Important coordinates Effective potential Effective Potentials for Protein Folding and Binding With 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, (2004)

AGBNP 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 Born Surface area modelBorn radius-based estimator

Generalized Born Model Charging Free Energy in linear dielectric medium: B i is the Born radius of atom i defined by:

AGBNP: Pairwise Descreening Scheme i Born radii: rescaled pairwise descreening approximation: Rescale according to self-volume of j: Self-volume of j (Poincarè formula, ca. 1880): E. Gallicchio, R. Levy, J. Comp. Chem. (2004) Hawkins, Cramer, and Truhlar, JPC 1996 Schaefer and Karplus, JPC 1996 Qiu, Shenkin, Hollinger, and Still, JPC 1997 j

Accuracy of Born Radii: Ligand Binding (free - bound) (AGBNP) [Å -1 ] (Numerical) [Å -1 ]

Non-Polar Hydration Free Energy Non-polar hydration free energy estimator: : Surface area of atom i : Estimator based on Born radius : Surface tension and van der Waals adjustable parameters 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 Solvation Emilio 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 (A 2 ) U vdW (kcal/mol) 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 A 2. 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 A 2. 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  G eff =  U int +  G AGB +  G np  G np =  i  k A i +  k (  16  i  i 6 / 3B i 3 ) where k indicates atomtype of atom i Z-score: Z n = ave(  G i   G n )/  d Maximize: Z n  2

Summary of Fitting Results (in kcal/mol)

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, 1999 Nussinov, JMB, 2000 Garcia et al., Proteins, 2001 Zhou & Berne, PNAS, 2002 Dinner, Lazaridis, Karplus, PNAS, 1999 Pande et al., JMB, 2001 Zhou & Berne, PNAS, 2002

Replica 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 10 6 step/processor = 80 x 10 6 steps Time series of the temperature for one replicaTime series of the replicas for one Temp., T = 442 K * 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 S charged =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 S charged =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 WHAMT-WHAM  G max =5 kcal/mol  G max =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;T i ). T-WHAM A way to combine data from simulations at various temperatures to obtain properties at one given temperature. Energy distribution: - Given P(E j ;T 0 ) can predict histogram of energies n(E j ;T i ) at any temperature. - Select P(E j ;T 0 ) that best reproduces observed histograms (maximum likelihood solution assuming multinomial-distributed counts). WHAM equations: { Same derivation for joint probability P(x,E;T).

Alternative Coordinates for the  -Hairpin Projections onto the first four principal components

Alternative Coordinates for the  -Hairpin Temperature dependence T = 298 KT = 400 K T = 328 KT = 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  coil native 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-terminus of B1 domain of protein G  -Helix of C-peptide of ribonuclease A GEWTYDDATKTFTVTEKETAAAKFERQHM

Important coordinates Effective potential Effective Potentials for Protein Folding and Binding With 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 coordinates Effective potential Effective Potentials for Protein Folding and Binding With Thermodynamic Constraints