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Workshop on Recent Developments in Computer Simulation Studies in Condensed Matter Physics

作者： Mitsutake, Ayori Mori, Yoshiharu Okamoto, Yuko Nagoya Univ Dept Phys Aichi 4648602 Japan Keio Univ Dept Phys Kanagawa 2238522 Japan Nagoya Univ Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Struct Biol Res Ctr Nagoya Aichi 4648602 Japan

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E-0 by adding any physical quantity V of interest as a new energy term with a coupling constant lambda. We then perform a multi-dimensional multicanonical simulation where a random walk in E-0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter lambda is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter lambda corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized. (C) 2010 Published by Elsevier B.V.

关键词： Generalized-ensemble algorithms multicanonical algorithm simulated tempering replica-exchange method parallel tempering Mont Carlo molecular dynamics

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Multi-dimensional multicanonical algorithm, simulated tempering, replica-exchange method, and all that

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Physics Procedia 2010年 4卷 89-105页

作者： Ayori Mitsutake Yoshiharu Mori Yuko Okamoto Department of Physics Keio University Yokohama Kanagawa 223-8522 Japan Department of Physics Nagoya University Nagoya Aichi 464-8602 Japan Structural Biology Research Center Nagoya University Nagoya Aichi 464-8602 Japan

We discuss multi-dimensional generalizations of multicanonical algorithm, simulated tempering, and replica-exchange method. We generalize the original potential energy function E 0 by adding any physical quantity V of interest as a new energy term with a coupling constant λ . We then perform a multi-dimensional multicanonical simulation where a random walk in E 0 and V space is realized. We can alternately perform a multi-dimensional simulated-tempering simulation where a random walk in temperature T and parameter λ is realized. The results of the multi-dimensional replica-exchange simulations can be used to determine the weight factors for these multi-dimensional multicanonical and simulated tempering simulations. Two examples of the above methods are presented for biomoleculr systems where the parameter λ corresponds to the solvation parameter and the pressure. In the former, a random walk in the conformational energy and solvation free energy is performed, and in the latter, a random walk in the potential energy and volume is realized.

关键词： Generalized-ensemble algorithms multicanonical algorithm Simulated tempering Replica-exchange method Parallel tempering Mont Carlo Molecular dynamics

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Enhanced Sampling algorithms

Enhanced Sampling Algorithms

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作者： Ayori Mitsutake Yoshiharu Mori Yuko Okamoto

In biomolecular systems (especially all-atom models) with many degrees of freedom such as proteins and nucleic acids, there exist an astronomically large number of local-minimum-energy states. Conventional simulations in the canonical ensemble are of little use, because they tend to get trapped in states of these energy local minima. Enhanced conformational sampling techniques are thus in great demand. A simulation in generalized ensemble performs a random walk in potential energy space and can overcome this difficulty. From only one simulation run, one can obtain canonical-ensemble averages of physical quantities as functions of temperature by the single-histogram and/or multiple-histogram reweighting techniques. In this article we review uses of the generalized-ensemble algorithms in biomolecular systems. Three well-known methods, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are given. We then present various extensions of these three generalized-ensemble algorithms. The effectiveness of the methods is tested with short peptide and protein systems. less

关键词： Molecular Dynamics Simulation Monte Carlo Generalized-ensemble algorithm Replica-exchange method Simulated tempering multicanonical algorithm

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Residual entropy of ordinary ice calculated from multicanonical Monte Carlo simulations

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MOLECULAR SIMULATION 2012年第11期38卷 856-860页

作者： Berg, Bernd A. Muguruma, Chizuru Okamoto, Yuko Nagoya Univ Grad Sch Sci Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Sci Struct Biol Res Ctr Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Engn Ctr Computat Sci Nagoya Aichi 4648603 Japan Chukyo Univ Dept Int Liberal Studies Toyota Aichi 4700393 Japan Florida State Univ Dept Phys Tallahassee FL 32306 USA

In this article, we calculated the residual entropy of ice I (ordinary ice) by multicanonical Monte Carlo simulations of two simple models with nearest neighbour interactions on 3D hexagonal lattices. Our estimate is found to be within 0.13% of an analytical approximation by Nagle, which is an improvement of Pauling's result from 1935. We pose it as a challenge to experimentalists to improve on the accuracy of a 1936 measurement by Giauque and Stout by about one order of magnitude, which would allow one to identify corrections to Pauling's value unambiguously. It is straightforward to transfer our methods to other crystal systems.

关键词： residual entropy ice ice rules multicanonical algorithm generalised-ensemble algorithms

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Molecular simulations in generalised ensemble

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MOLECULAR SIMULATION 2012年第14-15期38卷 1282-1296页

作者： Okamoto, Yuko Nagoya Univ Grad Sch Sci Dept Phys Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Sci Struct Biol Res Ctr Nagoya Aichi 4648602 Japan Nagoya Univ Grad Sch Engn Ctr Computat Sci Nagoya Aichi 4648603 Japan

In this article, we review the generalised-ensemble algorithms. Three well-known methods, namely multicanonical algorithm, simulated tempering and replica-exchange method, are described first. Both Monte Carlo and molecular dynamics versions of the algorithms are presented. We then present further extensions of the above three methods. Finally, we discuss the relations among multicanonical algorithm, Wang-Landau method and metadynamics.

