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

TL;DR

This paper models two-state protein folding using a harmonic Gibbs energy well approach, revealing non-Arrhenius kinetics and the influence of solvent interactions, transition state positioning, and temperature range limitations.

Contribution

It introduces a harmonic Gibbs energy well model to analyze non-Arrhenius folding kinetics and the physical constraints of two-state systems.

Findings

Two-state systems are physically valid only within a finite temperature range.

Maximum stability occurs when denatured conformers minimize solvent exposure at the transition state.

Gibbs barriers are not solely due to enthalpy-entropy compensation.

Abstract

A model which treats the denatured and the native conformers as being confined to harmonic Gibbs energy wells has been used to analyse the non-Arrhenius behaviour of spontaneously folding fixed two-state systems. The results demonstrate that when pressure and solvent are constant: (i) a two-state system is physically defined only for a finite temperature range; (ii)irrespective of the primary sequence, the 3-dimensional structure of the native conformer, the residual structure in the denatured state, and the magnitude of the folding and unfolding rate constants, the equilibrium stability of a two-state system is a maximum when its denatured conformers bury the least amount of solvent accessible surface area (SASA) to reach the activated state; (iii) the Gibbs barriers to folding and unfolding are not always due to the incomplete compensation of the activation enthalpies and entropies; (iv) the difference in heat capacity between the reaction-states is due to both the size of the solvent-shell and the noncovalent interactions; (v) the position of the transition state ensemble along the reaction coordinate (RC) depends on the choice of the RC; and (vi) the atomic structure of the transiently populated reaction-states cannot be inferred from perturbation-induced changes in their energetics.