Quantifying extrinsic noise in gene expression using the maximum entropy framework

TL;DR

This paper introduces a maximum entropy approach to distinguish intrinsic and extrinsic noise in gene expression, providing a method to analyze how extrinsic factors influence gene product variability using experimental data.

Contribution

The paper develops a novel maximum entropy framework to quantify extrinsic noise in gene expression solely from expression profiles, advancing understanding of gene expression variability.

Findings

Extrinsic factors significantly influence gene expression distribution.

The framework accurately models mRNA distribution in E. coli.

Predictions made by the model align with some existing experimental data.

Abstract

We present a maximum entropy framework to separate intrinsic and extrinsic contributions to noisy gene expression solely from the profile of expression. We express the experimentally accessible probability distribution of the copy number of the gene product (mRNA or protein) by accounting for possible variations in extrinsic factors. The distribution of extrinsic factors is estimated using the maximum entropy principle. Our results show that extrinsic factors qualitatively and quantitatively affect the probability distribution of the gene product. We work out, in detail, the transcription of mRNA from a constitutively expressed promoter in {\it E. coli}. We suggest that the variation in extrinsic factors may account for the observed {\it wider than Poisson} distribution of mRNA copy numbers. We successfully test our framework on a numerical simulation of a simple gene expression scheme that accounts for the variation in extrinsic factors. We also make falsifiable predictions, some of which are tested on previous experiments in {\it E. coli} while others need verification. Application of the current framework to more complex situations is also discussed.