Unbiased sampling of globular lattice proteins in three dimensions

TL;DR

This paper introduces an efficient Monte Carlo algorithm for unbiased sampling of Hamiltonian walks on a cubic lattice, modeling globular proteins, and explores their interactions and boundary effects.

Contribution

The paper presents a novel Monte Carlo method that efficiently and unbiasedly samples Hamiltonian walks, applicable to modeling globular proteins in three dimensions.

Findings

Algorithm is ergodic with dynamical exponent z=0

Studied interactions between polymer endpoints

Analyzed boundary effects on large polymers

Abstract

We present a Monte Carlo method that allows efficient and unbiased sampling of Hamiltonian walks on a cubic lattice. Such walks are self-avoiding and visit each lattice site exactly once. They are often used as simple models of globular proteins, upon adding suitable local interactions. Our algorithm can easily be equipped with such interactions, but we study here mainly the flexible homopolymer case where each conformation is generated with uniform probability. We argue that the algorithm is ergodic and has dynamical exponent z=0. We then use it to study polymers of size up to 64^3 = 262144 monomers. Results are presented for the effective interaction between end points, and the interaction with the boundaries of the system.