Gene-gene cooperativity in small networks

TL;DR

This paper introduces a binary spin model to simplify the analysis of small, noisy gene regulatory networks, effectively capturing gene interactions and correlations.

Contribution

It develops a mapping from molecular to binary variables, enabling reduced descriptions and phase diagrams for gene interactions in stochastic networks.

Findings

Binary model accurately reproduces gene expression probabilities

Phase diagram identifies conditions for gene independence and coupling

Model applicable to larger self-regulatory gene systems

Abstract

We show how to construct a reduced description of interacting genes in noisy, small regulatory networks using coupled binary "spin" variables. Treating both the protein number and gene expression state variables stochastically and on equal footing we propose a mapping which connects the molecular level description of networks to the binary representation. We construct a phase diagram indicating when genes can be considered to be independent and when the coupling between them cannot be neglected leading to synchrony or correlations. We find that an appropriately mapped boolean description reproduces the probabilities of gene expression states of the full stochastic system very well and can be transfered to examples of self-regulatory systems with a larger number of gene copies.