Protein Folding as a Physical Stochastic Process

TL;DR

This paper models protein folding as a stochastic process using a conditioned self-avoiding walk approach, incorporating physical interactions and simulated via Monte Carlo methods to explore folding pathways and structural properties.

Contribution

It introduces CSAW, a novel model combining SAW and physical interactions, with a mathematical basis in Langevin equations, for simulating protein folding.

Findings

Demonstrates folding pathways and elastic properties

Shows helix formation and collective modes

Validates model flexibility through examples

Abstract

We model protein folding as a physical stochastic process as follows. The unfolded protein chain is treated as a random coil described by SAW (self-avoiding walk). Folding is induced by hydrophobic forces and other interactions, such as hydrogen bonding, which can be taken into account by imposing conditions on SAW. The resulting model is termed CSAW (conditioned self-avoiding walk. Conceptually, the mathematical basis is a generalized Langevin equation. In practice, the model is implemented on a computer by combining SAW and Monte Carlo. To illustrate the flexibility and capabilities of the model, we consider a number of examples, including folding pathways, elastic properties, helix formation, and collective modes.