The dynamics of simple gene-network motifs subject to extrinsic fluctuations

TL;DR

This paper presents an analytical framework to quantify how extrinsic environmental fluctuations influence gene-network motifs, enhancing understanding of cellular variability beyond intrinsic noise effects.

Contribution

The authors develop a generic analytical method to model bounded extrinsic noise as an auxiliary species, applicable to various gene-expression motifs and not limited by noise magnitude.

Findings

Extrinsic noise significantly impacts gene expression variability.

The formalism quantifies effects of noise magnitude, correlation time, and distribution.

Results aid in interpreting single-cell gene-expression data.

Abstract

Cellular processes do not follow deterministic rules; even in identical environments genetically identical cells can make random choices leading to different phenotypes. This randomness originates from fluctuations present in the biomolecular interaction networks. Most previous work has been focused on the intrinsic noise (IN) of these networks. Yet, especially for high-copy-number biomolecules, extrinsic or environmental noise (EN) has been experimentally shown to dominate the variation. Here, we develop an analytical formalism that allows for calculation of the effect of EN on gene-expression motifs. We introduce a method for modeling bounded EN as an auxiliary species in the master equation. The method is fully generic and is not limited to systems with small EN magnitudes. We focus our study on motifs that can be viewed as the building blocks of genetic switches: a nonregulated gene, a self-inhibiting gene, and a self-promoting gene. The role of the EN properties (magnitude, correlation time, and distribution) on the statistics of interest are systematically investigated, and the effect of fluctuations in different reaction rates is compared. Due to its analytical nature, our formalism can be used to quantify the effect of EN on the dynamics of biochemical networks and can also be used to improve the interpretation of data from single-cell gene-expression experiments.