How input fluctuations reshape the dynamics of a biological switching system

TL;DR

This paper investigates how stochastic fluctuations in input signals influence the switching behavior of a biological system, revealing that noise can suppress transition rates especially under large, slow fluctuations.

Contribution

It introduces an analytically tractable model using a mean-reverting diffusion process to study input noise effects on biological switches, extending previous work.

Findings

Input noise suppresses transition rates in the biological switch.

Large amplitude and slow reversion of input fluctuations enhance suppression.

The model provides analytical insights into stochastic regulation of biochemical switches.

Abstract

An important task in quantitative biology is to understand the role of stochasticity in biochemical regulation. Here, as an extension of our recent work [Phys. Rev. Lett. 107, 148101 (2011)], we study how input fluctuations affect the stochastic dynamics of a simple biological switch. In our model, the on transition rate of the switch is directly regulated by a noisy input signal, which is described as a nonnegative mean-reverting diffusion process. This continuous process can be a good approximation of the discrete birth-death process and is much more analytically tractable. Within this new setup, we apply the Feynman-Kac theorem to investigate the statistical features of the output switching dynamics. Consistent with our previous findings, the input noise is found to effectively suppress the input-dependent transitions. We show analytically that this effect becomes significant when the input signal fluctuates greatly in amplitude and reverts slowly to its mean.