Improved Sampling for Biological Molecules Using Shadow Hybrid Monte Carlo

Shadow Hybrid Monte Carlo (SHMC) is a new method for sampling the phase space of large biological molecules. It improves sampling by allowing larger time steps and system sizes in the molecular dynamics (MD) step of Hybrid Monte Carlo (HMC). This is achieved by sampling from high order approximations to the modified Hamiltonian, which is exactly integrated by a symplectic MD integrator. SHMC requires extra storage, modest computational overhead, and a reweighting step to obtain averages from the canonical ensemble. Numerical experiments are performed on biological molecules, ranging from a small peptide with 66 atoms to a large solvated protein with 14281 atoms. Experimentally, SHMC achieves an order magnitude speedup in sampling efficiency for medium sized proteins.

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

[2]  R. Skeel,et al.  Langevin stabilization of molecular dynamics , 2001 .

[3]  Berend Smit,et al.  Understanding Molecular Simulation , 2001 .

[4]  Rafael de la Llave,et al.  Dynamics of algorithms , 2000 .

[5]  J. Andrew McCammon,et al.  Molecular dynamics of cryptophane and its complexes with tetramethylammonium and neopentane using a continuum solvent model , 1999 .

[6]  Paul B. Mackenze.  An Improved Hybrid Monte Carlo Method , 1989 .

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

[8]  J. Izaguirre.  Longer Time Steps for Molecular Dynamics , 1999 .

[9]  P. Deuflhard,et al.  A Direct Approach to Conformational Dynamics Based on Hybrid Monte Carlo , 1999 .

[10]  Heermann,et al.  Hybrid Monte Carlo method for condensed-matter systems. , 1992, Physical review. B, Condensed matter.

[11]  Paul D. Kirchhoff,et al.  Structural Fluctuations of a Cryptophane Host: A Molecular Dynamics Simulation , 1996 .

[12]  J. Pablo,et al.  Structure of binary polymer blends: Multiple time step hybrid Monte Carlo simulations and self‐consistent integral‐equation theory , 1995 .

[13]  Thierry Matthey,et al.  Framework Design, Parallelization and Force Computation in Molecular Dynamics , 2002 .

[14]  C. Schütte.  Conformational Dynamics: Modelling, Theory, Algorithm, and Application to Biomolecules , 1999 .

[15]  B. Brooks,et al.  Constant pressure molecular dynamics simulation: The Langevin piston method , 1995 .

[16]  J. M. Sanz-Serna,et al.  Numerical Hamiltonian Problems , 1994 .

[17]  Creutz.  Global Monte Carlo algorithms for many-fermion systems. , 1988, Physical review. D, Particles and fields.

[18]  Scott Hampton.  Improved Sampling of Configuration Space of Biomolecules Using Shadow Hybrid Monte Carlo , 2004 .

[19]  B. Berne,et al.  Novel methods of sampling phase space in the simulation of biological systems. , 1997, Current opinion in structural biology.

[20]  Thierry Matthey,et al.  ProtoMol, an object-oriented framework for prototyping novel algorithms for molecular dynamics , 2004, TOMS.

[21]  Ernst Hairer,et al.  Asymptotic expansions and backward analysis for numerical integrators , 2000 .

[22]  A new hybrid Monte Carlo algorithm for protein potential function test and structure refinement , 1999, Proteins.

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

[24]  H. Scheraga,et al.  On the multiple-minima problem in the conformational analysis of molecules: deformation of the potential energy hypersurface by the diffusion equation method , 1989 .

[25]  E A Merritt,et al.  Raster3D: photorealistic molecular graphics. , 1997, Methods in enzymology.

[26]  Hybrid Monte Carlo with adaptive temperature in mixed‐canonical ensemble: Efficient conformational analysis of RNA , 1998 .

[27]  Radford M. Neal.  An improved acceptance procedure for the hybrid Monte Carlo algorithm , 1992, hep-lat/9208011.

[28]  D. L. Freeman,et al.  Reducing Quasi-Ergodic Behavior in Monte Carlo Simulations by J-Walking: Applications to Atomic Clusters , 1990 .

[29]  Robert D. Skeel,et al.  Practical Construction of Modified Hamiltonians , 2001, SIAM J. Sci. Comput..

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

[31]  A. Kennedy,et al.  Hybrid Monte Carlo , 1988 .

[32]  Jesús A. Izaguirre,et al.  Targeted Mollified Impulse: A Multiscale Stochastic Integrator for Long Molecular Dynamics Simulations , 2003, Multiscale Model. Simul..

[33]  B M Pettitt,et al.  A sampling problem in molecular dynamics simulations of macromolecules. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[34]  A. Kennedy,et al.  Acceptances and autocorrelations in hybrid Monte Carlo , 1991 .

[35]  Stephen S. Lavenberg,et al.  A Perspective on the Use of Control Variables to Increase the Efficiency of Monte Carlo Simulations , 1981 .

[36]  B. Berne,et al.  Smart walking: A new method for Boltzmann sampling of protein conformations , 1997 .

[37]  R W Hockney,et al.  Computer Simulation Using Particles , 1966 .

[38]  Stephen D. Bond,et al.  The Nosé-Poincaré Method for Constant Temperature Molecular Dynamics , 1999 .

[39]  B. Pendleton,et al.  Hybrid Monte Carlo simulations theory and initial comparison with molecular dynamics , 1993 .