Advanced potential energy surfaces for condensed phase simulation.

Computational modeling at the atomistic and mesoscopic levels has undergone dramatic development in the past 10 years to meet the challenge of adequately accounting for the many-body nature of intermolecular interactions. At the heart of this challenge is the ability to identify the strengths and specific limitations of pairwise-additive interactions, to improve classical models to explicitly account for many-body effects, and consequently to enhance their ability to describe a wider range of reference data and build confidence in their predictive capacity. However, the corresponding computational cost of these advanced classical models increases significantly enough that statistical convergence of condensed phase observables becomes more difficult to achieve. Here we review a hierarchy of potential energy surface models used in molecular simulations for systems with many degrees of freedom that best meet the trade-off between accuracy and computational speed in order to define a sweet spot for a given scientific problem of interest.

[1]  Nohad Gresh,et al.  Inclusion of the ligand field contribution in a polarizable molecular mechanics: SIBFA‐LF , 2003, J. Comput. Chem..

[2]  Margaret E. Johnson,et al.  Current status of the AMOEBA polarizable force field. , 2010, The journal of physical chemistry. B.

[3]  Jacopo Tomasi,et al.  A new definition of cavities for the computation of solvation free energies by the polarizable continuum model , 1997 .

[4]  Alexander D. MacKerell,et al.  CHARMM fluctuating charge force field for proteins: II Protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model , 2004, J. Comput. Chem..

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

[6]  T. Straatsma,et al.  THE MISSING TERM IN EFFECTIVE PAIR POTENTIALS , 1987 .

[7]  W. V. van Gunsteren,et al.  On the Calculation of Atomic Forces in Classical Simulation Using the Charge-on-Spring Method To Explicitly Treat Electronic Polarization. , 2007, Journal of chemical theory and computation.

[8]  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..

[9]  Nathan A. Baker,et al.  iAPBS: a programming interface to the adaptive Poisson–Boltzmann solver , 2012 .

[10]  P. Fowler,et al.  Central or distributed multipole moments? Electrostatic models of aromatic dimers , 1991 .

[11]  C. Sagui,et al.  Molecular dynamics simulations of DNA with polarizable force fields: convergence of an ideal B-DNA structure to the crystallographic structure. , 2006, The journal of physical chemistry. B.

[12]  Anthony J. Stone,et al.  Distributed multipole analysis, or how to describe a molecular charge distribution , 1981 .

[13]  C. Breneman,et al.  Determining atom‐centered monopoles from molecular electrostatic potentials. The need for high sampling density in formamide conformational analysis , 1990 .

[14]  Michael W. Mahoney,et al.  A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions , 2000 .

[15]  T. Head-Gordon,et al.  Optimizing Protein-Solvent Force Fields to Reproduce Intrinsic Conformational Preferences of Model Peptides. , 2011, Journal of chemical theory and computation.

[16]  J. Madura,et al.  Solubility of simple, nonpolar compounds in TIP4P-Ew. , 2006, The Journal of chemical physics.

[17]  M. Levitt,et al.  Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme. , 1976, Journal of molecular biology.

[18]  D Fincham,et al.  Shell model simulations by adiabatic dynamics , 1993 .

[19]  Ad Bax,et al.  An empirical backbone-backbone hydrogen-bonding potential in proteins and its applications to NMR structure refinement and validation. , 2004, Journal of the American Chemical Society.

[20]  Michael Mascagni,et al.  Numerical Optimization of a Walk-on-Spheres Solver for the Linear Poisson-Boltzmann Equation , 2013 .

[21]  Rebecca C Wade,et al.  Biomolecular diffusional association. , 2002, Current opinion in structural biology.

[22]  R. Best,et al.  Protein simulations with an optimized water model: cooperative helix formation and temperature-induced unfolded state collapse. , 2010, The journal of physical chemistry. B.

[23]  Kazuo Kitaura,et al.  Theoretical Background of the Fragment Molecular Orbital (FMO) Method and Its Implementation in GAMESS , 2009 .

[24]  Thomas A. Halgren,et al.  The representation of van der Waals (vdW) interactions in molecular mechanics force fields: potential form, combination rules, and vdW parameters , 1992 .

[25]  Pengyu Y. Ren,et al.  Ion solvation thermodynamics from simulation with a polarizable force field. , 2003, Journal of the American Chemical Society.

