Numerical computation of effective thermal equilibrium in Stochastically Switching Langevin Systems

TL;DR

This paper develops a numerical method to compute the effective thermal equilibrium in stochastically switching Langevin systems, enabling analysis of stability and transitions in biological models with switching forces.

Contribution

It introduces a quasipotential framework for switching Langevin systems and modifies existing algorithms to address numerical challenges, extending energy landscape analysis.

Findings

Validated quasipotential calculations against Monte Carlo transition times.

Identified and addressed numerical challenges in computing transition paths.

Demonstrated the method on an idealized system with consistent results.

Abstract

Stochastically switching force terms appear frequently in models of biological systems under the action of active agents such as proteins. The interaction of switching force and Brownian motion can create an "effective thermal equilibrium" even though the system does not obey a potential function. In order to extend the field of energy landscape analysis to understand stability and transitions in switching systems, we derive the quasipotential that defines this effective equilibrium for a general overdamped Langevin system with a force switching according to a continuous-time Markov chain process. Combined with the string method for computing most-probable transition paths, we apply our method to an idealized system and show the appearance of previously unreported numerical challenges. We present modifications to the algorithms to overcome these challenges, and show validity by demonstrating agreement between our computed quasipotential barrier and asymptotic Monte Carlo transition times in the system.