Communication: Transition-path velocity as an experimental measure of barrier crossing dynamics

Abstract

Experimental observation of transition paths—short events when the system of interest crosses the free energy barrier separating reactants from products—provides an opportunity to probe the dynamics of barrier crossing. Yet limitations in the experimental time resolution usually result in observing trajectories that are smoothed out, recross the transition state fewer times, and exhibit apparent velocities that are much lower than the instantaneous ones. Here we show that it is possible to define (and measure) an effective transition-path velocity which preserves exact information about barrier crossing dynamics in the following sense: the exact transition rate can be written in a form resembling that given by transition-state theory, with the mean thermal velocity replaced by the transition-path velocity. In addition, the transition-path velocity (i) ensures the exact local value of the unidirectional reactive flux at equilibrium and (ii) leads to the exact mean transition-path time required for the system to cross the barrier region separating reactants from products. We discuss the coordinate dependence of the transition path velocity and derive analytical expressions for it in the case of diffusive dynamics. These results can be used to discriminate among models of barrier crossing dynamics in single-molecule force spectroscopy studies.

Transition Path Dynamics of a Dielectric Particle in a Bistable Optical Trap

“…5(f)], which characterizes the dynamics of barrier crossing in terms of the time derivative of the average shape. Consistent with the model of diffusive crossing of a parabolic barrier, these profiles are monotonic functions of the coordinate with a minimum at the barrier top [35,38,39].…”

“…(f) The transition-path velocity as defined in Ref. [39] [Eq. (5)] (black symbols) compared with the theoretical prediction [red line, Eq.…”

Frictional Effects on RNA Folding: Speed Limit and Kramers Turnover

“…Transmission Coefficients: The ratio κ = kF kTST shown in Figure 4 can be as small as ≈ 10 −3 , in the high viscosity region. Recently, based on transition path velocity as a measure of recrossing dynamics [61], the values of κ have been measured in single molecule pulling experiments [62] for several DNA hairpins. By fixing the mechanical force at the transition midpoint, where the probability of being folded and unfolded are equal, the folding trajectories were used to estimate that κ ≈ 10 −5 [62].…”

Single-file diffusion in a bi-stable potential: Signatures of memory in the barrier-crossing of a tagged-particle

“…From a theoretical point of view, the most detailed and precise results were obtained in the context of relaxation phenomena [20][21][22][23][24][25][26] and first passage time statistics [27][28][29][30][31][32][33][34] in Markovian (i.e., memoryless) systems. However, physical observables typically correspond to lower-dimensional projections, and the observed dynamics is Markovian only under quite restrictive conditions on the nature of the projection.…”