Variational Optimization of an All-Atom Implicit Solvent Force Field to Match Explicit Solvent Simulation Data.

The development of accurate implicit solvation models with low computational cost is essential for addressing many large-scale biophysical problems. Here, we present an efficient solvation term based on a Gaussian solvent-exclusion model (EEF1) for simulations of proteins in aqueous environment, with the primary aim of having a good overlap with explicit solvent simulations, particularly for unfolded and disordered states - as would be needed for multiscale applications. In order to achieve this, we have used a recently proposed coarse-graining procedure based on minimization of an entropy-related objective function to train the model to reproduce the equilibrium distribution obtained from explicit water simulations. Via this methodology, we have optimized both a charge screening parameter and a backbone torsion term against explicit solvent simulations of an α-helical and a β-stranded peptide. The performance of the resulting effective energy function, termed EEF1-SB, is tested with respect to the properties of folded proteins, the folding of small peptides or fast-folding proteins, and NMR data for intrinsically disordered proteins. The results show that EEF1-SB provides a reasonable description of a wide range of systems, but its key advantage over other methods tested is that it captures very well the structure and dimension of disordered or weakly structured peptides. EEF1-SB is thus a computationally inexpensive (~ 10 times faster than Generalized-Born methods) and transferable approximation for treating solvent effects.

[1]  H. Scheraga,et al.  Accessible surface areas as a measure of the thermodynamic parameters of hydration of peptides. , 1987, Proceedings of the National Academy of Sciences of the United States of America.

[2]  V. Muñoz,et al.  Folding dynamics and mechanism of β-hairpin formation , 1997, Nature.

[3]  G. Voth,et al.  Solvent Free Ionic Solution Models from Multiscale Coarse-Graining. , 2013, Journal of chemical theory and computation.

[4]  Carsten Kutzner,et al.  GROMACS 4:  Algorithms for Highly Efficient, Load-Balanced, and Scalable Molecular Simulation. , 2008, Journal of chemical theory and computation.

[5]  J. Warwicker,et al.  Calculation of the electric potential in the active site cleft due to alpha-helix dipoles. , 1982, Journal of molecular biology.

[6]  Michael Feig,et al.  Modeling solvent environments : applications to simulations of biomolecules , 2010 .

[7]  D. Tobias,et al.  The dynamics of protein hydration water: a quantitative comparison of molecular dynamics simulations and neutron-scattering experiments. , 2000, Biophysical journal.

[8]  Robert W Woody,et al.  Solvent dependence of PII conformation in model alanine peptides. , 2004, Journal of the American Chemical Society.

[9]  R. Bryant,et al.  The dynamics of water-protein interactions. , 1996, Annual review of biophysics and biomolecular structure.

[10]  P. Privalov,et al.  Contribution of hydration to protein folding thermodynamics. II. The entropy and Gibbs energy of hydration. , 1993, Journal of molecular biology.

[11]  Oliver F. Lange,et al.  Recognition Dynamics Up to Microseconds Revealed from an RDC-Derived Ubiquitin Ensemble in Solution , 2008, Science.

[12]  R. Zwanzig High‐Temperature Equation of State by a Perturbation Method. I. Nonpolar Gases , 1954 .

[13]  C. Sander,et al.  An effective solvation term based on atomic occupancies for use in protein simulations , 1993 .

[14]  K. Sharp,et al.  Protein-solvent interactions. , 2006, Chemical reviews.

[15]  P. J. Steinbach,et al.  Exploring peptide energy landscapes: A test of force fields and implicit solvent models , 2004, Proteins.

[16]  Samuel L. DeLuca,et al.  Practically Useful: What the Rosetta Protein Modeling Suite Can Do for You , 2010, Biochemistry.

[17]  T. Lazaridis,et al.  On the unfolding of α‐lytic protease and the role of the pro region , 2000, Proteins.

[18]  F. Ding,et al.  Ab initio folding of proteins with all-atom discrete molecular dynamics. , 2008, Structure.

[19]  M Scott Shell,et al.  A new multiscale algorithm and its application to coarse-grained peptide models for self-assembly. , 2012, The journal of physical chemistry. B.

[20]  M Scott Shell,et al.  The relative entropy is fundamental to multiscale and inverse thermodynamic problems. , 2008, The Journal of chemical physics.

[21]  M. Karplus,et al.  Effective energy function for proteins in solution , 1999, Proteins.

[22]  D. Chandler Interfaces and the driving force of hydrophobic assembly , 2005, Nature.

[23]  Urs Haberthür,et al.  FACTS: Fast analytical continuum treatment of solvation , 2008, J. Comput. Chem..

[24]  Gregory A Voth,et al.  Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: a new method for force-matching. , 2004, The Journal of chemical physics.

[25]  Themis Lazaridis,et al.  Orientational correlations and entropy in liquid water , 1996 .

