Reaction coordinates for the flipping of genetic switches

TL;DR

This paper uses Forward Flux Sampling to analyze the switching dynamics of genetic toggle switches, revealing how reaction rates influence stability and pathways, with distinctions between exclusive and general switch models.

Contribution

It provides a detailed kinetic and mechanistic analysis of genetic switch flipping, highlighting the effects of reaction rates on switching pathways and stability in different models.

Findings

TF-operator binding rate influences switching pathways in the exclusive switch.

Dimerisation rate affects switching rate but not pathway in the exclusive switch.

Switching pathways in the general switch are robust to rate changes, unlike in the exclusive switch.

Abstract

We present a detailed analysis, based on the Forward Flux Sampling (FFS) simulation method, of the switching dynamics and stability of two models of genetic toggle switches, consisting of two mutually-repressing genes encoding transcription factors (TFs); in one model (the exclusive switch), they mutually exclude each other's binding, while in the other model (general switch) the two transcription factors can bind simultaneously to the shared operator region. We assess the role of two pairs of reactions that influence the stability of these switches: TF-TF homodimerisation and TF-DNA association/dissociation. We factorise the flipping rate k into the product of the probability rho(q*) of finding the system at the dividing surface (separatrix) between the two stable states, and a kinetic prefactor R. In the case of the exclusive switch, the rate of TF-operator binding affects both rho(q*) and R, while the rate of TF dimerisation affects only R. In the case of the general switch both TF-operator binding and TF dimerisation affect k, R and rho(q*). To elucidate this, we analyse the transition state ensemble (TSE). For the exclusive switch, varying the rate of TF-operator binding can drastically change the pathway of switching, while changing the rate of dimerisation changes the switching rate without altering the mechanism. The switching pathways of the general switch are highly robust to changes in the rate constants of both TF-operator and TF-TF binding, even though these rate constants do affect the flipping rate; this feature is unique for non-equilibrium systems.