• Proteins are dynamic systems

Concerted motions of the p53binding domain of MDM2

• protein dynamics:– Timescale: from s to fs.

– Inhomogeneity within same structure.

– Conformational substates

– Temperature dependence.

Motions of tyrosine kinase

Observation of protein dynamics

– Mössbauer spectroscopy: based on the interaction between x-ray (e. g. synchrotron radiation) and atomic nucleus in solids or some liquids (nuclear resonance scattering).

Lamb-Mössbauer factor f:

22

0 xkef

– Incoherent neutron scattering:

j

xkj

jeII22

0 j jj xIx 2

02

Experimental observation

• Linear up to about Tc=180K.

• T>Tc: a dramatic increase of the slope new modes of motion contribute to MSD, even in dry Mb.

• This phenomenon has been found in a large number of proteins.

Data from incoherent neutron scattering (open symbols), and Mössbauer absorption (full symbols) with different Mb-crystals.

Experimental observation

How fast are these new modes of motion?– Consider the relation of

energy and time resolution:

The new protein specific motions (T>Tc) occur on a

timesacle < 4ps!

meVE 1 st 12104/1

Symbols: data from several Mössbauer experiments"—": calculated data from phonon density.

Example: photosystem II of spinach

Average mean square displacements of iron in photosystem II of spinach (•) and efficiency of the electron transfer from quinone A to quinone B as a function of temperature.

Proteins and glasses

• Glasses are better studied and much simpler than proteins, so they can serve as guides to formulate concepts and theories for proteins.

Attributes Glass Protein

Structurally disordered Many mimina in the

energy landscape -, -relaxation

Glass transition• Unlike crystalline solids,

glasses do not have a certain melting temperature.

• The viscosity changes gradually with increasing temperature.

• Glass transition temperature Tg: At which the viscosity of a material reaches 10^13p = poise (=0.1kg/ms).

SiO2 crystal

SiO2 glass

Glass transition

• T<Tg: „Frozen“ in one of many local minima, very little mobility.

• T>Tg: The energy barriers can be overcome and other local minima explored.

Energy landscape

Glass-like transition in proteins

• Proteins also possess a glass transition temperature Tg:– Near Tg: Dynamical transition to a glass-like solid,

– T<Tg: Quenched anharmonic motions and long-range correlated motion. (functionally relevant motions)

• From computer simulations: Glassy behaviour of solvent drives the transition of protein.

Atomic-Detail Computer Simulation

Model System

Molecular Mechanics Potential

ji ij

ji

ji ij

ij

ij

ijij

impropersdihedrals

N

n

n

anglesbondsb

Dr

qq

rr

KnK

kbbkV

,,

612

20

1

20

20

4

cos1

Energy Surface Exploration by Simulation..

Mountain Landscape

Energy Landscapes

More realistic pictures of energy landscapes

kTVV

j

i jieN

N /)(

Dynamical Transition

Mean-Square Displacement Nonlinear in T

The Protein Glass Transition

d

d

nn

Onset of Protein Function

Harmonic

Liquid

Glass

Dynamics & Activity of Glutamate Dehydrogenasein a Cryosolvent

[70% MeOD; 30%; D2O]

VALERIE REATRACHEL DUNNROY DANIELJOHN FINNEY

.

Principal Component Analysis of the Myoglobin Glass Transition

ALEXTOURNIER

7500

jjiiij rtrrtrA )()(

ALEX TOURNIER

Anharmonicity Factor= N/ P

Normal Mode Frequency, N

Principal Mode Frequency, P

N

P

Good Fit

Bad Fit

Error in Gaussian Fit

P(r)

P(r)

Free Energy Profiles of Dominant Principal Components

Mode Incipient at Myoglobin Glass Transition

Low temperature onset of anharmonic dynamics

Simulation details :Simulation details :

• Hydrated Myoglobin crystalHydrated Myoglobin crystal

• 10 ns MD trajectory (NPT)10 ns MD trajectory (NPT)

• Methyl dynamics at 150 KMethyl dynamics at 150 K

Mean Square DisplacementMean Square Displacement

• Protein dynamical transition~220KProtein dynamical transition~220K

• Onset of anharmonic dynamics~150KOnset of anharmonic dynamics~150K

Methyl dynamic heterogeneityMethyl dynamic heterogeneity

Site-specific spectral analysisSite-specific spectral analysis

• Low frequency methyl dynamics Low frequency methyl dynamics is sensitive to local packing is sensitive to local packing

Role of Xenon cavitiesRole of Xenon cavities

• Mobile CH3 groups Mobile CH3 groups are populated near are populated near xenon cavitiesxenon cavities

Dynamical Transition in an Isolated ProteinIsolated Protein:MD Simulation of Myoglobin.

