Eigenvalues of the Homogeneous Finite Linear One Step Master Equation: Applications to Downhill Folding

TL;DR

This paper analyzes the eigenvalues of a finite linear master equation model to understand the kinetics of downhill protein folding, demonstrating a transition from single to multi-exponential behavior with increasing bias.

Contribution

It provides a mathematical proof linking the absence of energy barriers to kinetic behavior changes in protein folding models.

Findings

Transition from single to multi-exponential kinetics at sufficient bias

Eigenvalue analysis confirms theoretical predictions

Implications for interpreting downhill folding experiments

Abstract

Motivated by claims about the nature of the observed timescales in protein systems said to fold downhill, we have studied the finite, linear master equation which is a model of the downhill process. By solving for the system eigenvalues, we prove the often stated claim that in situations where there is no free energy barrier, a transition between single and multi-exponential kinetics occurs at sufficient bias (towards the native state). Consequences for protein folding, especially the downhill folding scenario, are briefly discussed.