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, including 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 as well as the average transition path times and discuss the similarities and differences with the high friction limit.

Protein folding transition path times from single molecule FRET

“…ref [87–91]. For the slower transition path times found for nucleic acids, advances in single molecule force spectroscopy now permit resolution of the duration of a single barrier crossing, making it possible to obtain a complete distribution of transition path times [92–97]. This is more difficult for single molecule FRET experiments of proteins, where currently only the very longest individual transition path times can be observed (HS Chung and WA Eaton, unpublished results) because of bleaching of the fluorophores at the high illumination intensities that must be employed.…”

Non-Markovian barrier crossing with two-time-scale memory is dominated by the faster memory component

“…2 (a), i.e. for τ m /τ D 1 and τ Γ /τ D 1, the barrier crossing is diffusive, meaning that the particle fluctuates in a potential well for a long time until a single barrier-crossing event occurs with a transition path time that is much shorter than the mean first-passage time [45,46]. In contrast, if the friction is low or if the memory time is long, i.e.…”

Effect of Memory and Active Forces on Transition Path Time Distributions

“…The G(t) in the inertial case is more complex and is given in Ref. 18 For short times G(t) ≈ √ 2x 0 /σ(t), which diverges as a consequence of the the initial condition x(0) = −x 0 , implying σ(t) → 0. This leads to a TPT distribution vanishing with an essential singularity as t → 0.…”

“…We can however get an approximation for βE sufficiently large. In that limit the integrals in (18) are determined by the large t-limit of G(t). The average TPT is then given by (for details, see Appendix )…”