Transition Path Times in Asymmetric Barriers

TL;DR

This study investigates how asymmetry in energy barriers affects transition path times in biomolecular conformational changes, revealing that asymmetric barriers can be well-fitted by symmetric models but yield different parameter estimates.

Contribution

It introduces a family of asymmetric potential models and analyzes their impact on TPT distributions, clarifying discrepancies in barrier height estimations.

Findings

Asymmetric barriers can be fitted by symmetric models with adjusted parameters.

Fitted barrier heights and diffusion coefficients differ from original input values.

Eigenvalue spectrum analysis explains the effects of barrier asymmetry on TPT.

Abstract

Biomolecular conformational transitions are usually modeled as barrier crossings in a free energy landscape. The transition paths connect two local free energy minima and transition path times (TPT) are the actual durations of the crossing events. The simplest model employed to analyze TPT and to fit empirical data is that of a stochastic particle crossing a parabolic barrier. Motivated by some disagreement between the value of the barrier height obtained from the TPT distributions as compared to the value obtained from kinetic and thermodynamic analyses, we investigate here TPT for barriers which deviate from the symmetric parabolic shape. We introduce a continuous set of potentials, that starting from a parabolic shape, can be made increasingly asymmetric by tuning a single parameter. The TPT distributions obtained in the asymmetric case are very well-fitted by distributions generated by parabolic barriers. The fits, however, provide values for the barrier heights and diffusion coefficients which deviate from the original input values. We show how these findings can be understood from the analysis of the eigenvalues spectrum of the Fokker-Planck equation and highlight connections with experimental results.