Transition path time distributions

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.

16 pages, 5 figures

References in corpus (4)

• Quantitative Protein Dynamics from Dominant Folding Pathways
• The mean shape of transition and first-passage paths
• Anomalous dynamics of DNA hairpin folding
• Non-Markovian dynamics of reaction coordinate in polymer folding

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• Transition Path Times in Asymmetric Barriers
• Nonreciprocality of a micromachine driven by a catalytic chemical reaction
• Sampling constrained stochastic trajectories using Brownian bridges
• Experimental measurement of mean transition path velocities of colloidal particles surmounting energy barriers
• Transition path time over a barrier of a colloidal particle in a viscoelastic bath
• Estimating the Most Probable Transition Time for Stochastic Dynamical Systems
• Controlling reaction dynamics in chemical model systems through external driving
• Cycle completion times probe interactions with environment
• Two-Dimensional Active Brownian Particles Crossing a Parabolic Barrier: Transition-Path Times, Survival Probability, and First-Passage Time
• Markov-bridge generation of transition paths and its application to cell-fate choice