Simulation of Lattice Polymers with Multi-Self-Overlap Ensemble

Abstract

A novel family of dynamical Monte Carlo algorithms for lattice polymers is proposed. Our central idea is to simulate an extended ensemble in which the self-avoiding condition is systematically weakened. The degree of self-overlap is controlled in a similar manner as the multicanonical ensemble. As a consequence, the ensemble -the multi-self-overlap ensemble -contains adequate portions of self-overlapping conformations as well as higher energy ones. It is shown that the multi-self-overlap ensemble algorithm correctly reproduces the canonical averages at finite temperatures of the HP model of lattice proteins. Moreover, it is superior in performance to the standard multicanonical algorithm when applied to a complicated problem of a polymer with eight-stickers. An alternative algorithm based on the exchange Monte Carlo method is also discussed.KEYWORDS: heteropolymers, Monte Carlo, slow relaxation, self-avoidance, extended ensemble, multicanonical, exchange Monte Carlo 3327Monte Carlo simulations of lattice polymers are an important subject in various fields of scientific research, for example, statistical physics, physical chemistry and theoretical biology. Simulations of lattice heteropolymers, which consist of several different types of monomers, are particularly interesting because they are minimal models of protein folding.1, 2) Such simulations, however, often suffer from slow relaxation and metastability caused by the competition between short-ranged interactions and connectivity constraints among the monomers. For other systems with metastability, such as a spin system which exhibits a first-order phase transition, the multicanonical ensemble method is known to work well.3, 4) But for the lattice heteropolymer, the multicanonical ensemble is not the best solution. In fact, even a self-avoiding walk, which is the simplest lattice polymer, is difficult to generate, 5) although no interaction energy is assumed between monomers other than the constraint of self-avoidance.In this letter, we propose a novel approach to the dynamical Monte Carlo simulation of lattice polymers. The present approach is a variant of Monte Carlo algorithms based on extended ensembles 3,4,[6][7][8][9][10][11][12][13] and can be applied to a wide range of models including lattice heteropolymers and protein models on lattices. Our starting point is the introduction of an artificial ensemble that contains conformations with finite self-overlaps. With this relaxation of the self-avoidance constraint, the conformations with self-overlaps play the role of "bridges" between metastable states and a rapid mixing of the Markov chain is expected. In fact, Shakhnovich et al. have reported that folding becomes considerably faster than usual in the lattice protein model that allowed double and triple self-overlapping conformations. 14, 15)But it is not easy to produce an adequate amount of * E-mail: iba@ism.ac.jp * * E-mail: chikenji@hyperion.phys.sci.osaka-u.ac.jp self-avoiding conformations. Consider a dynamical simulation of a self-avoiding walk....

Multidimensional replica-exchange method for free-energy calculations

“…The expectation values were calculated from Eq. (28). We find that the average reaction coordinate, or the average end-to-end distance, grows as the temperature is raised, reflecting the unfolding of the peptide upon increased thermal fluctuations.…”

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

“…Red arrows are inter-Cα atomic vectors from 11 Lys to 17 Cys of the two molecules. Blue arrows are those from 2 Arg to that of 7 Ser for the two molecules. Two unit vectors e a1 and e a2 are parallel to one of red arrows, respectively.…”

“…Similarly, e b1 and e b2 (blue vectors in Fig. 10(a)) are unit vectors from the Cα atom of 2 Arg to that of 7 Ser for the first and second KR-CSH-ET1 molecules, respectively. Consequently, e a and e b approximately represent the respective orientations of the helix and strand in each KR-CSH-ET1 molecule.…”

“…Recently, generalized ensemble methods have been developed for sampling large-scale motions of polypeptides. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] A multicanonical Monte Carlo sampling, was introduced to study a physical system, a two-dimensional Potts model, 16 and was subsequently applied to biological systems. [17][18][19] Nakajima et al extended the multicanonical sampling to molecular dynamics (MD), which solves the equations of motion in a Cartesian coordinate space.…”

Thermodynamics of Aggregation of Two Proteins

“…For efficient sampling of the configurations, we use multi-selfoverlap-ensemble Monte Carlo (MSOE) method proposed by Chikenji et al; 10,11) in fact, this is the first application of MSOE to a multi-protein system. The paper is organized as follows: The model and the method will be described in the next section.…”