Empirical Classical Force Fields for Molecular Systems

With the continuing increase of the power of computers, the past decades have seen a rapid increase in the number, performance and accuracy of theoretical computational methods in chemistry (van Gunsteren et al., 1989 ff, Lipkowitz & Boyd, 1990ff). One can distinguish three major classes of methods for the theoretical study of molecular properties, listed in order of decreasing computational expenses: (i) ab initio molecular-orbital methods (Hehre et al., 1986), (ii) semi-empirical molecular-orbital methods (Zerner, 1991), and (iii) empirical classical force-field methods. Since the available computing resources are most often the true limiting factor to numerical calculations, it has become clear that there is no universal method able to solve all possible problems, but that one should rather select the method that is the most suitable to a problem of interest. The properties of the observable (s) and system under consideration that will, together with the available computing power, largely determine which type of method can be used are (van Gunsteren & Berendsen, 1990): (i) the required system size, (ii) the required volume of conformational space that has to be searched or sampled (in terms of dynamics: the required time-scale), (iii) the required resolution in terms of particles (determined by the smallest entity, subatomic particle, atom, or group of atoms, treated explicitly in the model), and (iv) the required energetical accuracy of the interaction function. These requirements may be incompatible, in which case the observable cannot be computed adequately with the currently available computer resources (van Gunsteren et al., 1995b). When requirements (i) and (ii) are in conflict with requirement (iii), this conflict may be resolved by the design of hierarchical or hybrid models, where only the relevant degrees of freedom are treated with a more expensive, higher resolution method. This is often done, for example, in the study of acid- or base-catalysed, organic or enzymatic reactions in the bulk phase (Warshel, 1991, Field, 1993, Whitnell & Wilson, 1993, Liu et al., 1996a).

[1]  J. A. Barker.  Reaction field, screening, and long-range interactions in simulations of ionic and dipolar systems , 1994 .

[2]  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 .

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

[4]  Anthony K. Rappé,et al.  Reply to Comment on: van der Waals functional forms for molecular simulations , 1993 .

[5]  Francesc X. Avilés,et al.  Free energies of transfer of Trp analogs from chloroform to water: Comparison of theory and experiment and the importance of adequate treatment of electrostatic and internal interactions , 1996 .

[6]  Charles L. Brooks,et al.  The influence of long-range force truncation on the thermodynamics of aqueous ionic solutions , 1987 .

[7]  J. Hermans,et al.  REACTION FIELD MOLECULAR DYNAMICS SIMULATION WITH FRIEDMAN'S IMAGE CHARGE METHOD , 1995 .

[8]  Wilfred F. van Gunsteren,et al.  A generalized reaction field method for molecular dynamics simulations , 1995 .

[9]  Wilfred F. van Gunsteren,et al.  Computer Simulation of Biomolecular Systems: Theoretical and Experimental Applications , 1989 .

[10]  Ming-Jing Hwang,et al.  Derivation of class II force fields. I. Methodology and quantum force field for the alkyl functional group and alkane molecules , 1994, J. Comput. Chem..

[11]  Norman L. Allinger,et al.  Molecular mechanics. The MM3 force field for hydrocarbons. 2. Vibrational frequencies and thermodynamics , 1989 .

[12]  János G. Ángyán,et al.  Common theoretical framework for quantum chemical solvent effect theories , 1992 .

[13]  Martin Karplus,et al.  Empirical force field study of geometries and conformational transitions of some organic molecules , 1992 .

[14]  Arnold T. Hagler,et al.  Computer simulation of the conformational properties of oligopeptides. Comparison of theoretical methods and analysis of experimental results , 1979 .

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

[16]  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.

[17]  Norman L. Allinger,et al.  Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms , 1977 .

[18]  A. T. Hagler,et al.  Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 2. A benchmark for the objective comparison of alternative force fields , 1979 .

[19]  R. Cramer,et al.  Validation of the general purpose tripos 5.2 force field , 1989 .

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

[21]  Lennart Nilsson,et al.  Empirical energy functions for energy minimization and dynamics of nucleic acids , 1986 .

[22]  T. Keith,et al.  Inclusion of Explicit Solvent Molecules in a Self-Consistent-Reaction Field Model of Solvation , 1994 .

[23]  Paul R. Gerber,et al.  MAB, a generally applicable molecular force field for structure modelling in medicinal chemistry , 1995, J. Comput. Aided Mol. Des..

[24]  J. A. Barker,et al.  Monte Carlo studies of the dielectric properties of water-like models , 1973 .

[25]  A. Warshel,et al.  Calculations of electrostatic energies in proteins. The energetics of ionized groups in bovine pancreatic trypsin inhibitor. , 1985, Journal of molecular biology.

