Sparse essential interactions in model networks of gene regulation

TL;DR

This paper presents a simple model explaining why gene regulatory networks tend to be sparse, showing that functional constraints naturally lead to low in-degree and essential interactions, with implications for network robustness.

Contribution

The study introduces a minimal model demonstrating how functional constraints induce sparsity and essential interactions in gene regulatory networks.

Findings

Sparse networks emerge from functional constraints.

Mutations have heterogeneous effects due to network sparsity.

Model aligns with observed low in-degree in real gene networks.

Abstract

Gene regulatory networks typically have low in-degrees, whereby any given gene is regulated by few of the genes in the network. What mechanisms might be responsible for these low in-degrees? Starting with an accepted framework of the binding of transcription factors to DNA, we consider a simple model of gene regulatory dynamics. In this model, we show that the constraint of having a given function leads to the emergence of minimum connectivities compatible with function. We exhibit mathematically this behavior within a limit of our model and show that it also arises in the full model. As a consequence, functionality in these gene networks is parsimonious, i.e., is concentrated on a sparse number of interactions as measured for instance by their essentiality. Our model thus provides a simple mechanism for the emergence of sparse regulatory networks, and leads to very heterogeneous effects of mutations.