Implicit Solvent Electrostatics in Biomolecular Simulation

We give an overview of how implicit solvent models are currently used in protein simulations. The emphasis is on numerical algorithms and approximations: since even folded proteins sample many distinct configurations, it is of considerable importance to be both accurate and efficient in estimating the energetic consequences of this dynamical behavior. Particular attention is paid to calculations of pH-dependent behavior, as a paradigm for the analysis of electrostatic interactions in complex systems.

[1]  J. Tomasi,et al.  Thirty years of continuum solvation chemistry: a review, and prospects for the near future , 2004 .

[2]  D. D. Yue,et al.  Theory of Electric Polarization , 1974 .

[3]  Ronald M. Levy,et al.  AGBNP: An analytic implicit solvent model suitable for molecular dynamics simulations and high‐resolution modeling , 2004, J. Comput. Chem..

[4]  S A Allison,et al.  Modeling the electrophoresis of rigid polyions: application to lysozyme. , 1995, Biophysical journal.

[5]  Charles Tanford,et al.  Theory of Protein Titration Curves. II. Calculations for Simple Models at Low Ionic Strength , 1957 .

[6]  J. Kirkwood,et al.  Theory of Solutions of Molecules Containing Widely Separated Charges with Special Application to Zwitterions , 1934 .

[7]  D. Braess.  Finite Elements: Theory, Fast Solvers, and Applications in Solid Mechanics , 1995 .

[8]  Paul Tavan,et al.  Continuum description of ionic and dielectric shielding for molecular-dynamics simulations of proteins in solution. , 2004, The Journal of chemical physics.

[9]  R. Alberty.  Thermodynamics of Biochemical Reactions: Alberty/Thermodynamics , 2005 .

[10]  A. McCoy,et al.  Electrostatic complementarity at protein/protein interfaces. , 1997, Journal of molecular biology.

[11]  P. Hünenberger,et al.  Explicit-solvent molecular dynamics simulation at constant pH: Methodology and application to small amines , 2001 .

[12]  J. Mccammon,et al.  Brownian dynamics simulation of diffusion‐influenced bimolecular reactions , 1984 .

[13]  P. Kollman,et al.  Calculating structures and free energies of complex molecules: combining molecular mechanics and continuum models. , 2000, Accounts of chemical research.

[14]  Carmay Lim,et al.  Absolute pKa calculations with continuum dielectric methods , 1991 .

[15]  J. Antosiewicz,et al.  Constant-pH molecular dynamics simulations: a test case of succinic acid , 2004 .

[16]  Michael J. Holst,et al.  A New Paradigm for Parallel Adaptive Meshing Algorithms , 2000, SIAM J. Sci. Comput..

[17]  B Honig,et al.  Electrostatic contributions to protein–protein interactions: Fast energetic filters for docking and their physical basis , 2001, Protein science : a publication of the Protein Society.

[18]  J Novotny,et al.  Electrostatic fields in antibodies and antibody/antigen complexes. , 1992, Progress in biophysics and molecular biology.

[19]  C. Soares,et al.  Constant-pH molecular dynamics using stochastic titration , 2002 .

[20]  Michael J. Holst,et al.  The adaptive multilevel finite element solution of the Poisson-Boltzmann equation on massively parallel computers , 2001, IBM J. Res. Dev..

[21]  Andrew J. Bordner,et al.  Boundary element solution of the linear Poisson–Boltzmann equation and a multipole method for the rapid calculation of forces on macromolecules in solution , 2003, J. Comput. Chem..

[22]  Charles L. Brooks,et al.  λ‐dynamics: A new approach to free energy calculations , 1996 .

[23]  P. Hünenberger,et al.  pH-Dependent Stability of a Decalysine α-Helix Studied by Explicit-Solvent Molecular Dynamics Simulations at Constant pH , 2004 .

[24]  Ronald M. Levy,et al.  The SGB/NP hydration free energy model based on the surface generalized born solvent reaction field and novel nonpolar hydration free energy estimators , 2002, J. Comput. Chem..

[25]  Gregory D. Hawkins,et al.  Pairwise solute descreening of solute charges from a dielectric medium , 1995 .