[26]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[27]  M Scott Shell,et al.  Relative entropy as a universal metric for multiscale errors. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  M. Karplus,et al.  Simulation of activation free energies in molecular systems , 1996 .

[29]  Franca Fraternali,et al.  Implicit Solvation Parameters Derived from Explicit Water Forces in Large-Scale Molecular Dynamics Simulations , 2012, Journal of chemical theory and computation.

[30]  Jianpeng Ma,et al.  CHARMM: The biomolecular simulation program , 2009, J. Comput. Chem..

[31]  J. P. Garrahan,et al.  Comparison of implicit solvent models and force fields in molecular dynamics simulations of the PB1 domain , 2011 .

[32]  Francesca Fanelli,et al.  Wordom: A User-Friendly Program for the Analysis of Molecular Structures, Trajectories, and Free Energy Surfaces , 2010, J. Comput. Chem..

[33]  M. Vendruscolo,et al.  Determination of protein structures consistent with NMR order parameters. , 2004, Journal of the American Chemical Society.

[34]  Berk Hess,et al.  LINCS: A linear constraint solver for molecular simulations , 1997 .

[35]  Wilfred F van Gunsteren,et al.  A refined, efficient mean solvation force model that includes the interior volume contribution. , 2011, The journal of physical chemistry. B.

[36]  Gerhard Hummer,et al.  Molecular Theories and Simulation of Ions and Polar Molecules in Water , 1998 .

[37]  M. Karplus,et al.  A Comprehensive Analytical Treatment of Continuum Electrostatics , 1996 .

[38]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[39]  A. Roitberg,et al.  Smaller and faster: the 20-residue Trp-cage protein folds in 4 micros. , 2002, Journal of the American Chemical Society.

[40]  L. Serrano,et al.  A short linear peptide that folds into a native stable β-hairpin in aqueous solution , 1994, Nature Structural Biology.

[41]  M. Gruebele,et al.  Computational design and experimental testing of the fastest-folding β-sheet protein. , 2011, Journal of molecular biology.

[42]  G. Hummer,et al.  Optimized molecular dynamics force fields applied to the helix-coil transition of polypeptides. , 2009, The journal of physical chemistry. B.

[43]  Ian W. Davis,et al.  RosettaLigand docking with full ligand and receptor flexibility. , 2009, Journal of molecular biology.

[44]  G. Bouvignies,et al.  Exploring multiple timescale motions in protein GB3 using accelerated molecular dynamics and NMR spectroscopy. , 2007, Journal of the American Chemical Society.

[45]  H. Schwalbe,et al.  Structure and dynamics of the homologous series of alanine peptides: a joint molecular dynamics/NMR study. , 2007, Journal of the American Chemical Society.

[46]  A. D. McLachlan,et al.  Solvation energy in protein folding and binding , 1986, Nature.

[47]  E. Stellwagen,et al.  Distribution of Helicity within the Model Peptide Acetyl(AAQAA)3amide , 1994 .

[48]  A. Irbäck,et al.  Folding thermodynamics of peptides. , 2004, Biophysical journal.

[49]  Andreas Vitalis,et al.  ABSINTH: A new continuum solvation model for simulations of polypeptides in aqueous solutions , 2009, J. Comput. Chem..

[50]  Collin M. Stultz,et al.  Conformational sampling with implicit solvent models: application to the PHF6 peptide in tau protein. , 2007, Biophysical journal.

[51]  W. L. Jorgensen Quantum and statistical mechanical studies of liquids. 10. Transferable intermolecular potential functions for water, alcohols, and ethers. Application to liquid water , 2002 .

[52]  Lee-Ping Wang,et al.  Systematic Parametrization of Polarizable Force Fields from Quantum Chemistry Data. , 2013, Journal of chemical theory and computation.

[53]  M Scott Shell,et al.  Coarse-graining errors and numerical optimization using a relative entropy framework. , 2011, The Journal of chemical physics.

[54]  Michele Vendruscolo,et al.  Protein structure determination from NMR chemical shifts , 2007, Proceedings of the National Academy of Sciences.

[55]  R. Best,et al.  Balance between alpha and beta structures in ab initio protein folding. , 2010, The journal of physical chemistry. B.

[56]  J. Hofrichter,et al.  Sub-microsecond protein folding. , 2006, Journal of molecular biology.

[57]  R. Best,et al.  Free‐energy landscape of the GB1 hairpin in all‐atom explicit solvent simulations with different force fields: Similarities and differences , 2011, Proteins.

[58]  Alexander D. MacKerell,et al.  Optimization of the additive CHARMM all-atom protein force field targeting improved sampling of the backbone φ, ψ and side-chain χ(1) and χ(2) dihedral angles. , 2012, Journal of chemical theory and computation.

