
soth
atth
eA
CF
from
anM
Dsi
mul
atio
nis
:
Cf(j
∆t)
=1
N−j
N−
1−
j ∑ i=0
f(i
∆t)f((i+j)
∆t)
(8.9
)
whe
reN
isth
enu
mbe
rofa
vaila
ble
time
fram
esfo
rthe
calc
ulat
ion.
The
resu
lting
AC
Fis
obvi
ousl
yon
lyav
aila
ble
attim
epo
ints
with
the
sam
ein
terv
al∆t.
Sin
cefo
rm
any
appl
icat
ions
itis
nece
ssar
yto
know
the
shor
ttim
ebe
havi
orof
the
AC
F(e
.g.t
hefir
st10
ps)
this
ofte
nm
eans
that
we
have
tosa
veth
eat
omic
coor
dina
tes
with
shor
tint
erva
ls.
Ano
ther
impl
icat
ion
ofeq
n.8.
9is
that
inpr
inci
ple
we
can
notc
ompu
teal
lpoi
nts
ofth
eA
CF
with
the
sam
eac
cura
cy,s
ince
we
have
N−
1da
tapo
ints
forC
f(∆t)
but
only
1fo
rCf((N−
1)∆t)
.H
owev
er,
ifw
ede
cide
toco
mpu
teon
lyan
AC
Fof
leng
thM
∆t,
whe
reM
≤N/2
we
can
com
pute
allp
oint
sw
ithth
esa
me
stat
istic
alac
cura
cy:
Cf(j
∆t)
=1 M
N−
1−
M ∑ i=0
f(i
∆t)f((i+j)
∆t)
(8.1
0)
here
ofco
ursej<M
.M
isso
met
imes
refe
rred
toas
the
time
lag
ofth
eco
rrel
atio
nfu
nctio
n.W
hen
we
deci
deto
doth
is,w
ein
tent
iona
llydo
notu
seal
lthe
avai
labl
epo
ints
for
very
shor
ttim
e
5.6
.F
ilefo
rma
ts9
1
Like
inth
ehy
drog
enda
taba
se(s
ee5.5.
1),
whe
nm
ore
then
one
atom
isco
nnec
ted
toan
exis
ting
one,
anu
mbe
rw
illbe
appe
nded
toth
een
dof
the
atom
nam
e.
•[
de
lete
]de
lete
exis
ting
atom
s.O
neat
omna
me
per
line.
•[
bo
nd
s]
,[a
ng
les
],[
dih
ed
rals
]an
d[
imp
rop
ers
]ad
dad
ditio
nalb
onde
dpa
ram
eter
s.T
hefo
rmat
isid
entic
alto
that
used
inth
eff?
??
.rtp
,se
e5.5
.1.
5.6
File
form
ats
5.6.
1To
polo
gyfil
e
The
topo
logy
file
isbu
iltfo
llow
ing
the
GR
OM
AC
Ssp
ecifi
catio
nfo
ra
mol
ecul
arto
polo
gy.
A*.
top
file
can
bege
nera
ted
bypd
b2
gm
x.
Des
crip
tion
ofth
efil
ela
yout
:
•se
mic
olon
(;)
and
new
line
surr
ound
com
men
ts
•on
alin
een
ding
with\
the
new
line
char
acte
ris
igno
red.
•di
rect
ives
are
surr
ound
edby[
and
]
•th
eto
polo
gyco
nsis
tsof
thre
ele
vels
:
–th
epa
ram
eter
leve
l(se
eTa
ble
5.3)
–th
em
olec
ule
leve
l,w
hich
shou
ldco
ntai
non
eor
mor
em
olec
ule
defin
ition
s(s
eeTa
-bl
e5.
4)
–th
esy
stem
leve
l:[sy
ste
m]
,[m
ole
cule
s]
•ite
ms
shou
ldbe
sepa
rate
dby
spac
esor
tabs
,not
com
mas
•at
oms
inm
olec
ules
shou
ldbe
num
bere
dco
nsec
utiv
ely
star
ting
at1
•th
efil
eis
pars
edon
ceon
lyw
hich
impl
ies
that
nofo
rwar
dre
fere
nces
can
betr
eate
d:ite
ms
mus
tbe
defin
edbe
fore
they
can
beus
ed
•ex
clus
ions
can
bege
nera
ted
from
the
bond
sor
over
ridde
nm
anua
lly
•th
ebo
nded
forc
ety
pes
can
bege
nera
ted
from
the
atom
type
sor
over
ridde
npe
rbo
nd
•de
scrip
tive
com
men
tlin
esan
dem
pty
lines
are
high
lyre
com
men
ded
•us
ing
one
ofth
e[a
tom
s]
,[
bo
nd
s]
,[
pa
irs
],
[a
ng
les
],
etc.
with
out
havi
ngus
ed[
mo
lecu
lety
pe
]be
fore
ism
eani
ngle
ssan
dge
nera
tes
aw
arni
ng.
•us
ing
[m
ole
cule
s]
with
out
havi
ngus
ed[
syst
em
]be
fore
ism
eani
ngle
ssan
dge
nera
tes
aw
arni
ng.
92
Ch
ap
ter
5.
Top
olog
ies
Param
etersinteraction
directive#
f.param
eterspert
typeat.
tp
ma
nd
ato
ryd
efa
ults
non-bondedfunction
type;com
binationrule;
generatepairs
(no/yes);fudge
LJ();fudge
()m
an
da
tory
ato
mtyp
es
atomtype;m
(u);q(e);particle
type;c6
(kJm
ol −1nm
6);c12
(kJm
ol −1nm
12)
bo
nd
type
s(see
Table5.4,directiveb
on
ds
)co
nstra
inttyp
es
(seeTable5.4,directive
con
strain
ts)
pa
irtype
s(see
Table5.4,directivep
airs
)a
ng
letyp
es
(seeTable5.4,directive
an
gle
s)
properdih.
dih
ed
raltyp
es
2(b
)1
θm
ax
(deg);fc(kJ
mol −
1);mult
X(a
)
improper
dih.d
ihe
dra
ltype
s2(c
)2
θ0
(deg);fc(kJ
mol −
1rad −2)
XR
Bdihedral
dih
ed
raltyp
es
2(b
)3
C0 ,C
1 ,C2 ,C
3 ,C4 ,C
5(kJ
mol −
1)LJ
no
nb
on
dp
ara
ms
21
c6(kJ
mol −
1nm6);c
12
(kJm
ol −1nm
12)
Buckingham
no
nb
on
dp
ara
ms
22
a(kJ
mol −
1);b(nm
−1);
c6
(kJm
ol −1nm
6)
Molecule
definition(s)
oneor
more
molecule
definitionsas
describedin
Table5.4
(nextpage)
System
ma
nd
ato
rysyste
msystem
name
ma
nd
ato
rym
ole
cule
sm
oleculenam
e;number
ofmolecules
’#at’is
thenum
berofatom
types’f.
tp’isfunction
type’pert’indicates
ifthisinteraction
typecan
beperturbed
duringfree
energycalculations
(a)
multiplicities
cannotbe
perturbed(b
)the
innertw
oatom
sin
thedihedral
(c)
theouter
two
atoms
inthe
dihedralF
orfree
energycalculations,the
parameters
fortopology
’B’(lam
bda=
1)should
beadded
onthe
same
line,afterthe
normalparam
eters,inthe
same
orderas
thenorm
alparameters.
Table5.3:
The
topology(*.to
p)
file.
8.5
.C
orre
latio
nfu
nctio
ns
13
7
r
r+dr
r+dr
rθ+
dθθ
e
ABD
CF
igure8.2:
Definition
ofslicesing
rdf
:A
.gA
B(r).
B.g
AB
(r,θ).T
heslices
arecolored
grey.C
.N
ormalization〈ρ
B 〉lo
cal .
D.N
ormalization〈ρ
B 〉lo
cal,
θ .N
ormalization
volumes
arecolored
grey.
Usually
thevalue
ofrm
ax
ishalf
ofthe
boxlength.
The
averagingis
alsoperform
edin
time.
Inpractice
theanalysis
programgrd
fdivides
thesystem
intosphericalslices
(fromrtor+dr,see
Fig.8.2A
)and
makes
ahistogram
instead
oftheδ-function.
An
example
ofthe
rdfof
Oxygen-
Oxygen
inS
PC
-water
[48]isgiven
inF
ig.8.3.
With
grd
fitis
alsopossible
tocalculate
anangle
dependentrdfgA
B(r,θ),w
herethe
angleθis
definedw
ithrespectto
acertain
laboratoryaxise,see
Fig.8.2B
.
gA
B(r,θ)
=1
〈ρB 〉
loca
l,θ
1NA
NA∑i∈
A
NB∑j∈
B
δ(rij −
r)δ(θij −
θ)2πr2sin(θ)
(8.4)
cos(θij )
=rij ·e
‖rij ‖
‖e‖(8.5)
This
gA
B(r,θ)
isusefulforanalyzing
anisotropicsystem
s.N
otethatin
thiscase
thenorm
alization〈ρ
B 〉lo
cal,
θis
theaverage
densityin
allangleslices
fromθ
toθ+
dθ
uptorm
ax ,so
angledependent,
seeF
ig.8.2D.
8.5C
orrelationfunctions
8.5.1T
heoryofcorrelation
functions
The
theoryofcorrelation
functionsis
wellestablished
[65].
How
everw
ew
anttodescribe
herethe
implem
entationofthe
variouscorrelation
functionflavors
inthe
GR
OM
AC
Scode.
The
definitionofthe
autocorrelationfunction
(AC
F)Cf (t)
fora
propertyf(t)is
Cf (t)
=〈f(ξ)f(ξ
+t)〉
ξ(8.6)
13
6C
ha
pte
r8
.A
na
lysi
s
Fig
ure
8.1:
The
win
dow
ofng
mx
show
ing
abo
xof
wat
er.
ase
tof
ener
gies
,lik
epo
tent
ial,
kine
ticor
tota
lene
rgy,
orin
divi
dual
cont
ribut
ions
,lik
eLe
nnar
d-Jo
nes
ordi
hedr
alen
ergi
es.
The
cen
ter-
of-
ma
ssve
loci
ty,defi
ned
as vco
m=
1 M
N ∑ i=1
miv
i(8
.2)
withM
=∑ N i=
1m
ith
eto
talm
ass
ofth
esy
stem
,can
bem
onito
red
intim
eby
the
prog
ram
gco
m.
Itis
how
ever
reco
mm
ende
dto
rem
ove
the
cent
er-o
f-m
ass
velo
city
ever
yst
ep(s
eech
apte
r3)
!
8.4
Rad
iald
istr
ibut
ion
func
tions
g_
rdf
The
rad
iald
istr
ibu
tion
fun
ctio
n(rd
f)or
pair
corr
elat
ion
func
tiong
AB
(r)
betw
een
part
icle
sof
type
Aan
dB
isde
fined
inth
efo
llow
ing
way
:
g AB
(r)
=〈ρ
B(r
)〉〈ρ
B〉 lo
cal
=1
〈ρB〉 lo
cal
1 NA
NA ∑ i∈A
NB ∑ j∈B
δ(r i
j−r)
4πr2
(8.3
)
with
〈ρB
(r)〉
the
part
icle
dens
ityof
typeB
ata
dist
ancer
arou
ndpa
rtic
lesA
,an
d〈ρ
B〉 lo
cal
the
part
icle
dens
ityof
typeB
aver
aged
over
all
sphe
res
arou
ndpa
rtic
les
Aw
ithra
diusr m
ax
(see
Fig
.8.2
C).
5.6
.F
ilefo
rma
ts9
3
Mol
ecul
ede
finiti
onin
tera
ctio
ndi
rect
ive
#f.
para
met
ers
pert
type
at.
tp
ma
nd
ato
rym
ole
cule
typ
em
olec
ule
nam
e;ex
clud
ene
ighb
ors
#bo
nds
away
for
non-
bond
edin
tera
ctio
nsm
an
da
tory
ato
ms
1at
omty
pe;r
esid
uenu
mbe
r;re
sidu
ena
me;
atom
nam
e;ch
arge
grou
pnu
mbe
r;q
(e);
m(u
)X
(b)
bond
bo
nd
s(c
,d)
21
b 0(n
m);
f c(k
Jm
ol−
1nm
−2)
XG
96bo
ndb
on
ds
(c,d
)2
2b 0
(nm
);f c
(kJ
mol−
1nm
−4)
Xm
orse
bo
nd
s(c
,d)
23
b 0(n
m);
D(k
Jm
ol−1);β
(nm−
1)
cubi
cbo
ndb
on
ds
(c,d
)2
4b 0
(nm
);C 2
(kJ
mol−
1nm
−2);
C3
(kJ
mol−
1nm
−3)
conn
ectio
nb
on
ds
(c)
25
harm
onic
pot.
bo
nd
s2
6b 0
(nm
);f c
(kJ
mol−
1nm
−2)
XLJ
1-4
pa
irs
21
c 6(k
Jm
ol−
1nm
6);
c 12
(kJ
mol−
1nm
12)
Xan
gle
an
gle
s(d
)3
1θ 0
(deg
);f c
(kJ
mol−
1ra
d−2)
XG
96an
gle
an
gle
s(d
)3
2θ 0
(deg
);f c
(kJ
mol−
1)
Xpr
oper
dih.
dih
ed
rals
41
θ max
(deg
);f c
(kJ
mol−
1);
mul
tX
(a)
impr
oper
dih.
dih
ed
rals
42
θ 0(d
eg);
f c(k
Jm
ol−
1ra
d−2)
XR
Bdi
hedr
ald
ihe
dra
ls4
3C 0
,C1,C
2,C
3,C
4,C
5(k
Jm
ol−
1)
cons
trai
ntco
nst
rain
ts2
1b 0
(nm
)X
cons
tr.n.
c.co
nst
rain
ts2
2b 0
(nm
)X
settl
ese
ttle
s3
1d O
H,d
HH
(nm
)du
mm
y2d
um
mie
s23
1a
()du
mm
y3d
um
mie
s34
1a,
b()
dum
my3
fdd
um
mie
s34
2a
();d
(nm
)du
mm
y3fa
dd
um
mie
s34
3θ
(deg
);d
(nm
)du
mm
y3ou
td
um
mie
s34
4a,
b()
;c(n
m−1)
dum
my4
fdd
um
mie
s45
1a,
b()
;d(n
m);
posi
tion
res.
po
sitio
nre
stra
ints
11
k x,k
y,k
z(k
Jm
ol−
1nm
−2)
dist
ance
res.
dis
tan
cere
stra
ints
21
type
;ind
ex;l
ow,u
p 1,up
2(n
m);
fact
or()
angl
ere
s.a
ng
lere
stra
ints
41
θ 0(d
eg);
f c(k
Jm
ol−
1);
mul
tX
(a)
angl
ere
s.z
an
gle
rest
rain
tsz
21
θ 0(d
eg);
f c(k
Jm
ol−
1);
mul
tX
(a)
excl
usio
nse
xclu
sio
ns
1on
eor
mor
eat
omin
dice
s
’#at
’is
the
num
ber
ofat
omin
dice
s’f.
tp’i
sfu
nctio
nty
pe’p
ert’
indi
cate
sif
this
inte
ract
ion
type
can
bepe
rtur
bed
durin
gfr
eeen
ergy
calc
ulat
ions
(a)
mul
tiplic
ities
can
notb
epe
rtur
bed
(b)
only
the
atom
type
,cha
rge
and
mas
sca
nbe
pert
urbe
d(c
)us
edby
gro
mp
pfo
rge
nera
ting
excl
usio
ns(d
)ca
nbe
conv
erte
dto
cons
trai
nts
bygro
mp
pF
orfr
eeen
ergy
calc
ulat
ions
,the
para
met
ers
for
topo
logy
’B’(
lam
bda
=1)
shou
ldbe
adde
don
the
sam
elin
e,af
ter
the
norm
alpa
ram
eter
s,in
the
sam
eor
der
asth
eno
rmal
para
met
ers.
Tabl
e5.
4:T
hem
olec
ule
defin
ition
.
94
Ch
ap
ter
5.