[26]  H. Berendsen,et al.  COMPUTER-SIMULATION OF MOLECULAR-DYNAMICS - METHODOLOGY, APPLICATIONS, AND PERSPECTIVES IN CHEMISTRY , 1990 .

[27]  Peter A. Kollman,et al.  AMBER: Assisted model building with energy refinement. A general program for modeling molecules and their interactions , 1981 .

[28]  Martin Neumann,et al.  Pair correlations in an NACL-SPC water model simulations versus extended rism computations (Molecular Physics, Vol 77, Pg 769, 1992). , 1992 .

[29]  Daan Frenkel.  Monte Carlo simulations: a primer , 1993 .

[30]  Martin Neumann,et al.  Consistent calculation of the static and frequency-dependent dielectric constant in computer simulations , 1984 .

[31]  W. V. Gunsteren,et al.  Molecular dynamics free energy calculation in four dimensions , 1994 .

[32]  A. T. Hagler,et al.  Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 3. The C:O.cntdot..cntdot..cntdot.H-O hydrogen bond and the analysis of the energetics and packing of carboxylic acids , 1979 .

[33]  Wilfred F. van Gunsteren,et al.  Molecular Dynamics with a Quantum‐Chemical Potential: Solvent Effects on an SN2 Reaction at Nitrogen , 1996 .

[34]  S. Engelsen,et al.  THE CONSISTENT FORCE FIELD. II: AN OPTIMIZED SET OF POTENTIAL ENERGY FUNCTIONS FOR THE ALKANES , 1994 .

[35]  Warren J. Hehre,et al.  AB INITIO Molecular Orbital Theory , 1986 .

[36]  Ming-Jing Hwang,et al.  Derivation of Class II Force Fields. III. Characterization of a Quantum Force Field for Alkanes , 1994 .

[37]  A. Mark,et al.  Fluctuation and cross-correlation analysis of protein motions observed in nanosecond molecular dynamics simulations. , 1995, Journal of molecular biology.

[38]  David Fincham,et al.  Optimisation of the Ewald Sum for Large Systems , 1994 .

[39]  W F van Gunsteren,et al.  Molecular mechanics in biology: from structure to function, taking account of solvation. , 1994, Annual review of biophysics and biomolecular structure.

[40]  Jan L. M. Dillen,et al.  An empirical force field. I. Alkanes , 1995, J. Comput. Chem..

[41]  Shoshana J. Wodak,et al.  Computer simulations of liquid water: treatment of long-range interactions , 1990 .

[42]  Can Simple Quantum-Chemical Continuum Models Explain the Gauche Effect in Poly(ethylene oxide)? , 1994 .

[43]  David T. Jones,et al.  De novo protein design using pairwise potentials and a genetic algorithm , 1994, Protein science : a publication of the Protein Society.

[44]  J. Mccammon,et al.  Dynamics of Proteins and Nucleic Acids , 2018 .

[45]  Arnold T. Hagler,et al.  On the use of quantum energy surfaces in the derivation of molecular force fields , 1994 .

[46]  Andrew E. Torda,et al.  Local elevation: A method for improving the searching properties of molecular dynamics simulation , 1994, J. Comput. Aided Mol. Des..

[47]  R. Wood.  Continuum electrostatics in a computational universe with finite cutoff radii and periodic boundary conditions: Correction to computed free energies of ionic solvation , 1995 .

[48]  Douglas A. Smith.  Modeling the hydrogen bond , 1994 .

[49]  W F van Gunsteren,et al.  A structure refinement method based on molecular dynamics in four spatial dimensions. , 1993, Journal of molecular biology.

[50]  M. J. Field,et al.  The Simulation of Chemical Reactions , 1995 .

[51]  M J Elrod,et al.  Many-body effects in intermolecular forces. , 1994, Chemical reviews.

[52]  O. Steinhauser,et al.  Taming cut-off induced artifacts in molecular dynamics studies of solvated polypeptides. The reaction field method. , 1992, Journal of molecular biology.

[53]  Wilfred F. van Gunsteren,et al.  A molecular dynamics simulation study with a combined quantum mechanical and molecular mechanical potential energy function: Solvation effects on the conformational equilibrium of dimethoxyethane , 1995 .

[54]  B. Montgomery Pettitt,et al.  Effects of truncating long-range interactions in aqueous ionic solution simulations , 1988 .

[55]  M. Levitt,et al.  Molecular dynamics of native protein. I. Computer simulation of trajectories. , 1983, Journal of molecular biology.