[26]  Christian Holm,et al.  Electrostatic effects in soft matter and biophysics , 2001 .

[27]  D. Case,et al.  Constant pH molecular dynamics in generalized Born implicit solvent , 2004, J. Comput. Chem..

[28]  Jacopo Tomasi,et al.  Molecular Interactions in Solution: An Overview of Methods Based on Continuous Distributions of the Solvent , 1994 .

[29]  Barry Honig,et al.  Calculating total electrostatic energies with the nonlinear Poisson-Boltzmann equation , 1990 .

[30]  C. Brooks,et al.  Novel generalized Born methods , 2002 .

[31]  Peijuan Zhu,et al.  Implementation and testing of stable, fast implicit solvation in molecular dynamics using the smooth‐permittivity finite difference Poisson–Boltzmann method , 2004, J. Comput. Chem..

[32]  S Karlin,et al.  Clusters of charged residues in protein three-dimensional structures. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[33]  Huan-Xiang Zhou,et al.  Comparison of calculation and experiment implicates significant electrostatic contributions to the binding stability of barnase and barstar. , 2003, Biophysical journal.

[34]  C. Chothia,et al.  The atomic structure of protein-protein recognition sites. , 1999, Journal of molecular biology.

[35]  B. Honig,et al.  Calculation of electrostatic potentials in an enzyme active site , 1987, Nature.

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

[37]  D. Chipman.  Computation of p K a from Dielectric Continuum Theory , 2002 .

[38]  J. Andrew Grant,et al.  A smooth permittivity function for Poisson–Boltzmann solvation methods , 2001, J. Comput. Chem..

[39]  Federico Fogolari,et al.  On the variational approach to Poisson–Boltzmann free energies , 1997 .

[40]  Razif R. Gabdoulline,et al.  Protein interaction property similarity analysis , 2001 .

[41]  B. Roux,et al.  Implicit solvent models. , 1999, Biophysical chemistry.

[42]  P. Tavan,et al.  Continuum description of solvent dielectrics in molecular-dynamics simulations of proteins , 2003 .

[43]  M. L. Connolly.  Solvent-accessible surfaces of proteins and nucleic acids. , 1983, Science.

[44]  P. E. Dyshlovenko.  Adaptive numerical method for Poisson-Boltzmann equation and its application , 2002 .

[45]  D. Case,et al.  Exploring protein native states and large‐scale conformational changes with a modified generalized born model , 2004, Proteins.

[46]  W. Im,et al.  Continuum solvation model: Computation of electrostatic forces from numerical solutions to the Poisson-Boltzmann equation , 1998 .

[47]  C. Chothia,et al.  The structure of protein-protein recognition sites. , 1990, The Journal of biological chemistry.

[48]  J. Goldman,et al.  Theory of titration curves , 1963 .

[49]  Goran Neshich,et al.  Analysis of the black‐eyed pea trypsin and chymotrypsin inhibitor‐α‐chymotrypsin complex , 1997 .

[50]  Malcolm E. Davis,et al.  Electrostatics in biomolecular structure and dynamics , 1990 .

[51]  A J Olson,et al.  Electrostatic orientation of the electron-transfer complex between plastocyanin and cytochrome c. , 1991, The Journal of biological chemistry.

[52]  M L Connolly,et al.  The molecular surface package. , 1993, Journal of molecular graphics.

[53]  L. R. Scott,et al.  Electrostatics and diffusion of molecules in solution: simulations with the University of Houston Brownian dynamics program , 1995 .

[54]  R C Wade,et al.  Simulation of the diffusional association of barnase and barstar. , 1997, Biophysical journal.

[55]  F. Gurd,et al.  pH-dependent processes in proteins. , 1985, CRC critical reviews in biochemistry.

[56]  D. Case,et al.  Modification of the Generalized Born Model Suitable for Macromolecules , 2000 .

[57]  Yutaka Ishikawa,et al.  Scientific Computing in Object-Oriented Parallel Environments , 1997, Lecture Notes in Computer Science.

[58]  Marcia O. Fenley,et al.  Hybrid boundary element and finite difference method for solving the nonlinear Poisson–Boltzmann equation , 2004, J. Comput. Chem..

