A simple model for calculating the kinetics of protein folding from three-dimensional structures

Abstract

An elementary statistical mechanical model was used to calculate the folding rates for 22 proteins from their known three-dimensional structures. In this model, residues come into contact only after all of the intervening chain is in the native conformation. An additional simplifying assumption is that native structure grows from localized regions that then fuse to form the complete native molecule. The free energy function for this model contains just two contributions—conformational entropy of the backbone and the energy of the inter-residue contacts. The matrix of inter-residue interactions is obtained from the atomic coordinates of the three-dimensional structure. For the 18 proteins that exhibit two-state equilibrium and kinetic behavior, profiles of the free energy versus the number of native peptide bonds show two deep minima, corresponding to the native and denatured states. For four proteins known to exhibit intermediates in folding, the free energy profiles show additional deep minima. The calculated rates of folding the two-state proteins, obtained by solving a diffusion equation for motion on the free energy profiles, reproduce the experimentally determined values surprisingly well. The success of these calculations suggests that folding speed is largely determined by the distribution and strength of contacts in the native structure. We also calculated the effect of mutations on the folding kinetics of chymotrypsin inhibitor 2, the most intensively studied two-state protein, with some success.