important coordinates effective potential effective potentials for protein folding and binding with...
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Important coordinates
Eff
ecti
ve p
oten
tial
Effective Potentials for Protein Folding and BindingWith Thermodynamic Constraints
• The AGBNP effective solvation potential
•Optimization for structure prediction
•Free energy surfaces for -hairpin and -helical peptide folding
•Dynamics and kinetics
Roadmap to GB/NP Effective Potential Models for Solvation
•Electrostatic Component—Dielectric Continuum approximation. Generalized Born models—Parameterization (atomic radii) against FEP explicit solvent calculations with OPLS-AA force field
•Non-Polar Component—Novel non-polar estimator from FEP explicit solvent studies—Parameterization against experimental gas solubilities of small molecules—Parameterization for macromolecules: binding, folding
R.M. Levy, L. Y. Zhang, E. Gallicchio, and A.K. Felts, JACS, 125, 9523 (2003)
E. Gallicchio, L. Y. Zhang, and R.M. Levy, JCC, 23, 517, (2002)
E. Gallicchio, M. Kubo, and R.M. Levy, JPC, 104, 6271 (2000)
The AGBNP Implicit Solvent Model
AGBNP: Analytical Generalized Born + Non-Polar
Requirements:• Applicable to small ligands and large biomolecules,
many different functional groups• Applicable to study small and large conformational
changes: sensitive to molecular geometry.• Analytical with analytical gradients: MD sampling
E. Gallicchio, R. Levy, J. Comp. Chem., 25, 479-499 (2004)
AGBNP
Gsolv Gelec Gnp
Gcav GvdW
• Novel pairwise descreening Generalized Born model.• Separate models for cavity free energy and solute-solvent van der Waals interaction energy.• Fully analytical.• Sensitive to conformational change.• Equally applicable to small molecules and macromolecules.
Generalized BornSurface area model Born radius-based estimator
Generalized Born Model
Charging Free Energy in linear dielectric medium:
Gelec 12
1 in
1w
qiq j
fij (rij )ij
fij rij2 BiB j exp
rij2
4Bi Bj
1/ 2
Bi is the Born radius of atom i defined by:
Gsinglei 1
21 in
1w
qi2
Bi 1
81 in
1w
qi2
r ri4
V d3r
AGBNP: Pairwise Descreening Scheme
i
Born radii: rescaled pairwise descreening approximation:
1
Bi
1
Ri 1
4 s jQijj
Rescale according to self-volume of j:
s j Vj (self)
Vj
Vj (self) Vj 1
2 Vjkk 1
3 Vjklkl
Self-volume of j (Poincarè formula, ca. 1880):
E. Gallicchio, R. Levy, J. Comp. Chem. (2004)Hawkins, Cramer, and Truhlar, JPC 1996Schaefer and Karplus, JPC 1996Qiu, Shenkin, Hollinger, and Still, JPC 1997
j
Accuracy of Born Radii:Ligand Binding (free - bound)
Bi 1
(AGBNP)[Å-1]
Bi 1
(Numerical)[Å-1]
Non-Polar Hydration Free Energy
Gnp i Ai iW(Bi ) i
Non-polar hydration free energy estimator:
Gnp Gcav GvdW
Wi w-4i i
6
| r ri |6slv. 16wi i
6
3Ci3
Ci 3
41
| r - ri |6slv.
1/ 3
Bi
: Surface area of atom i
: Estimator based on Born radius
: Surface tension and van der Waals adjustable parameters
Ai
W(Bi )
i ,i
R.M. Levy, L. Y. Zhang, E. Gallicchio, and A.K. Felts, JACS, 125, 9523 (2003)
E. Gallicchio, M. Kubo, and R.M. Levy, JPC, 104, 6271 (2000)
Enthalpy-Entropy and Cavity Decomposition of Alkane Hydration Free Energies: Numerical Results and
Implications for Theories of Hydrophobic SolvationEmilio Gallicchio, Masahito Kubo, Ronald Levy, J. Phys. Chem., 104, 6271 (2000)
Solute-Solvent van der Waals Energy of Proteins: Comparison of Surface Area and Continuum Solvent Models
SASA (A2) SASA (A2)
Uvd
W (
kca
l/m
ol)
Figure: Continuum solvent solute-solvent van der Waals interaction energies of various peptides and proteins conformations plotted against their accessible surface area. (A) Data with accessible surface area between 3000 and 12000 A2. Filled circles denote 98 native peptide and protein conformations, open triangles denote 12 extended protein conformations, and filled triangles denote 273 decoy conformations of 4 native proteins. (B) Data with accessible surface area between 6000 and 10000 A2. Filled triangles denote decoy conformations of of protein lz1 (the native conformation of lz1 is circled).The lines are the linear least square fit to all native and extended protein conformations examined, respectively.
(A) (B)
Optimization of the AGBNP Effective Potential for Structure Prediction with thermodynamic constraints
Geff = Uint + GAGB + Gnp
Gnp = i k Ai + k(16ii6 / 3Bi
3)
where k indicates atomtype of atom i
Z-score: Zn = ave(Gi Gn)/d
Maximize: Zn 2
Summary of Fitting Results (in kcal/mol)Molecular class Number of Fit Prediction molecules
Compounds containing only C and Halkanes 19 0.21 0.24alkenes and dienes 11 0.16 0.22alkynes 6 0.20 0.33arenes 21 0.38 0.44Subtotal 57 0.26 0.32
Compounds containing only C, H and Oalcohols 27 0.25 0.28ethers 17 0.62 0.66ketones and aldehydes 22 0.23 0.26carboxylic acids 3 0.23 0.44esters 15 0.23 0.25Subtotal 103 0.29 0.33
Compounds containing only C, H, O and Namines 23 0.27 0.33amides 5 0.19 0.40nitriles 5 0.42 1.15nitro compounds 6 0.78 2.57nitrogen heterocyclic 13 0.33 1.22Subtotal 52 0.35 0.89
Compounds containing C, H, O, N and Sthiols 3 0.72 1.24sulfides 3 0.43 0.74Subtotal 6 0.57 0.99
Total 199 0.32 0.50
Protein Loops Modeling
7RSA (13-24)
Prediction of native loop conformation using the OPLS/AGBNP effective energy function
AGBNP: Applications
• Protein Folding- Peptides.- Protein Decoys.
