On the Diffusion Time Evolution of Folding Chains in the Heteropolymer Model

TL;DR

This paper mathematically models the time evolution of protein folding chains in a heteropolymer model, revealing a power-law relationship and how randomness affects the folding dynamics.

Contribution

It introduces a mathematical description of folding chain evolution and analyzes the impact of coupling constant randomness on the power-law exponent.

Findings

Folding amino acid chains follow a power law D ~ t^ν.

The exponent ν decreases from approximately 0.666 to 0.5 with increased randomness.

The model links the degree of randomness to the folding dynamics.

Abstract

In this paper, we mathematically describe the time evolution of protein folding features via Iori et al.'s heteropolymer model. More specifically, we identify that the folding amino acid chain evolve according to a power law $D \sim t^{\nu}$. The power $\nu$ decreases from $0.\overline{66}$ to $0.5$ when the randomness of the coupling constants in the Lennard-Jones potential increases.