Top
olog
ies
•after[
system
]the
onlyallow
eddirective
is[m
ole
cule
s]
•using
anunknow
nstring
in[]
causesallthe
datauntilthe
nextdirective
tobe
ignored,and
generatesa
warning.
Here
isan
example
ofatopology
file,u
rea
.top
:
;;E
xam
ple
top
olo
gy
file;;
Th
efo
rcefie
ldfile
sto
be
inclu
de
d#
inclu
de
"ffgm
x.itp"
[m
ole
cule
type
];
na
me
nre
xclU
rea
3
[a
tom
s]
;n
rtyp
ere
snr
resid
ua
tom
cgn
rch
arg
e1
C1
UR
EA
C1
10
.68
32
O1
UR
EA
O2
1-0
.68
33
NT
1U
RE
AN
32
-0.6
22
4H
1U
RE
AH
42
0.3
46
5H
1U
RE
AH
52
0.2
76
6N
T1
UR
EA
N6
3-0
.62
27
H1
UR
EA
H7
30
.34
68
H1
UR
EA
H8
30
.27
6
[b
on
ds
];
ai
aj
fun
ctb
0kb
34
11
.00
00
00
e-0
13
.74
46
80
e+
05
35
11
.00
00
00
e-0
13
.74
46
80
e+
05
67
11
.00
00
00
e-0
13
.74
46
80
e+
05
68
11
.00
00
00
e-0
13
.74
46
80
e+
05
12
11
.23
00
00
e-0
15
.02
08
00
e+
05
13
11
.33
00
00
e-0
13
.76
56
00
e+
05
16
11
.33
00
00
e-0
13
.76
56
00
e+
05
[p
airs
];
ai
aj
fun
ctc6
c12
24
10
.00
00
00
e+
00
0.0
00
00
0e
+0
02
51
0.0
00
00
0e
+0
00
.00
00
00
e+
00
27
10
.00
00
00
e+
00
0.0
00
00
0e
+0
02
81
0.0
00
00
0e
+0
00
.00
00
00
e+
00
37
10
.00
00
00
e+
00
0.0
00
00
0e
+0
03
81
0.0
00
00
0e
+0
00
.00
00
00
e+
00
46
10
.00
00
00
e+
00
0.0
00
00
0e
+0
05
61
0.0
00
00
0e
+0
00
.00
00
00
e+
00
[a
ng
les
];
ai
aj
ak
fun
ctth
0cth
13
41
1.2
00
000
e+
02
2.9
28
80
0e
+0
2
8.2
.L
oo
king
atyo
ur
traje
ctory
13
5
Sid
eC
ha
inprotein
sidechain
atoms;
thatis
allatoms
exceptN
,C
α ,C
,O
,backbone
amide
hydrogen,oxygens
inC
-terminus
andhydrogens
onthe
N-term
inus
Sid
eC
ha
in-H
proteinside
chainatom
sexcluding
allhydrogens
Pro
t-Ma
sses
proteinatom
sexcluding
dumm
ym
asses(as
usedin
dumm
yatom
constructionsof
NH
3
groupsand
Tryptophane
sidechains),seealso
sec.5.2.2;this
groupis
onlyincluded
when
itdiffers
fromthe
’Pro
tein
’group
No
n-P
rote
inallnon-protein
atoms
DN
AallD
NA
atoms
mo
lecu
len
am
efor
allresidues/m
oleculesw
hichare
notrecognized
asprotein
orD
NA
,one
groupper
residue/molecule
name
isgenerated
Oth
erallatom
sw
hichare
neitherprotein
norD
NA
.
Em
ptygroups
willnotbe
generated.
8.2Looking
atyourtrajectory
ng
mx
Before
analyzingyour
trajectoryit
isoften
informative
tolook
atyour
trajectoryfirst.
Grom
acscom
esw
itha
simple
trajectoryview
ern
gm
x;theadvantage
with
thisone
isthatitdoes
notrequireO
penGL,w
hichusually
isn’tpresente.g.on
supercomputers.
Itisalso
possibleto
generatea
hard-copy
inE
ncapsulatedP
ostscriptformat,
seeF
ig.8.1.
Ifyouw
antafaster
andm
orefancy
viewer
thereare
severalprograms
thatcan
readthe
GR
OM
AC
Strajectory
formats
–have
alook
atour
homepagew
ww
.gromacs.orgfor
updatedlinks.
8.3G
eneralproperties
g_
en
erg
yg
_co
m
Toanalyze
some
orallen
erg
iesand
otherproperties,
suchastota
lp
ressu
re,p
ressu
rete
nso
r,d
en
sity,bo
x-volu
meand
bo
x-sizes,use
theprogramg
en
erg
y.
Achoice
canbe
made
froma
list
13
4C
ha
pte
r8
.A
na
lysi
s
Gro
ups
can
ther
efor
eco
nsis
tof
ase
ries
ofa
tom
nu
mb
ers,
but
inso
me
case
sal
soofm
ole
cule
nu
mb
ers.
Itis
also
poss
ible
tosp
ecify
ase
ries
ofan
gles
bytrip
les
ofa
tom
nu
mb
ers,
dihe
dral
sby
qu
ad
rup
leso
fa
tom
nu
mb
ersa
ndbo
nds
orve
ctor
s(in
am
olec
ule)
bypairs
ofa
tom
nu
mb
ers.
Whe
nap
prop
riate
the
type
ofin
dex
file
will
besp
ecifi
edfo
rth
efo
llow
ing
anal
ysis
prog
ram
s.To
help
crea
ting
such
inde
xfil
es(
ind
ex.
nd
x),
ther
ear
ea
coup
leof
prog
ram
sto
gene
rate
them
,us
ing
eith
eryo
urin
put
confi
gura
tion
orth
eto
polo
gy.
Toge
nera
tean
inde
xfil
eco
nsis
ting
ofa
serie
sof
ato
mn
um
be
rs(as
inth
eex
ampl
eofg
AB
)us
ema
ken
dx
.To
gene
rate
anin
dex
file
with
angl
esor
dihe
dral
s,us
emk
an
gn
dx
.O
fco
urse
you
can
also
mak
eth
emby
hand
.T
hege
nera
lfo
rmat
ispr
esen
ted
here
:
[O
xyg
en
]1
47
[H
ydro
ge
n]
23
56
89
Firs
tth
egr
oup
nam
eis
writ
ten
betw
een
squa
rebr
acke
ts.
The
follo
win
gat
omnu
mbe
rsm
aybe
spre
adou
tove
ras
man
ylin
esas
you
like.
The
atom
num
berin
gst
arts
at1.
8.1.
1D
efau
ltG
roup
s
Whe
nno
inde
xfil
eis
supp
lied
toan
alys
isto
ols,
anu
mbe
rof
defa
ult
grou
psca
nbe
gene
rate
dto
choo
sefr
om:
Sys
tem al
lato
ms
inth
esy
stem
Pro
tein al
lpro
tein
atom
s
Pro
tein
-Hpr
otei
nat
oms
excl
udin
ghy
drog
ens
C-a
lph
a Cα
atom
s
Ba
ckb
on
epr
otei
nba
ckbo
neat
oms;
N,C α
and
C
Ma
inC
ha
inpr
otei
nm
ain
chai
nat
oms:
N,C α
,Can
dO
,inc
ludi
ngox
ygen
sin
C-t
erm
inus
Ma
inC
ha
in+
Cb
prot
ein
mai
nch
ain
atom
sin
clud
ing
Cβ
Ma
inC
ha
in+
Hpr
otei
nm
ain
chai
nat
oms
incl
udin
gba
ckbo
neam
ide
hydr
ogen
and
hydr
ogen
son
the
N-
term
inus
5.6
.F
ilefo
rma
ts9
5
13
51
1.2
00
00
0e
+0
22
.92
88
00
e+
02
43
51
1.2
00
00
0e
+0
23
.34
72
00
e+
02
16
71
1.2
00
00
0e
+0
22
.92
88
00
e+
02
16
81
1.2
00
00
0e
+0
22
.92
88
00
e+
02
76
81
1.2
00
00
0e
+0
23
.34
72
00
e+
02
21
31
1.2
15
00
0e
+0
25
.02
08
00
e+
02
21
61
1.2
15
00
0e
+0
25
.02
08
00
e+
02
31
61
1.1
70
00
0e
+0
25
.02
08
00
e+
02
[d
ihe
dra
ls]
;a
ia
ja
ka
lfu
nct
ph
icp
mu
lt2
13
41
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
06
13
41
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
02
13
51
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
06
13
51
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
02
16
71
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
03
16
71
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
02
16
81
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
03
16
81
1.8
00
00
0e
+0
23
.34
72
00
e+
01
2.0
00
00
0e
+0
0
[d
ihe
dra
ls]
;a
ia
ja
ka
lfu
nct
q0
cq3
45
12
0.0
00
00
0e
+0
01
.67
36
00
e+
02
67
81
20
.00
00
00
e+
00
1.6
73
60
0e
+0
21
36
22
0.0
00
00
0e
+0
01
.67
36
00
e+
02
[p
osi
tion
_re
stra
ints
];
you
wo
uld
n’t
no
rma
llyu
seth
isfo
ra
mo
lecu
lelik
eU
rea
,;
bu
tit’
sh
ere
for
did
act
ica
lp
urp
ose
s;
ai
fun
ctfc
11
10
00
10
00
10
00
;R
est
rain
toa
po
int
21
10
00
01
00
0;
Re
stra
into
alin
e(Y
-axi
s)3
11
00
00
0;
Re
stra
into
ap
lan
e(Y
-Z-p
lan
e)
;In
clu
de
SP
Cw
ate
rto
polo
gy
#in
clu
de
"sp
c.itp
"
[sy
ste
m]
Ure
ain
Wa
ter
[m
ole
cule
s]
;mo
lecu
len
am
en
r.U
rea
1S
OL
10
00
Her
efo
llow
sth
eex
plan
ator
yte
xt.
[d
efa
ults
]:
•no
n-bo
ndty
pe=
1(L
enna
rd-J
ones
)or
2(B
ucki
ngha
m)
note
:w
hen
usin
gth
eB
ucki
ngha
mpo
tent
ial
noco
mbi
natio
nru
leca
nbe
used
,an
da
full
inte
ract
ion
mat
rixm
ustb
epr
ovid
edun
der
the
no
nb
on
dp
ara
ms
sect
ion.
96
Ch
ap
ter
5.
Top
olog
ies
•com
binationrule
=1
(supplyC(6
)and
C(1
2),σ
ij=√σ
i σj ),
2(supply
σand
ε,σ
ij=
12 (σi +
σj ))
or3
(supplyσand
ε,σij
=√σ
i σj )
•generate
pairs=
no(get1-4
interactionsfrom
pairlist)oryes(generate
1-4interactions
fromnorm
alLennard-Jonesparam
etersusing
FudgeLJ
andF
udgeQQ
)
•F
udgeLJ=
factorto
changeLennard-Jones
1-4interactions
•F
udgeQQ
=factor
tochange
electrostatic1-4
interactions
note:FudgeLJ
andF
udgeQQ
onlyneed
tobe
specifiedw
hengenerate
pairsis
setto’yes’.
#in
clud
e"ffg
mx.itp
":
thisincludes
thebonded
andnon-bonded
GR
OM
AC
Sparam
eters,the
gm
xin
ffgm
xw
illbereplaced
bythe
name
oftheforce
fieldyou
areactually
using.
[m
ole
cule
type
]:
definesthe
name
ofyourm
oleculein
this*.to
pand
nrexcl=3
standsfor
excludingnon-bonded
interactionsbetw
eenatom
sthatare
nofurther
than3
bondsaw
ay.
[a
tom
s]
:defines
them
olecule,w
herenrand
type
arefixed,
therest
isuser
defined.S
oa
tom
canbe
named
asyou
like,cgnr
made
largeror
smaller
(ifpossible,
thetotalcharge
ofa
chargegroup
shouldbe
zero),andcharges
canbe
changedhere
too.
[b
on
ds
]:
nocom
ment.
[p
airs
]:
1-4interactions
[a
ng
les
]:
nocom
ment
[d
ihe
dra
ls]
:in
thiscase
thereare
9proper
dihedrals(funct
=1),
3im
proper(funct
=2)
andno
Ryckaert-B
ellemans
typedihedrals.
Ifyou
want
toinclude
Ryckaert-B
ellemans
typedihedrals
ina
topology,dothe
following
(incase
ofe.g.decane):
[d
ihe
dra
ls]
;a
ia
ja
ka
lfu
nct
c0c1
c21
23
43
23
45
3
anddo
notforgettoera
seth
e1
-4in
tera
ctionin
[p
airs
]!!
[p
ositio
nre
strain
ts]
:harm
onicallyrestrain
theselected
particlesto
referenceposi-
tions(sec.4.2.9).
The
referencepositions
areread
froma
separatecoordinate
fileby
grompp.
#in
clud
e"sp
c.itp"
:includes
atopology
filethat
was
alreadyconstructed
(seenext
sec-tion,m
olecule.itp).
[syste
m]
:title
ofyoursystem
,userdefined
[m
ole
cule
s]
:this
definesthe
totalnumber
of(sub)m
oleculesin
yoursystem
thatare
de-fined
inthis*.to
p.
Inthis
example
fileit
standsfor
1urea
molecules
dissolvedin
1000w
aterm
olecules.T
hem
oleculetype
SO
Lis
definedin
thesp
c.itpfile.
5.6.2M
olecule.itpfile
Ifyou
constructa
topologyfile
youw
illusem
oreoften
(likea
water
molecule,
spc.itp
)it
isbetter
tom
akeam
ole
cule
.itpfile,w
hichonly
liststhe
information
ofthem
olecule:
Chapter
8
Analysis
Inthis
chapterdifferentw
aysofanalyzing
yourtrajectory
aredescribed.
The
names
ofthecorre-
spondinganalysis
programs
aregiven.
Specific
infoon
thein-and
outputoftheseprogram
scan
befound
inthe
on-linem
anualatwww
.gromacs.org.
The
outputfilesare
oftenproduced
asfinished
Grace/X
mgr
graphs.
First
insec.8.1
thegroup
conceptin
analysisis
explained.T
henthe
differentanalysis
toolsare
presented.
8.1G
roupsin
Analysis.
ma
ke_
nd
xm
k_a
ng
nd
x
Inchapter3
itw
asexplained
howgro
up
so
fa
tom
scanbe
usedin
theM
D-program
.In
most
analysisprogram
sgroups
ofatom
sare
neededto
work
on.M
ostprogram
scan
generateseveral
defaultindexgroups,butgroups
canalw
aysbe
readfrom
anindex
file.Let’s
considerasim
ulationof
abinary
mixture
ofcom
ponentsA
andB
.W
henw
ew
antto
calculatethe
radialdistribution
function(rdf)g
AB
(r)ofA
with
respecttoB
,we
haveto
calculate
4πr2g
AB
(r)=
VN
A∑i∈
A
NB∑j∈
B
P(r)
(8.1)
whereV
isthe
volume
andP(r)
isthe
probabilityto
finda
Batom
atadistance
rfrom
anA
atom.
By
havingthe
userdefine
theatom
nu
mb
ersfor
groupsA
andB
ina
simple
filew
ecan
calculatethis
gA
Bin
them
ostgeneral
way,
without
havingto
make
anyassum
ptionsin
therdf-program
aboutthetype
ofparticles.
13
2C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
dods
spas
sign
sse
cond
ary
stru
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ates
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ated
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oss
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eor
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ater
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ecto
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alm
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eof
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ribed
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evio
usse
ctio
n,bu
tthi
stim
eyo
uon
lyne
edto
incl
ude
files
:
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he
forc
efie
ldfil
es
tob
ein
clu
de
d#
incl
ud
e"f
fgm
x.itp
"
;In
clu
de
ure
ato
po
log
y
98
Ch
ap
ter
5.
