Stability and Structural Properties of Gene Regulation Networks with Coregulation Rules

TL;DR

This paper introduces a formal framework for modeling gene coregulation in gene regulatory networks using Random Boolean Networks, analyzing how coregulation influences network stability and properties.

Contribution

It develops specific models for transcription factor networks with modular and hierarchical structures, and provides a mean-field analysis of their stability.

Findings

Autoregulated multi-input modules (MIM) enhance stability.

Hierarchical gene complexes increase network robustness.

Steady-state distributions factorize as Bayesian networks.

Abstract

Coregulation of the expression of groups of genes has been extensively demonstrated empirically in bacterial and eukaryotic systems. Such coregulation can arise through the use of shared regulatory motifs, which allow the coordinated expression of modules (and module groups) of functionally related genes across the genome. Coregulation can also arise through the physical association of multi-gene complexes through chromosomal looping, which are then transcribed together. We present a general formalism for modeling coregulation rules in the framework of Random Boolean Networks (RBN), and develop specific models for transcription factor networks with modular structure (including module groups, and multi-input modules (MIM) with autoregulation) and multi-gene complexes (including hierarchical differentiation between multi-gene complex members). We develop a mean-field approach to analyse the stability of large networks incorporating coregulation, and show that autoregulated MIM and hierarchical gene-complex models can achieve greater stability than networks without coregulation whose rules have matching activation frequency. We provide further analysis of the stability of small networks of both kinds through simulations. We also characterize several general properties of the transients and attractors in the hierarchical coregulation model, and show using simulations that the steady-state distribution factorizes hierarchically as a Bayesian network in a Markov Jump Process analogue of the RBN model.