Transition path time distributions

TL;DR

This paper derives the full transition path time distribution for a particle crossing a parabolic barrier in the underdamped regime, highlighting the influence of inertia on short-time dynamics relevant to biomolecular folding experiments.

Contribution

It provides the first analytical derivation of transition path time distribution including inertial effects in the underdamped regime, extending previous overdamped models.

Findings

Inertia affects short-time transition path dynamics.

Derived explicit transition path time distribution for underdamped systems.

Compared underdamped and overdamped regimes highlighting key differences.

Abstract

Biomolecular folding, at least in simple systems, can be described as a two state transition in a free energy landscape with two deep wells separated by a high barrier. Transition paths are the short part of the trajectories that cross the barrier. Average transition path times and, recently, their full probability distribution have been measured for several biomolecular systems, e.g. in the folding of nucleic acids or proteins. Motivated by these experiments, we have calculated the full transition path time distribution for a single stochastic particle crossing a parabolic barrier, focusing on the underdamped regime. Our analysis thus includes inertial terms, which were neglected in previous studies. These terms influence the short time scale dynamics of a stochastic system, and can be of experimental relevance in view of the short duration of transition paths. We derive the full transition path time distribution in the underdamped case and discuss the similarities and differences with the high friction (overdamped) limit.