Enhancement of canonical sampling by virtual-state transitions.

A novel method was developed to enhance canonical sampling. A system is divided into virtually introduced sub-states, called "virtual states," which does not exist in reality. The configuration sampling is achieved by a standard canonical sampling method, the Metropolis Monte Carlo method, and confined in a virtual state for a while. In contrast, inter-virtual state motions are controlled by transition probabilities, which can be set arbitrarily. A simple recursive equation was introduced to determine the inter-virtual state transition probabilities, by which the sampling is enhanced considerably. We named this method "virtual-system coupled canonical Monte Carlo (VcMC) sampling." A simple method was proposed to reconstruct a canonical distribution function at a certain temperature from the resultant VcMC sampling data. Two systems, a one-dimensional double-well potential and a three-dimensional ligand-receptor binding/unbinding model, were examined. VcMC produced an accurate canonical distribution much more quickly than a conventional canonical Monte Carlo simulation does.

[1]  Benoît Roux,et al.  Extension to the weighted histogram analysis method: combining umbrella sampling with free energy calculations , 2001 .

[2]  Haruki Nakamura,et al.  Verifying trivial parallelization of multicanonical molecular dynamics for conformational sampling of a polypeptide in explicit water , 2009 .

[3]  H. Scheraga,et al.  Prediction of the native conformation of a polypeptide by a statistical‐mechanical procedure. I. Backbone structure of enkephalin , 1985, Biopolymers.

[4]  Berg,et al.  Multicanonical ensemble: A new approach to simulate first-order phase transitions. , 1992, Physical review letters.

[5]  Mahmoud Moradi,et al.  Adaptively Biased Molecular Dynamics: An Umbrella Sampling Method With a Time-Dependent Potential , 2009 .

[6]  J. Straub,et al.  Statistical-temperature Monte Carlo and molecular dynamics algorithms. , 2006, Physical review letters.

[7]  A. Kidera,et al.  Enhanced conformational sampling in Monte Carlo simulations of proteins: application to a constrained peptide. , 1995, Proceedings of the National Academy of Sciences of the United States of America.

[8]  Hidetoshi Kono,et al.  Adaptive lambda square dynamics simulation: An efficient conformational sampling method for biomolecules , 2014, J. Comput. Chem..

[9]  Akira R Kinjo,et al.  Wang-Landau molecular dynamics technique to search for low-energy conformational space of proteins. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Johannes Kästner,et al.  An algorithm to find minimum free-energy paths using umbrella integration. , 2012, The Journal of chemical physics.

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

[12]  George Chikenji,et al.  Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble , 1998 .

[13]  Haruki Nakamura,et al.  A virtual-system coupled multicanonical molecular dynamics simulation: principles and applications to free-energy landscape of protein-protein interaction with an all-atom model in explicit solvent. , 2013, The Journal of chemical physics.

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

[15]  Christian Bartels,et al.  Multidimensional adaptive umbrella sampling: Applications to main chain and side chain peptide conformations , 1997 .

[16]  A. Laio,et al.  Escaping free-energy minima , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[17]  A Mitsutake,et al.  Generalized-ensemble algorithms for molecular simulations of biopolymers. , 2000, Biopolymers.

[18]  Multicanonical molecular dynamics algorithm employing an adaptive force-biased iteration scheme. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  A. Kidera,et al.  Multicanonical Ensemble Generated by Molecular Dynamics Simulation for Enhanced Conformational Sampling of Peptides , 1997 .

[20]  M. Mezei.  Adaptive umbrella sampling: Self-consistent determination of the non-Boltzmann bias , 1987 .

[21]  R. Swendsen,et al.  THE weighted histogram analysis method for free‐energy calculations on biomolecules. I. The method , 1992 .

[22]  G. Torrie,et al.  Monte Carlo free energy estimates using non-Boltzmann sampling: Application to the sub-critical Lennard-Jones fluid , 1974 .

[23]  Haruki Nakamura,et al.  Virtual‐system‐coupled adaptive umbrella sampling to compute free‐energy landscape for flexible molecular docking , 2015, J. Comput. Chem..

[24]  A. Laio,et al.  Predicting crystal structures: the Parrinello-Rahman method revisited. , 2002, Physical review letters.

[25]  Haruki Nakamura,et al.  Theory for trivial trajectory parallelization of multicanonical molecular dynamics and application to a polypeptide in water , 2011, J. Comput. Chem..

[26]  Johannes Kästner.  Umbrella integration with higher-order correction terms. , 2012, The Journal of chemical physics.

[27]  R. Hooft,et al.  An adaptive umbrella sampling procedure in conformational analysis using molecular dynamics and its application to glycol , 1992 .

[28]  D. Landau,et al.  Determining the density of states for classical statistical models: a random walk algorithm to produce a flat histogram. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[29]  Haruki Nakamura,et al.  Flexible binding simulation by a novel and improved version of virtual-system coupled adaptive umbrella sampling , 2016 .

[30]  Yilin Meng,et al.  Self-Learning Adaptive Umbrella Sampling Method for the Determination of Free Energy Landscapes in Multiple Dimensions. , 2013, Journal of chemical theory and computation.

[31]  Shoji Takada,et al.  Folding energy landscape and network dynamics of small globular proteins , 2009, Proceedings of the National Academy of Sciences.

[32]  Yuko Okamoto,et al.  Prediction of peptide conformation by multicanonical algorithm: New approach to the multiple‐minima problem , 1993, J. Comput. Chem..

[33]  Haruki Nakamura,et al.  Enhanced conformational sampling to visualize a free-energy landscape of protein complex formation , 2016, The Biochemical journal.

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

[35]  Y. Okamoto,et al.  Molecular dynamics, Langevin, and hybrid Monte Carlo simulations in multicanonical ensemble , 1996, physics/9710018.

[36]  D. Landau,et al.  Efficient, multiple-range random walk algorithm to calculate the density of states. , 2000, Physical review letters.

[37]  Haruki Nakamura,et al.  A free-energy landscape for coupled folding and binding of an intrinsically disordered protein in explicit solvent from detailed all-atom computations. , 2011, Journal of the American Chemical Society.

[38]  Haruki Nakamura,et al.  Enhanced and effective conformational sampling of protein molecular systems for their free energy landscapes , 2012, Biophysical Reviews.

[39]  Benoît Roux,et al.  Calculation of Free Energy Landscape in Multi-Dimensions with Hamiltonian-Exchange Umbrella Sampling on Petascale Supercomputer. , 2012, Journal of chemical theory and computation.

[40]  Eric F Darve,et al.  Calculating free energies using average force , 2001 .

[41]  Lee,et al.  New Monte Carlo algorithm: Entropic sampling. , 1993, Physical review letters.