[26]  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..

[27]  Benoît Roux,et al.  Modeling induced polarization with classical Drude oscillators: Theory and molecular dynamics simulation algorithm , 2003 .

[28]  Jules W. Moskowitz,et al.  Water Molecule Interactions , 1970 .

[29]  Harry A. Stern,et al.  Development of a polarizable force field for proteins via ab initio quantum chemistry: First generation model and gas phase tests , 2002, J. Comput. Chem..

[30]  C. Vega,et al.  A general purpose model for the condensed phases of water: TIP4P/2005. , 2005, The Journal of chemical physics.

[31]  Guo-Wei Wei,et al.  Matched interface and boundary (MIB) method for elliptic problems with sharp-edged interfaces , 2007, J. Comput. Phys..

[32]  Pengyu Y. Ren,et al.  Polarizable Atomic Multipole Water Model for Molecular Mechanics Simulation , 2003 .

[33]  Alexander D. MacKerell,et al.  A simple polarizable model of water based on classical Drude oscillators , 2003 .

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

[35]  Michael R. Shirts,et al.  Extremely precise free energy calculations of amino acid side chain analogs: Comparison of common molecular mechanics force fields for proteins , 2003 .

[36]  John E. Sader,et al.  Electrical Double-Layer Interaction between Heterogeneously Charged Colloidal Particles: A Superposition Formulation , 1998 .

[37]  P. Fowler,et al.  The long range model of intermolecular forces , 1983 .

[38]  Michael J. Holst,et al.  The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation , 2007, SIAM J. Numer. Anal..

[39]  Paul D. Adams,et al.  On macromolecular refinement at subatomic resolution with interatomic scatterers , 2007, Acta Crystallographica Section D: Biological Crystallography.

[40]  Teresa Head-Gordon,et al.  Calculating the Bimolecular Rate of Protein-Protein Association with Interacting Crowders. , 2013, Journal of chemical theory and computation.

[41]  Piotr Cieplak,et al.  Polarization effects in molecular mechanical force fields , 2009, Journal of physics. Condensed matter : an Institute of Physics journal.

[42]  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 .

[43]  Norman L. Allinger,et al.  Molecular mechanics. The MM3 force field for hydrocarbons. 1 , 1989 .

[44]  Timothy D. Fenn,et al.  Polarizable atomic multipole X-ray refinement: application to peptide crystals , 2009, Acta crystallographica. Section D, Biological crystallography.

[45]  George D. J. Phillies,et al.  Effects of intermacromolecular interactions on diffusion. II. Three‐component solutions , 1974 .

[46]  Brad A. Bauer,et al.  Exploring ion permeation energetics in gramicidin A using polarizable charge equilibration force fields. , 2009, Journal of the American Chemical Society.

[47]  C. Zukoski,et al.  The Electrostatic Interaction of Rigid, Globular Proteins with Arbitrary Charge Distributions. , 1998, Journal of colloid and interface science.

[48]  A. Warshel,et al.  Consistent Force Field for Calculations of Conformations, Vibrational Spectra, and Enthalpies of Cycloalkane and n‐Alkane Molecules , 1968 .

[49]  Lauren Wickstrom,et al.  Evaluating the performance of the ff99SB force field based on NMR scalar coupling data. , 2009, Biophysical journal.

[50]  Nathan A. Baker,et al.  Biomolecular electrostatics and solvation: a computational perspective , 2012, Quarterly Reviews of Biophysics.

[51]  P. Kollman,et al.  A well-behaved electrostatic potential-based method using charge restraints for deriving atomic char , 1993 .

[52]  Ian R. McDonald,et al.  Introduction of the shell model of ionic polarizability into molecular dynamics calculations , 1974 .

[53]  Teresa Head-Gordon,et al.  An Analytical Electrostatic Model for Salt Screened Interactions between Multiple Proteins. , 2006, Journal of chemical theory and computation.

[54]  Adrian H. Elcock,et al.  Diffusion, Crowding & Protein Stability in a Dynamic Molecular Model of the Bacterial Cytoplasm , 2010, PLoS Comput. Biol..

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

[56]  J. R. Carl,et al.  Atom dipole interaction model for molecular polarizability. Application to polyatomic molecules and determination of atom polarizabilities , 1972 .

