Replica-Permutation Method with the Suwa-Todo Algorithm beyond the Replica-Exchange Method.

We propose a new method for molecular dynamics and Monte Carlo simulations, which is referred to as the replica-permutation method (RPM), to realize more efficient sampling than the replica-exchange method (REM). In RPM, not only exchanges between two replicas but also permutations among more than two replicas are performed. Furthermore, instead of the Metropolis algorithm, the Suwa-Todo algorithm is employed for replica-permutation trials to minimize its rejection ratio. We applied RPM to particles in a double-well potential energy, Met-enkephalin in a vacuum, and a C-peptide analog of ribonuclease A in explicit water. For comparison purposes, replica-exchange molecular dynamics simulations were also performed. As a result, RPM sampled not only the temperature space but also the conformational space more efficiently than REM for all systems. From our simulations of C-peptide, we obtained the α-helix structure with salt bridges between Gly2 and Arg10, which is known in experiments. Calculating its free-energy landscape, the folding pathway was revealed from an extended structure to the α-helix structure with the salt bridges. We found that the folding pathway consists of the two steps: The first step is the "salt-bridge formation step," and the second step is the "α-helix formation step."

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

[2]  N. Metropolis,et al.  Equation of State Calculations by Fast Computing Machines , 1953, Resonance.

[3]  F. Young.  Biochemistry , 1955, The Indian Medical Gazette.

[4]  M. H. Quenouille.  NOTES ON BIAS IN ESTIMATION , 1956 .

[5]  Rupert G. Miller.  The jackknife-a review , 1974 .

[6]  H. Berendsen,et al.  ALGORITHMS FOR MACROMOLECULAR DYNAMICS AND CONSTRAINT DYNAMICS , 1977 .

[7]  William G. Hoover,et al.  High-strain-rate plastic flow studied via nonequilibrium molecular dynamics , 1982 .

[8]  W. Kabsch,et al.  Dictionary of protein secondary structure: Pattern recognition of hydrogen‐bonded and geometrical features , 1983, Biopolymers.

[9]  W. L. Jorgensen,et al.  Comparison of simple potential functions for simulating liquid water , 1983 .

[10]  Denis J. Evans,et al.  Computer ‘‘experiment’’ for nonlinear thermodynamics of Couette flow , 1983 .

[11]  S. Nosé.  A unified formulation of the constant temperature molecular dynamics methods , 1984 .

[12]  S. Nosé.  A molecular dynamics method for simulations in the canonical ensemble , 1984 .

[13]  P. S. Kim,et al.  Nature of the charged-group effect on the stability of the C-peptide helix. , 1985, Proceedings of the National Academy of Sciences of the United States of America.

[14]  Hoover,et al.  Canonical dynamics: Equilibrium phase-space distributions. , 1985, Physical review. A, General physics.

[15]  Robert L. Baldwin,et al.  Tests of the helix dipole model for stabilization of α-helices , 1987, Nature.

[16]  C. Brooks.  Computer simulation of liquids , 1989 .

[17]  Alan M. Ferrenberg,et al.  Optimized Monte Carlo data analysis. , 1989, Physical Review Letters.

[18]  P E Wright,et al.  1H NMR studies of the solution conformations of an analogue of the C-peptide of ribonuclease A. , 1989, Biochemistry.

[19]  R. L. Baldwin,et al.  The Glu 2- ... Arg 10+ side-chain interaction in the C-peptide helix of ribonuclease A. , 1990, Biophysical chemistry.

[20]  B. Berg,et al.  Multicanonical algorithms for first order phase transitions , 1991 .

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

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

[23]  R A Sayle,et al.  RASMOL: biomolecular graphics for all. , 1995, Trends in biochemical sciences.

[24]  P. Kollman,et al.  A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules , 1995 .

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

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

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

[28]  J. M. Scholtz,et al.  2,3-Methanoamino acid analogs of Arg stabilize secondary structures of a 13 amino acid peptide in aqueous solution , 1998 .

[29]  U H Hansmann,et al.  Temperature dependence of distributions of conformations of a small peptide. , 1998, Journal of molecular graphics & modelling.

[30]  Alexander D. MacKerell,et al.  All-atom empirical potential for molecular modeling and dynamics studies of proteins. , 1998, The journal of physical chemistry. B.

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

[32]  Y. Sugita,et al.  Multidimensional replica-exchange method for free-energy calculations , 2000, cond-mat/0009120.

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

[34]  S. Takada,et al.  On the Hamiltonian replica exchange method for efficient sampling of biomolecular systems: Application to protein structure prediction , 2002 .

[35]  Multioverlap simulations for transitions between reference configurations. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  Yuko Okamoto,et al.  Monte Carlo simulations in generalized isobaric-isothermal ensembles. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  Yuko Okamoto,et al.  Liquid-Gas Phase Transitions Studied by Multibaric-Multithermal Monte Carlo Simulations , 2004 .

[38]  Yuko Okamoto,et al.  Multi-overlap molecular dynamics methods for biomolecular systems , 2004 .

[39]  Yuko Okamoto,et al.  Molecular dynamics simulations in the multibaric–multithermal ensemble , 2004 .

[40]  H. Okumura,et al.  Monte Carlo simulations in multibaric–multithermal ensemble , 2004 .

[41]  Bernd A. Berg.  Markov Chain Monte Carlo Simulations and Their Statistical Analysis , 2004 .

[42]  Orlando E Acevedo,et al.  Amino acid propensities revisited. , 2005, Omics : a journal of integrative biology.

[43]  Yuko Okamoto,et al.  Theoretical studies of transition states by the multioverlap molecular dynamics methods. , 2006, The Journal of chemical physics.

[44]  Yuko Okamoto,et al.  Multibaric–multithermal ensemble molecular dynamics simulations , 2006, J. Comput. Chem..

[45]  V. Hornak,et al.  Comparison of multiple Amber force fields and development of improved protein backbone parameters , 2006, Proteins.

[46]  Yuko Okamoto,et al.  A new generalized-ensemble algorithm: multicanonical–multioverlap algorithm , 2007 .

[47]  Yuko Okamoto,et al.  Explicit symplectic integrators of molecular dynamics algorithms for rigid-body molecules in the canonical, isobaric-isothermal, and related ensembles. , 2007, The Journal of chemical physics.

[48]  Effective sampling in the configurational space of a small peptide by the multicanonical-multioverlap algorithm. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Yuko Okamoto,et al.  Generalized-ensemble algorithms for molecular dynamics simulations , 2007 .

[50]  Hisashi Okumura,et al.  Partial multicanonical algorithm for molecular dynamics and Monte Carlo simulations. , 2008, The Journal of chemical physics.

[51]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[52]  Yuko Okamoto,et al.  Replica-exchange method in van der Waals radius space: overcoming steric restrictions for biomolecules. , 2009, The Journal of chemical physics.

[53]  Synge Todo,et al.  Markov chain Monte Carlo method without detailed balance. , 2010, Physical review letters.

[54]  Hisashi Okumura,et al.  Optimization of partial multicanonical molecular dynamics simulations applied to an alanine dipeptide in explicit water solvent. , 2011, Physical chemistry chemical physics : PCCP.

[55]  Hisashi Okumura,et al.  Temperature and pressure denaturation of chignolin: Folding and unfolding simulation by multibaric‐multithermal molecular dynamics method , 2012, Proteins.