[56]  Peter A. Kollman,et al.  AMBER, a package of computer programs for applying molecular mechanics, normal mode analysis, molecular dynamics and free energy calculations to simulate the structural and energetic properties of molecules , 1995 .

[57]  P. Kollman,et al.  Molecular Dynamics Free Energy Perturbation Calculations: Influence of Nonbonded Parameters on the Free Energy of Hydration of Charged and Neutral Species , 1994 .

[58]  P. Weiner,et al.  Computer Simulation of Biomolecular Systems , 1997 .

[59]  S. L. Mayo,et al.  DREIDING: A generic force field for molecular simulations , 1990 .

[60]  M. Levitt,et al.  Potential energy function and parameters for simulations of the molecular dynamics of proteins and nucleic acids in solution , 1995 .

[61]  Jan L. M. Dillen,et al.  An empirical force field. II. Crystalline alkanes , 1995, J. Comput. Chem..

[62]  Reaction Field Effects on the Simulated Properties of Liquid Water , 1995 .

[63]  J. Kestin,et al.  Equilibrium and transport properties of the noble gases and their mixtures at low density , 1984 .

[64]  M. Karplus,et al.  Role of Electrostatics in the Structure, Energy, and Dynamics of Biomolecules: A Model Study of N-Methylalanylacetamide , 1985 .

[65]  B. Brooks,et al.  The effects of truncating long‐range forces on protein dynamics , 1989, Proteins.

[66]  P. Kollman,et al.  Molecular dynamics free energy simulations: Influence of the truncation of long‐range nonbonded electrostatic interactions on free energy calculations of polar molecules , 1994 .

[67]  A. Warshel,et al.  Consistent Force Field Calculations. II. Crystal Structures, Sublimation Energies, Molecular and Lattice Vibrations, Molecular Conformations, and Enthalpies of Alkanes , 1970 .

[68]  S. Lifson,et al.  Consistent force field studies of intermolecular forces in hydrogen-bonded crystals. 1. Carboxylic acids, amides, and the C:O.cntdot..cntdot..cntdot.H- hydrogen bonds , 1979 .

[69]  Norman L. Allinger,et al.  Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals' potentials and crystal data for aliphatic and aromatic hydrocarbons , 1989 .

[70]  B. Montgomery Pettitt,et al.  Efficient Ewald electrostatic calculations for large systems , 1995 .

[71]  F. B. Brown,et al.  Dissociation potential for breaking a CH bond in methane , 1985 .

[72]  Bernard R. Brooks,et al.  New spherical‐cutoff methods for long‐range forces in macromolecular simulation , 1994, J. Comput. Chem..

[73]  A. Mark,et al.  Computational approaches to study protein unfolding: Hen egg white lysozyme as a case study , 1995, Proteins.

[74]  Arieh Warshel,et al.  A surface constrained all‐atom solvent model for effective simulations of polar solutions , 1989 .

[75]  W. L. Jorgensen,et al.  The OPLS [optimized potentials for liquid simulations] potential functions for proteins, energy minimizations for crystals of cyclic peptides and crambin. , 1988, Journal of the American Chemical Society.

[76]  Kjeld Rasmussen,et al.  The Consistent Force Field , 1977 .

[77]  W F van Gunsteren,et al.  Protein structure prediction force fields: Parametrization with quasi‐newtonian dynamics , 1997, Proteins.

[78]  H Liu,et al.  A combined quantum/classical molecular dynamics study of the catalytic mechanism of HIV protease. , 1996, Journal of molecular biology.

[79]  Ming-Jing Hwang,et al.  Derivation of Class II Force Fields. 2. Derivation and Characterization of a Class II Force Field, CFF93, for the Alkyl Functional Group and Alkane Molecules , 1994 .

[80]  Wilfred F. van Gunsteren,et al.  Calculating Electrostatic Interactions Using the Particle−Particle Particle−Mesh Method with Nonperiodic Long-Range Interactions , 1996 .

[81]  Kjeld Rasmussen,et al.  The Consistent Force Field. 1. Methods and Strategies for Optimization of Empirical Potential Energy Functions. , 1994 .

[82]  W. Goddard,et al.  UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations , 1992 .

[83]  Norman L. Allinger,et al.  Conformational analysis—CI , 1974 .

[84]  Angelo Vedani,et al.  YETI: An interactive molecular mechanics program for small‐molecule protein complexes , 1988 .

[85]  B. Montgomery Pettitt,et al.  Structural and energetic effects of truncating long ranged interactions in ionic and polar fluids , 1985 .

[86]  W F van Gunsteren,et al.  On the interpretation of biochemical data by molecular dynamics computer simulation. , 1992, European journal of biochemistry.

