First-Passage Time Distributions in Two-State Protein Folding Kinetics: Exploring the Native-Like States vs Overcoming the Free Energy Barrier

TL;DR

This study investigates how native-like state exploration influences two-state protein folding kinetics, revealing that first-passage time distributions are mostly exponential and that exploration time significantly impacts folding rates.

Contribution

It demonstrates that native-like state exploration duration affects folding kinetics and provides a detailed analysis of first-passage time distributions in two-state protein folding.

Findings

FPT distributions are essentially exponential for barrier crossing and native state finding.

Exploration of native-like states influences the mean folding time more than the free energy barrier height.

MFPT to reach native state increases with temperature, explaining the U-shaped temperature dependence.

Abstract

Using a beta-hairpin protein as a representative example of two-state folders, we studied how the exploration of native-like states affects the folding kinetics. It has been found that the first-passage time (FPT) distributions are essentially single-exponential not only for the times to overcome the free energy barrier that separates unfolded and native-like states but also for the times to find the native state among the native-like ones. If the protein explores native-like states for a time much longer than the time to overcome the free energy barrier, which was found to be characteristic of high temperatures, the resulting FPT distribution to reach the native state remains close to exponential but the mean FPT (MFPT) is determined not by the height of the free energy barrier but by the time to explore native-like states. The mean time to overcome the free energy barrier is found to be in reasonable agreement with the Kramers rate formula and generally far shorter than the MFPT to reach the native state. The time to find the native state among native-like ones increases with temperature, which explains the known U-shape dependence of the MFPTs on temperature.