[59]  Charles L. Brooks,et al.  New analytic approximation to the standard molecular volume definition and its application to generalized Born calculations , 2003, J. Comput. Chem..

[60]  C. Brooks,et al.  Constant‐pH molecular dynamics using continuous titration coordinates , 2004, Proteins.

[61]  J. Antosiewicz,et al.  Constant-pH molecular dynamics study of protonation-structure relationship in a heptapeptide derived from ovomucoid third domain. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[62]  James B. Matthew,et al.  [17] Calculation of electrostatic interactions in proteins , 1986 .

[63]  Nathan A. Baker,et al.  Adaptive multilevel finite element solution of the Poisson–Boltzmann equation I. Algorithms and examples , 2000 .

[64]  Alexander D. MacKerell,et al.  Computational Biochemistry and Biophysics , 2001 .

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

[66]  R. Friesner,et al.  Generalized Born Model Based on a Surface Integral Formulation , 1998 .

[67]  K. Sharp,et al.  Electrostatic interactions in macromolecules: theory and applications. , 1990, Annual review of biophysics and biophysical chemistry.

[68]  C. Tanford,et al.  Interpretation of protein titration curves. Application to lysozyme. , 1972, Biochemistry.

[69]  Nathan A. Baker,et al.  Adaptive multilevel finite element solution of the Poisson–Boltzmann equation II. Refinement at solvent‐accessible surfaces in biomolecular systems , 2000 .

[70]  E. Knapp,et al.  Accurate pKa determination for a heterogeneous group of organic molecules. , 2004, Chemphyschem : a European journal of chemical physics and physical chemistry.

[71]  Charles L. Brooks,et al.  Performance comparison of generalized born and Poisson methods in the calculation of electrostatic solvation energies for protein structures , 2004, J. Comput. Chem..

[72]  D. Case,et al.  A novel view of pH titration in biomolecules. , 2001, Biochemistry.

[73]  J. Mccammon,et al.  On the evaluation and optimization of protein X‐ray structures for pKa calculations , 2003, Protein science : a publication of the Protein Society.

[74]  D. Beglov,et al.  Atomic Radii for Continuum Electrostatics Calculations Based on Molecular Dynamics Free Energy Simulations , 1997 .

[75]  B. Montgomery Pettitt,et al.  Numerical Considerations in the Computation of the Electrostatic Free Energy of Interaction within the Poisson-Boltzmann Theory , 1997 .

[76]  Federico Fogolari,et al.  Protocol for MM/PBSA molecular dynamics simulations of proteins. , 2003, Biophysical journal.

[77]  M. Schaefer,et al.  A precise analytical method for calculating the electrostatic energy of macromolecules in aqueous solution. , 1990, Journal of molecular biology.

[78]  B. Lee,et al.  The interpretation of protein structures: estimation of static accessibility. , 1971, Journal of molecular biology.

[79]  Ann M. Richard,et al.  Quantitative comparison of molecular electrostatic potentials for structure‐activity studies , 1991 .

[80]  B. García-Moreno E.,et al.  Structural interpretation of pH and salt-dependent processes in proteins with computational methods. , 2004, Methods in enzymology.

[81]  H. Berendsen,et al.  The electric potential of a macromolecule in a solvent: A fundamental approach , 1991 .

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

[83]  Wei Zu Chen,et al.  Protein molecular dynamics with electrostatic force entirely determined by a single Poisson‐Boltzmann calculation , 2002, Proteins.

[84]  Jim Warwicker,et al.  Improved pKa calculations through flexibility based sampling of a water‐dominated interaction scheme , 2004, Protein science : a publication of the Protein Society.

[85]  W. Guida,et al.  Accurate Prediction of Acidity Constants in Aqueous Solution via Density Functional Theory and Self-Consistent Reaction Field Methods , 2002 .

[86]  Michael J. Holst,et al.  Adaptive Numerical Treatment of Elliptic Systems on Manifolds , 2001, Adv. Comput. Math..

[87]  D. Case,et al.  Thermodynamics of a reverse turn motif. Solvent effects and side-chain packing. , 1997, Journal of molecular biology.

