Elastic Energy and Phase Structure in a Continuous Spin Ising Chain with Applications to the Protein Folding Problem

TL;DR

This paper uses Monte Carlo simulations of a continuous spin Ising chain to explore phase transitions relevant to protein folding, identifying distinct phases and comparing model predictions with elastic energy formulas.

Contribution

It introduces a numerical analysis of a continuous spin Ising model for proteins, revealing phase behavior and transitions relevant to folding mechanisms.

Findings

Identifies collapsed, random walk, and self-avoiding phases depending on temperature.

Confirms a phase transition between collapsed and random walk phases.

Shows the model's predictions align with phenomenological elastic energy formulas.

Abstract

We present a numerical Monte Carlo analysis of a continuos spin Ising chain that can describe the statistical proterties of folded proteins. We find that depending on the value of the Metropolis temperature, the model displays the three known nontrivial phases of polymers: At low temperatures the model is in a collapsed phase, at medium temperatures it is in a random walk phase, and at high temperatures it enters the self-avoiding random walk phase. By investigating the temperature dependence of the specific energy we confirm that the transition between the collapsed phase and the random walk phase is a phase transition, while the random walk phase and self-avoiding random walk phase are separated from each other by a cross-over transition. We also compare the predictions of the model to a phenomenological elastic energy formula, proposed by Huang and Lei to describe folded proteins.