First-Passage Time Distribution and Non-Markovian Diffusion Dynamics of Protein Folding

TL;DR

This paper analyzes the non-Markovian diffusion dynamics of protein folding, deriving the first-passage time distribution and revealing temperature-dependent behaviors, including a V-shaped MFPT and a transition from Poisson to Lévy-like distributions.

Contribution

It provides a detailed analytical study of the first-passage time distribution in protein folding with non-Markovian dynamics, highlighting the temperature effects and energy landscape influence.

Findings

MFPT has a V-shaped dependence on temperature.

Higher energy gap shortens the MFPT.

At high temperature, FPT distribution is Poisson-like; at low temperature, Lévy-like.

Abstract

We study the kinetics of protein folding via statistical energy landscape theory. We concentrate on the local-connectivity case, where the configurational changes can only occur among neighboring states, with the folding progress described in terms of an order parameter given by the fraction of native conformations. The non-Markovian diffusion dynamics is analyzed in detail and an expression for the mean first-passage time (MFPT) from non-native unfolded states to native folded state is obtained. It was found that the MFPT has a V-shaped dependence on the temperature. We also find that the MFPT is shortened as one increases the gap between the energy of the native and average non-native folded states relative to the fluctuations of the energy landscape. The second- and higher-order moments are studied to infer the first-passage time (FPT) distribution. At high temperature, the distribution becomes close to a Poisson distribution, while at low temperatures the distribution becomes a L\'evy-like distribution with power-law tails, indicating a non-self-averaging intermittent behavior of folding dynamics. We note the likely relevance of this result to single-molecule dynamics experiments, where a power law (L\'evy) distribution of the relaxation time of the underlined protein energy landscape is observed.