Classical molecular dynamics in a nutshell.

This chapter provides an overview of the various techniques that are commonly used in classical molecular dynamics simulations. It describes suitable algorithms for the integration of Newton's equation of motion over many time steps for systems containing a large number of particles, different choices of boundary conditions as well as available force fields for biological systems, that is, the mathematical description of the interactions of atoms and molecules with each other. It also illustrates algorithms used to simulate systems at constant temperature and/or pressure and discusses their advantages and disadvantages. It presents a few methods to save CPU time and a summary of popular software for biomolecular molecular dynamics simulations.

[1]  N. Kampen,et al.  Stochastic processes in physics and chemistry , 1981 .

[2]  T. Schlick,et al.  Special stability advantages of position-Verlet over velocity-Verlet in multiple-time step integration , 2001 .

[3]  Mark E. Tuckerman,et al.  Reversible multiple time scale molecular dynamics , 1992 .

[4]  J. Krumhansl,et al.  Superposition Assumption. II. High Density Fluid Argon , 1972 .

[5]  M. Klein,et al.  Nosé-Hoover chains : the canonical ensemble via continuous dynamics , 1992 .

[6]  S. Harvey,et al.  The flying ice cube: Velocity rescaling in molecular dynamics leads to violation of energy equipartition , 1998, J. Comput. Chem..

[7]  Berend Smit,et al.  Understanding molecular simulation: from algorithms to applications , 1996 .

[8]  M. Parrinello,et al.  Polymorphic transitions in single crystals: A new molecular dynamics method , 1981 .

[9]  K. Kremer,et al.  Dissipative particle dynamics: a useful thermostat for equilibrium and nonequilibrium molecular dynamics simulations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[11]  H. C. Andersen Rattle: A “velocity” version of the shake algorithm for molecular dynamics calculations , 1983 .

[12]  G. Ciccotti,et al.  Non-Hamiltonian molecular dynamics: Generalizing Hamiltonian phase space principles to non-Hamiltonian systems , 2001 .

[13]  B. Berne,et al.  Efficient molecular dynamics and hybrid Monte Carlo algorithms for path integrals , 1993 .

[14]  William D. Mattson,et al.  Near-neighbor calculations using a modified cell-linked list method , 1999 .

[15]  X. Daura,et al.  Parametrization of aliphatic CHn united atoms of GROMOS96 force field , 1998 .

[16]  Markus S. Miettinen Computational modeling of cationic lipid bilayers in saline solutions , 2010 .

[17]  D. van der Spoel,et al.  GROMACS: A message-passing parallel molecular dynamics implementation , 1995 .

[18]  Marcus Mueller,et al.  Biological and synthetic membranes: What can be learned from a coarse-grained description? , 2006 .

[19]  T. Schneider,et al.  Molecular-dynamics study of a three-dimensional one-component model for distortive phase transitions , 1978 .

[20]  R. Friesner,et al.  Evaluation and Reparametrization of the OPLS-AA Force Field for Proteins via Comparison with Accurate Quantum Chemical Calculations on Peptides† , 2001 .

[21]  G. Grest,et al.  Dynamics of entangled linear polymer melts: A molecular‐dynamics simulation , 1990 .

[22]  Steve Plimpton,et al.  Fast parallel algorithms for short-range molecular dynamics , 1993 .

[23]  Richard H. Miller,et al.  A horror story about integration methods , 1991 .

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

[25]  Yuefan Deng,et al.  Error and timing analysis of multiple time-step integration methods for molecular dynamics , 2007, Comput. Phys. Commun..

[26]  F. Lasagni Canonical Runge-Kutta methods , 1988 .

[27]  J. Marsden,et al.  Lie-Poisson Hamilton-Jacobi theory and Lie-Poisson integrators , 1988 .

[28]  J. Tersoff,et al.  New empirical approach for the structure and energy of covalent systems. , 1988, Physical review. B, Condensed matter.

[29]  Klaus Schulten,et al.  Accelerating Molecular Modeling Applications with GPU Computing , 2009 .

[30]  S. Jackson,et al.  How do small single-domain proteins fold? , 1998, Folding & design.

[31]  Wojciech Rozmus,et al.  A symplectic integration algorithm for separable Hamiltonian functions , 1990 .

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

[33]  Laxmikant V. Kalé,et al.  Scalable molecular dynamics with NAMD , 2005, J. Comput. Chem..

[34]  Gerrit Groenhof,et al.  GROMACS: Fast, flexible, and free , 2005, J. Comput. Chem..

[35]  L. Verlet Computer "Experiments" on Classical Fluids. I. Thermodynamical Properties of Lennard-Jones Molecules , 1967 .

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

[37]  I. Vattulainen,et al.  How would you integrate the equations of motion in dissipative particle dynamics simulations , 2003 .

[38]  H. Berendsen,et al.  Molecular dynamics with coupling to an external bath , 1984 .

[39]  M. Mandell On the properties of a periodic fluid , 1976 .

[40]  H. Trotter On the product of semi-groups of operators , 1959 .

[41]  W. C. Swope,et al.  A computer simulation method for the calculation of equilibrium constants for the formation of physi , 1981 .

[42]  S. Nosé,et al.  Constant pressure molecular dynamics for molecular systems , 1983 .