[57]  Pengyu Y. Ren,et al.  Systematic improvement of a classical molecular model of water. , 2013, The journal of physical chemistry. B.

[58]  Greg L. Hura,et al.  Development of an improved four-site water model for biomolecular simulations: TIP4P-Ew. , 2004, The Journal of chemical physics.

[59]  B. Thole Molecular polarizabilities calculated with a modified dipole interaction , 1981 .

[60]  Steven J. Stuart,et al.  Fluctuating charge force fields for aqueous solutions , 1995 .

[61]  D. Wemmer,et al.  Differences in β-strand populations of monomeric Aβ40 and Aβ42. , 2013, Biophysical journal.

[62]  Teresa Head-Gordon,et al.  Effects of co-solvents on peptide hydration water structure and dynamics. , 2010, Physical chemistry chemical physics : PCCP.

[63]  Charles L Brooks,et al.  Revisiting the hexane-water interface via molecular dynamics simulations using nonadditive alkane-water potentials. , 2006, The Journal of chemical physics.

[64]  Marcia O. Fenley,et al.  Fast Boundary Element Method for the Linear Poisson-Boltzmann Equation , 2002 .

[65]  Alan Grossfield,et al.  Simulation of Ca2+ and Mg2+ solvation using polarizable atomic multipole potential. , 2006, The journal of physical chemistry. B.

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

[67]  Wei Wang,et al.  Fast evaluation of polarizable forces. , 2005, The Journal of chemical physics.

[68]  Hermann Stoll,et al.  On the direct calculation of localized HF orbitals in molecule clusters, layers and solids , 1977 .

[69]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[70]  D. Truhlar,et al.  Self-Consistent Polarization of the Boundary in the Redistributed Charge and Dipole Scheme for Combined Quantum-Mechanical and Molecular-Mechanical Calculations. , 2007, Journal of chemical theory and computation.

[71]  Wei Zu Chen,et al.  A Stochastic Dynamics Simulation Study Associated with Hydration Force and Friction Memory Effect , 2000 .

[72]  S. Lifson,et al.  Energy functions for peptides and proteins. II. The amide hydrogen bond and calculation of amide crystal properties. , 1974, Journal of the American Chemical Society.

[73]  Michael R. Shirts,et al.  Solvation free energies of amino acid side chain analogs for common molecular mechanics water models. , 2005, The Journal of chemical physics.

[74]  T. Head-Gordon,et al.  Optimizing solute-water van der Waals interactions to reproduce solvation free energies. , 2012, The journal of physical chemistry. B.

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

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

[77]  Charles L. Brooks,et al.  CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations , 2004, J. Comput. Chem..

[78]  Harry A. Stern,et al.  Fluctuating Charge, Polarizable Dipole, and Combined Models: Parameterization from ab Initio Quantum Chemistry , 1999 .

[79]  Pengyu Y. Ren,et al.  Consistent treatment of inter‐ and intramolecular polarization in molecular mechanics calculations , 2002, J. Comput. Chem..

[80]  Wei Zhang,et al.  Strike a balance: Optimization of backbone torsion parameters of AMBER polarizable force field for simulations of proteins and peptides , 2006, J. Comput. Chem..

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

[82]  Michiel Sprik,et al.  A polarizable model for water using distributed charge sites , 1988 .

[83]  F. Jiang,et al.  Influence of side chain conformations on local conformational features of amino acids and implication for force field development. , 2010, The journal of physical chemistry. B.

[84]  Robert B. Hermann,et al.  Theory of hydrophobic bonding. II. Correlation of hydrocarbon solubility in water with solvent cavity surface area , 1972 .

[85]  L. Greengard,et al.  A new version of the fast multipole method for screened Coulomb interactions in three dimensions , 2002 .

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

[87]  Nikolay Galkin,et al.  Application of a polarizable force field to calculations of relative protein–ligand binding affinities , 2008, Proceedings of the National Academy of Sciences.

[88]  Nicolas L. Fawzi,et al.  Homogeneous and heterogeneous tertiary structure ensembles of amyloid-β peptides. , 2011, Biochemistry.

[89]  Margaret E. Johnson,et al.  Hydration water dynamics near biological interfaces. , 2009, The journal of physical chemistry. B.

[90]  Alexander D. MacKerell,et al.  Development of a polarizable intermolecular potential function (PIPF) for liquid amides and alkanes. , 2007, Journal of chemical theory and computation.

