arXiv subjects

Yuko Okamoto

Publications and source records attributed to Yuko Okamoto.

At least 37 records · Page 2Linked to original sources

arXiv2009

Replica-Exchange Method in van der Waals Radius Space: Overcoming Steric Restrictions for Biomolecules

We present a new type of the Hamiltonian replica-exchange method, in which not temperatures but the van der Waals radius parameter is exchanged. By decreasing the van der Waals radii that control spatial sizes of atoms, this Hamiltonian replica-exchange method overcomes the steric restrictions and energy barriers. Furthermore, the simulation based on this method escapes from the local-minimum free-energy states and realizes effective sampling in the conformational space. We applied this method to an alanine dipeptide in aqueous solution and showed the effectiveness of the method by comparing the results with those obtained from the conventional canonical method.

cond-mat.stat-mech↗

arXiv2008

Multicanonical Algorithm, Simulated Tempering, Replica-Exchange Method, and All That

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.

cond-mat.stat-mech↗

arXiv2008

Thermodynamics of two lattice ice models in three dimensions

In a recent paper we introduced two Potts-like models in three dimensions, which share the following properties: (A) One of the ice rules is always fulfilled (in particular also at infinite temperature). (B) Both ice rules hold for groundstate configurations. This allowed for an efficient calculation of the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. Here we present the thermodynamics of these models. Despite their similarities with Potts models, no sign of a disorder-order phase transition is found.

cond-mat.stat-mech↗

arXiv2007

Generalized-Ensemble Algorithms for Protein Folding Simulations

Conventional simulations of complex systems in the canonical ensemble suffer from the quasi-ergodicity problem. A simulation in generalized ensemble overcomes this difficulty by performing a random walk in potential energy space and other parameter space. 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 the generalized-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 given. We then present further extensions of the above three methods.

cond-mat.stat-mech↗

arXiv2007

Residual Entropy of Ordinary Ice from Multicanonical Simulations

We introduce two simple models with nearest neighbor interactions on 3D hexagonal lattices. Each model allows one to calculate the residual entropy of ice I (ordinary ice) by means of multicanonical simulations. This gives the correction to the residual entropy derived by Linus Pauling in 1935. Our estimate is found to be within less than 0.1% of an analytical approximation by Nagle, which is an improvement of Pauling's result. 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.

cond-mat.stat-mech↗

arXiv2006

Explicit Symplectic Integrators of Molecular Dynamics Algorithms for Rigid-Body Molecules in the Canonical, Isothermal-Isobaric, and Related Ensembles

We propose explicit symplectic integrators of molecular dynamics (MD) algorithms for rigid-body molecules in the canonical and isothermal-isobaric ensembles. We also present a symplectic algorithm in the constant normal pressure and lateral surface area ensemble and that combined with the Parrinello-Rahman algorithm. Employing the symplectic integrators for MD algorithms, there is a conserved quantity which is close to Hamiltonian. Therefore, we can perform a MD simulation more stably than by conventional nonsymplectic algorithms. We applied this algorithm to a TIP3P pure water system at 300 K and compared the time evolution of the Hamiltonian with those by the nonsymplectic algorithms. We found that the Hamiltonian was conserved well by the symplectic algorithm even for a time step of 4 fs. This time step is longer than typical values of 0.5-2 fs which are used by the conventional nonsymplectic algorithms.

cond-mat.stat-mech↗

arXiv2006

Effective Sampling in the Configurational Space by the Multicanonical-Multioverlap Algorithm

We propose a new generalized-ensemble algorithm, which we refer to as the multicanonical-multioverlap algorithm. By utilizing a non-Boltzmann weight factor, this method realizes a random walk in the multi-dimensional, energy-overlap space and explores widely in the configurational space including specific configurations, where the overlap of a configuration with respect to a reference state is a measure for structural similarity. We apply the multicanonical-multioverlap molecular dynamics method to a penta peptide, Met-enkephalin, in vacuum as a test system. We also apply the multicanonical and multioverlap molecular dynamics methods to this system for the purpose of comparisons. We see that the multicanonical-multioverlap molecular dynamics method realizes effective sampling in the configurational space including specific configurations more than the other two methods. From the results of the multicanonical-multioverlap molecular dynamics simulation, furthermore, we obtain a new local-minimum state of the Met-enkephalin system.

