Distribution of essential interactions in model gene regulatory networks under mutation-selection balance

TL;DR

This paper models gene regulatory networks under mutation-selection balance, showing how selection shapes sparse in-degree, broad out-degree distributions, and the evolvability of network structures.

Contribution

It introduces a simple model demonstrating how selection influences degree distributions and essential interactions in gene regulatory networks.

Findings

Selection leads to minimal in-degree in networks.

Mutations cause broad out-degree distributions.

Networks remain evolvable under mutation-selection balance.

Abstract

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. They also tend to have broad distributions for the out-degree. What mechanisms might be responsible for these degree distributions? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. There, we show that selection for a target expression pattern leads to the emergence of minimum connectivities compatible with the selective constraint. As a consequence, these gene networks have low in-degree, and "functionality" is parsimonious, i.e. is concentrated on a sparse number of interactions as measured for instance by their essentiality. Furthermore, we find that mutations of the transcription factors drive the networks to have broad out-degrees. Finally, these classes of models are evolvable, i.e. significantly different genotypes can emerge gradually under mutation-selection balance.