A Space-Time Multiscale Method for Molecular Dynamics Simulations of Biomolecules

A novel multiscale approach for molecular-dynamics simulations is developed. The goal of this method is to reduce the time cost of molecular-dynamics simulations without loss of accuracy in the quantities of interest. The proposed approach consists of the waveform relaxation scheme aimed at capturing the high-frequency motions and a coarse-scale solution in space and time aimed at resolving smooth features (in both space and time domains) of the system. The use of proper orthogonal decomposition (POD) modes at the coarse-grained level has been found to accelerate convergence of the waveform relaxation scheme. The accuracy and efficiency of this method are reported by applying it to a model problem of chain of fi-D-glucopyranose monomers.

[1]  Robert D. Skeel,et al.  Multiple grid methods for classical molecular dynamics , 2002, J. Comput. Chem..

[2]  R. Hockney,et al.  Shaping the force law in two-dimensional particle-mesh models , 1974 .

[3]  P. P. Ewald Die Berechnung optischer und elektrostatischer Gitterpotentiale , 1921 .

[4]  J. Edward Jackson,et al.  A User's Guide to Principal Components. , 1991 .

[5]  A. Cooper Dynamics of Proteins and Nucleic Acids , 1988 .

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

[7]  Akio Kitao,et al.  Conformational dynamics of polypeptides and proteins in the dihedral angle space and in the cartesian coordinate space: Normal mode analysis of deca‐alanine , 1991 .

[8]  B. Ravindra,et al.  COMMENTS ON “ON THE PHYSICAL INTERPRETATION OF PROPER ORTHOGONAL MODES IN VIBRATIONS” , 1999 .

[9]  J. E. Jackson A User's Guide to Principal Components , 1991 .

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

[11]  O. Nevanlinna,et al.  Convergence of dynamic iteration methods for initial value problems , 1987 .

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

[13]  Kevin J. Naidoo,et al.  Carbohydrate solution simulations: Producing a force field with experimentally consistent primary alcohol rotational frequencies and populations , 2002, J. Comput. Chem..

[14]  Earl H. Dowell,et al.  Modal reduction of mathematical models of biological molecules , 2006 .

[15]  Haim Waisman,et al.  A Space-Time Multilevel Method For Molecular Dynamics Simulations , 2006 .

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

[17]  Berend Smit,et al.  Understanding Molecular Simulations: from Algorithms to Applications , 2002 .

[18]  Tamar Schlick,et al.  Inherent speedup limitations in multiple time step/particle mesh Ewald algorithms , 2003, J. Comput. Chem..

[19]  Bernhard Steffen,et al.  A particle-particle particle-multigrid method for long-range interactions in molecular simulations , 2005, Comput. Phys. Commun..

[20]  Leslie Greengard,et al.  A fast algorithm for particle simulations , 1987 .

[21]  Andrew Lumsdaine,et al.  Waveform Iterative Techniques for Device Transient Simulation on Parallel Machines , 1993, PPSC.

[22]  G. Kerschen,et al.  PHYSICAL INTERPRETATION OF THE PROPER ORTHOGONAL MODES USING THE SINGULAR VALUE DECOMPOSITION , 2002 .

[23]  Robert E. Rudd,et al.  COARSE-GRAINED MOLECULAR DYNAMICS AND THE ATOMIC LIMIT OF FINITE ELEMENTS , 1998 .

[24]  Resve A. Saleh,et al.  Accelerating relaxation algorithms for circuit simulation using waveform-Newton and step-size refinement , 1988, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[25]  C. Sagui,et al.  Multigrid methods for classical molecular dynamics simulations of biomolecules , 2001 .

[26]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[27]  Kevin Burrage,et al.  Parallel and sequential methods for ordinary differential equations , 1995, Numerical analysis and scientific computation.