Replica exchange with nonequilibrium switches: enhancing equilibrium sampling by increasing replica overlap.

We describe a replica exchange strategy where trial swap configurations are generated by nonequilibrium switching simulations. By devoting simulation time to the switching simulations, one can systematically increase an effective overlap between replicas, which leads to an increased exchange acceptance rate and less correlated equilibrium samples. In this paper, we derive our method for a general class of stochastic dynamics, and discuss various strategies for enhancing replica overlap through novel dynamical schemes and prudent choices of switching protocols. We then demonstrate our method on a model system of alanine dipeptide in implicit solvent, characterizing decreases in data correlations and gains in sampling efficiency.

[1]  Christophe Chipot,et al.  Good practices in free-energy calculations. , 2010, The journal of physical chemistry. B.

[2]  Wang,et al.  Replica Monte Carlo simulation of spin glasses. , 1986, Physical review letters.

[3]  J. Schofield,et al.  Extended state-space Monte Carlo methods. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[4]  Charles H. Bennett,et al.  Efficient estimation of free energy differences from Monte Carlo data , 1976 .

[5]  C. Jarzynski,et al.  Escorted free energy simulations. , 2011, The Journal of chemical physics.

[6]  Michael W Deem,et al.  Parallel tempering: theory, applications, and new perspectives. , 2005, Physical chemistry chemical physics : PCCP.

[7]  C. Jarzynski Equilibrium free-energy differences from nonequilibrium measurements: A master-equation approach , 1997, cond-mat/9707325.

[8]  G. Crooks Nonequilibrium Measurements of Free Energy Differences for Microscopically Reversible Markovian Systems , 1998 .

[9]  W. C. Still,et al.  Semianalytical treatment of solvation for molecular mechanics and dynamics , 1990 .

[10]  G. Crooks Entropy production fluctuation theorem and the nonequilibrium work relation for free energy differences. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[11]  Radford M. Neal Sampling from multimodal distributions using tempered transitions , 1996, Stat. Comput..

[12]  C. Jarzynski Targeted free energy perturbation. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[13]  David A. Kofke,et al.  ARTICLES On the acceptance probability of replica-exchange Monte Carlo trials , 2002 .

[14]  W. C. Still,et al.  The GB/SA Continuum Model for Solvation. A Fast Analytical Method for the Calculation of Approximate Born Radii , 1997 .

[15]  Berend Smit,et al.  Accelerating Monte Carlo Sampling , 2002 .

[16]  Vijay S. Pande,et al.  Accelerating molecular dynamic simulation on graphics processing units , 2009, J. Comput. Chem..

[17]  D. Zuckerman,et al.  Single-ensemble nonequilibrium path-sampling estimates of free energy differences. , 2004, The Journal of chemical physics.

[18]  H. Stern Molecular simulation with variable protonation states at constant pH. , 2007, The Journal of chemical physics.

[19]  Ronald M. Levy,et al.  Long-time conformational transitions of alanine dipeptide in aqueous solution: Continuous and discrete-state kinetic models , 2004 .

[20]  U. Seifert,et al.  Optimal finite-time processes in stochastic thermodynamics. , 2007, Physical review letters.

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

[22]  Andrew J Ballard,et al.  Replica exchange with nonequilibrium switches , 2009, Proceedings of the National Academy of Sciences.

[23]  David E Shaw,et al.  Improving Sampling by Exchanging Hamiltonians with Efficiently Configured Nonequilibrium Simulations. , 2012, Journal of chemical theory and computation.

[24]  Mark A. Miller,et al.  Efficient free energy calculations by variationally optimized metric scaling: Concepts and applications to the volume dependence of cluster free energies and to solid–solid phase transitions , 2000 .

[25]  Jerome Nilmeier,et al.  Monte Carlo Sampling with Hierarchical Move Sets: POSH Monte Carlo. , 2009, Journal of chemical theory and computation.

[26]  Christoph Dellago,et al.  Optimum protocol for fast-switching free-energy calculations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[27]  M. Athènes Computation of a chemical potential using a residence weight algorithm. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[28]  H. G. Petersen,et al.  Error estimates on averages of correlated data , 1989 .

[29]  C. Jarzynski,et al.  Escorted free energy simulations: improving convergence by reducing dissipation. , 2008, Physical review letters.

[30]  C. Dellago,et al.  Equilibrium free energies from fast-switching trajectories with large time steps. , 2005, The Journal of chemical physics.

[31]  K. Hukushima,et al.  Exchange Monte Carlo Method and Application to Spin Glass Simulations , 1995, cond-mat/9512035.

[32]  Scott Brown,et al.  Cool walking: A new Markov chain Monte Carlo sampling method , 2003, J. Comput. Chem..

[33]  Y. Sugita,et al.  Replica-exchange molecular dynamics method for protein folding , 1999 .