[43]  G. R. Luckhurst,et al.  Computer simulation studies of anisotropic systems: VIII. The Lebwohl-Lasher model of nematogens revisited , 1982 .

[44]  Gary P. Morriss,et al.  Statistical Mechanics of Nonequilibrium Liquids , 2008 .

[45]  H. C. Andersen Molecular dynamics simulations at constant pressure and/or temperature , 1980 .

[46]  G. Ciccotti,et al.  Molecular Dynamics of Complex Systems: Non-Hamiltonian, Constrained, Quantum-Classical , 2004 .

[47]  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 .

[48]  R. Impey,et al.  On the calculation of the orientational correlation parameter g 2 , 1981 .

[49]  András Baranyai,et al.  New algorithm for constrained molecular-dynamics simulation of liquid benzene and naphthalene , 1990 .

[50]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[51]  Weber,et al.  Computer simulation of local order in condensed phases of silicon. , 1985, Physical review. B, Condensed matter.

[52]  Hans-Jörg Limbach,et al.  ESPResSo - an extensible simulation package for research on soft matter systems , 2006, Comput. Phys. Commun..

[53]  Klaus Schulten,et al.  Multilevel summation of electrostatic potentials using graphics processing units , 2009, Parallel Comput..

[54]  R. Hockney,et al.  Quiet high resolution computer models of a plasma , 1974 .

[55]  M. Tuckerman,et al.  On the classical statistical mechanics of non-Hamiltonian systems , 1999 .

[56]  S. Edwards,et al.  The computer study of transport processes under extreme conditions , 1972 .

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

[58]  Denis J. Evans,et al.  Constrained molecular dynamics: Simulations of liquid alkanes with a new algorithm , 1986 .

[59]  P. Kollman,et al.  Settle: An analytical version of the SHAKE and RATTLE algorithm for rigid water models , 1992 .

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

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

[62]  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.

[63]  G. Ciccotti,et al.  Numerical Integration of the Cartesian Equations of Motion of a System with Constraints: Molecular Dynamics of n-Alkanes , 1977 .

[64]  G. Strang On the Construction and Comparison of Difference Schemes , 1968 .

[65]  S. Nosé,et al.  An extension of the canonical ensemble molecular dynamics method , 1986 .

[66]  G. Vignoles,et al.  Molecular dynamics evidences of the full graphitization of a nanodiamond annealed at 1500 K , 2008 .

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

[68]  D. C. Rapaport,et al.  The Art of Molecular Dynamics Simulation , 1997 .

[69]  Creutz,et al.  Higher-order hybrid Monte Carlo algorithms. , 1989, Physical review letters.

[70]  S. Nosé A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[71]  Fiona Reid,et al.  On the performance of molecular dynamics applications on current high-end systems , 2005, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

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

[73]  A. Leach Molecular Modelling: Principles and Applications , 1996 .

[74]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

[75]  T. Schlick,et al.  Overcoming stability limitations in biomolecular dynamics. I. Combining force splitting via extrapolation with Langevin dynamics in LN , 1998 .

[76]  Berk Hess,et al.  GROMACS 3.0: a package for molecular simulation and trajectory analysis , 2001 .

[77]  Joshua A. Anderson,et al.  General purpose molecular dynamics simulations fully implemented on graphics processing units , 2008, J. Comput. Phys..

[78]  O. G. Mouritsen,et al.  Fluctuation-Induced First-Order Phase Transition in an Anisotropic Planar Model of N 2 on Graphite , 1982 .

[79]  Priya Vashishta,et al.  Structural Transitions in Superionic Conductors , 1983 .

[80]  Wilfred F. van Gunsteren,et al.  An improved GROMOS96 force field for aliphatic hydrocarbons in the condensed phase , 2001, J. Comput. Chem..

[81]  Collapses and explosions in self-gravitating systems. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[82]  M. Parrinello,et al.  Canonical sampling through velocity rescaling. , 2007, The Journal of chemical physics.

[83]  Holger Gohlke,et al.  The Amber biomolecular simulation programs , 2005, J. Comput. Chem..

[84]  M. Tuckerman,et al.  A Liouville-operator derived measure-preserving integrator for molecular dynamics simulations in the isothermal–isobaric ensemble , 2006 .

[85]  C. Lowe,et al.  An alternative approach to dissipative particle dynamics , 1999 .

[86]  Philippe H. Hünenberger,et al.  A fast pairlist‐construction algorithm for molecular simulations under periodic boundary conditions , 2004, J. Comput. Chem..

[87]  P. Morse Diatomic Molecules According to the Wave Mechanics. II. Vibrational Levels , 1929 .

[88]  Pedro Gonnet,et al.  A simple algorithm to accelerate the computation of non‐bonded interactions in cell‐based molecular dynamics simulations , 2007, J. Comput. Chem..

[89]  D. Adams,et al.  Computer simulation of ionic systems: The distorting effects of the boundary conditions , 1979 .

[90]  A. Arnold,et al.  Harvesting graphics power for MD simulations , 2007, 0709.3225.

[91]  M. Tuckerman,et al.  Understanding Modern Molecular Dynamics: Techniques and Applications , 2000 .