[91]  Donald E. Williams Representation of the molecular electrostatic potential by atomic multipole and bond dipole models , 1988 .

[92]  Alexander H Boschitsch,et al.  A Fast and Robust Poisson-Boltzmann Solver Based on Adaptive Cartesian Grids. , 2011, Journal of chemical theory and computation.

[93]  Clifford E. Dykstra,et al.  Electrostatic interaction potentials in molecular force fields , 1993 .

[94]  John M Herbert,et al.  A generalized many-body expansion and a unified view of fragment-based methods in electronic structure theory. , 2012, The Journal of chemical physics.

[95]  Steven J. Stuart,et al.  Dynamical fluctuating charge force fields: Application to liquid water , 1994 .

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

[97]  Christos Boutsidis,et al.  Atomic-level characterization of the ensemble of the Aβ(1-42) monomer in water using unbiased molecular dynamics simulations and spectral algorithms. , 2011, Journal of molecular biology.

[98]  Benzhuo Lu,et al.  Order N algorithm for computation of electrostatic interactions in biomolecular systems , 2006, Proceedings of the National Academy of Sciences.

[99]  M. V. Subbotin,et al.  A quantum mechanical polarizable force field for biomolecular interactions , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[100]  D. J. Price,et al.  A modified TIP3P water potential for simulation with Ewald summation. , 2004, The Journal of chemical physics.

[101]  Haibo Yu,et al.  Accounting for polarization in molecular simulation , 2005, Comput. Phys. Commun..

[102]  S. Lifson,et al.  Energy functions for peptides and proteins. I. Derivation of a consistent force field including the hydrogen bond from amide crystals. , 1974, Journal of the American Chemical Society.

[103]  Anastassia N Alexandrova,et al.  Polarization Effects for Hydrogen-Bonded Complexes of Substituted Phenols with Water and Chloride Ion. , 2007, Journal of chemical theory and computation.

[104]  M. Head‐Gordon,et al.  Examination of the hydrogen-bonding networks in small water clusters (n = 2-5, 13, 17) using absolutely localized molecular orbital energy decomposition analysis. , 2012, Physical chemistry chemical physics : PCCP.

[105]  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.

[106]  Brad A. Bauer,et al.  Properties of water along the liquid-vapor coexistence curve via molecular dynamics simulations using the polarizable TIP4P-QDP-LJ water model. , 2009, The Journal of chemical physics.

[107]  Weidong Xin,et al.  A boundary element formulation of protein electrostatics with explicit ions , 2007, J. Comput. Phys..

[108]  Many-body force field models based solely on pairwise Coulomb screening do not simultaneously reproduce correct gas-phase and condensed-phase polarizability limits. , 2004, The Journal of chemical physics.

[109]  B. Derjaguin,et al.  Theory of the stability of strongly charged lyophobic sols and of the adhesion of strongly charged particles in solutions of electrolytes , 1993 .

[110]  Donald G Truhlar,et al.  Electrostatically embedded many-body method for dipole moments, partial atomic charges, and charge transfer. , 2012, Physical chemistry chemical physics : PCCP.

[111]  Wilfred F. van Gunsteren,et al.  Development of a simple, self-consistent polarizable model for liquid water , 2003 .

[112]  Jacob K. White,et al.  Accurate solution of multi‐region continuum biomolecule electrostatic problems using the linearized Poisson–Boltzmann equation with curved boundary elements , 2009, J. Comput. Chem..

[113]  H. Berendsen,et al.  Interaction Models for Water in Relation to Protein Hydration , 1981 .

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

[115]  E. Verwey,et al.  Theory of the stability of lyophobic colloids. , 1955, The Journal of physical and colloid chemistry.

[116]  Kenneth D Jordan,et al.  Theoretical characterization of the (H2O)21 cluster: application of an n-body decomposition procedure. , 2006, The journal of physical chemistry. B.

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

[118]  C. Vega,et al.  Relation between the melting temperature and the temperature of maximum density for the most common models of water. , 2005, The Journal of chemical physics.

[119]  G. Hummer,et al.  Are current molecular dynamics force fields too helical? , 2008, Biophysical journal.

[120]  W. V. van Gunsteren,et al.  New Interaction Parameters for Oxygen Compounds in the GROMOS Force Field: Improved Pure-Liquid and Solvation Properties for Alcohols, Ethers, Aldehydes, Ketones, Carboxylic Acids, and Esters. , 2011, Journal of chemical theory and computation.

