Estimation of Protein Folding Rate from Monte Carlo Simulations and Entropy Capacity

Oxana      V. Galzitskaya

Abstract

The problem of protein self-organization is one of the most important problems of molecular biology nowadays. Despite the recent success in the understanding of general principles of protein folding, details of this process are yet to be elucidated. Moreover, the prediction of protein folding rates has its own practical value due to the fact that aggregation directly depends on the rate of protein folding. The time of folding has been calculated for 67 proteins with known experimental data at the point of thermodynamic equilibrium between unfolded and native states using a Monte Carlo model where each residue is considered to be either folded as in the native state or completely disordered. The times of folding for 67 proteins which reach the native state within the limit of 108 Monte Carlo steps are in a good correlation with the experimentally measured folding rate at the mid-transition point (the correlation coefficient is -0.82). Theoretical consideration of a capillarity model for the process of protein folding demonstrates that the difference in the folding rate for proteins sharing more spherical and less spherical folds is the result of differences in the conformational entropy due to a larger surface of the boundary between folded and unfolded phases in the transition state for proteins with more spherical fold. The capillarity model allows us to predict the folding rate at the same level of correlation as by Monte Carlo simulations. The calculated model entropy capacity (conformational entropy per residue divided by the average contact energy per residue) for 67 proteins correlates by about 78% with the experimentally measured folding rate at the mid-transition point.

Keywords: Two-state and multi-state kinetics, structural class, compactness, radius of cross-section, entropy capacity, Protein Folding Rate, Monte Carlo Simulations, protein self-organization, multiple regression technique, SH3 domains, cold shock proteins, fibronectin domains, conformational entropy, alpha-helical proteins, amino acid residues, native state, unfolded state, rate-limiting step of folding, Ferredoxin-like Fold, native topology, mid-transition