Top
olog
ies
#in
clud
e"u
rea
.itp"
;In
clud
eS
PC
wa
ter
top
olo
gy
#in
clud
e"sp
c.itp"
[syste
m]
Ure
ain
Wa
ter
[m
ole
cule
s]
;mo
lecu
len
am
en
um
be
rU
rea
1S
OL
10
00
5.6.3Ifdefoption
Avery
powerful
featurein
GR
OM
AC
Sis
theuse
of#
ifde
fstatem
entsin
your*.top
file.B
ym
akinguse
ofthis
statement,
differentparam
etersfor
onem
oleculecan
beused
inthe
same
*.top
file.A
nexam
pleis
givenfor
TF
E,w
herethere
isan
optionto
usedifferentcharges
onthe
atoms:
chargesderived
byD
eLoof
eta
l.[62]orby
VanB
uurenand
Berendsen
[43].
Infactyou
canuse
alltheoptions
oftheC
-Preprocessor,
cpp
,becausethis
isused
toscan
thefile.
The
way
tom
akeuse
ofthe#ifd
ef
optionis
asfollow
s:
•in
gro
mp
p.m
dp
(theG
RO
MA
CS
preprocessorinputparam
eters)use
theoption
de
fine
=-D
De
loo
ford
efin
e=
•putthe#
ifde
fstatem
entsin
your*.top
,asshow
nbelow
:
...
[a
tom
s]
;n
rtyp
ere
snr
resid
ua
tom
cgn
rch
arg
em
ass
#ifd
ef
De
Lo
of
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seC
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rge
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10
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#e
lse;
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Ch
arg
es
from
Va
nB
uu
ren
1C
1T
FE
C1
0.5
92
F1
TF
EF
1-0
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EF
1-0
.24
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TF
EF
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.25
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TF
EC
H2
10
.26
6O
A1
TF
EO
A1
-0.5
5
7.4
.P
rogra
ms
by
top
ic1
31
Distances
instructures
overtim
e
gm
indistcalculates
them
inimum
distancebetw
eentw
ogroups
gdist
calculatesthe
distancesbetw
eenthe
centersofm
assoftw
ogroups
gm
dmat
calculatesresidue
contactmaps
grm
sdistcalculates
atompair
distancesaveraged
with
power
2,-3or
-6
Mass
distributionproperties
overtim
e
gtraj
plotsx,v,f,box,tem
peratureand
rotationalenergyg
gyratecalculates
theradius
ofgyrationg
msd
calculatesm
eansquare
displacements
grotacf
calculatesthe
rotationalcorrelationfunction
form
oleculesg
rdfcalculates
radialdistributionfunctions
Analyzing
bondedinteractions
gbond
calculatesbond
lengthdistributions
mk
angndxgenerates
indexfiles
forgangle
gangle
calculatesdistributions
andcorrelations
forangles
anddihedrals
gdih
analyzesdihedraltransitions
Structuralproperties
ghbond
computes
andanalyzes
hydrogenbonds
gsaltbr
computes
saltbridgesg
sascom
putessolventaccessible
surfacearea
gorder
computes
theorder
parameter
peratom
forcarbon
tailsg
sganglecom
putesthe
angleand
distancebetw
eentw
ogroups
gsorient
analyzessolventorientation
aroundsolutes
gbundle
analyzesbundles
ofaxes,e.g.helicesg
disreanalyzes
distancerestraints
Kinetic
properties
gtraj
plotsx,v,f,box,tem
peratureand
rotationalenergyg
velacccalculates
velocityautocorrelation
functionsg
tcafcalculates
viscositiesofliquids
Electrostatic
properties
geniongenerates
mono
atomic
ionson
energeticallyfavorable
positionsg
potentialcalculates
theelectrostatic
potentialacrossthe
boxg
dipolescom
putesthe
totaldipoleplus
fluctuationsg
dielectriccalculates
frequencydependentdielectric
constants
Protein
specificanalysis
13
0C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
geni
onge
nera
tes
mon
oat
omic
ions
onen
erge
tical
lyfa
vora
ble
posi
tions
genc
onf
mul
tiplie
sa
conf
orm
atio
nin
’rand
om’o
rient
atio
nsge
npr
gene
rate
spo
sitio
nre
stra
ints
for
inde
xgr
oups
prot
onat
epr
oton
ates
stru
ctur
es
Run
ning
asi
mul
atio
ngr
ompp
mak
esa
run
inpu
tfile
tpbc
onv
mak
esa
run
inpu
tfile
for
rest
artin
ga
cras
hed
run
mdr
unpe
rfor
ms
asi
mul
atio
nxm
drun
perf
orm
ssi
mul
atio
nsw
ithex
tra
expe
rimen
talf
eatu
res
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win
gtr
ajec
torie
sng
mx
disp
lays
atr
ajec
tory
trjc
onv
conv
erts
traj
ecto
ries
toe.
g.pd
bw
hich
can
bevi
ewed
with
e.g.
rasm
ol
Pro
cess
ing
ener
gies
gen
ergy
writ
esen
ergi
esto
xvg
files
and
disp
lays
aver
ages
gen
emat
extr
acts
anen
ergy
mat
rixfr
oman
ener
gyfil
em
drun
with
-rer
un(r
e)ca
lcul
ates
ener
gies
for
traj
ecto
ryfr
ames
Con
vert
ing
files
editc
onf
conv
erts
and
man
ipul
ates
stru
ctur
efil
estr
jcon
vco
nver
tsan
dm
anip
ulat
estr
ajec
tory
files
trjc
atco
ncat
enat
estr
ajec
tory
files
enec
onv
conv
erts
ener
gyfil
esxm
p2ps
conv
erts
XP
Mm
atric
esto
enca
psul
ated
post
scrip
t(or
XP
M)
Tool
s mak
end
xm
akes
inde
xfil
esm
kan
gndx
gene
rate
sin
dex
files
for
gangl
egm
xche
ckch
ecks
and
com
pare
sfil
esgm
xdum
pm
akes
bina
ryfil
eshu
man
read
able
gtr
ajpl
ots
x,v
and
fofs
elec
ted
atom
s/gr
oups
(and
mor
e)fr
oma
traj
ecto
ryg
anal
yze
anal
yzes
data
sets
trjo
rder
orde
rsm
olec
ules
acco
rdin
gto
thei
rdi
stan
ceto
agr
oup
Dis
tanc
esbe
twee
nst
ruct
ures
grm
sca
lcul
ates
rmsd
’sw
itha
refe
renc
est
ruct
ure
and
rmsd
mat
rices
gco
nfrm
sfit
stw
ost
ruct
ures
and
calc
ulat
esth
erm
sdg
clus
ter
clus
ters
stru
ctur
esg
rmsf
calc
ulat
esat
omic
fluct
uatio
ns
5.6
.F
ilefo
rma
ts9
9
7H
O1
TF
EH
O1
0.3
#e
nd
if
[b
on
ds
];
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aj
fun
ctc0
c16
71
1.0
00
00
0e
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00
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21
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... 5.6.
4F
ree
ener
gyca
lcul
atio
ns
Fre
een
ergy
diffe
renc
esbe
twee
ntw
osy
stem
sA
and
Bca
nbe
calc
ulat
edas
desc
ribed
inse
c.3.
12.
The
syst
ems
Aan
dB
are
desc
ribed
byto
polo
gies
cons
istin
gof
the
sam
enu
mbe
rof
mol
ecul
esw
ithth
esa
me
num
ber
ofat
oms.
Mas
ses
and
non-
bond
edin
tera
ctio
nsca
nbe
pert
urbe
dby
addi
ngB
para
met
ers
inth
e[a
tom
s]
field
.B
onde
din
tera
ctio
nsca
nbe
pert
urbe
dby
addi
ngB
pa-
ram
eter
sto
the
bond
edty
pes
orth
ebo
nded
inte
ract
ions
.T
hepa
ram
eter
sth
atca
nbe
pert
urbe
dar
elis
ted
inTa
ble5
.3an
dTa
ble5
.4.
Theλ
-dep
ende
nce
ofth
ein
tera
ctio
nsis
desc
ribed
inse
ctio
nse
c.4.
3.B
elow
isan
exam
ple
ofa
topo
logy
whi
chch
ange
sfr
om20
0pr
opan
ols
to20
0pe
ntan
esus
ing
the
GR
OM
OS
-96
forc
efie
ld.
;In
clu
de
forc
efie
ldp
ara
me
ters
#in
clu
de
"ffG
43
a1
.itp
"
[m
ole
cule
typ
e]
;N
am
en
rexc
lP
rop
Pe
nt
3
[a
tom
s]
;n
rty
pe
resn
rre
sid
ue
ato
mcg
nr
cha
rge
ma
ssty
pe
Bch
arg
eB
ma
ssB
1H
1P
RO
PP
H1
0.3
98
1.0
08
CH
30
.01
5.0
35
2O
A1
PR
OP
PO
1-0
.54
81
5.9
99
4C
H2
0.0
14
.02
73
CH
21
PR
OP
PC
11
0.1
50
14
.02
7C
H2
0.0
14
.02
74
CH
21
PR
OP
PC
22
0.0
00
14
.02
75
CH
31
PR
OP
PC
32
0.0
00
15
.03
5
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on
ds
];
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fun
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ar_
Ap
ar_
B1
22
gb
_1
gb
_2
62
32
gb
_1
7g
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gb
_2
64
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_2
6
[p
airs
];
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fun
ct1
41
25
1
10
0C
ha
pte
r5
.To
po
logie
s
[a
ng
les
];
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aj
ak
fun
ctp
ar_
Ap
ar_
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23
2g
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11
ga
_1
42
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ga
_1
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2g
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ga
_1
4
[d
ihe
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ls]
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ia
ja
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nct
pa
r_A
pa
r_B
12
34
1g
d_
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gd
_1
72
34
51
gd
_1
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17
[syste
m]
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eP
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ol
toP
en
tan
e
[m
ole
cule
s]
;C
om
po
un
d#
mo
lsP
rop
Pe
nt
20
0
Atom
sthat
arenot
perturbed,PC2
andP
C3,
donot
needB
parameter
specifications,the
Bpa-
rameters
willbe
copiedfrom
theA
parameters.
Bonded
interactionsbetw
eenatom
sthat
arenot
perturbeddo
notneed
Bparam
eterspecifications,
herethis
isthe
casefor
thelast
bond.Topolo-
giesusing
theG
RO
MA
CS
forcefield
needno
bondedparam
etersat
all,since
boththe
Aand
Bparam
etersare
determined
bythe
atomtypes.
Non-bonded
interactionsinvolving
oneor
two
per-turbed
atoms
usethe
free-energyperturbation
functionalforms.
Non-bonded
interactionbetw
eentw
onon-perturbed
atoms
usethe
normalfunctionalform
s.T
hism
eansthat
when,
forinstance,
onlythe
chargeofa
particleis
perturbed,itsLennard-Jones
interactionsw
illalsobe
affectedw
henlam
bdais
notequaltozero
orone.
Note
thatthistopology
usesthe
GR
OM
OS
-96force
field,inw
hichthe
bondedinteractions
arenot
determined
bythe
atomtypes.
The
bondedinteraction
stringsare
convertedby
theC
-preprocessor.T
heforce
fieldparam
eterfiles
containlines
like:
#d
efin
eg
b_
26
0.1
53
07
.15
00
e+
06
#d
efin
eg
d_
17
0.0
00
5.8
63
5.6.5C
onstraintforce
The
constraintforce
between
two
atoms
inone
molecule
canbe
calculatedw
iththe
freeenergy
perturbationcode
byadding
aconstraint
between
thetw
oatom
s,w
itha
differentlength
inthe
Aand
Btopology.
When
theB
lengthis
1nanom
eterlonger
thanthe
Alength
andlam
bdais
keptconstant
atzero,
thederivative
ofthe
Ham
iltonianw
ithrespect
tolam
bdais
theconstraint
force.F
orconstraintsbetw
eenm
oleculesthe
pullcodecan
beused,see
sec.6.1.
Below
isan
example
forcalculating
theconstraint
forceat
0.7nanom
eterbetw
eentw
om
ethanesin
water,
bycom
biningthe
two
methanes
intoone
molecule.
The
addedconstraintis
offunctiontype
2,which
means
thatitis
notusedfor
generatingexclusions
(see5.3.5).
;In
clud
efo
rcefie
ldp
ara
me
ters
7.4
.P
rogra
ms
by
top
ic1
29
freezegrps:G
roupsthat
areto
befrozen
(i.e.their
X,
Y,and/or
Zposition
will
notbe
updated;e.g.
Lip
idS
OL
).freezedim
specifiesfor
which
dimension
thefreezing
applies.You
might
wantto
useenergy
groupexclusions
forcom
pletelyfrozen
groups.
freezedim:
dimensions
forw
hichgroups
infreezegrpsshouldbe
frozen,specifyY
orN
forX
,Y
andZ
andfor
eachgroup
(e.g.YY
NN
NNm
eansthatparticles
inthe
firstgroupcan
move
onlyin
Zdirection.
The
particlesin
thesecond
groupcan
move
inany
direction).
cosacceleration:
(0)[nm
ps −2]
theam
plitudeofthe
accelerationprofile
forcalculating
theviscosity.
The
accelerationis
inthe
X-direction
andthe
magnitude
iscosaccelerationcos(2
piz/boxheight).Tw
oterm
sare
addedto
theenergy
file:the
amplitude
ofthevelocity
profileand
1/viscosity.
7.3.19E
lectricfields
Ex
;Ey
;Ez:
Ifyouw
anttouse
anelectric
fieldin
adirection,enter
3num
bersafter
theappropriate
E*,
thefirstnum
ber:the
number
ofcosines,only1
isim
plemented
(with
frequency0)
soenter
1,the
secondnum
ber:the
strengthof
theelectric
fieldin
Vnm
−1,
thethird
number:
thephase
ofthecosine,you
canenter
anynum
berhere
sincea
cosineoffrequency
zerohas
nophase.
Ext;E
yt;Ezt:
notimplem
entedyet
7.3.20U
serdefined
thingies
user1grps
;user2grps:
userint1(0);userint2
(0);userint3(0);userint4:
(0)
userreal1(0);userreal2
(0);userreal3(0);userreal4:
(0)T
heseyou
canuse
ifyouhack
outcode.You
canpass
integersand
realsto
yoursubroutine.
Check
theinputrec
definitioninsrc/in
clud
e/typ
es/in
pu
trec.h
7.4P
rograms
bytopic
Generating
topologiesand
coordinatespdb2gm
xconverts
pdbfiles
totopology
andcoordinate
filesx2top
generatesa
primitive
topologyfrom
coordinateseditconf
editsthe
boxand
writes
subgroupsgenbox
solvatesa
system
12
8C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
disr
efc
:(1
000)
[kJ
mol−
1nm
−2]
forc
eco
nsta
ntfo
rdi
stan
cere
stra
ints
,whi
chis
mul
tiplie
dby
a(p
ossi
bly)
diffe
rent
fact
orfo
rea
chre
stra
int
disr
eta
u:(0
)[p
s]tim
eco
nsta
ntfo
rdi
stan
cere
stra
ints
runn
ing
aver
age
nstd
isre
out:
(100
)[s
teps
]fr
eque
ncy
tow
rite
the
runn
ing
time
aver
aged
and
inst
anta
neou
sdi
stan
ces
ofal
lato
mpa
irsin
volv
edin
rest
rain
tsto
the
ener
gyfil
e(c
anm
ake
the
ener
gyfil
eve
ryla
rge)
7.3.
17F
ree
Ene
rgy
Per
turb
atio
n
free
ener
gy:
noO
nly
use
topo
logy
A.
yes
Inte
rpol
ate
betw
een
topo
logy
A(la
mbd
a=0)
toto
polo
gyB
(lam
bda=
1)an
dw
rite
the
deriv
ativ
eof
the
Ham
ilton
ian
with
resp
ectt
ola
mbd
ato
the
ener
gyfil
ean
dto
dg
dl.x
vg.
The
pote
ntia
ls,
bond
-leng
ths
and
angl
esar
ein
terp
olat
edlin
early
asde
scrib
edin
the
man
ual.