[121]  Jory Z. Ruscio,et al.  Structure and dynamics of the Abeta(21-30) peptide from the interplay of NMR experiments and molecular simulations. , 2008, Journal of the American Chemical Society.

[122]  Terry P. Lybrand,et al.  Calculation of free energy changes in ion–water clusters using nonadditive potentials and the Monte Carlo method , 1987 .

[123]  Chandrajit L. Bajaj,et al.  An Efficient Higher-Order Fast Multipole Boundary Element Solution for Poisson-Boltzmann-Based Molecular Electrostatics , 2011, SIAM J. Sci. Comput..

[124]  Gregory K. Schenter,et al.  Excited States of the Bacteriochlorophyll b Dimer of Rhodopseudomonas viridis: A QM/MM Study of the Photosynthetic Reaction Center That Includes MM Polarization , 1995 .

[125]  Walter Thiel,et al.  Solvent Boundary Potentials for Hybrid QM/MM Computations Using Classical Drude Oscillators: A Fully Polarizable Model. , 2012, Journal of chemical theory and computation.

[126]  O Engkvist,et al.  Accurate Intermolecular Potentials Obtained from Molecular Wave Functions: Bridging the Gap between Quantum Chemistry and Molecular Simulations. , 2000, Chemical reviews.

[127]  Edward Teller,et al.  Interaction of the van der Waals Type Between Three Atoms , 1943 .

[128]  D. Baker,et al.  An orientation-dependent hydrogen bonding potential improves prediction of specificity and structure for proteins and protein-protein complexes. , 2003, Journal of molecular biology.

[129]  Carlos Vega,et al.  Simulating water with rigid non-polarizable models: a general perspective. , 2011, Physical chemistry chemical physics : PCCP.

[130]  Andrew T. Fenley,et al.  An analytical approach to computing biomolecular electrostatic potential. I. Derivation and analysis. , 2008, The Journal of chemical physics.

[131]  Teresa Head-Gordon,et al.  A New and Efficient Poisson-Boltzmann Solver for Interaction of Multiple Proteins. , 2010, Journal of chemical theory and computation.

[132]  Andrew T. Fenley,et al.  An analytical approach to computing biomolecular electrostatic potential. II. Validation and applications. , 2008, The Journal of chemical physics.

[133]  R. Zauhar,et al.  A new method for computing the macromolecular electric potential. , 1985, Journal of molecular biology.

[134]  Frank Jensen,et al.  Force field modeling of conformational energies: Importance of multipole moments and intramolecular polarization , 2007 .

[135]  Anthony J. Stone,et al.  The Theory of Intermolecular Forces , 2013 .

[136]  Alexander D. MacKerell,et al.  Simulating Monovalent and Divalent Ions in Aqueous Solution Using a Drude Polarizable Force Field. , 2010, Journal of chemical theory and computation.

[137]  Kim Palmo,et al.  Inclusion of charge and polarizability fluxes provides needed physical accuracy in molecular mechanics force fields , 2006 .

[138]  Pengyu Y. Ren,et al.  Calculation of protein–ligand binding free energy by using a polarizable potential , 2008, Proceedings of the National Academy of Sciences.

[139]  Jie Li,et al.  Development of polarizable models for molecular mechanical calculations II: induced dipole models significantly improve accuracy of intermolecular interaction energies. , 2011, The journal of physical chemistry. B.

[140]  Jacob Kongsted,et al.  The polarizable embedding coupled cluster method. , 2011, Journal of Chemical Physics.

[141]  David L Mobley,et al.  Small molecule hydration free energies in explicit solvent: An extensive test of fixed-charge atomistic simulations. , 2009, Journal of chemical theory and computation.

[142]  G. Beran,et al.  Accurate Molecular Crystal Lattice Energies from a Fragment QM/MM Approach with On-the-Fly Ab Initio Force Field Parametrization. , 2011, Journal of chemical theory and computation.

[143]  Spencer R Pruitt,et al.  Fragmentation methods: a route to accurate calculations on large systems. , 2012, Chemical reviews.

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

[145]  Yue Shi,et al.  Multipole electrostatics in hydration free energy calculations , 2011, J. Comput. Chem..