[88]  B Honig,et al.  Membrane binding of peptides containing both basic and aromatic residues. Experimental studies with peptides corresponding to the scaffolding region of caveolin and the effector region of MARCKS. , 2000, Biochemistry.

[89]  W. Im,et al.  Optimized atomic radii for protein continuum electrostatics solvation forces. , 1999, Biophysical chemistry.

[90]  L. Onsager.  Electric Moments of Molecules in Liquids , 1936 .

[91]  P Beroza,et al.  Calculations of proton-binding thermodynamics in proteins. , 1998, Methods in enzymology.

[92]  P. Kollman,et al.  Continuum Solvent Studies of the Stability of DNA, RNA, and Phosphoramidate−DNA Helices , 1998 .

[93]  J. Andrew McCammon,et al.  Conformational sampling with Poisson–Boltzmann forces and a stochastic dynamics/Monte Carlo method: Application to alanine dipeptide , 1997 .

[94]  R. Alberty.  Thermodynamics of Biochemical Reactions , 2003 .

[95]  David A. Case,et al.  Effective Born radii in the generalized Born approximation: The importance of being perfect , 2002, J. Comput. Chem..

[96]  A. Elcock.  Prediction of functionally important residues based solely on the computed energetics of protein structure. , 2001, Journal of molecular biology.

[97]  E. Alexov,et al.  Combining conformational flexibility and continuum electrostatics for calculating pK(a)s in proteins. , 2002, Biophysical journal.

[98]  Jung-Hsin Lin,et al.  Bridging implicit and explicit solvent approaches for membrane electrostatics. , 2002, Biophysical journal.

[99]  G. K. Ackers,et al.  Electrostatic contributions to the energetics of dimer-tetramer assembly in human hemoglobin: pH dependence and effect of specifically bound chloride ions. , 1981, Biochemistry.

[100]  H. Scheraga,et al.  A fast adaptive multigrid boundary element method for macromolecular electrostatic computations in a solvent , 1997 .

[101]  C. Brooks,et al.  Recent advances in the development and application of implicit solvent models in biomolecule simulations. , 2004, Current opinion in structural biology.

[102]  Richard H. Henchman,et al.  Revisiting free energy calculations: a theoretical connection to MM/PBSA and direct calculation of the association free energy. , 2004, Biophysical journal.

[103]  Nathan A. Baker,et al.  Electrostatics of nanosystems: Application to microtubules and the ribosome , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[104]  D. Poland.  Free energy of proton binding in proteins , 2003, Biopolymers.

[105]  Barry Honig,et al.  Electrostatic control of the membrane targeting of C2 domains. , 2002, Molecular cell.

[106]  P. Colella,et al.  A Finite Difference Domain Decomposition Method Using Local Corrections for the Solution of Poisson's Equation , 1999 .

[107]  O. Axelsson,et al.  Finite element solution of boundary value problemes - theory and computation , 2001, Classics in applied mathematics.

[108]  Ruhong Zhou,et al.  Comment on: Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? The Poisson-Boltzmann equation by Zhou, R. et al. , 2004 .

[109]  J. Apostolakis,et al.  Continuum Electrostatic Energies of Macromolecules in Aqueous Solutions , 1997 .

[110]  D. A. Dunnett.  Classical Electrodynamics , 2020, Nature.

[111]  A. Baptista.  Comment on “Explicit-solvent molecular dynamics simulation at constant pH: Methodology and application to small amines” [J. Chem. Phys. 114, 9706 (2001)] , 2002 .

[112]  M. Born.  Volumen und Hydratationswärme der Ionen , 1920 .

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

[114]  G. Lamm,et al.  The Poisson–Boltzmann Equation , 2003 .

[115]  D. Case,et al.  Generalized born models of macromolecular solvation effects. , 2000, Annual review of physical chemistry.

[116]  Benoît Roux,et al.  Solvation of complex molecules in a polar liquid: An integral equation theory , 1996 .

[117]  J. Andrew McCammon,et al.  Computation of electrostatic forces on solvated molecules using the Poisson-Boltzmann equation , 1993 .

[118]  K. Sharp,et al.  Protein folding and association: Insights from the interfacial and thermodynamic properties of hydrocarbons , 1991, Proteins.