Whe
nsc
alph
ais
larg
erth
anze
ro,
soft-
core
pote
ntia
lsar
eus
edfo
rth
eLJ
and
Cou
lom
bin
tera
ctio
ns.
init
lam
bda:
(0)
star
ting
valu
efo
rla
mbd
a
delta
lam
bda:
(0)
incr
ease
per
time
step
for
lam
bda
scal
pha:
(0)
the
soft-
core
para
met
er,
ava
lue
of0
resu
ltsin
linea
rin
terp
olat
ion
ofth
eLJ
and
Cou
lom
bin
tera
ctio
ns
scsi
gma:
(0.3
)[n
m]
the
soft-
core
sigm
afo
rpa
rtic
les
whi
chha
vea
C6
orC
12pa
ram
eter
equa
lto
zero
7.3.
18N
on-e
quili
briu
mM
D
acc
grps
:gr
oups
for
cons
tant
acce
lera
tion
(e.g
.:P
rote
inS
ol
)al
lato
ms
ingr
oups
Pro
tein
and
Sol
will
expe
rienc
eco
nsta
ntac
cele
ratio
nas
spec
ified
inth
eac
cele
rate
line
acce
lera
te:
(0)
[nm
ps−
2]
acce
lera
tion
fora
ccgr
ps;
x,y
and
zfo
rea
chgr
oup
(e.g
.0.1
0.0
0.0
-0.1
0.0
0.0
mea
nsth
atfir
stgr
oup
has
cons
tant
acce
lera
tion
of0.
1nm
ps−
2in
Xdi
rect
ion,
seco
ndgr
oup
the
oppo
site
).
5.6
.F
ilefo
rma
ts1
01
#in
clu
de
"ffG
43
a1
.itp
"
[m
ole
cule
typ
e]
;N
am
en
rexc
lM
eth
an
es
1
[a
tom
s]
;n
rty
pe
resn
rre
sid
ua
tom
cgn
rch
arg
em
ass
1C
H4
1C
H4
C1
10
16
.04
32
CH
41
CH
4C
22
01
6.0
43
[co
nst
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ts]
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nct
leng
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ng
th_
B1
22
0.7
1.7
#in
clu
de
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c.itp
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[sy
ste
m]
;N
am
eM
eth
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es
inW
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[m
ole
cule
s]
;C
om
po
un
d#
mo
lsM
eth
an
es
1S
OL
20
02
5.6.
6C
oord
inat
efil
e
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ithth
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rofil
eex
tens
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ain
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olec
ular
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ctur
ein
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OM
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rmat
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ple
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uded
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w:
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rs,
refo
rma
tst
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ug
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Thi
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rmat
isfix
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llco
lum
nsar
ein
afix
edpo
sitio
n.If
you
wan
tto
read
such
afil
ein
your
own
prog
ram
with
outu
sing
the
GR
OM
AC
Slib
rarie
syo
uca
nus
eth
efo
llow
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form
ats:
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2C
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pte
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po
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s
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bo
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],bo
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],bo
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],bo
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],bo
x[Z][X
],bo
x[Z][Y
]
Fortran
format:
(i5,2
a5
,i5,3
f8.3
,3f8
.4)
So
con
fin.g
rois
theG
RO
MA
CS
coordinatefile
andis
almost
thesam
eas
theG
RO
MO
S-
87file
(forG
RO
MO
Susers:
when
usedw
ithntx=
7).T
heonly
differenceis
thebox
forw
hichG
RO
MA
CS
usesa
tensor,notavector.
7.3
.R
un
Pa
ram
ete
rs1
27
morse:no
bondsare
representedby
aharm
onicpotential
yesbonds
arerepresented
bya
Morse
potential
7.3.15E
nergygroup
exclusions
energygrpexcl:
Pairs
ofenergygroups
forw
hichallnon-bonded
interactionsare
excluded.A
nexam
ple:if
youhave
two
energygroupsPro
tein
andS
OL,specifying
en
erg
ye
xcl=
Pro
tein
Pro
tein
SO
LS
OL
would
giveonly
thenon-bonded
interactionsbetw
eenthe
proteinand
thesolvent.
This
isespecially
usefulforspeedingup
energycalculations
with
md
run
-reru
nand
forexclud-ing
interactionsw
ithinfrozen
groups.
7.3.16N
MR
refinement
disre:nono
distancerestraints
(ignoredistance
restraintsinform
ationin
topologyfile)
simplesim
ple(per-m
olecule)distance
restraints
ensemble
distancerestraints
overan
ensemble
ofmolecules
disrew
eighting:
equaldividethe
restraintforceequally
overallatom
pairsin
therestraint
conservativethe
forcesare
thederivative
ofthe
restraintpotential,
thisresults
inan
r−
7w
eightingofthe
atompairs
disrem
ixed:
nothe
violationused
inthe
calculationofthe
restraintforceis
thetim
eaveraged
violation
yesthe
violationused
inthe
calculationofthe
restraintforceis
thesquare
rootofthetim
eaveraged
violationtim
esthe
instantaneousviolation
12
6C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
7.3.
14B
onds
cons
trai
nts:
none
No
cons
trai
nts,
i.e.b
onds
are
repr
esen
ted
bya
harm
onic
ora
Mor
sepo
tent
ial(
depe
nd-
ing
onth
ese
tting
ofmor
se)
and
angl
esby
aha
rmon
icpo
tent
ial.
hbon
ds Onl
yco
nstr
ain
the
bond
sw
ithH
-ato
ms.
all-b
onds
Con
stra
inal
lbon
ds.
h-an
gles
Con
stra
inal
lbo
nds
and
cons
trai
nth
ean
gles
that
invo
lve
H-a
tom
sby
addi
ngbo
nd-
cons
trai
nts.
all-a
ngle
sC
onst
rain
allb
onds
and
cons
trai
nal
lang
les
byad
ding
bond
-con
stra
ints
.
cons
trai
ntal
gorit
hm:
lincs
LIN
earC
onst
rain
tSol
ver.
The
accu
racy
inse
twithlin
csor
der,
whi
chse
tsth
enu
mbe
rof
mat
rices
inth
eex
pans
ion
for
the
mat
rixin
vers
ion,
4is
enou
ghfo
ra
”nor
mal
”M
Dsi
mul
atio
n,8
isne
eded
forB
Dw
ithla
rge
time-
step
s.T
heac
cura
cyof
the
cons
trai
nts
ispr
inte
dto
the
log
file
ever
ynstlo
gst
eps.
Ifa
bond
rota
tes
mor
eth
anlincs
war
nang
le[d
egre
es]
inon
est
ep,
aw
arni
ngw
illbe
prin
ted
both
toth
elo
gfil
ean
dto
std
err
.Li
ncs
shou
ldno
tbe
used
with
coup
led
angl
eco
nstr
aint
s.
shak
e Sha
keis
slow
eran
dle
ssst
able
than
Linc
s,bu
tdoe
sw
ork
with
angl
eco
nstr
aint
s.T
here
lativ
eto
lera
nce
isse
twiths
hake
tol,
0.00
01is
ago
odva
lue
for
”nor
mal
”M
D.
unco
nstr
aine
dst
art:
noap
ply
cons
trai
nts
toth
est
artc
onfig
urat
ion
yes
dono
tapp
lyco
nstr
aint
sto
the
star
tcon
figur
atio
n
shak
eto
l:(0
.000
1)re
lativ
eto
lera
nce
for
shak
e
lincs
orde
r:(4
)H
ighe
stor
der
inth
eex
pans
ion
ofth
eco
nstr
aint
coup
ling
mat
rix.
lincs
orde
ris
also
used
for
the
num
ber
ofLi
ncs
itera
tions
durin
gen
ergy
min
imiz
atio
n,on
lyon
eite
ratio
nis
used
inM
D.
lincs
war
nang
le:
(30)
[deg
rees
]m
axim
uman
gle
that
abo
ndca
nro
tate
befo
reLi
ncs
will
com
plai
n
Cha
pter
6
Spe
cial
Topi
cs
6.1
Cal
cula
ting
pote
ntia
lsof
mea
nfo
rce:
the
pull
code
The
rear
ea
num
ber
ofop
tions
toca
lcul
ate
pote
ntia
lsof
mea
nfo
rce
and
rela
ted
topi
cs.
Inth
ecu
rren
tver
sion
ofG
RO
MA
CS
this
isim
plem
ente
dth
roug
hso
me
extr
afil
esfo
rm
dru
n.
6.1.
1O
verv
iew
Fou
rdi
ffere
ntty
pes
ofca
lcul
atio
nar
esu
ppor
ted:
1.C
onst
rain
tfor
ces
The
dist
ance
betw
een
the
cent
ers
ofm
ass
oftw
ogr
oups
ofat
oms
can
beco
nstr
aine
dan
dth
eco
nstr
aint
forc
em
onito
red.
The
dist
ance
can
bein
1,2,
or3
dim
ensi
ons.
Thi
sm
etho
dus
esth
eS
HA
KE
algo
rithm
but
only
need
s1
itera
tion
tobe
exac
tif
only
two
grou
psar
eco
nstr
aine
d.
2.U
mbr
ella
sam
plin
gA
sim
ple
umbr
ella
sam
plin
gw
ithan
harm
onic
umbr
ella
pote
ntia
ltha
tac
tson
the
cent
erof
mas
sof
agr
oup
ofat
oms.
3.A
FM
pulli
ngA
sprin
gis
conn
ecte
dto
anat
oman
dsl
owly
retr
acte
d.T
his
has
the
effe
ctof
pulli
ngan
atom
orgr
oup
ofat
oms
away
from
itsin
itial
loca
tion.
The
rate
cons
tant
and
sprin
gco
nsta
ntfo
rth
esp
ring
can
beva
ried
tost
udy
e.g.
the
unbi
ndin
gof
apr
otei
nan
da
ligan
d(s
eefig
ure6
.1).
4.S
tart
ing
stru
ctur
esT
his
optio
ncr
eate
sa
num
bero
fsta
rtin
gst
ruct
ures
forp
oten
tialo
fmea
nfo
rce
calc
ulat
ions
,mov
ing
1or
2gr
oups
ofat
oms
ata
spec
ified
rate
tow
ards
oraw
ayfr
oma
refe
renc
egr
oup,
writ
ing
out
aco
ordi
nate
file
atsp
ecifi
edin
terv
als.
Not
eth
atth
egr
oups
give
nin
the
inde
xfil
ear
etr
ansl
ated
asp
ecifi
eddi
stan
ceea
chst
ep,
but
inad
ditio
nal
soun
derg
oth
eno
rmal
MD
,su
bjec
tto
defin
ition
sofe.g.
tem
pera
ture
coup
ling
grou
ps,
free
zegr
oups
and
the
like.
Inth
eca
lcul
atio
ns,
ther
eha
sto
be1
refe
renc
egr
oup
and
1or
2ot
her
grou
psof
atom
s.F
orco
nstr
aine
dru
ns,
the
dist
ance
betw
een
the
refe
renc
egr
oup
and
the
othe
rgr
oups
iske
ptco
nsta
nt
10
4C
ha
pte
r6
.S
pe
cialTo
pics
V
zz
linkspring rup
Figure
6.1:S
chematic
pictureof
pullinga
lipidout
ofa
lipidbilayer
with
AF
Mpulling.
Vrup
isthe
velocityatw
hichthe
springis
retracted,Z
link
isthe
atomto
which
thespring
isattached
andZ
sprin
gis
thelocation
ofthespring.
atthedistance
theyhave
inthe
inputcoordinatefile
(.tp
r)
file.
6.1.2U
sage
Inputfiles
The
md
run
programs
needs4
additionalfiles:2
inputfilesand
2outputfiles.
-pi
pu
ll.pp
aIfthis
fileis
specifiedthe
pullcodew
illbeused.
Itcontainsthe
parameters
thatcontrolwhat
typeofcalculation
isdone.
Afullexplanation
ofalltheoptions
isgiven
below.
-pn
ind
ex.n
dx
This
filedefines
thedifferentgroups
foruse
inallpullcalculations.
The
groupsare
referredto
bynam
e,sothe
indexfile
cancontain
othergroups
thatarenotused
asw
ell.
-po
pu
llou
t.pp
aA
formatted
copyofthe
inputparameter
filew
iththe
parameters
thatwere
actuallyused
inthe
run.
-pd
op
ull.p
do
The
datafile
with
thecalculated
forces(A
FM
pulling,constraint
force)or
positions(um
-brella
sampling).
Definition
ofgroups
The
way
thereference
groupsand
differentreference
typesw
orkis
summ
arizedin
figure6.2.
There
arefour
differentpossibilitiesfor
thereference
group.
7.3
.R
un
Pa
ram
ete
rs1
25
compressibility:
[bar −1
]com
pressibility(N
OT
E:
thisis
nowreally
inbar−
1)F
orw
aterat
1atm
and300
Kthe
compressibility
is4.5e-5
[bar −1].
refp:
[bar]
referencepressure
forcoupling
7.3.12S
imulated
annealing
annealing:
noN
osim
ulatedannealing.
yesS
imulated
annealingto
0[K
]at
timezero
temp
time
(ps).R
eferencetem
peraturefor
theB
erendsen-thermostat
isreft
x(1
-tim
e/zero
temp
time),
time
constantis
taut
[ps].N
otethat
thereference
temperature
willnot
gobelow
0[K
],i.e.
afterzero
temp
time
(ifit
ispositive)
thereference
temperature
will
be0
[K].
Negative
zerotem
ptim
eresults
inheating,w
hichw
illgoon
indefinitely.
zerotem
ptim
e:(0)
[ps]tim
eatw
hichtem
peraturew
illbezero
(canbe
negative).Tem
peratureduring
therun
canbe
seenas
astraightline
goingthrough
T=
reft[K
]att=0
[ps],andT
=0
[K]att=zero
temp
time
[ps].Look
inour
FAQ
fora
schematic
graphoftem
peratureversus
time.
7.3.13V
elocitygeneration
genvel:
noD
onotgenerate
velocitiesatstartup.
The
velocitiesare
settozero
when
thereare
novelocities
inthe
inputstructurefile.
yesG
eneratevelocities
accordingto
aM
axwelldistribution
attemperature
gentem
p[K
],w
ithrandom
seedgenseed.
This
isonly
meaningfulw
ithintegratormd.
gentem
p:(300)
[K]
temperature
forM
axwelldistribution
genseed:
(173529)[integer]
usedto
initializerandom
generatorfor
randomvelocities,
whengen
seedisset
to-1,
theseed
iscalculated
as(time
()+
ge
tpid
())%
10
00
00
0
12
4C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
noN
opr
essu
reco
uplin
g.T
his
mea
nsa
fixed
box
size
.
bere
ndse
nE
xpon
entia
lrel
axat
ion
pres
sure
coup
ling
with
time
cons
tant
tau
p[p
s].
The
box
issc
aled
ever
ytim
este
p.It
has
been
argu
edth
atth
isdo
esno
tyie
lda
corr
ectt
herm
ody-
nam
icen
sem
ble,
but
itis
the
mos
tef
ficie
ntw
ayto
scal
ea
box
atth
ebe
ginn
ing
ofa
run.
Par
inel
lo-R
ahm
anE
xten
ded-
ense
mbl
epr
essu
reco
uplin
gw
here
the
box
vect
ors
are
subj
ectt
oan
equa
tion
ofm
otio
n.T
heeq
uatio
nof
mot
ion
for
the
atom
sis
coup
led
toth
is.
No
inst
anta
neou
ssc
alin
gta
kes
plac
e.A
sfo
rNos
e-H
oove
rtem
pera
ture
coup
ling
the
time
cons
tant
tau
p[p
s]is
the
perio
dof
pres
sure
fluct
uatio
nsat
equi
libriu
m.
Thi
sis
prob
ably
abe
tter
met
hod
whe
nyo
uw
ant
toap
ply
pres
sure
scal
ing
durin
gda
taco
llect
ion,
but
bew
are
that
you
can
getv
ery
larg
eos
cilla
tions
ifyo
uar
est
artin
gfr
oma
diffe
rent
pres
sure
.
pcou
plty
pe:
isot
ropi
cIs
otro
pic
pres
sure
coup
ling
with
time
cons
tanttau
p[p
s].
The
com
pres
sibi
lity
and
refe
renc
epr
essu
rear
ese
tw
ithcom
pres
sibi
lity
[bar−
1]
and
ref
p[b
ar],
one
valu
eis
need
ed.
sem
iisot
ropi
cP
ress
ure
coup
ling
whi
chis
isot
ropi
cin
the
xan
dy
dire
ctio
n,bu
tdi
ffere
ntin
the
zdi
rect
ion.
