Analysis of Two-State Folding Using Parabolic Approximation I: Hypothesis

TL;DR

This paper introduces a harmonic Gibbs energy-well model for two-state protein folding, describing denatured and native states with parabolas and linking transition state properties to ensemble distributions.

Contribution

It presents a novel parabolic approximation model for two-state folding, connecting energy landscapes to folding kinetics and stability.

Findings

Gibbs energy functions modeled as parabolas

Transition state position determined by parabola intersection

Equilibrium and rate constants linked to Gaussian distributions

Abstract

A model which treats the denatured and native conformers of spontaneously-folding fixed two-state systems as being confined to harmonic Gibbs energy-wells has been developed.Within the assumptions of this model the Gibbs energy functions of the denatured (DSE) and the native state (NSE) ensembles are described by parabolas, with the mean length of the reaction coordinate (RC) being given by the temperature-invariant denaturant m value.Consequently, the ensemble-averaged position of the transition state ensemble (TSE) along the RC, and the ensemble-averaged Gibbs energy of the TSE are determined by the intersection of the DSE and the NSE-parabolas. The equations derived enable equilibrium stability and the rate constants to be rationalized in terms of the mean and the variance of the Gaussian distribution of the solvent accessible surface area of the conformers in the DSE and the NSE. The implications of this model for protein folding are discussed.