Bimodality in gene expression without feedback: From Gaussian white noise to log-normal coloured noise

TL;DR

This paper explores how different types of noise, especially non-Gaussian and nonlinear, influence bimodal gene expression dynamics, challenging traditional Gaussian white noise assumptions and introducing a new nonlinear noise filtering approach.

Contribution

It introduces a novel nonlinear noise filtering methodology and demonstrates its effectiveness in analyzing noise-induced bimodal transitions in gene expression models.

Findings

Non-Gaussian and nonlinear noises significantly affect bimodal gene expression.

The new filtering approach captures transitions not explained by Gaussian noise.

System nonlinearity influences the impact of different noise types.

Abstract

Extrinsic noise-induced transitions to bimodal dynamics have been largely investigated in a variety of chemical, physical, and biological systems. In the standard approach in physical and chemical systems, the key properties that make these systems mathematically tractable are that the noise appears linearly in the dynamical equations, and it is assumed Gaussian and white. In biology, the Gaussian approximation has been successful in specific systems, but the relevant noise being usually non-Gaussian, non-white, and nonlinear poses serious limitations to its general applicability. Here we revisit the fundamental features of linear Gaussian noise, pinpoint its limitations, and review recent new approaches based on nonlinear bounded noises, which highlight novel mechanisms to account for transitions to bimodal behaviour. We do this by considering a simple but fundamental gene expression model, the repressed gene, which is characterized by linear and nonlinear dependencies on external parameters. We then review a general methodology introduced recently, so-called nonlinear noise filtering, which allows the investigation of linear, nonlinear, Gaussian and non-Gaussian noises. We also present a derivation of it, which highlights its dynamical origin. Testing the methodology on the repressed gene confirms that the emergence of noise-induced transitions appears to be strongly dependent on the type of noise adopted, and on the degree of nonlinearity present in the system.