Thi
sca
nbe
usef
ulfo
rm
embr
ane
sim
ulat
ions
.2
valu
esar
ene
eded
for
x/y
and
zdi
rect
ions
resp
ectiv
ely.
anis
otro
pic
Idem
,bu
t6
valu
esar
ene
eded
for
xx,
yy,
zz,
xy/y
x,xz
/zx
and
yz/z
yco
mpo
nent
sre
spec
tivel
y.W
hen
the
off-
diag
onal
com
pres
sibi
litie
sar
ese
tto
zero
,are
ctan
gula
rbox
will
stay
rect
angu
lar.
Bew
are
that
anis
otro
pic
scal
ing
can
lead
toex
trem
ede
form
atio
nof
the
sim
ulat
ion
box.
surf
ace-
tens
ion
Sur
face
tens
ion
coup
ling
for
surf
aces
para
llelt
oth
exy
-pla
ne.
Use
sno
rmal
pres
sure
coup
ling
for
the
z-di
rect
ion,
whi
leth
esu
rfac
ete
nsio
nis
coup
led
toth
ex/
ydi
men
-si
ons
ofth
ebo
x.T
hefir
stref
pva
lue
isth
ere
fere
nce
surf
ace
tens
ion
times
the
num
-be
rof
surf
aces
[bar
nm],
the
seco
ndva
lue
isth
ere
fere
nce
z-pr
essu
re[b
ar].
The
two
com
pres
sibi
lity
[bar−
1]
valu
esar
eth
eco
mpr
essi
bilit
yin
the
x/y
and
zdi
rect
ion
re-
spec
tivel
y.T
heva
lue
for
the
z-co
mpr
essi
bilit
ysh
ould
bere
ason
ably
accu
rate
sinc
eit
influ
ence
sth
eco
nver
geof
the
surf
ace-
tens
ion,
itca
nal
sobe
sett
oze
roto
have
abo
xw
ithco
nsta
nthe
ight
.
tric
linic Ful
lydy
nam
icbo
x-
supp
orte
d,bu
tex
perim
enta
l.Yo
ush
ould
prov
ide
six
valu
esfo
rth
eco
mpr
essi
bilit
yan
dre
fere
nce
pres
sure
.
tau
p:(1
)[p
s]tim
eco
nsta
ntfo
rco
uplin
g
6.1
.C
alc
ula
ting
po
ten
tials
ofm
ea
nfo
rce
:th
ep
ull
cod
e1
05
�
��
��
Fig
ure
6.2:
Ove
rvie
wof
the
diffe
rent
refe
renc
egr
oup
poss
ibili
ties,
appl
ied
toin
terf
ace
syst
ems.
Cis
the
refe
renc
egr
oup.
The
circ
les
repr
esen
tth
ece
nter
ofm
ass
of2
grou
pspl
usth
ere
fere
nce
grou
p,an
ddc
isth
ere
fere
nce
dist
ance
.
com
The
cent
erof
mas
sof
the
grou
pgi
ven
unde
rre
fere
nce
gro
up
,ca
lcul
ated
each
step
from
the
curr
entc
oord
inat
es.
com
t0 The
cent
erof
mas
sof
the
grou
pgi
ven
unde
rre
fere
nce
gro
up
,ca
lcul
ated
each
step
from
the
curr
ent
coor
dina
tes,
but
corr
ecte
dfo
rat
oms
that
have
cros
sed
the
box.
Ifth
ere
f-er
ence
grou
pco
nsis
tsof
allt
hew
ater
mol
ecul
esin
the
syst
em,a
nda
sing
lew
ater
mol
ecul
em
oves
acro
ssth
ebo
xan
den
ters
from
the
othe
rsi
de,
the
c.o.
m.
will
show
asl
ight
jum
p.T
his
issi
mpl
ydu
eto
the
perio
dic
boun
dary
cond
ition
s,an
dsh
ows
that
the
cent
erof
mas
sin
asi
mul
atio
nin
perio
dic
boun
dary
cond
ition
sis
illde
fined
ifth
egr
oup
used
toca
lcul
ate
itis
e.g.
asl
abof
liqui
d.If
the
’real
’pos
ition
sar
eus
edin
stea
dof
the
coor
dina
tes
that
have
been
rese
tto
bein
side
the
box,
the
cent
erof
mas
sof
the
who
lesy
stem
isco
nser
ved.
dyn
am
ic Ina
phos
phol
ipid
bila
yer
syst
emit
may
beof
inte
rest
toca
lcul
ate
the
pmf
ofa
lipid
asfu
nctio
nof
itsdi
stan
cefr
omth
ew
hole
bila
yer.
The
who
lebi
laye
rca
nbe
take
nas
refe
renc
egr
oup
inth
atca
se,
but
itm
ight
also
beof
inte
rest
tode
fine
the
reac
tion
coor
dina
tefo
rth
epm
fm
ore
loca
lly.d
yna
mic
does
not
use
allt
heat
oms
ofth
erefe
ren
ceg
rou
p,
but
inst
ead
only
thos
ew
ithin
acy
linde
rw
ithra
diusr
belo
wth
em
ain
grou
p.T
his
only
wor
ksfo
rdi
stan
ces
defin
edin
1di
men
sion
,an
dth
ecy
linde
ris
orie
nted
with
itslo
ngax
isal
ong
this
1di
men
sion
.A
seco
ndcy
linde
rca
nbe
defin
edw
ithrc
,w
itha
linea
rsw
itch
func
tion
that
wei
ghs
the
cont
ribut
ion
ofat
oms
betw
een
ran
drc
with
dist
ance
.T
his
smoo
thes
the
effe
cts
ofat
oms
mov
ing
inan
dou
tof
the
cylin
der
(whi
chca
uses
jum
psin
the
cons
trai
ntfo
rces
).
dyn
am
ict0
The
sam
easd
yna
mic
,but
the
coor
dina
tes
are
corr
ecte
dfo
rbo
xcro
ssin
gslik
ein
com
t0.
10
6C
ha
pte
r6
.S
pe
cialTo
pics
Note
thatstrictlyspeaking
thisis
notcorrectifthereference
groupis
notthew
holesystem
,including
thegroups
definedw
ithgrou
p1
andg
rou
p2
.
Tofurther
smooth
rapidlyfluctuating
distancesbetw
eenthe
referencegroup
andthe
othergroups,
theaverage
distancecan
beconstrained
insteadof
theinstanteneous
distance.T
hisis
definedby
settingre
flag
tothe
number
ofstepsto
averageover.
How
ever,usingthis
optionis
notstrictlycorrectfor
calculatingpotentials
ofmean
forcefrom
theaverage
constraintforce.
The
parameter
file
verb
ose
=n
oIf
thisis
setto
yes
,a
largeam
ountof
detailedinform
ationis
sentto
stde
rr,
which
isonly
usefulfordiagnostic
purposes.T
he.p
do
filealso
becomes
more
detailed,w
hichis
notnecessaryfor
normaluse.
run
type
=co
nstra
int
Options
arestart,
afm
,co
nstra
int,
um
bre
lla.
This
selectsthe
typeof
cal-culation:
making
startingstructures,A
FM
pulling,constraintforcecalculation
orum
brellasam
pling.
gro
up
1=
MB
21
1
gro
up
2=
MB
21
2T
hegroups
with
theatom
sto
acton.T
hefirstgroup
ism
andatory,thesecond
optional.
refe
ren
ceg
rou
p=
OC
TA
The
referencegroup.
Distances
arecalculated
betweeeng
rou
p1
(andg
rou
p2
ifspec-
ified)and
thisgroup.
Ife.g.the
constraintforce
between
two
ionsis
needed,you
would
specifiygro
up
1as
agroup
with
1ion,andre
fere
nce
gro
up
asthe
otherion.
reftyp
e=
com
The
typeofreference
group.O
ptionsareco
m,
com
t0,
dyn
am
ic,d
yna
mic
t0as
explainedabove.
refla
g=
1T
heposition
ofthereference
groupcan
betaken
asaverage
overanum
berofsteps,specifiedby
refla
g(see
above).
dire
ction
=0
.00
.01
.0D
istancesare
calculatedw
eightedby
x,y,
zas
specifiedin
dire
ction
.S
ettingthem
allto
1.0calculates
thedistance
between
two
groups,setting
thefirst
two
to0.0
andthe
thirdto
1.0calculates
thedistance
inthe
zdirection
only.
reve
rse=
tore
fere
nce
This
optionselects
thedirection
inw
hichthe
groupsare
moved
with
respecttothe
referencegroup
forA
FM
pullingand
startingstructure
calculations.C
hoicesare
tore
fere
nce
,fro
mre
fere
nce
.
7.3
.R
un
Pa
ram
ete
rs1
23
pme
order(4)
Interpolationorder
forP
ME
.4equals
cubicinterpolation.
Youm
ighttry6/8/10
when
run-ning
inparalleland
simultaneously
decreasegrid
dimension.
ewald
rtol(1e-5)T
herelative
strengthofthe
Ew
ald-shifteddirectpotentialatthe
cutoffisgiven
byew
aldrtol.
Decreasing
thisw
illgivea
more
accuratedirectsum
,butthenyou
needm
orew
avevectors
forthe
reciprocalsum.
optimize
fft:
noD
on’tcalculatethe
optimalF
FT
planfor
thegrid
atstartup.
yesC
alculatethe
optimalF
FT
planfor
thegrid
atstartup.
This
savesa
fewpercent
forlong
simulations,buttakes
acouple
ofminutes
atstart.
7.3.10Tem
peraturecoupling
tcoupl:noN
otem
peraturecoupling.
berendsenTem
peraturecoupling
with
aB
erendsen-thermostat
toa
bathw
ithtem
peratureref
t[K
],with
time
constanttaut
[ps].S
everalgroupscan
becoupled
separately,theseare
specifiedin
thetcgrps
fieldseparated
byspaces.
nose-hooverTem
peraturecoupling
with
aby
usinga
Nose-H
ooverextended
ensemble.
The
refer-ence
temperature
andcoupling
groupsare
selectedas
above,butinthis
casetau
t[ps]
controlsthe
periodof
thetem
peraturefluctuations
atequilibrium
,w
hichis
slightlydifferentfrom
arelaxation
time.
tcgrps:groups
tocouple
separatelyto
temperature
bath
taut:
[ps]
time
constantforcoupling
(onefor
eachgroup
intc
grps)
reft:
[K]
referencetem
peraturefor
coupling(one
foreach
groupin
tcgrps)
7.3.11P
ressurecoupling
pcoupl:
12
2C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
vdw
type
:
Cut
-off Tw
inra
nge
cut-
off’s
with
neig
hbor
list
cut-
offrli
stan
dV
dWcu
t-of
frvd
w,
whe
rerv
dw>
rlist
.
Shi
ftT
heLJ
(not
Buc
king
ham
)po
tent
iali
sde
crea
sed
over
the
who
lera
nge
and
the
forc
esde
cay
smoo
thly
toze
robe
twee
nrvdw
switc
han
drv
dw.
The
neig
hbor
sear
chcu
t-of
frli
stsh
ould
be0.
1to
0.3
nmla
rger
thanrv
dwto
acco
mm
odat
efo
rth
esi
zeof
char
gegr
oups
and
diffu
sion
betw
een
neig
hbor
listu
pdat
es.
Use
r md
run
will
now
expe
ctto
find
two
files
with
user
-defi
ned
func
tions
:rt
ab
.xvg
for
Rep
ulsi
on,d
tab
.xvg
for
Dis
pers
ion.
The
sefil
essh
ould
cont
ain
5co
lum
ns:
the
xva
lue,
f(x)
,-f
(1) (
x),
f(2
) (x)
and
-f(3
) (x)
,w
here
f(n
) (x)
deno
tes
then
th
deriv
ativ
eof
func
tionf
(x)
with
resp
ect
tox
.T
hex
shou
ldru
nfr
om0
[nm
]to
rlist
+0
.5[n
m],
with
asp
acin
gof
0.0
02
[nm
]w
hen
you
run
insi
ngle
prec
isio
n,or
0.0
00
5[n
m]
whe
nyo
uru
nin
doub
lepr
ecis
ion.
The
func
tion
valu
eat
x=0
isno
tim
port
ant.
Whe
nyo
uw
ant
tous
eLJ
corr
ectio
n,m
ake
sure
that
rvdw
corr
espo
nds
toth
ecu
t-of
fin
the
user
-defi
ned
func
tion.
rvdw
switc
h:(0
)[n
m]
whe
reto
star
tsw
itchi
ngth
eLJ
pote
ntia
l
rvdw
:(1
)[n
m]
dist
ance
for
the
LJor
Buc
king
ham
cut-
off
Dis
pCor
r:
nodo
n’ta
pply
any
corr
ectio
n
Ene
rPre
sap
ply
long
rang
edi
sper
sion
corr
ectio
nsfo
rE
nerg
yan
dP
ress
ure
Ene
r appl
ylo
ngra
nge
disp
ersi
onco
rrec
tions
for
Ene
rgy
only
four
iers
paci
ng:
(0.1
2)[n
m]
The
max
imum
grid
spac
ing
fort
heF
FT
grid
whe
nus
ing
PP
PM
orP
ME
.For
ordi
nary
Ew
ald
the
spac
ing
times
the
box
dim
ensi
ons
dete
rmin
esth
ehi
ghes
tm
agni
tude
tous
ein
each
di-
rect
ion.
Inal
lca
ses
each
dire
ctio
nca
nbe
over
ridde
nby
ente
ring
ano
n-ze
rova
lue
for
four
ier
n*.
four
ier
nx(0
);f
ourie
rny
(0)
;fou
rier
nz:
(0)
Hig
hest
mag
nitu
deof
wav
eve
ctor
sin
reci
proc
alsp
ace
whe
nus
ing
Ew
ald.
Grid
size
whe
nus
ing
PP
PM
orP
ME
.The
seva
lues
over
ride
four
iers
paci
ngpe
rdi
rect
ion.
The
best
choi
ceis
pow
ers
of2,
3,5
and
7.A
void
larg
epr
imes
.
6.1
.C
alc
ula
ting
po
ten
tials
ofm
ea
nfo
rce
:th
ep
ull
cod
e1
07
r=
0 Ifdy
nam
icre
fere
nce
grou
psar
ese
lect
ed(
dyn
am
ic,
dyn
am
ict0
),r
isth
era
dius
ofth
ecy
linde
rus
edto
defin
ew
hich
atom
sar
epa
rtof
the
refe
renc
egr
oup
(see
abov
e).
rc=
0 With
dyna
mic
refe
renc
egr
oups
,th
ecy
linde
rca
nbe
smoo
thly
switc
hed
soth
atat
oms
that
fall
betw
eenr
and
rcar
ew
eigh
ted
linea
rlyfr
om1
to0
goin
gfr
omrto
rc.
As
reas
onab
lein
itial
valu
esw
esu
gges
tr=
1.0
and
rc=
1.5
but
this
will
depe
ndst
rong
lyon
the
exac
tsys
tem
ofin
tere
st.
up
da
te=
1T
hefr
eque
ncy
with
whi
chth
edy
nam
icre
fere
nce
grou
psar
ere
calc
ulat
ed.
Usu
ally
ther
eis
nore
ason
tous
ean
ythi
ngot
her
than
1.
pu
llra
te=
0.0
00
05
The
pull
rate
innm
/tim
este
pfo
rA
FM
pulli
ng.
forc
eco
nst
an
t=
10
0T
hefo
rce
cons
tant
for
the
sprin
gin
AF
Mpu
lling
,in
kJm
ol−
1nm
−2.
wid
th=
0W
idth
ofth
eum
brel
lasa
mpl
ing
pote
ntia
lin
kJm
ol−
1nm
−2.
r0g
rou
p2
=0
.00
.03
.30
0T
hein
itial
loca
tion
ofth
egr
oups
with
resp
ect
toth
ere
fere
nce
grou
p.O
nly
coor
dina
tes
sele
cted
with
dire
ctio
nar
eta
ken
into
acco
unt.