关键词： multicanonical algorithm simulated tempering replica-exchange method Wang-Landau method metadynamics

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Generalized-ensemble algorithms for molecular dynamics simulations

Generalized-ensemble algorithms for molecular dynamics simul...

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Symposium on Progress and Future Prospects in Molecular Dynamics Simulation

作者： Itoh, Satoru G. Okumura, Hisashi Okamoto, Yuko Nagoya Univ Sch Sci Dept Phys Nagoya Aichi 4648602 Japan

In complex systems with many degrees of freedom such as biomolecular systems, conventional Monte Carlo and molecular dynamics simulations in canonical ensemble or isobaric-isothermal ensemble suffer from the multiple-minima problem, resulting in entrapment in states of energy local minima. A simulation in generalized ensemble performs a random walk in specified variables and overcomes this difficulty. In this article we review the generalized-ensemble algorithms. multicanonical algorithm is described first. In this method, a random walk in potential energy space is realized and the simulation can avoid the multiple-minima problem. We then present two new generalized-ensemble algorithms, namely multioverlap algorithm and multibaric-multithermal algorithm, which are multi-variable/multi-dimensional extensions of the multicanonical algorithm. In the former method, a random walk in overlap space is realized, and in the latter that in both potential energy space and volume space is obtained. Emphasis is laid in the description of the molecular dynamics versions of these algorithms.

关键词： molecular dynamics simulation generalized-ensemble algorithms multicanonical algorithm multioverlap algorithm multibaric-multithermal algorithm

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Generalized-ensemble algorithms for molecular dynamics simulations

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MOLECULAR SIMULATION 2007年第1-2期33卷 47-56页

作者： Itoh, Satoru G. Okumura, Hisashi Okamoto, Yuko Nagoya Univ Sch Sci Dept Phys Nagoya Aichi 4648602 Japan

关键词： molecular dynamics simulation generalized-ensemble algorithms multicanonical algorithm multioverlap algorithm multibaric-multithermal algorithm

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A generalized Wang-Landau algorithm for Monte Carlo computation

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JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION 2005年第472期100卷 1311-1327页

作者： Liang, FM Texas A&M Univ Dept Stat College Stn TX 77843 USA

Inference for a complex system with a rough energy landscape is a central topic in Monte Carlo computation. Motivated by the successes of the Wang-Landau algorithm in discrete systems, we generalize the algorithm to continuous systems. The generalized algorithm has some features that conventional Monte Carlo algorithms do not have. First, it provides a new method for Monte Carlo integration based on stochastic approximation;second, it is an excellent tool for Monte Carlo optimization. In an appropriate setting, the algorithm can lead to a random walk in the energy space, and thus it can sample relevant parts of the sample space, even in the presence of many local energy minima. The generalized algorithm can be conveniently used in many problems of Monte Carlo integration and optimization, for example, normalizing constant estimation, model selection, highest posterior density interval construction, and function optimization. Our numerical results show that the algorithm outperforms simulated annealing and parallel tempering in optimization for the system with a rough energy landscape. Some theoretical results on the convergence of the algorithm are provided.

关键词： 1/k-ensemble sampling importance sampling Markov chain Monte Carlo Monte Carlo integration Monte Carlo optimization multicanonical algorithm Wang-Landau algorithm

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multicanonical simulations step by step

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COMPUTER PHYSICS COMMUNICATIONS 2003年第3期153卷 397-406页

作者： Berg, BA Florida State Univ Dept Phys Tallahassee FL 32306 USA

The purpose of this article is to provide a starter kit for multicanonical simulations in statistical physics. Fortran code for the q-state Potts model in d = 2, 3,... dimensions can be downloaded from the Web and this paper describes simulation results, which are in all details reproducible by running prepared programs. To allow for comparison with exact results, the internal energy, the specific heat, the free energy and the entropy are calculated for the d = 2 Ising (q = 2) and the q = 10 Potts model. Analysis programs, relying on an all-log jackknife technique, which is suitable for handling sums of very large numbers, are introduced to calculate our final estimators. (C) 2003 Elsevier B.V. All rights reserved.

关键词： multicanonical algorithm Fortran code all-log jackknife technique internal energy free energy entropy

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Generalized-ensemble simulations of spin systems and protein systems

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COMPUTER PHYSICS COMMUNICATIONS 2002年第1期146卷 69-76页

作者： Nagasima, T Sugita, Y Mitsutake, A Okamoto, Y Inst Mol Sci Dept Theoret Studies Okazaki Aichi 4448585 Japan Grad Univ Adv Studies Dept Funct Mol Sci Okazaki Aichi 4448585 Japan Keio Univ Fac Sci & Technol Dept Phys Yokohama Kanagawa 2238522 Japan

In complex systems such as spin systems and protein systems, conventional simulations in the canonical ensemble will get trapped in states of energy local minima. We employ the generalized-ensemble algorithms in order to overcome this multiple-minima problem. Three well-known generalized-ensemble algorithms, namely, multicanonical algorithm, simulated tempering, and replica-exchange method, are described. We then present three new generalized-ensemble algorithms based on the combinations of the three methods. Effectiveness of the new methods are tested with a Potts model and protein systems. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： Potts model protein folding generalized-ensemble algorithm multicanonical algorithm simulated tempering replica-exchange method

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