Emergent Bistability : Effects of Additive and Multiplicative Noise

TL;DR

This paper investigates how additive and multiplicative noise influence emergent bistability in gene expression, using stochastic formalisms to analyze steady states and transition times, with implications for natural and synthetic biological systems.

Contribution

It introduces a detailed stochastic analysis of emergent bistability, highlighting the effects of noise on system dynamics and steady state distributions, which was not previously explored.

Findings

Bimodal distributions are a mixture of lognormal and Gaussian forms.

Noise strength affects the variances and weights of the distributions.

Results are relevant for understanding gene regulation in natural and synthetic contexts.

Abstract

Positive feedback and cooperativity in the regulation of gene expression are generally considered to be necessary for obtaining bistable expression states. Recently, a novel mechanism of bistability termed emergent bistability has been proposed which involves only positive feedback and no cooperativity in the regulation. An additional positive feedback loop is effectively generated due to the inhibition of cellular growth by the synthesized proteins. The mechanism, demonstrated for a synthetic circuit, may be prevalent in natural systems also as some recent experimental results appear to suggest. In this paper, we study the effects of additive and multiplicative noise on the dynamics governing emergent bistability. The calculational scheme employed is based on the Langevin and Fokker-Planck formalisms. The steady state probability distributions of protein levels and the mean first passage times are computed for different noise strengths and system parameters. In the region of bistability, the bimodal probability distribution is shown to be a linear combination of a lognormal and a Gaussian distribution. The variances of the individual distributions and the relative weights of the distributions are further calculated for varying noise strengths and system parameters. The experimental relevance of the model results is also pointed out.