The
grou
psar
em
oved
toth
ese
initi
alpo
sitio
nsbe
fore
the
actu
alcr
eatio
nof
ase
ries
ofst
artin
gst
ruct
ures
com
men
ces.
tole
ran
ce=
0.0
01
The
accu
racy
with
whi
chth
eac
tual
posi
tion
ofth
egr
oups
mus
tm
atch
the
calc
ulat
edid
eal
posi
tions
for
ast
artin
gst
ruct
ure
(innm
).
tra
nsl
atio
nra
te=
0.0
00
01
The
rate
oftr
ansl
atio
nin
alld
irect
ions
(nm
/ste
p).
As
men
tione
dab
ove,
norm
alM
Dfo
rce
calc
ulat
ions
and
posi
tion
upda
tes
also
acto
nth
egr
oups
.
tra
nss
tep
=0
.2T
hein
terv
alin
nmat
whi
chst
ruct
ures
are
writ
ten
out.
6.1.
3O
utpu
t
The
outp
utfil
eis
ate
xtfil
ew
ithfo
rces
orpo
sitio
ns,
one
per
line.
Ifth
ere
are
two
grou
psth
eyal
tern
ate
inth
eou
tput
file.
Cur
rent
lyth
ere
isno
supp
orte
dan
alys
ispr
ogra
mto
read
this
file,
buti
tis
sim
ple
topa
rse.
6.1.
4Li
mita
tions
Apa
rtfr
omob
viou
slim
itatio
nsth
atar
esi
mpl
yno
tim
plem
ente
d(
e.g.
abe
tter
umbr
ella
sam
plin
gan
dan
alys
issc
hem
e),
ther
eis
one
impo
rtan
tlim
itatio
n:co
nstr
aint
forc
esca
non
lybe
calc
ulat
ed
10
8C
ha
pte
r6
.S
pe
cialTo
pics
between
molecules
orgroups
ofm
olecules.If
agroup
containspart
ofa
molecule
ofw
hichthe
bondlengthsare
constrained,S
HA
KE
orLIN
CS
andthe
constraintforce
calculationhere
will
interferew
itheach
other,m
akingthe
resultsunreliable.
Ifa
constraintforce
isw
antedbetw
eentw
oatom
s,thiscan
bedone
throughthe
freeenergy
perturbationcode.
Insum
mary:
•pullcode:betw
eenm
oleculesor
groupsofm
olecules.
•free
energyperturbation
code:between
singleatom
s.
•not
possiblecurrently:
between
groupsof
atoms
thatare
partof
alarger
molecule
forw
hichthe
bondsare
constrainedw
ithS
HA
KE
orLIN
CS
.
6.1.5Im
plementation
The
codefor
theoptions
describedabove
canbe
foundin
thefiles
pu
ll.c,p
ullin
it.c,p
ullio
.c,p
ullu
til.cand
theheaderfilespu
ll.hand
pu
lls.h.
This
lastfiledefines
afew
datatypes,pull.h
explainsthe
main
functions.
6.1.6F
uturedevelopm
ent
There
areseveraladditionalfeatures
thatwould
beuseful,including
more
advancedum
brellasam
-pling,an
analysistoolto
analysethe
outputofthepullcode,incorporation
oftheinputparam
etersand
indexfile
intotheg
rom
pp
programinputfiles,extension
tom
oregroups,m
oreflexible
defi-nition
ofareaction
coordinate,extensionto
groupsthatare
partsofm
oleculesthatuse
SH
AK
Eor
LINC
S,and
acom
binationofthe
startingstructure
calculationw
ithconstraints
forfaster
conver-gence
ofstartingstructures.
6.2R
emoving
fastestdegreesoffreedom
The
maxim
umtim
estep
inM
Dsim
ulationsis
limited
bythe
smallest
oscillationperiod
thatcan
befound
inthe
simulated
system.
Bond-stretching
vibrationsare
intheir
quantum-m
echanicalground
stateand
aretherefore
betterrepresented
bya
constraintthanby
aharm
onicpotential.
For
therem
ainingdegrees
offreedom
,the
shortestoscillation
periodas
measured
froma
simu-
lationis
13fs
forbond-angle
vibrationsinvolving
hydrogenatom
s.Taking
asa
guidelinethat
with
aVerlet(leap-frog)integration
scheme
am
inimum
of5num
ericalintegrationsteps
shouldbe
performed
perperiod
ofa
harmonic
oscillationin
orderto
integrateit
with
reasonableaccuracy,
them
aximum
time
stepw
illbeabout3
fs.D
isregardingthese
veryfastoscillations
ofperiod13
fsthe
nextshortestperiodsare
around20
fs,which
willallow
am
aximum
time
stepofabout4
fs
Rem
ovingthe
bond-angledegrees
offreedom
fromhydrogen
atoms
canbest
bedone
bydefin-
ingthem
asdum
my
atoms
instead
ofnorm
alatoms.
Where
anorm
alatoms
isconnected
tothe
molecule
with
bonds,angles
anddihedrals,
adum
my
atom’s
positionis
calculatedfrom
thepo-
sitionof
threenearby
heavyatom
sin
apredefined
manner
(seealso
sec.4.5).
For
thehydrogens
inw
aterand
inhydroxyl,sulfhydrylor
amine
groups,nodegrees
offreedomcan
berem
oved,be-cause
rotationalfreedomshould
bepreserved.
The
onlyother
optionavailable
toslow
down
these
7.3
.R
un
Pa
ram
ete
rs1
21
PM
EF
astP
article-Mesh
Ew
aldelectrostatics.
Direct
spaceis
similar
tothe
Ew
aldsum
,w
hilethe
reciprocalpartisperform
edw
ithF
FT
s.G
riddim
ensionsare
controlledw
ithfourierspacing
andthe
interpolationorder
withpm
eorder.
With
agrid
spacingof
0.1nm
andcubic
interpolationthe
electrostaticforces
havean
accuracyof
2-3e-4.S
incethe
errorfrom
thevdw
-cutoffis
largerthan
thisyou
might
try0.15
nm.
When
runningin
paralleltheinterpolation
parallelizesbetter
thanthe
FF
T,sotry
decreasinggrid
dimensions
while
increasinginterpolation.
PP
PMP
article-Particle
Particle-M
eshalgorithm
forlong
rangeelectrostatic
interactions.U
seforexam
plerlist=1
.0,rcoulom
bsw
itch=0
.0,rcoulom
b=
0.8
5,rvdw
switch=
1.0
andrvdw
=1
.0.
The
griddim
ensionsare
controlledbyfourierspacing.
Reasonable
gridspacing
forP
PP
Mis
0.05-0.1nm
.S
eeS
hift
forthe
detailsof
theparticle-
particlepotential.
NO
TE
:thepressure
inincorrectw
henusing
PP
PM
.
Reaction-F
ieldR
eactionfield
with
Coulom
bcut-offrcoulom
b,wherercoulom
b>
rvdw>
rlist.T
hedielectric
constantbeyond
thecut-off
isepsilonr.
The
dielectricconstant
canbe
setto
infinityby
settingepsilonr=
0.
Generalized-R
eaction-Field
Generalized
reactionfield
with
Coulom
bcut-off
rcoulomb,w
herercoulomb>
rvdw>
rlist.T
hedielectric
constantbeyond
thecut-off
isepsilon
r.T
heionic
strengthis
computed
fromthe
number
ofcharged(i.e.w
ithnon
zerocharge)
chargegroups.
The
temperature
forthe
GR
Fpotentialis
setwithref
t[K
].
ShiftT
heC
oulomb
potentialisdecreased
overthew
holerange
andthe
forcesdecay
smoothly
tozero
betweenrcoulom
bsw
itchand
rcoulomb.
The
neighborsearch
cut-offrlistshould
be0.1
to0.3
nmlarger
thanrcoulomb
toaccom
modate
forthe
sizeof
chargegroups
anddiffusion
between
neighborlistupdates.
UserS
pecifyrshort
andrlong
tothe
same
value,md
run
will
nowexpect
tofind
afile
ctab
.xvgw
ithuser-defined
functions.T
hisfile
shouldcontain
5colum
ns:the
xvalue,f(x)
,-f
(1)(x)
,f
(2)(x)
and-f
(3)(x)
,w
heref
(n)(x)
denotesthen
th
derivativeof
functionf(x)w
ithrespect
tox.
The
xshould
runfrom
0[nm
]to
rlist+0
.5[nm
],w
itha
spacingof0
.00
2[nm
]w
henyou
runin
singleprecision,
or0
.00
05
[nm]
when
yourun
indouble
precision.T
hefunction
valueat
x=0
isnot
important.
rcoulomb
switch:
(0)[nm
]w
hereto
startswitching
theC
oulomb
potential
rcoulomb:
(1)[nm
]distance
forthe
Coulom
bcut-off
epsilonr:
(1)dielectric
constant
12
0C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
xtc
grps
:gr
oup(
s)to
writ
eto
xtc
traj
ecto
ry,d
efau
ltth
ew
hole
syst
emis
writ
ten
(ifns
txtc
outi
sla
rger
than
zero
)
ener
gygr
ps:
grou
p(s)
tow
rite
toen
ergy
file
7.3.
8N
eigh
bor
sear
chin
g
nstli
st:
(10)
[ste
ps]
Fre
quen
cyto
upda
teth
ene
ighb
orlis
t(a
ndth
elo
ng-r
ange
forc
es,
whe
nus
ing
twin
-ran
gecu
t-of
f’s).
Whe
nth
isis
0,th
ene
ighb
orlis
tis
mad
eon
lyon
ce.
nsty
pe:
grid
Mak
ea
grid
inth
ebo
xan
don
lych
eck
atom
sin
neig
hbor
ing
grid
cells
whe
nco
nstr
uct-
ing
ane
wne
ighb
orlis
teve
rynst
lists
teps
.In
larg
esy
stem
sgr
idse
arch
ism
uch
fast
erth
ansi
mpl
ese
arch
.
sim
ple C
heck
ever
yat
omin
the
box
whe
nco
nstr
uctin
ga
new
neig
hbor
liste
very
nstli
stst
eps.
pbc:
xyz
Use
perio
dic
boun
dary
cond
ition
sin
alld
irect
ions
.
noU
seno
perio
dic
boun
dary
cond
ition
s,ig
nore
the
box.
Tosi
mul
ate
with
outc
ut-o
ffs,s
etal
lcut
-offs
to0
andn
stlis
t=0.
rlist
:(1
)[n
m]
cut-
offd
ista
nce
for
the
shor
t-ra
nge
neig
hbor
list
7.3.
9E
lect
rost
atic
san
dV
dW
coul
ombt
ype:
Cut
-off Tw
inra
nge
cut-
off’s
with
neig
hbor
list
cut-
offrli
stan
dC
oulo
mb
cut-
offrc
oulo
mb,
whe
rerli
st<
rvdw
<rc
oulo
mb.
The
diel
ectr
icco
nsta
ntis
setw
itheps
ilon
r.
Ew
ald C
lass
ical
Ew
ald
sum
elec
tros
tatic
s.U
see.
g.rli
st=
0.9,
rvdw
=0.
9,rc
oulo
mb=
0.9.
The
high
est
mag
nitu
deof
wav
eve
ctor
sus
edin
reci
proc
alsp
ace
isco
ntro
lled
byfo
uri-
ersp
acin
g.T
here
lativ
eac
cura
cyof
dire
ct/r
ecip
roca
lspa
ceis
cont
rolle
dby
ewal
drt
ol.
NO
TE
:E
wal
dsc
ales
asO
(N3/2)
and
isth
usex
trem
ely
slow
for
larg
esy
stem
s.It
isin
clud
edm
ainl
yfo
rre
fere
nce
-in
mos
tcas
esP
ME
will
perf
orm
muc
hbe
tter.
6.2
.R
em
ovin
gfa
ste
std
egre
es
off
ree
do
m1
09
D
d
α
d BA
C
���������� ����������
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��
��
��
���������� ����������
� ���
�����
�����
�����
�����
���������� ����������
Fig
ure
6.3:
The
diffe
rent
type
sof
dum
my
atom
cons
truc
tions
used
forh
ydro
gen
atom
s.T
heat
oms
used
inth
eco
nstr
uctio
nof
the
dum
my
atom
(s)a
rede
pict
edas
blac
kci
rcle
s,du
mm
yat
oms
asgr
eyon
es.
Hyd
roge
nsar
esm
alle
rth
anhe
avy
atom
s.A
:fixe
dbo
ndan
gle,
note
that
here
the
hydr
ogen
isno
tadu
mm
yat
om;B:i
nth
epl
ane
ofth
ree
atom
s,w
ithfix
eddi
stan
ce;
C:i
nth
epl
ane
ofth
ree
atom
s,w
ithfix
edan
gle
and
dist
ance
;D
:con
stru
ctio
nfo
ram
ine
grou
ps(
-NH
2or
-NH
+ 3),
see
text
for
deta
ils.
mot
ions
,is
toin
crea
seth
em
ass
ofth
ehy
drog
enat
oms
atth
eex
pens
eof
the
mas
sof
the
conn
ecte
dhe
avy
atom
.T
his
will
incr
ease
the
mom
ent
ofin
ertia
ofth
ew
ater
mol
ecul
esan
dth
ehy
drox
yl,
sulfh
ydry
lor
amin
egr
oups
,w
ithou
taf
fect
ing
the
equi
libriu
mpr
oper
ties
ofth
esy
stem
and
with
-ou
taffe
ctin
gth
edy
nam
ical
prop
ertie
sto
om
uch.
The
seco
nstr
uctio
nsw
illsh
ortly
bede
scrib
edin
sec.
6.2.
1an
dha
vepr
evio
usly
been
desc
ribed
infu
llde
tail
[63
].
Usi
ngbo
thdu
mm
yat
oms
and
mod
ified
mas
ses,
the
next
bottl
enec
kis
likel
yto
befo
rmed
byth
eim
prop
erdi
hedr
als
(whi
char
eus
edto
pres
erve
plan
arity
orch
iralit
yof
mol
ecul
argr
oups
)an
dth
epe
ptid
edi
hedr
als.
The
pept
ide
dihe
dral
cann
otbe
chan
ged
with
out
affe
ctin
gth
eph
ysic
albe
-ha
vior
ofth
epr
otei
n.T
heim
prop
erdi
hedr
als
that
pres
erve
plan
arity
,m
ostly
deal
with
arom
atic
resi
dues
.B
onds
,ang
les
and
dihe
dral
sin
thes
ere
sidu
esca
nal
sobe
repl
aced
with
som
ewha
tela
b-or
ate
dum
my
atom
cons
truc
tions
,as
will
bede
scrib
edin
sec.
6.2.
2[6
4].
All
mod
ifica
tions
desc
ribed
inth
isse
ctio
nca
nbe
perf
orm
edus
ing
the
GR
OM
AC
Sto
polo
gybu
ild-
ing
tool
pd
b2
gm
x.
Sep
arat
eop
tions
exis
tto
incr
ease
hydr
ogen
mas
ses,
dum
mify
allh
ydro
gen
atom
sor
also
dum
mify
alla
rom
atic
resi
dues
.N
ote
that
whe
nal
lhyd
roge
nat
oms
are
dum
mifi
ed,
also
thos
ein
side
the
arom
atic
resi
dues
will
bedu
mm
ified
,i.e
.hyd
roge
nsin
the
arom
atic
resi
dues
are
trea
ted
diffe
rent
lyde
pend
ing
onth
etr
eatm
ento
fthe
arom
atic
resi
dues
.
Par
amet
ers
for
the
dum
my
cons
truc
tions
for
the
hydr
ogen
atom
sar
ein
ferr
edfr
omth
efo
rcefi
eld
para
met
ers
(vis.
bond
leng
ths
and
angl
es)
dire
ctly
bygro
mp
pw
hile
proc
essi
ngth
eto
polo
gyfil
e.T
heco
nstr
uctio
nsfo
rth
ear
omat
icre
sidu
esar
eba
sed
onth
ebo
ndle
ngth
san
dan
gles
for
the
geom
etry
asde
scrib
edin
the
forc
efiel
ds,b
utth
ese
para
met
ers
are
hard
-cod
edin
top
db
2g
mx
due
toth
eco
mpl
exna
ture
ofth
eco
nstr
uctio
nne
eded
for
aw
hole
arom
atic
grou
p.
