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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” )