Homeostasis in Gene Regulatory Networks

TL;DR

This paper investigates the principles of homeostasis in gene regulatory networks by analyzing the dynamics of mRNA and protein concentrations through a bipartite graph framework, linking network topology to homeostasis behavior.

Contribution

It introduces a novel bipartite graph approach to classify and relate homeostasis types in gene regulatory networks and their associated protein-mRNA networks.

Findings

Established a correspondence between homeostasis types of GRNs and PRNs.

Characterized homeostasis types unique to PRNs without GRN counterparts.

Provided a framework for analyzing complex gene regulatory networks.

Abstract

In this paper, we use the framework of infinitesimal homeostasis to study general design principles for the occurrence of homeostasis in gene regulatory networks. We assume that the dynamics of the genes explicitly includes both transcription and translation, keeping track of both mRNA and protein concentrations. Given a GRN we construct an associated Protein-mRNA Network (PRN), where each individual (mRNA and protein) concentration corresponds to a node and the edges are defined in such a way that the PRN becomes a bipartite directed graph. By simultaneously working with the GRN and the PRN we are able to apply our previous results about the classification of homeostasis types (i.e., topologically defined homeostasis generating mechanism) and their corresponding homeostasis patterns. Given an arbitrarily large and complex GRN $\mathcal{G}$ and its associated PRN $\mathcal{R}$, we obtain a correspondence between all the homeostasis types (and homeostasis patterns) of $\mathcal{G}$ and a subset the homeostasis types (and homeostasis patterns) of $\mathcal{R}$. Moreover, we completely characterize the homeostasis types of the PRN that do not have GRN counterparts.