Isolating intrinsic noise sources in a stochastic genetic switch

TL;DR

This paper analyzes a stochastic gene circuit model to identify how different intrinsic noise sources influence state transitions, using perturbation methods to compare effects of protein and promotor state fluctuations.

Contribution

It introduces a perturbation-based approach to isolate and compare the effects of specific intrinsic noise sources in a stochastic genetic switch model.

Findings

Protein noise significantly alters the stability landscape.

Fluctuations in promotor states dominate small-time dynamics.

Protein noise impacts transition times and system stability.

Abstract

The stochastic mutual repressor model is analysed using perturbation methods. This simple model of a gene circuit consists of two genes and three promotor states. Either of the two protein products can dimerize, forming a repressor molecule that binds to the promotor of the other gene. When the repressor is bound to a promotor, the corresponding gene is not transcribed and no protein is produced. Either one of the promotors can be repressed at any given time or both can be unrepressed, leaving three possible promotor states. This model is analysed in its bistable regime in which the deterministic limit exhibits two stable fixed points and an unstable saddle, and the case of small noise is considered. On small time scales, the stochastic process fluctuates near one of the stable fixed points, and on large time scales, a metastable transition can occur, where fluctuations drive the system past the unstable saddle to the other stable fixed point. To explore how different intrinsic noise sources affect these transitions, fluctuations in protein production and degradation are eliminated, leaving fluctuations in the promotor state as the only source of noise in the system. Perturbation methods are then used to compute the stability landscape and the distribution of transition times, or first exit time density. To understand how protein noise affects the system, small magnitude fluctuations are added back into the process, and the stability landscape is compared to that of the process without protein noise. It is found that significant differences in the random process emerge in the presence of protein noise.