[87]  M. Levitt,et al.  Energy refinement of hen egg-white lysozyme. , 1974, Journal of molecular biology.

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

[89]  S. Harvey.  Treatment of electrostatic effects in macromolecular modeling , 1989, Proteins.

[90]  R. Christoffersen,et al.  Development of a flexible intra‐ and intermolecular empirical potential function for large molecular systems , 1981 .

[91]  A. Beckwith,et al.  New potential energy function for bond extensions , 1989 .

[92]  H. Schreiber,et al.  Molecular dynamics studies of solvated polypeptides: Why the cut-off scheme does not work , 1992 .

[93]  T. Halgren.  Maximally diagonal force constants in dependent angle-bending coordinates: Part I. Mathematical formulation , 1988 .

[94]  C. Cramer,et al.  An SCF Solvation Model for the Hydrophobic Effect and Absolute Free Energies of Aqueous Solvation , 1992, Science.

[95]  W. F. van Gunsteren,et al.  Effect of constraints on the dynamics of macromolecules , 1982 .

[96]  Wang Lu,et al.  ON THE APPROXIMATION OF SOLVENT EFFECTS ON THE CONFORMATION AND DYNAMICS OF CYCLOSPORIN A BY STOCHASTIC DYNAMICS SIMULATION TECHNIQUES , 1988 .

[97]  J. Banavar,et al.  Computer Simulation of Liquids , 1988 .

[98]  Paul R. Gerber,et al.  Peptide mechanics: A force field for peptides and proteins working with entire residues as smallest units , 1992 .

[99]  A. Rappé,et al.  van der Waals functional forms for molecular simulations , 1992 .

[100]  Alan E. Mark,et al.  Computer simulation of protein motion , 1995 .

[101]  Wilfred F. van Gunsteren,et al.  Lattice‐sum methods for calculating electrostatic interactions in molecular simulations , 1995 .

[102]  A. Mark,et al.  Avoiding singularities and numerical instabilities in free energy calculations based on molecular simulations , 1994 .

[103]  P. Kollman,et al.  An all atom force field for simulations of proteins and nucleic acids , 1986, Journal of computational chemistry.

[104]  A. Hagler,et al.  Derivation of force fields for molecular mechanics and dynamics from ab initio energy surfaces. , 1988, Proceedings of the National Academy of Sciences of the United States of America.

[105]  Alexander D. MacKerell,et al.  An all-atom empirical energy function for the simulation of nucleic acids , 1995 .

[106]  Nonadditivity of interaction in hydrated copper(1+) and copper(2+) clusters , 1990 .

[107]  Ronald M. Levy,et al.  On finite‐size effects in computer simulations using the Ewald potential , 1995 .

[108]  M Levitt,et al.  Molecular dynamics of native protein. II. Analysis and nature of motion. , 1983, Journal of molecular biology.

[109]  U. Singh,et al.  A NEW FORCE FIELD FOR MOLECULAR MECHANICAL SIMULATION OF NUCLEIC ACIDS AND PROTEINS , 1984 .

[110]  Martin Neumann,et al.  Dipole moment fluctuation formulas in computer simulations of polar systems , 1983 .

[111]  O. Steinhauser,et al.  Cutoff size does strongly influence molecular dynamics results on solvated polypeptides. , 1992, Biochemistry.

[112]  Thomas A. Halgren,et al.  Maximally diagonal force constants in dependent angle-bending coordinates. II. Implications for the design of empirical force fields , 1990 .

[113]  S. Lifson,et al.  Born–Oppenheimer energy surfaces of similar molecules: Interrelations between bond lengths, bond angles, and frequencies of normal vibrations in alkanes , 1982 .

[114]  F. Momany,et al.  Validation of the general purpose QUANTA ®3.2/CHARMm® force field , 1992 .

[115]  Jonathan W. Essex,et al.  An empirical boundary potential for water droplet simulations , 1995, J. Comput. Chem..

[116]  Arnold T. Hagler,et al.  On the functional representation of bond energy functions , 1994, J. Comput. Chem..

[117]  H. Scheraga,et al.  Energy parameters in polypeptides. 10. Improved geometrical parameters and nonbonded interactions for use in the ECEPP/3 algorithm, with application to proline-containing peptides , 1994 .

[118]  Arnold T. Hagler,et al.  New combining rules for rare gas van der waals parameters , 1993, J. Comput. Chem..

[119]  D. Beglov,et al.  Finite representation of an infinite bulk system: Solvent boundary potential for computer simulations , 1994 .

[120]  M. Karplus,et al.  CHARMM: A program for macromolecular energy, minimization, and dynamics calculations , 1983 .