KRZYSZTOF KUCZERAMARTIN KARPLUS

100 150 200 250 3000.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

6 8 10 12 14 16 18 20 22

0.001

0.002

0.003

0.004

0.005

0 - 8Å 8 - 12Å 12 - 16Å 16 - 20Å 20 - 26Å

u2 si

de-c

hain

s [Å

2]

Temperature [K]

slo

pe [Å

2 K-1]

D [Å]

5 4 32 1

Radial Dependence of Dynamical TransitionJIANCONG XUALEX TOURNIER

Hydrated Myoglobin

54

3

2

1

System

Heatbaths

Prot Solv.

kTQ

pp

pQ

PdNkT

mp

kQ

p

Q

P

m

N

i i

i

kk

iii

i

ii

k

1

21

121

2

1

2

2

1

1

2,1

p

pFp

pr

t thermostaof Mass :

Momentum Thermostat:

variableThermostat:

Q

p

aim eTemperatur :T

particles ofNumber : N

constant sBoltzmann' :k

Nose-Hoover-Chain Multiple Heatbath Simulation Algorithm

System

1st Heatbath

2nd Heatbath

Prot Solv.

Canonical Distribution ofTemperatures

KEEP COLD

VARY T

T1

T2

DUAL HEAT-BATH SIMULATIONS

e.g.

ALEX TOURNIER

100 150 200 250 3000.0

0.5

1.0

1.5

2.0

(b)

(a) Protein 300K Control Protein fixed

D [

10

5 Å2 s-

1 ]

150 200 250 30010

1

102

103

104

105

106

107

108

109

Protein fixed Control Protein 300K

Dip

ole

co

rre

latio

n t

ime

[p

s]

Tem perature [K ]

Translation

Rotation

Water Diffusionon a Protein Surface

TranslationALEXTOURNIER

160 180 200 220 240 260 280 300101

102

103

104

105

Fig. 3

Control

Dip

ole

co

rre

latio

n tim

e (

ps)

Temperature (K)

Water Diffusion and the Glass Transition

ALEXTOURNIER

Protein

Water Translational Diffusion

Protein Fluctuations

160 180 200 220 240 260 280 300101

102

103

104

105

Fig. 3

Control

Dip

ole

co

rre

latio

n tim

e (

ps)

Temperature (K)

Rotation

Effect of Approximations in Experimental Neutron Scattering Data Analysis

u2 1 ns

Low-q, 20 eV resolution

‘High’-q, (0q2 23Å-2),20 eV resolution

‘Low’-q (0q2 1.44Å-2) perfect resolution

Harmonic

JENNIFERHAYWARD

22

3

1

0,Luq

L

incLinc ebqS

GERALD KNELLER

FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY

TRAJECTORY OF RIGID BODIES

6 5 4 36 2 1Atomic Dynamicsas a function of

Distance from Protein Centre

Concentric Shells

SERGE DELLERUE,ANDREI PETRESCU,MARIE-CLAIRE BELLISSENT-FUNEL

10-1 100 101 102 103

t (ps)

0.0

0.2

0.4

0.6

0.8

1.0A

I(q,t)

B

0.0

0.2

0.4

0.6

0.8

1.0

I(q,t)

10-1 100 101 102 103

t (ps)

Derivation of

Simplified Dynamical Description from

Molecular Dynamics Simulation Data:

Fit of a Stretched Exponential Model

to the

Intermediate Scattering Function.

Radially-Softening Dynamical Model

Rav= radius of sphere in which atom diffuses. = dynamical correlation time = stretch factor (range of timescales spanned)

)q(A)t,q()q(A1)t,q(Iinc

t

etq,

Atom in Sphere

Some “Predictions” for the Spallation Neutron Source….

