Insight into peptide folding

role of solvent and hydrophobicity dynamics of conformational transitions

Hydration thermodynamics of purely hydrophobic solutes

Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: 640-647

• Small molecules• Bulk-like water (~4 hydrogen

bonds)

• “WET” hydration

• Clusters

• Fewer hydrogen bonds

• DEWETTING - “DRY” regime

Hydration thermodynamics of purely hydrophobic solutes

Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: 640-647

R r

Hydration thermodynamics of purely hydrophobic solutes

Chandler, D. et al. (2005). “Interfaces and the driving force of hydrophobic assembly", Nature 437: 640-647

~4/3R3

~4R2

4R2

Isabella Daidone

Total free energy of solvation:

SOL NPpolG G GD = D +D

Non-polar term

Polar term

Chothia, C. (1974). “Hydrophobic bonding and accessible surface area in proteins”. Nature 248:338-339

Solvent accessible surface areaEffective surface tension

gD = åNP i ii

G S

Implicit solvent model: GB/SA

in

ex

– Linear isotropic dielectric– Solute: Solvent:

( )e r

in( )e e=r ex( )e e=r

[ ( ) ( )] 4 ( )e f prÑ Ñ = -r r r Poisson-Boltzmann equation

in

ex

– Linear isotropic dielectric– Solute: Solvent:

( )e r

in( )e e=r ex( )e e=r

Implicit solvent model: GB/SA

Generalized Born formula for an arbitrary charge distribution ,

11

2i j

poli jex ij

qqG

fe

æ ö÷ç ÷D = - -ç ÷ç ÷çè øå

Still, W. C., A. Tempczyk, et al. (1990). "Semianalytical Treatment of Solvation for Molecular Mechanics and Dynamics." JACS 112(16): 6127-6129

Met109

Lys 110

His111

Met 112

Ala 113

Gly 114

Ala 115

Ala 116

Ala 117

Ala 118

Gly 119

Ala 120

Val 121

Val 122

Inouye, H and Kirschner, DA. (1998). “Polypeptide chain folding in the hydrophobic core of hamster scrapie prion: analysis by X-ray diffraction”. J. Struct. Biol. 122:247-255

Prion Protein H1 peptide

H1 peptide molecular dynamics simulations

Total simulation time of 1.1 s

240+850300water (SPC)-helix

Length (ns)Temp (K)SolventStarting structure

•PME•N,V,T

•periodic truncated octahedron•1 nm explicit solvent on all sides

*

*Gromos96 force field, GROMACS software package

0 1

MDpme

Time (s) 0.24

V121

G114 A115

A116A113

H111 A118

G119M109

M112A117

V122

A120

K110

A115

A116

A117A118

A120

V121

A113

M112

M109

V122Daidone I. et al. (2005). “Theoretical characterization of -helix and -hairpin folding kinetics”. J. Am. Chem. Soc. 127: 14825-14832

0.50.25 0.75

0

0

1

1

Time (s)

Implicit GB/SA

Explicit

0.24

Both simulations are performed with Gromos96 force field

MD simulations of the H1 peptide

Thermodynamic properties

Acoil k = -RT lnpk pcoil

pk , pcoil probability of the system

of being in state k,coil

Helmholtz free energy

coil

coil helix

~1 kJ/mol

~ 10 kJ/mol

~ 8 kJ/mol

A

ExplicitImplici

t

Explicit

Implicit

coil helixcoil

A

Acoil k = -RT lnpk

pcoil

pk , pcoil probability of the system

of being in state k,coil

Helmholtz free energy

statistical error < 0.5 kJ/mol

1 kJ/mol

10 kJ/mol

8 kJ/mol

A

ExplicitImplici

t

Explicit

Implicitcoil helix

coil

A

V121

G114 A115

A116A113

H111 A118

G119M109

M112A117

V122

A120

K110

Characterization of the -hairpin state

Acoil k = -RT lnpk pcoil

2 HB

1 HBcoil

coil...

Characterization of the -hairpin state

Characterization of the -hairpin state

V121

M109

Solvent density at the hydrophobic surface

R=0.9-1.0 nm

“DRY”

Solvent density at the hydrophobic surface

Hydrophobic Solvent Exposed Surface Area (nm2)

Firs

t Hyd

rati

on S

hell

Den

sity

(nm

-2)

around hydrophilic

around hydrophobic

hydrophobic analog

“DRY”“WET”

Influence of hydration density on peptide thermodynamics

Met 109 (H) –Val 121 (O) (nm) 0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Influence of hydration density on peptide thermodynamics

Dynamic characterization of the Dynamic characterization of the

conformational transitionsconformational transitions

““Reaction coordinates”: principal componentsReaction coordinates”: principal components

ij i i j j C x x x x Positional fluctuationsPositional fluctuationscovariance matrixcovariance matrix

Eigenvectors of fluctuationsEigenvectors of fluctuationsand corresponding eigenvaluesand corresponding eigenvaluesCTTΛ T

q first essential eigenvector

A. Amadei et al., PROTEINS, 17:412-425, 1993. “Essential dynamics of proteins”

Mean square displacement along qMean square displacement along q

time (s)

q (

nm

)

-3-3

-2-2

-1-1

00

11

projection of the trajectory on qprojection of the trajectory on q

00 11

D and D0 are the long and short-time diffusion constants, respectively1 , 2, 3 are the relaxation times of the switching modes

mean square displacement <q2(t)> (nm2/ps)

Free diffusion along qFree diffusion along q

slope=2D0

slope=2D00

00 10001000

1 2 32 ( / ) ( / ) ( / )0 1 1 0 2 2 0 3 32 2( ) (1 ) 2( ) (1 ) 2( ) (1 )t t tq D t D A e D A e D A et t tt t t- - -

¥D = + - - + - - + - -

Isabella Daidone

implicit

explicit

Conformational dynamics of the H1 peptide

Dnm2ps-1

D0

nm2ps-1

5.5 10-5

(0.5 10-5)

0.09(0.001)

Implicit

2.6 10-5

(0.5 10-5)

0.02(0.001)

Explicit

3

ps

2

ps

1

ps

43 (4)

-

<1

102 (5)

7 (1)

<1

8

water-peptide

Hydrogen bond life times

Conformational dynamics of the H1 peptide

Dnm2ps-1

D0

nm2ps-1

5.5 10-5

(0.5 10-5)

0.09

(0.001)

Implicit

2.6 10-5

(0.5 10-5)

Explicit

3

ps

2

ps

1

ps

43 (4)

-

<1

102 (5)

7 (1)

<1

8

0.02

(0.001)

ImplicitExplicit

49 (10)

-

132 (21)

8 (3)

pp

ps

wp

ps

intra-peptide

Acknowledgments

Jeremy

Alfredo Di Nola(University “La Sapienza” of Rome)

Andrea Amadei (University of Rome “Tor Vergata” )