6.2.
1H
ydro
gen
bond
-ang
levi
brat
ions
Con
stru
ctio
nof
Dum
my
Ato
ms
The
goal
ofde
finin
ghy
drog
enat
oms
asdu
mm
yat
oms
isto
rem
ove
allh
igh-
freq
uenc
yde
gree
sof
free
dom
from
them
.In
som
eca
ses
not
alld
egre
esof
free
dom
ofa
hydr
ogen
atom
shou
ldbe
rem
oved
,e.
g.in
the
case
ofhy
drox
ylor
amin
egr
oups
the
rota
tiona
lfr
eedo
mof
the
hydr
ogen
11
0C
ha
pte
r6
.S
pe
cialTo
pics
atom(s)
shouldbe
preserved.C
areshould
betaken
thatno
unwanted
correlationsare
introducedby
theconstruction
ofdum
my
atoms,
e.g.bond-angle
vibrationbetw
eenthe
constructingatom
scould
translateinto
hydrogenbond-length
vibration.A
dditionally,since
dumm
yatom
sare
bydefinition
mass-less,in
orderto
preservetotalsystem
mass,the
mass
ofeachhydrogen
atomthat
istreated
asdum
my
atomshould
beadded
tothe
bondedheavy
atom.
Takinginto
accounttheseconsiderations,the
hydrogenatom
sin
aprotein
naturallyfallinto
severalcategories,each
requiringa
differentapproach,seealso
Fig.
6.3:
•h
ydro
xyl(-O
H)
or
sulfh
ydryl
(-SH
)h
ydroge
n:T
heonly
internaldegree
offreedom
ina
hydroxylgroupthat
canbe
constrainedis
thebending
ofthe
C-O
-Hangle.
This
angleis
fixedby
definingan
additionalbondofappropriate
length,seeF
ig.6.3A
.This
removes
thehigh
frequencyangle
bending,butleavesthe
dihedralrotationalfreedom.
The
same
goesfor
asulfhydrylgroup.
Note
thatinthese
casesthe
hydrogenis
nottreatedas
adum
my
atom.
•sin
gle
am
ine
or
am
ide
(-NH
-)a
nd
aro
ma
tich
ydroge
ns
(-C
H-):
The
positionof
thesehy-
drogenscannot
beconstructed
froma
linearcom
binationof
bondvectors,
becauseof
theflexibility
oftheangle
between
theheavy
atoms.
Instead,the
hydrogenatom
ispositioned
ata
fixeddistance
fromthe
bondedheavy
atomon
aline
goingthrough
thebonded
heavyatom
anda
pointonthe
linethrough
bothsecond
bondedatom
s,seeF
ig.6.3B
.
•p
lan
ar
am
ine
(-NH
2 )h
ydroge
ns:T
hem
ethodused
forthe
singleam
idehydrogen
isnot
wellsuited
forplanar
amine
groups,because
nosuitable
two
heavyatom
scan
befound
todefine
thedirection
ofthehydrogen
atoms.
Instead,
thehydrogen
isconstructed
atafixed
distancefrom
thenitrogen
atom,w
itha
fixedangle
tothe
carbonatom
,inthe
planedefined
byone
oftheother
heavyatom
s,seeF
ig.6.3C
.
•a
min
eg
rou
p(u
mb
rella-N
H2
or
-NH
+3)
hyd
rogen
s:Am
inehydrogens
with
rotationalfree-dom
cannotbe
constructedas
dumm
yatom
sfrom
theheavy
atoms
theyare
connectedto,
sincethis
would
resultin
lossof
therotationalfreedom
ofthe
amine
group.To
preservethe
rotationalfreedomw
hilerem
ovingthe
hydrogenbond-angle
degreesof
freedom,
two
“dumm
ym
asses”are
constructedw
iththe
same
totalmass,m
omentofinertia
(forrotation
aroundtheC
-Nbond)
andcenter
ofm
assas
theam
inegroup.
These
dumm
ym
asseshave
nointeraction
with
anyother
atom,exceptfor
thefactthatthey
areconnected
tothe
carbonand
toeach
other,resultingin
arigid
triangle.F
romthese
threeparticles
thepositions
ofthenitrogen
andhydrogen
atoms
areconstructed
aslinearcom
binationsofthe
two
carbon-mass
vectorsand
theirouter
product,resultingin
anam
inegroup
with
rotationalfreedomintact,
butwithoutother
internaldegreesoffreedom
.S
eeF
ig.6.3D
.
6.2.2O
ut-of-planevibrations
inarom
aticgroups
The
planararrangem
entsin
theside
chainsof
thearom
aticresidues
lendsitself
perfectlyfor
adum
my-atom
construction,giving
aperfectly
planargroup
without
theinherently
instablecon-
straintsthatare
necessaryto
keepnorm
alatoms
ina
plane.T
hebasic
approachis
todefine
threeatom
sor
dumm
ym
assesw
ithconstraints
between
themto
fixthe
geometry
andcreate
therestof
theatom
sas
simple
dumm
ytype
3atom
s(see
sec.4.5)
fromthese
three.E
achof
thearom
aticresidues
requirea
differentapproach:
7.3
.R
un
Pa
ram
ete
rs1
19
7.3.5E
nergym
inimization
emtol:
(100.0)[kJ
mol −
1nm
−1]
them
inimization
isconverged
when
them
aximum
forceis
smaller
thanthis
value
emstep:
(0.01)[nm
]initialstep-size
nstcgsteep:(1000)
[steps]frequency
ofperforming
1steepestdescentstep
while
doingconjugate
gradientenergym
in-im
ization.
7.3.6S
hellMolecular
Dynam
ics
The
shellmoleculardynam
icsprogramxm
drunoptim
izesthe
positionsofthe
shellsatevery
time
stepuntileitherthe
RM
Sforce
onthe
shellsis
lessthan
emtol,ora
maxim
umnum
berofiterations(niter)
hasbeen
reached
emtol:
(100.0)[kJ
mol −
1nm
−1]
them
inimization
isconverged
when
them
aximum
forceis
smaller
thanthis
value.F
orshell
MD
thisvalue
shouldbe
1.0atm
ost,butsincethe
variableis
usedfor
energym
inimization
asw
ellthedefaultis
100.0.
niter:(20)m
aximum
number
ofiterationsfor
optimizing
theshellpositions.
7.3.7O
utputcontrol
nstxout:(100)
[steps]frequency
tow
ritecoordinates
tooutputtrajectory
file,thelastcoordinates
arealw
aysw
rit-ten
nstvout:(100)
[steps]frequency
tow
ritevelocities
tooutputtrajectory,the
lastvelocitiesare
always
written
nstfout:(0)
[steps]frequency
tow
riteforces
tooutputtrajectory.
nstlog:(100)
[steps]frequency
tow
riteenergies
tolog
file,thelastenergies
arealw
aysw
ritten
nstenergy:(100)
[steps]frequency
tow
riteenergies
toenergy
file,thelastenergies
arealw
aysw
ritten
nstxtcout:(0)
[steps]frequency
tow
ritecoordinates
toxtc
trajectory
xtcprecision:
(1000)[real]
precisionto
write
toxtc
trajectory
11
8C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
sdA
leap
-fro
gst
ocha
stic
dyna
mic
sin
tegr
ator
.T
hete
mpe
ratu
refo
rone
orm
ore
grou
psof
atom
s(tc
grps
)is
setw
ithre
ft
[K],
the
inve
rse
fric
tion
cons
tant
for
each
grou
pis
set
with
tau
t[p
s].
The
para
met
ertco
upli
sig
nore
d.T
hera
ndom
gene
rato
ris
initi
aliz
edw
ithld
seed
.
NO
TE
:tem
pera
ture
devi
atio
nsde
cay
twic
eas
fast
asw
itha
Ber
ends
enth
erm
osta
twith
the
sam
etau
t.
bdA
nE
uler
inte
grat
orfo
rB
row
nian
orpo
sitio
nLa
ngev
indy
nam
ics,
the
velo
city
isth
efo
rce
divi
ded
bya
fric
tion
coef
ficie
nt(bd
fric
[am
ups−
1])
plus
rand
omth
erm
alno
ise
(bd
tem
p[K
]).
Whe
nbd
fric
=0,
the
fric
tion
coef
ficie
ntfo
rea
chpa
rtic
leis
calc
u-la
ted
asm
ass/ta
ut,
asfo
rth
ein
tegr
ators
d.
The
rand
omge
nera
tor
isin
itial
ized
with
ldse
ed.
tinit:
(0)
[ps]
star
ting
time
for
your
run
(onl
ym
akes
sens
efo
rin
tegr
ator
sm
d,sd
and
bd
)
dt:
(0.0
01)
[ps]
time
step
for
inte
grat
ion
(onl
ym
akes
sens
efo
rin
tegr
ator
sm
d,sd
and
bd
)
nste
ps:
(1)
max
imum
num
ber
ofst
eps
toin
tegr
ate
nstc
omm
:(1
)[s
teps
]if
posi
tive:
freq
uenc
yfo
rce
nter
ofm
ass
mot
ion
rem
oval
ifne
gativ
e:fr
eque
ncy
for
cent
erof
mas
sm
otio
nan
dro
tatio
nalm
otio
nre
mov
al(s
houl
don
lybe
used
for
vacu
umsi
mul
atio
ns)
com
mgr
ps:
grou
p(s)
for
cent
erof
mas
sm
otio
nre
mov
al,
defa
ult
isth
ew
hole
syst
em,
rota
tion
rem
oval
can
only
bedo
neon
the
who
lesy
stem
7.3.
4La
ngev
indy
nam
ics
bdte
mp:
(300
)[K
]te
mpe
ratu
rein
Bro
wni
andy
nam
ics
run
(con
trol
sth
erm
alno
ise
leve
l).W
hen
bdfr
ic=
0,re
ft
isus
edin
stea
d.
bdfr
ic:
(0)
[am
ups
−1]
Bro
wni
andy
nam
ics
fric
tion
coef
ficie
nt.
Whe
nbdfr
ic=
0,th
efr
ictio
nco
effic
ient
for
each
part
icle
isca
lcul
ated
asm
ass/tau
t.
ldse
ed:
(199
3)[in
tege
r]us
edto
initi
aliz
era
ndom
gene
rato
rfo
rth
erm
alno
ise
for
stoc
hast
ican
dB
row
nian
dyna
m-
ics.
Whe
nld
seed
isse
tto
-1,
the
seed
isca
lcul
ated
as(tim
e()
+g
etp
id()
)%
10
00
00
0
6.3
.V
isco
sity
calc
ula
tion
11
1
ε
η
ζδ
ε
γ
ε
δε
δεδ γ
ζε
η
εδ
γ
Ph
eT
yrH
isT
rp
ζ
ε
ζ
εδ
γ
δδ
���������� ����������
���������� �������������������� ����������
���������� �������������� ����
���������� ����������
� ������������� ����������
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���������� ����������
���������� ����������
���������� ����������
Fig
ure
6.4:
The
diffe
rent
type
sof
dum
my
atom
cons
truc
tions
used
for
arom
atic
resi
dues
.T
heat
oms
used
inth
eco
nstr
uctio
nof
the
dum
my
atom
(s)
are
depi
cted
asbl
ack
circ
les,
dum
my
atom
sas
grey
ones
.H
ydro
gens
are
smal
ler
than
heav
yat
oms.
A:
phen
ylal
anin
e;B
:ty
rosi
ne(n
ote
that
the
hydr
oxyl
hydr
ogen
isno
tadu
mm
yat
om);C
:try
ptop
hane
;D:h
istid
ine.
•P
he
nyl
ala
nin
e:C
γ,C
ε1an
dCε2
are
kept
asno
rmal
atom
s,bu
twith
each
am
ass
ofon
eth
irdth
eto
talm
ass
ofth
eph
enyl
grou
p.S
eeF
ig.
6.3A
.
•Ty
rosi
ne
:The
ring
istr
eate
did
entic
alto
the
phen
ylal
anin
erin
g.A
dditi
onal
ly,
cons
trai
nts
are
defin
edbe
twee
nCε1
and
Cε2
and
Oη.
The
orig
inal
impr
oper
dihe
dral
angl
esw
illke
epbo
thtr
iang
les
(one
for
the
ring
and
one
withO
η)
ina
plan
e,bu
tdue
toth
ela
rger
mom
ents
ofin
ertia
this
cons
truc
tion
will
bem
uch
mor
est
able
.T
hebo
ndan
gle
inth
ehy
drox
ylgr
oup
will
beco
nstr
aine
dby
aco
nstr
aint
betw
een
Cγ
and
Hη,n
ote
that
the
hydr
ogen
isno
ttre
ated
asa
dum
my
atom
.S
eeF
ig.
6.3B
.
•T
ryp
top
ha
ne
:Cβ
iske
ptas
ano
rmal
atom
and
two
dum
my
mas
ses
are
crea
ted
atth
ece
nter
ofm
ass
ofea
chof
the
rings
,eac
hw
itha
mas
seq
ualt
oth
eto
talm
ass
ofth
ere
spec
tive
ring
(Cδ2
and
Cε2
are
each
coun
ted
half
for
each
ring)
.T
his
keep
sth
eov
eral
lcen
ter
ofm
ass
and
the
mom
ento
fine
rtia
alm
ost(
butn
otqu
ite)
equa
lto
wha
titw
as.
See
Fig
.6.
3C.
•H
istid
ine
:C
γ,
Cε1
and
Nε2
are
kept
asno
rmal
atom
s,bu
tw
ithm
asse
sre
dist
ribut
edsu
chth
atth
ece
nter
ofm
ass
ofth
erin
gis
pres
erve
d.S
eeF
ig.
6.3D
.
6.3
Vis
cosi
tyca
lcul
atio
n
The
shea
rvi
scos
ityis
apr
oper
tyof
liqui
dw
hich
can
bede
term
ined
easi
lyby
expe
rimen
t.It
isus
eful
for
para
met
eriz
ing
the
forc
efiel
d,be
caus
eit
isa
kine
ticpr
oper
ty,w
hile
mos
toth
erpr
oper
-tie
sw
hich
are
used
for
para
met
eriz
atio
nar
eth
erm
odyn
amic
.T
hevi
scos
ityis
also
anim
port
ant
prop
erty
,si
nce
itis
ofin
fluen
ceon
the
rate
sof
conf
orm
atio
nalc
hang
esof
mol
ecul
esso
lvat
edin
the
liqui
d.
The
visc
osity
can
beca
lcul
ated
from
aneq
uilib
rium
sim
ulat
ion
usin
gan
Ein
stei
nre
latio
n:
η=
1 2V
kBT
lim t→∞
d dt
⟨ ( ∫t 0
+t
t 0P
xz(t′ )
dt′) 2⟩
t 0
(6.1
)
Thi
sca
nbe
done
withg
en
erg
y.
Thi
sm
etho
dco
nver
ges
very
slow
ly.
Ana
nose
cond
sim
ulat
ion
mig
htno
tbe
long
enou
ghfo
ran
accu
rate
dete
rmin
inat
ion
ofth
evi
scoi
ty.
The
resu
ltis
very
depe
nden
ton
the
trea
tmen
tof
the
elec
tros
tatic
s.U
sing
a(s
hort
)cu
t-of
fre
sults
inla
rge
nois
eon
11
2C
ha
pte
r6
.S
pe
cialTo
pics
theoff-diagonal
pressureelem
ents,w
hichcan
increasethe
calculatedviscosity
byan
orderof
magnitude.
GR
OM
AC
Salso
hasa
non-equilibriumm
ethodfor
determining
theviscosity.
This
makes
useof
thefact
thatenergy,
which
isfed
intosystem
byexternalforces,
isdissipated
throughviscous
friction.T
hegenerated
heatisrem
ovedby
couplingto
aheatbath.