Pressure Transition in Protein Dynamics

LARS MEINHOLD

WATER

THE FREQUENCIES AFFECTED

PROTEINCrystalline

Staphylococcal Nuclease

solvent

Pressure-induced transition in protein dynamics

Meinhold, Smith. PRE 72:061908 (2005)

DoS: i ig )(

mode 1 mode 5 mode 30 mode 100

PMF:m

pTkG Bm lnprotein

22 )()()( tt kk rrrMSD:

t

r()

r(+t)

Protein:Protein Interactions.Vibrations at 150K

VANDANAKURKAL-SIEBERT

GERALD KNELLER

FIT RIGID REFERENCE STRUCTURES TO EACH FRAME OF FULLY-FLEXIBLE TRAJECTORY

TRAJECTORY OF RIGID BODIES

Scattering of X-Rays by Protein Crystals

Real Crystal =

IdealCrystal

+ Perturbations

STÉPHANIE HÉRYDANIEL GENESTSVEN LAMMERS

PROTEINFUNCTION

CollectiveMotions

Dynamics

Structure

NMR (13%) X-ray (87%)X-ray

beam

detector Bragg el(r)

phaseproblem

disorderstatic - dynamic

DIFFUSEScattering

'1)',( '

kk

quuq Tkk

T

ekkf

Diff. Scatt.(B factors)

CORRELATION

Rigid-Body Decomposition

Rigid-Body Fit(R-factor re: Full Trajectory = 5.3%)

Molecular Dynamics of Lysozyme Unit Cell

Experimental Full Trajectory

STÉPHANIE HÉRYDANIEL GENEST

X-Ray Diffuse Scattering

LARS MEINHOLD

Staphylococcal Nuclease

Staph nuclease S Gruner et al

still exposure diffuse scattering after removalof Bragg peaks

Staph nuclease S Gruner et al

h

l

k

Interpreting the experimental data …

datareduction3D – 2D – 1D

MD simulations

• unit cell: 15993 atoms 4 proteins 2115 TIP3P + 48

Cl-

• CHARMM (param:22)• PME• Nose-Hoover (300K,1bar)• 4 X10ns, t =1fs

Unit cell of Staphylococcal nuclease

Space group P41 (4 proteins)

Water box with unit cell dimensions (1972 molecules)

36 chloride ions

Total number of atoms 15540

S.LAMMERS

Intensity in hk0 plane Experimental intensity

distribution

Theoretical intensitydistribution

Scattering vector in hk0 plane

Intensity in hk0 plane

25 frames250 frames 2500 frames 12000 frames

R-factor for hk0 plane

LARS MEINHOLD

X-Ray Diffuse Scattering

1D

decomposition

unit cell scattering

protein scattering ''

'

eee

e

)(

)('

'

kkkk

kk

iii

ik

kkk ffI

uququuq

rrq

diff

Meinhold, Smith. PRL 95:218103 (2005)

2D

'' 1e)',(kk

Tkk

T

kkfIquuq

diff

variance-covariance matrix<ukuk’

T>

Which parts of the protein and which types ofmotion cause the intense scattering features?

pairs (k,k’) PCA

decomposition

decomposition

Protein Scattering

Solvent Scattering

LARS MEINHOLD

SolventRing ?

decomposition

Protein Scattering?

Solvent Scattering?

LARS MEINHOLD

PROTEIN

SOLVENT

Helix Repeat

Interstrand Distance

Water O…O

2D

Meinhold, Smith. PRL 95:218103 (2005)

'' 1e)',(kk

Tkk

T

kkfIquuq

diff

Specific Motions in Diffuse Scattering Pattern

Feature F2

LARS MEINHOLD

20vv

v

N. Calimet, CMB

Characterisation of PCA modes:

m

pTkG

M

Bm

mT

m

ln

vu2/1

3D

q

q

qq1q Exp

MDExp

I

IINR

without

hydrogensincluding

Agreement factor: EXP - MDMD scattering not converged

μs1log * ttR t

Meinhold, Smith. BiophysJ 88:2554 (2005)

TkE

T Bt exp

Convergence properties of collective variables

protein topology

Meinhold, Smith. BiophysJ 88:2554 (2005)

2'

2

'

''kk

kTk

uu

uu

kkTkk Cuu

an-isotropic isotropiclinear correlation

PROTEINFUNCTION

CollectiveMotions

??

temperaturepressure

Tournier, Smith. PRL 91:208106 (2003)

MD Simulation

s a m p l i n gp r o b l e m

brute force

replica exchange

conformational flooding

(T2,p2)(T1,p1)

Bragg & DiffuseX-ray Scattering

r e f i n e m e n t

PROTEINFUNCTION

DynamicsStructure

ComputerSimulation

NeutronScattering

4th generationX-ray sources

CollectiveMotions

- new concepts -

SystemsBiology- networks -

ab-initioFolding