[59]  Ad Bax,et al.  Validation of Protein Structure from Anisotropic Carbonyl Chemical Shifts in a Dilute Liquid Crystalline Phase , 1998 .

[60]  P. Privalov,et al.  Contribution of hydration to protein folding thermodynamics. I. The enthalpy of hydration. , 1993, Journal of molecular biology.

[61]  B. Honig,et al.  A rapid finite difference algorithm, utilizing successive over‐relaxation to solve the Poisson–Boltzmann equation , 1991 .

[62]  R. Constanciel Theoretical basis of the empirical reaction field approximations through continuum model , 1986 .

[63]  G. Hummer,et al.  HYDROPHOBIC FORCE FIELD AS A MOLECULAR ALTERNATIVE TO SURFACE-AREA MODELS , 1999 .

[64]  M Karplus,et al.  "New view" of protein folding reconciled with the old through multiple unfolding simulations. , 1997, Science.

[65]  S. Hassan,et al.  A General Treatment of Solvent Effects Based on Screened Coulomb Potentials , 2000 .

[66]  Lennart Nilsson,et al.  Implicit Solvent Models and Stabilizing Effects of Mutations and Ligands on the Unfolding of the Amyloid β-Peptide Central Helix. , 2013, Journal of chemical theory and computation.

[67]  T. Lazaridis Inhomogeneous Fluid Approach to Solvation Thermodynamics. 1. Theory , 1998 .

[68]  Ray Luo,et al.  Accelerated Poisson–Boltzmann calculations for static and dynamic systems , 2002, J. Comput. Chem..

[69]  R. Best,et al.  Tackling force-field bias in protein folding simulations: folding of Villin HP35 and Pin WW domains in explicit water. , 2010, Biophysical journal.

[70]  T. Creamer,et al.  Polyproline II helical structure in protein unfolded states: Lysine peptides revisited , 2002, Protein science : a publication of the Protein Society.

[71]  W. V. van Gunsteren,et al.  An efficient mean solvation force model for use in molecular dynamics simulations of proteins in aqueous solution. , 1996, Journal of molecular biology.

[72]  Kresten Lindorff-Larsen,et al.  Experimental parameterization of an energy function for the simulation of unfolded proteins. , 2008, Biophysical journal.

[73]  Y. Sugita,et al.  Replica-exchange molecular dynamics method for protein folding , 1999 .

[74]  T. Darden,et al.  The effect of long‐range electrostatic interactions in simulations of macromolecular crystals: A comparison of the Ewald and truncated list methods , 1993 .

[75]  Luyuan Zhang,et al.  Mapping hydration dynamics around a protein surface , 2007, Proceedings of the National Academy of Sciences.

[76]  K. Dill Dominant forces in protein folding. , 1990, Biochemistry.

[77]  A. Irbäck,et al.  An effective all-atom potential for proteins , 2009, PMC biophysics.

[78]  S. Hassan,et al.  A critical analysis of continuum electrostatics: The screened Coulomb potential–implicit solvent model and the study of the alanine dipeptide and discrimination of misfolded structures of proteins , 2002, Proteins.

[79]  Alexander D. MacKerell,et al.  Improved treatment of the protein backbone in empirical force fields. , 2004, Journal of the American Chemical Society.

[80]  Charles L. Brooks,et al.  Generalized born model with a simple smoothing function , 2003, J. Comput. Chem..

[81]  P. Privalov,et al.  Contribution of hydration and non-covalent interactions to the heat capacity effect on protein unfolding. , 1992, Journal of molecular biology.

[82]  J. Apostolakis,et al.  Evaluation of a fast implicit solvent model for molecular dynamics simulations , 2002, Proteins.

[83]  R. Dror,et al.  Systematic Validation of Protein Force Fields against Experimental Data , 2012, PloS one.

[84]  Robert B Best,et al.  Matching of additive and polarizable force fields for multiscale condensed phase simulations. , 2013, Journal of chemical theory and computation.

[85]  K. Lindorff-Larsen,et al.  How robust are protein folding simulations with respect to force field parameterization? , 2011, Biophysical journal.

[86]  Alexander D. MacKerell,et al.  Inclusion of many-body effects in the additive CHARMM protein CMAP potential results in enhanced cooperativity of α-helix and β-hairpin formation. , 2012, Biophysical journal.

[87]  C Sander,et al.  Excluded volume approximation to protein-solvent interaction. The solvent contact model. , 1990, Biophysical journal.

[88]  Ad Bax,et al.  Evaluation of backbone proton positions and dynamics in a small protein by liquid crystal NMR spectroscopy. , 2003, Journal of the American Chemical Society.

[89]  Themis Lazaridis,et al.  Inhomogeneous Fluid Approach to Solvation Thermodynamics. 2. Applications to Simple Fluids , 1998 .