[119]  J. Tomasi,et al.  Electrostatic interaction of a solute with a continuum. A direct utilizaion of AB initio molecular potentials for the prevision of solvent effects , 1981 .

[120]  Michael J. Holst,et al.  Multigrid solution of the Poisson—Boltzmann equation , 1992, J. Comput. Chem..

[121]  Michael Levitt,et al.  Finite‐difference solution of the Poisson–Boltzmann equation: Complete elimination of self‐energy , 1996, J. Comput. Chem..

[122]  Donald Bashford,et al.  Macroscopic electrostatic models for protonation states in proteins. , 2004, Frontiers in bioscience : a journal and virtual library.

[123]  Michael J. Holst,et al.  Numerical solution of the nonlinear Poisson–Boltzmann equation: Developing more robust and efficient methods , 1995, J. Comput. Chem..

[124]  Richard A. Friesner,et al.  Numerical solution of the Poisson–Boltzmann equation using tetrahedral finite‐element meshes , 1997 .

[125]  M. B. Pinto,et al.  Optimized δ expansion for relativistic nuclear models , 1997, nucl-th/9709049.

[126]  S. Petersen,et al.  Simulation of protein conformational freedom as a function of pH: constant‐pH molecular dynamics using implicit titration , 1997, Proteins.

[127]  Nathan A. Baker,et al.  Poisson-Boltzmann Methods for Biomolecular Electrostatics , 2004, Numerical Computer Methods, Part D.

[128]  Richard A. Friesner,et al.  An automatic three‐dimensional finite element mesh generation system for the Poisson–Boltzmann equation , 1997 .

[129]  M. Ondrechen,et al.  THEMATICS: A simple computational predictor of enzyme function from structure , 2001, Proceedings of the National Academy of Sciences of the United States of America.

[130]  B. Berne,et al.  Can a continuum solvent model reproduce the free energy landscape of a β-hairpin folding in water? , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[131]  K. Sharp,et al.  Accurate Calculation of Hydration Free Energies Using Macroscopic Solvent Models , 1994 .

[132]  P. Beroza,et al.  Protonation of interacting residues in a protein by a Monte Carlo method: application to lysozyme and the photosynthetic reaction center of Rhodobacter sphaeroides. , 1991, Proceedings of the National Academy of Sciences of the United States of America.

[133]  F. Gurd,et al.  Electrostatic effects in myoglobin. Hydrogen ion equilibria in sperm whale ferrimyoglobin. , 1974, Biochemistry.

[134]  Donald Bashford,et al.  An Object-Oriented Programming Suite for Electrostatic Effects in Biological Molecules , 1997, ISCOPE.

[135]  Gregory D. Hawkins,et al.  Parametrized Models of Aqueous Free Energies of Solvation Based on Pairwise Descreening of Solute Atomic Charges from a Dielectric Medium , 1996 .

[136]  R. Zauhar,et al.  The rigorous computation of the molecular electric potential , 1988 .

[137]  P. Schleyer.  Encyclopedia of computational chemistry , 1998 .

[138]  B. Honig,et al.  Classical electrostatics in biology and chemistry. , 1995, Science.

[139]  J. A. McCammon,et al.  Solving the finite difference linearized Poisson‐Boltzmann equation: A comparison of relaxation and conjugate gradient methods , 1989 .

[140]  Ray Luo,et al.  A Poisson–Boltzmann dynamics method with nonperiodic boundary condition , 2003 .

[141]  Emil Alexov,et al.  Rapid grid‐based construction of the molecular surface and the use of induced surface charge to calculate reaction field energies: Applications to the molecular systems and geometric objects , 2002, J. Comput. Chem..

[142]  Nathan A. Baker,et al.  Solvation forces on biomolecular structures: A comparison of explicit solvent and Poisson–Boltzmann models , 2004, J. Comput. Chem..

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

[144]  D. Case,et al.  Incorporating solvation effects into density functional theory: Calculation of absolute acidities , 1997 .

[145]  C. Tanford,et al.  Theory of Protein Titration Curves. I. General Equations for Impenetrable Spheres , 1957 .