The Principle of Stationary Action in Biophysics: Stability in Protein Folding

TL;DR

This paper applies the principle of stationary action to biophysics, specifically protein folding, providing a theoretical framework that explains stability, the energy funnel, and the uniqueness of folded states through stability theorems and critical points.

Contribution

It introduces a novel application of the action principle and stability theorems to understand protein folding dynamics and stability, linking physical principles to biological processes.

Findings

Explains the smooth energy funnel as a consequence of critical points in folding dynamics.

Provides a theoretical basis for why proteins fold reliably to unique states.

Shows how perturbation insensitivity arises from stability near critical points.

Abstract

Processes that proceed reliably from a variety of initial conditions to a unique final form, regardless of moderately changing conditions, are of obvious importance in biophysics. Protein folding is a case in point. We show that the action principle can be applied directly to study the stability of biological processes. The action principle in classical physics starts with the first variation of the action and leads immediately to the equations of motion. The second variation of the action leads in a natural way to powerful theorems that provide quantitative treatment of stability and focusing and also explain how some very complex processes can behave as though some seemingly important forces drop out. We first apply these ideas to the non-equilibrium states involved in two-state folding. We treat torsional waves and use the action principle to talk about critical points in the dynamics. For some proteins the theory resembles TST. We reach several quantitative and qualitative conclusions. Besides giving an explanation of why TST often works in folding, we find that the apparent smoothness of the energy funnel is a natural consequence of the putative critical points in the dynamics. These ideas also explain why biological proteins fold to unique states and random polymers do not. The insensitivity to perturbations which follows from the presence of critical points explains how folding to a unique shape occurs in the presence of dilute denaturing agents in spite of the fact that those agents disrupt the folded structure of the native state. This paper contributes to the theoretical armamentarium by directing attention to the logical progression from first physical principles to the stability theorems related to catastrophe theory as applied to folding. This can potentially have the same success in biophysics as it has enjoyed in optics.