Analysis of Two-State Folding Using Parabolic Approximation IV: Non-Arrhenius Kinetics of FBP28 WW Part-II

TL;DR

This paper presents a harmonic Gibbs energy well model to explain the non-Arrhenius kinetics of two-state protein folding, highlighting the thermodynamic conditions for rate maxima and minima.

Contribution

It introduces a parabolic approximation model that rationalizes non-Arrhenius folding kinetics and elucidates the thermodynamic compensation mechanisms involved.

Findings

Folding rate peaks when heat release balances desolvation heat absorption.

Unfolding rate is minimized when hydration heat offsets backbone and sidechain interactions.

Activation entropy is zero at optimal folding and unfolding conditions.

Abstract

A model which treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells has been used to rationalize the physical basis for the non-Arrhenius behaviour of spontaneously-folding fixed two-state systems. It is shown that at constant pressure and solvent conditions: (i) the rate constant for folding will be a maximum when the heat released upon formation of net molecular interactions is exactly compensated by the heat absorbed to desolvate net polar and non-polar solvent accessible surface area (SASA), as the denatured conformers driven by thermal noise bury their SASA and diffuse on the Gibbs energy surface to reach the activated state; (ii) the rate constant for unfolding will be a minimum when the heat absorbed by the native conformers to break various net backbone and sidechain interactions is exactly compensated by the heat of hydration released due to the net increase in SASA, as the native conformers unravel to reach the activated state; (iii) the activation entropy for folding will be zero, and the Gibbs barrier to folding will be a minimum, when the decrease in the backbone and the sidechain mobility is exactly compensated by the increase in entropy due to solvent-release, as the denatured conformers bury their SASA to reach the activated state; and (iv) the activation entropy for unfolding will be zero, and the Gibbs barrier to unfolding will be a maximum when the increase in the backbone and sidechain mobility is exactly compensated by the negentropy of solvent capture on the protein surface, as the native conformers unravel to reach the activated state.