Role of relaxation time scale in noisy signal transduction

TL;DR

This paper analytically examines how relaxation time scales influence noise and information transmission in gene regulatory networks, revealing their critical role in cellular fluctuation management and signal fidelity.

Contribution

It provides a novel analytical framework linking relaxation time to noise and information metrics in linear and branched gene network motifs.

Findings

Fano factor increases with chain length.

Mutual information decreases as chain length increases.

Intermediate components act as noise filters.

Abstract

Intracellular fluctuations, mainly triggered by gene expression, are an inevitable phenomenon observed in living cells. It influences generation of phenotypic diversity in genetically identical cells. Such variation of cellular components is beneficial in some contexts but detrimental in others. To quantify the fluctuations in a gene product, we undertake an analytical scheme for studying few naturally abundant linear as well as branched chain network motifs. We solve the Langevin equations associated with each motif under the purview of linear noise approximation and quantify Fano factor and mutual information. Both quantifiable expressions exclusively depend on the relaxation time (decay rate constant) and steady state population of the network components. We investigate the effect of relaxation time constraints on Fano factor and mutual information to indentify a time scale domain where a network can recognize the fluctuations associated with the input signal more reliably. We also show how input population affects both quantities. We extend our calculation to long chain linear motif and show that with increasing chain length, the Fano factor value increases but the mutual information processing capability decreases. In this type of motif, the intermediate components are shown to act as a noise filter that tune up input fluctuations and maintain optimum fluctuations in the output. For branched chain motifs, both quantities vary within a large scale due to their network architecture and facilitate survival of living system in diverse environmental conditions.