cond-mat.stat-mech↗

arXiv2005

Secondary-Structure Design of Proteins by a Backbone Torsion Energy

We propose a new backbone-torsion-energy term in the force field for protein systems. This torsion-energy term is represented by a double Fourier series in two variables, the backbone dihedral angles phi and psi. It gives a natural representation of the torsion energy in the Ramachandran space in the sense that any two-dimensional energy surface periodic in both phi and psi can be expanded by the double Fourier series. We can then easily control secondary-structure-forming tendencies by modifying the torsion-energy surface. For instance, we can increase/decrease the alpha-helix-forming-tendencies by lowering/raising the torsion-energy surface in the alpha-helix region and likewise increase/decrease the beta-sheet-forming tendencies by lowering/raising the surface in the beta-sheet region in the Ramachandran space. We applied our approach to AMBER parm94 and AMBER parm96 force fields and demonstrated that our modifications of the torsion-energy terms resulted in the expected changes of secondary-structure-forming-tendencies by performing folding simulations of alpha-helical and beta-hairpin peptides.

cond-mat.stat-mech↗

arXiv2003

Prediction of transmembrane helix configurations by replica-exchange simulations

We propose a method for predicting helical membrane protein structures by computer simulations. Our method consists of two parts. In the first part, amino-acid sequences of the transmembrane helix regions are obtained from one of existing WWW servers. In the second part, we perform a replica-exchange simulation of these transmembrane helices with some constraints and identify the predicted structure as the global-minimum-energy state. We have tested the method with the dimeric transmembrane domain of glycophorin A. The structure obtained from the prediction was in close agreement with the experimental data.

cond-mat.stat-mech↗

arXiv2003

Molecular dynamics of C-peptide of ribonuclease A studied by replica-exchange Monte Carlo method and diffusion theory

Generalized-ensemble algorithm and diffusion theory have been combined in order to compute the dynamical properties monitored by nuclear magnetic resonance experiments from efficient and reliable evaluation of statistical averages. Replica-exchange Monte Carlo simulations have been performed with a C-peptide analogue of ribonuclease A, and Smoluchowski diffusion equations have been applied. A fairly good agreement between the calculated and measured $^1$H-NOESY NMR cross peaks has been obtained. The combination of these advanced and continuously improving statistical tools allows the calculation of a wide variety of dynamical properties routinely obtained by experiments.

cond-mat.stat-mech↗

arXiv2003

Optimization of protein force-field parameters with the Protein Data Bank

We propose a novel method to optimize existing force-field parameters for protein systems. The method consists of minimizing the summation of the square of the force acting on each atom in the proteins with the structures from the Protein Data Bank. We performed this optimization to the partial-charge and torsion-energy parameters of the AMBER parm96 force field, using 100 molecules from the Protein Data Bank. We then performed folding simulations of $α$-helical and $β$-hairpin peptides. The optimized force-field parameters gave structures more similar to the experimental implications than the original AMBER force field.

cond-mat.stat-mech↗

arXiv2003

Metropolis Algorithms in Generalized Ensemble

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. Two well-known generalized-ensemble algorithms, namely, multicanonical algorithm and replica-exchange method, are described. We then present four new generalized-ensemble algorithms as further extensions of the two methods. Effectiveness of the new methods are illustrated with a Potts model, Lennard-Jones fluid system, and protein system.

cond-mat.stat-mech↗

arXiv2000

Generalized-Ensemble Algorithms for Molecular Simulations of Biopolymers

In complex systems with many degrees of freedom such as peptides and proteins there exist a huge 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. 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. Three well-known methods, 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 three new generalized-ensemble algorithms which combine the merits of the above methods. The effectiveness of the methods for molecular simulations in the protein folding problem is tested with short peptide systems.

