Testing the transition state theory in stochastic dynamics of a genetic switch

TL;DR

This paper investigates the applicability of transition state theory to stochastic gene circuit dynamics, showing it works well generally but fails for states with very few proteins.

Contribution

It demonstrates that a transition state theory-like approach can estimate switching rates in stochastic gene circuits, with limitations for low-protein states.

Findings

The theory provides consistent estimates for most states.

It fails for states with extremely low protein numbers.

The method applies to non-equilibrium systems.

Abstract

Stochastic dynamics of chemical reactions in a mutually repressing two-gene circuit is numerically simulated. The circuit has a rich variety of different states when the kinetic change of DNA status is slow. The stochastic switching transition between those states are compared with the theoretical estimation of the switching rate derived from the idea similar to the transition state theory. Even though the circuit is kept far from equilibrium, the method gives a consistent explanation of the switching kinetics for a wide range of parameters. The transition state theory-like estimation, however, fails to describe transitions involving the state which has the extremely small numbers of protein molecules.