• Ligand binding- Binding Mode Prediction.- Binding Free Energy Prediction.
• Structure Prediction- Protein Loop Modeling.
The -Hairpin of B1 Domain of Protein G
The hydrophobic sidechains are in green.
Pande, PNAS, 1999Nussinov, JMB, 2000Garcia et al., Proteins, 2001Zhou & Berne, PNAS, 2002
Dinner, Lazaridis, Karplus, PNAS, 1999Pande et al., JMB, 2001Zhou & Berne, PNAS, 2002
Replica Exchange Sampling for -hairpin FoldingReplica Exchange Sampling for -hairpin Folding
• Replica exchange sampling* is a method to effectively sample rough energy landscapes which have high dimensionality - the hairpin has 768 degrees of freedom •~20 MD simulations of the -hairpin run in parallel over the temperature range 270 K -690 K.
• Every 50 MD steps MC replica exchange moves are attempted
• Total sampling time: 20 processors x 4 x 106 step/processor = 80 x 106 steps
Time series of the temperature for one replica Time series of the replicas for one Temp., T = 442 K
0
5
10
15
20
0 1 105
2 105
3 105
4 105
5 105
Th
e n
um
ber
of
pro
cess
or
Step number (fsec)
250
300
350
400
450
500
550
600
650
0 1 105
2 105
3 105
4 105
5 105
Tem
pe
ratu
re
Step number (fsec)
* Y. Sugita, and Y. Okamoto, Chem. Phys. Let., 314, 141 (1999)
The -Hairpin of B1 Domain of Protein G
The potential of mean force of the capped peptide.
Simple nonpolar model. AGB-NP with Scharged=0.5
A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 000 (2004)
The -Hairpin of B1 Domain of Protein G
The potential of mean force of the capped peptide.
Simple nonpolar model. AGB-NP with Scharged=0.5
A Felts, Y. Harano, E. Gallicchio, and R. Levy, Proteins, 56, 000 (2004)
Estimated -Hairpin and -Helical Populations(native peptide from protein G, T=298K)
No WHAM T-WHAM
Gmax=5 kcal/mol Gmax=10 kcal/mol
-hairpin > 90%-helix < 10%G ~ 2 kcal/mol
T-WHAM: PMF contains information from high temperature walkers
Solve for (E) and insert into
expression for P(E;Ti).
T-WHAM
• A way to combine data from simulations at various temperatures to obtain properties at one given temperature.
Energy distribution:
P(E;Ti ) Z(T0 )
Z(Ti )e (i 0 )E P(E;T0 )
P(E;T0 )(E) e 0E
Z(T0 )
- Given P(Ej;T0) can predict histogram of energies n(Ej;Ti) at any temperature. - Select P(Ej;T0) that best reproduces observed histograms (maximum likelihood solution assuming multinomial-distributed counts).
P(E j ;T0 ) n(E j ;Ti )i
Ni e fi e (i 0 )E j
ie fi
Z(Ti )
Z(T0 ) P(E j ;T0 )e
(i 0 )E jj
WHAM equations: {Same derivation for joint probability P(x,E;T).
Alternative Coordinates for the -HairpinProjections onto the first four principal components
Alternative Coordinates for the -HairpinTemperature dependence
T = 298 K T = 400 K
T = 328 K T = 488 K
Free Energy Surface of the Protein G -Hairpin With Respect to the (1,4) Principle Components
T-WHAM
In Silico Mutation Study of the protein G -Hairpin Sequence
Sequence coilnative GEWTYDDATKTFTVTE 88% 8% 4%
W43S mutant GESTYDDATKTFTVTE 42% 40% 18%Y45S mutant GEWTSDDATKTFTVTE 23% 71% 6%W43S, Y45S GESTSDDATKTFTVTE 0.1% 83% 17%
44% homol* GEQVAREALKHFAETE 0% 95% 5%
random #1 VTGADFTKYTTEDWTE 35% 4% 61% random #2 VYEWDGTTKTEFADTT 31% 13% 56%
*C-terminal -helix of 1b6g: 44% BLAST homology with sequence from protein G
Free Energy Surfaces Generated with REM and OPLS-AA/AGBNP
-Hairpin of C-terminusof B1 domain of protein G
-Helix of C-peptideof ribonuclease A
GEWTYDDATKTFTVTE KETAAAKFERQHM
Important coordinates
Eff
ecti
ve p
oten
tial
Effective Potentials for Protein Folding and BindingWith Thermodynamic Constraints
• The AGBNP effective solvation potential
Emilio Gallicchio, Tony Felts
• Optimization for structure prediction
Emilio Gallicchio, Tony Felts
• Free energy surfaces for -hairpin and -helical peptide folding
Yuichi Harano, Tony Felts, Emilio Gallicchio, M. Andrec
• Dynamics and kinetics
Dimitriy Chekmarev, Tateki Ishida, Michael Andrec
Important coordinatesE
ffec
tive
pot
enti
al
Effective Potentials for Protein Folding and BindingWith Thermodynamic Constraints
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