cond-mat.stat-mech↗

arXiv2000

Replica-exchange multicanonical algorithm and multicanonical replica-exchange method for simulating systems with rough energy landscape

We propose two efficient algorithms for configurational sampling of systems with rough energy landscape. The first one is a new method for the determination of the multicanonical weight factor. In this method a short replica-exchange simulation is performed and the multicanonical weight factor is obtained by the multiple-histogram reweighting techniques. The second one is a further extension of the first in which a replica-exchange multicanonical simulation is performed with a small number of replicas. These new algorithms are particularly useful for studying the protein folding problem.

cond-mat.stat-mech↗

arXiv2000

Multidimensional replica-exchange method for free-energy calculations

We have developed a new simulation algorithm for free-energy calculations. The method is a multidimensional extension of the replica-exchange method. While pairs of replicas with different temperatures are exchanged during the simulation in the original replica-exchange method, pairs of replicas with different temperatures and/or different parameters of the potential energy are exchanged in the new algorithm. This greatly enhances the sampling of the conformational space and allows accurate calculations of free energy in a wide temperature range from a single simulation run, using the weighted histogram analysis method.

cond-mat.stat-mech↗

arXiv1998

Stochastic dynamics simulations in a new generalized ensemble

We develop a formulation for molecular dynamics, Langevin, and hybrid Monte Carlo algorithms in the recently proposed generalized ensemble that is based on a physically motivated realisation of Tsallis weights. The effectiveness of the methods are tested with an energy function for a protein system. Simulations in this generalized ensemble by the three methods are performed for a penta peptide, Met-enkephalin. For each algorithm, it is shown that from only one simulation run one can not only find the global-minimum-energy conformation but also obtain probability distributions in canonical ensemble at any temperature, which allows the calculation of any thermodynamic quantity as a function of temperature.

physics.bio-ph↗

arXiv1998

Tertiary structure prediction of C-peptide of ribonuclease A by multicanonical algorithm

We have performed multicanonical Monte Carlo simulations of C-peptide of ribonuclease A. It is known by CD and NMR experiments that this peptide has high alpha-helix content in aqueous solution and that the side-chain charges of residues Glu-2$^-$ and His-12$^+$ play an important role in the stability of the alpha-helix. In order to confirm these experimental implications, we have used two analogues of the peptide with charged and neutral side chains of Glu-2 and His-12. Two dielectric functions, distance-dependent and constant, are considered to study the effects of solvent contributions. All the simulations were started from random initial conformations. Various thermodynamic quantities such as average helicity as a function of residue number and average distance between two side chains as a function of temperature are calculated. The results are found to be in accord with the implications of CD and NMR experiments. The lowest-energy conformation obtained has an alpha-helix from Ala-4 to Gln-11 in complete agreement with the corresponding structure deduced from an X-ray crystallography experiment of ribonuclease A. It is shown that the salt bridge between the side chains of Glu-2$^-$ and Arg-10$^+$, which is known to exist from both NMR and X-ray experiments, is formed only when the side chains are properly charged. Its formation is greatly enhanced when the distance-dependent dielectric function is used.

physics.chem-ph↗

arXiv1998

Characteristic Temperatures of Folding of a Small Peptide

We perform a generalized-ensemble simulation of a small peptide taking the interactions among all atoms into account. From this simulation we obtain thermodynamic quantities over a wide range of temperatures. In particular, we show that the folding of a small peptide is a multi-stage process associated with two characteristic temperatures, the collapse temperature T_θ and the folding temperature T_f. Our results give supporting evidence for the energy landscape picture and funnel concept. These ideas were previously developed in the context of studies of simplified protein models, and here for the first time checked in an all-atom Monte Carlo simulation.

physics.chem-ph↗