For
aN
ewtonian
liquidadding
asm
allforcew
illresultina
velocitygradientaccording
tothe
following
equation:
ax (z)
+ηρ
∂2v
x (z)∂z2
=0
(6.2)
herew
ehave
appliedan
accelerationa
x (z)in
thex
-direction,w
hichis
afunction
ofthez-
coordinate.In
GR
OM
AC
Sthe
accelerationprofile
is:
ax (z)
=A
cos (2πz
lz )(6.3)
where
lzis
theheightofthe
box.T
hegenerated
velocityprofile
is:
vx (z)
=V
cos (2πz
lz )(6.4)
V=Aρη (
lz2π )
2
(6.5)
The
viscositycan
becalculated
fromAand
V:
η=AVρ (
lz2π )
2
(6.6)
Inthe
simulationV
isdefined
as:V=
N∑i=1
mi v
i,x 2cos (
2πz
lz )N∑i=
1
mi
(6.7)
The
generatedvelocity
profileis
notcoupledto
theheatbath,also
thevelocity
profileis
excludedfrom
thekinetic
energy.O
new
ouldlikeV
tobe
aslarge
aspossible
togetgood
statistics.H
owever
theshear
rateshould
notbeso
highthatthe
systemgets
toofar
fromequilibrium
.T
hem
aximum
shearrate
occursw
herethe
cosineis
zero,therate
is:
shm
ax
=m
axz ∣∣∣∣ ∂vx (z)∂z ∣∣∣∣ =
Aρη
lz2π(6.8)
For
asim
ulationw
ith:η=
10−
3[kg
m−
1s −
1],ρ
=10
3[kg
m−
3]and
lz=
2π[nm
],shm
ax
=1
[psnm
−1]A
.T
hisshear
rateshould
besm
allerthan
oneover
thelongestcorrelation
time
inthe
system.
Form
ostliquidsthis
willbe
therotation
correlationtim
e,which
isaround
10picoseconds.
Inthis
caseAshould
besm
allerthan
0.1[nm
ps−
2].W
henthe
shearrate
istoo
high,theobserved
viscosityw
illbetoo
low.
BecauseV
isproportionalto
thesquare
ofthe
boxheight,
theoptim
al
7.3
.R
un
Pa
ram
ete
rs1
17
7.3R
unP
arameters
7.3.1G
eneral
Default
valuesare
givenin
parentheses.T
hefirst
optionis
always
thedefault
option.U
nitsare
givenin
squarebrackets
The
differencebetw
eena
dashand
anunderscore
isignored.
Asam
ple.m
dp
fileis
available.T
hisshould
beappropriate
tostarta
normalsim
ulation.E
ditittosuityour
specificneeds
anddesires.
7.3.2P
reprocessing
title:this
isredundant,so
youcan
typeanything
youw
ant
cpp:(/lib/cpp)your
preprocessor
include:directories
toinclude
inyour
topology.form
at:-I/h
om
e/jo
hn
/my
lib-I../m
ore
lib
define:()
definesto
passto
thepreprocessor,defaultis
nodefines.
Youcan
useany
definesto
controloptions
inyour
customized
topologyfiles.
Options
thatarealready
availableby
defaultare:
-DF
LEX
SP
CW
illtellgrompp
toinclude
FLE
XS
PC
instead
ofSP
Cinto
yourtopology,this
isnec-
essaryto
makeconjugate
gradientwork
andw
illallowsteepestdescentto
minim
izefurther.
-DP
OS
RE
Willtellgrom
ppto
includeposre.itp
intoyour
topology,usedfor
positionrestraints.
7.3.3R
uncontrol
integrator:
md
Aleap-frog
algorithmfor
integratingN
ewton’s
equations.
steepAsteepest
descentalgorithm
forenergy
minim
ization.T
hem
aximum
stepsize
isem
step[nm],the
toleranceisem
tol[kJm
ol −1
nm−
1].
cgA
conjugategradient
algorithmfor
energym
inimization,
thetolerance
isem
tol[kJm
ol −1
nm−
1].C
Gis
more
efficientwhen
asteepestdescentstep
isdone
everyonce
ina
while,this
isdeterm
inedbynstcgsteep.
11
6C
ha
pte
r7
.R
un
pa
ram
ete
rsa
nd
Pro
gra
ms
Def
ault
Def
ault
Nam
eE
xt.
Type
Opt
ion
Des
crip
tion
ato
mtp
.atp
Asc
Ato
mty
pefil
eus
edby
pdb2
gmx
eiw
it.b
rkA
sc-f
Bro
okha
ven
data
bank
file
nn
nic
e.d
at
Asc
Gen
eric
data
file
use
r.d
lgA
scD
ialo
gB
oxda
tafo
rng
mx
sam
.ed
iA
scE
Dsa
mpl
ing
inpu
tsa
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do
Asc
ED
sam
plin
gou
tput
en
er.
ed
rG
ener
icen
ergy
:edr
en
ee
ne
r.e
dr
xdr
Ene
rgy
file
inpo
rtab
lexd
rfo
rmat
en
er.
en
eB
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yfil
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iwit.
en
tA
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Ent
ryin
the
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ein
date
bank
plo
t.e
ps
Asc
Enc
apsu
late
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eg
tra
j.g8
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rom
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atco
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96
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oord
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mos
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eric
stru
ctur
e:gro
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tpr
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ou
t.g
ro-o
Gen
eric
stru
ctur
e:gro
g9
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db
con
f.g
roA
sc-c
Coo
rdin
ate
file
inG
rom
os-8
7fo
rmat
po
lar.
hd
bA
scH
ydro
gen
data
base
top
inc.
itpA
scIn
clud
efil
efo
rto
polo
gyru
n.lo
gA
sc-l
Log
file
ps.
m2
pA
scIn
putfi
lefo
rm
at2p
sss
.ma
pA
scF
ileth
atm
aps
mat
rixda
tato
colo
rsss
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atrix
Dat
afil
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rom
pp
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putfi
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ithM
Dpa
ram
eter
sh
ess
ian
.mtx
Bin
-mH
essi
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atrix
ind
ex.
nd
xA
sc-n
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xfil
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eric
outp
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ee
iwit.
pd
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tein
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file
pu
ll.p
do
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ldat
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tput
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pa
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ato
po
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top
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ble
xdr
run
inpu
tfile
tra
j.trj
Bin
Tra
ject
ory
file
(cpu
spec
ific)
tra
j.trr
Ful
lpre
cisi
ontr
ajec
tory
:trr
trj
tra
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ject
ory
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rtab
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rmat
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file
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trr
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gro
g9
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tra
j.xtc
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Com
pres
sed
traj
ecto
ry(p
orta
ble
xdr
form
at)
gra
ph
.xvg
Asc
-oxv
gr/x
mgr
file
Tabl
e7.
1:T
heG
RO
MA
CS
file
type
san
dho
wth
eyca
nbe
used
for
inpu
t/out
put.
6.4
.U
ser
spe
cifie
dp
ote
ntia
lfu
nct
ion
s1
13
box
isel
onga
ted
inth
ez-di
rect
ion.
Inge
nera
lasi
mul
atio
nle
ngth
of10
0pi
cose
cond
sis
enou
ghto
obta
inan
accu
rate
valu
efo
rth
evi
scos
ity.
The
heat
gene
rate
dby
the
visc
ous
fric
tion
isre
mov
edby
coup
ling
toa
heat
bath
.B
ecau
seth
isco
uplin
gis
not
inst
anta
neou
sth
ere
alte
mpe
ratu
reof
the
liqui
dw
illbe
slig
htly
low
erth
anth
eob
serv
edte
mpe
ratu
re.
Ber
ends
ende
rived
this
tem
pera
ture
shift
[20
],w
hich
can
bew
ritte
nin
term
sof
the
shea
rra
teas
:T
s=
ητ
2ρC
vsh
2 max
(6.9
)
whe
reτ
isth
eco
uplin
gtim
efo
rth
eB
eren
dsen
ther
mos
tat
and
Cv
isth
ehe
atca
paci
ty.
Usi
ngth
eva
lues
ofth
eex
ampl
eab
ove,τ
=10−
13
[s]
andC
v=
2·1
03[J
kg−
1K−
1],
we
get:T
s=
25[K
ps−
2]s
h2 max.
Whe
nw
ew
antt
hesh
ear
rate
tobe
smal
ler
than
1/10
[ps−
1],T
sis
smal
ler
than
0.25
[K],
whi
chis
negl
igib
le.
Not
eth
atth
esy
stem
has
tobu
ildup
the
velo
city
profi
lew
hen
star
ting
from
aneq
uilib
rium
stat
e.T
his
build
-up
time
isof
the
orde
rof
the
corr
elat
ion
time
ofth
eliq
uid.
Two
quan
titie
sar
ew
ritte
nto
the
ener
gyfil
e,al
ong
with
thei
rave
rage
san
dflu
ctua
tions
:V
and1/η
asob
tain
edfr
om(6.6)
.
6.4
Use
rsp
ecifi
edpo
tent
ialf
unct
ions
You
can
also
use
your
own
pote
ntia
lfun
ctio
nsw
ithou
tedi
ting
the
GR
OM
AC
Sco
de.
The
pote
ntia
lfu
nctio
nsh
ould
beac
cord
ing
toth
efo
llow
ing
equa
tion
V(r
ij)
=q iq j
4πε 0f(r
ij)+C
6g(r
ij)+C
12h(r
ij)
(6.1
0)
with
f,g,h
user
defin
edfu
nctio
ns.
Not
eth
atif
g(r)
repr
esen
tsa
norm
aldi
sper
sion
inte
ract
ion,
g(r)
shou
ldbe<
0.C
6,
C12
and
the
char
ges
are
read
from
the
topo
logy
.A
lso
note
that
com
bina
tion
rule
sar
eon
lysu
ppor
ted
for
Lenn
ard
Jone
san
dB
ucki
ngha
m,
and
that
your
tabl
essh
ould
mat
chth
epa
ram
eter
sin
the
bina
ryto
polo
gy.
Whe
nyo
uad
dth
efo
llow
ing
lines
inyo
ur.md
pfil
e:
rlis
t=
1.0
cou
lom
bty
pe
=U
ser
rco
ulo
mb
=1
.0vd
wty
pe
=U
ser
rvd
w=
1.0
the
MD
prog
ram
will
read
asi
ngle
file
(nam
eca
nbe
chan
ged
with
optio
n-t
ab
le)
with
seve
nco
lum
nsof
tabl
elo
okup
data
inth
eor
der:
x,f(
x),f
”(x)
,g(x
),g”
(x),
h(x)
,h”(
x).
The
xsh
ould
run
from
0to
r c+0.
5,w
itha
spac
ing
of0.
002
nmw
hen
you
run
insi
ngle
prec
isio
n,or
0.00
05w
hen
you
run
indo
uble
prec
isio
n.In
this
cont
extr
cde
note
sth
em
axim
umof
the
two
cut-
offsrvd
wan
drc
ou
lom
b(s
eeab
ove)
.T
hese
varia
bles
need
notb
eth
esa
me
(and
need
notb
e1.
0ei
ther
).S
ome
func
tions
used
for
pote
ntia
lsco
ntai
na
sing
ular
ityat
x=
0,bu
tsin
ceat
oms
are
norm
ally
notc
lose
rto
each
othe
rth
an0.
1nm
,the
func
tion
valu
eat
x=
0is
noti
mpo
rtan
tand
the
tabl
esca
nbe
star
ted
ate.
g.0.
02nm
.F
inal
ly,
itis
also
poss
ible
toco
mbi
nea
stan
dard
Cou
lom
bw
itha
mod
ified
LJ
11
4C
ha
pte
r6
.S
pe
cialTo
pics
potential(orvice
versa).O
nethen
specifiese.g.
coulombtype
=C
ut-offorcoulom
btype=
PM
E,
combined
with
vdwtype
=U
ser.T
hetable
filem
ustalw
ayscontain
the7
columns
however,
andm
eaningfuldata(i.e.
notzeroes)m
ustbeentered
inallcolum
ns.A
number
ofpre-builttablefiles
canbe
foundin
theG
MX
LIBdirectory,
for6-8,
6-9,6-10,
6-11,6-12
LennardJones
potentialscom
binedw
itha
normalC
oulomb.
6.5R
unningG
RO
MA
CS
inparallel
Ifyou
haveinstalled
theM
PI
(Message
Passing
Interface)on
yourcom
puter(s)you
cancom
pileG
RO
MA
CS
with
thislibrary
torun
simulations
inparallel.
Allsupercom
putersare
shippedw
ithM
PIlibraries
optimized
forthatparticular
platform,and
ifyouare
usinga
clusterofw
orkstationsthere
areseveralgood
freeM
PIim
plementations.
Youcan
findupdated
linksto
theseon
thegro-
macs
homepagew
ww
.gromacs.org.O
nceyou
havean
MP
Ilibraryinstalled
it’strivialto
compile
GR
OM
AC
Sw
ithM
PI
support:Just
setthe
option--en
ab
le-m
pi
tothe
configurescript
andrecom
pile.(B
utdon’t
forgetto
make
distcleanbefore
runningconfigure
ifyou
havepreviously
compiled
with
adifferentconfiguration.)
Ifyouare
usinga
supercomputer
youm
ightalsow
anttoturn
ofthedefaultnicing
ofthem
drunprocess
with
the--d
isab
le-n
iceoption.
There
isusually
aprogram
calledmpiru
nw
ithw
hichyou
canfire
upthe
parallelprocesses.A
typicalcomm
andline
lookslike:
%m
piru
n-p
go
ofu
s,do
ofu
s,fred
10
md
run
-sto
po
l-v
-N3
0this
runson
eachofthe
machines
goofus,doofus,fredw
ith10
processeson
each1.
Ifyou
havea
singlem
achinew
ithm
ultipleprocessors
youdon’t
haveto
usethe
mp
irun
com-
mand,butyou
cando
with
anextra
optionto
md
run
:%
md
run
-np
8-s
top
ol
-v-N
8In
thisexam
pleM
PI
readsthe
firstoption
fromthe
comm
andline.
Sincem
dru
nalso
wants
toknow
thenum
berofprocesses
youhave
totype
ittwice.
Check
yourlocalm
anuals(or
onlinem
anual)for
exactdetailsofyour
MP
Iimplem
entation.
Ifyouare
interestedin
programm
ingM
PIyourself,you
canfind
manuals
andreference
litteratureon
thew
ebatw
ww
.mcs.anl.gov/m
pi/index.html
.
1Exam
pletaken
fromS
iliconG
raphicsm
anual
Chapter
7
Run
parameters
andP
rograms
7.1O
nlineand
htmlm
anuals
Allthe
information
inthis
chaptercan
alsobe
foundin
HT
ML
format
inyour
GR
OM
AC
Sdata
directory.T
hepath
dependson
where
yourfiles
areinstalled,butthe
defaultlocationis
/usr/lo
cal/g
rom
acs/sh
are
/htm
l/on
line
.htm
lO
r,ifyouinstalled
fromLinux
packagesitcan
befound
as/u
sr/loca
l/sha
re/g
rom
acs/h
tml/o
nlin
e.h
tml
Youcan
alsouse
theonline
fromour
web
site,w
ww
.gromacs.org/docum
entation/reference3.0/online.htm
l
Inaddition,
we
installstandard
UN
IXm
anualsfor
allthe
programs.
Ifyou
havesourced
theG
MX
RCscriptin
theG
RO
MA
CS
binarydirectory
foryour
hosttheyshould
alreadybe
presentinyour$
MA
NP
AT
H,andyou
shouldbe
ableto
typee.g.m
an
gro
mp
p.
The
programm
anualpagescan
alsobe
foundin
Appendix
Ein
thism
anual.
7.2F
iletypes
Table7.1
liststhe
filetypes
usedby
GR
OM
AC
Salong
with
ashortdescription,and
youcan
finda
more
detaildescriptionfor
eachfile
inyour
HT
ML
reference,orin
ouronline
version.
GR
OM
AC
Sfiles
written
inxdr
format
canbe
readon
anyarchitecture
with
GR
OM
AC
Sversion
1.6orlaterifthe
configurationscriptfound
theX
DR
librarieson
yoursystem.
They
shouldalw
aysbe
presentonU
NIX
sincethey
arenecessary
forthe
network
filesystem
support.