Stability depends on positive autoregulation in Boolean gene regulatory networks.

Ricardo Pinho,Marcus W Feldman,Manuel Irimia,Victor Garcia,Marcel Salathé

doi:10.1371/journal.pcbi.1003916

Abstract

Network motifs have been identified as building blocks of regulatory networks, including gene regulatory networks (GRNs). The most basic motif, autoregulation, has been associated with bistability (when positive) and with homeostasis and robustness to noise (when negative), but its general importance in network behavior is poorly understood. Moreover, how specific autoregulatory motifs are selected during evolution and how this relates to robustness is largely unknown. Here, we used a class of GRN models, Boolean networks, to investigate the relationship between autoregulation and network stability and robustness under various conditions. We ran evolutionary simulation experiments for different models of selection, including mutation and recombination. Each generation simulated the development of a population of organisms modeled by GRNs. We found that stability and robustness positively correlate with autoregulation; in all investigated scenarios, stable networks had mostly positive autoregulation. Assuming biological networks correspond to stable networks, these results suggest that biological networks should often be dominated by positive autoregulatory loops. This seems to be the case for most studied eukaryotic transcription factor networks, including those in yeast, flies and mammals.

Highlights

Gene regulatory networks (GRNs) are believed to play a central role in organismal development and evolution [1,2,3]
Two rules relating the presence of feedback loops in gene regulatory networks (GRNs) to their dynamical properties have been proposed [13]: (i) a necessary condition for multistability is the existence of a positive circuit in the regulatory network; and (ii) a necessary condition for the existence of an attractive cycle in the dynamics is the existence of a negative circuit
Functional classes of cells can be attributed to the activation and repression of genes, which enable each cell type to support different functions within the organism. These patterns of activity have been studied by means of gene regulatory networks (GRNs)

Summary

Introduction

Gene regulatory networks (GRNs) are believed to play a central role in organismal development and evolution [1,2,3]. A direct autoregulation motif in transcriptional GRNs consists of a regulator that binds to the promoter region of its own gene, regulating its own transcription. It constitutes the simplest case of a feedback mechanism. Two thirds of E. coli’s transcriptional factors (TFs) are believed to be autoregulated [10]. Two rules relating the presence of feedback loops in GRNs to their dynamical properties have been proposed [13]: (i) a necessary condition for multistability (i.e., the existence of several stable fixed points in the dynamics) is the existence of a positive circuit in the regulatory network (the sign of a circuit being defined as the product of the signs of its edges); and (ii) a necessary condition for the existence of an attractive cycle in the dynamics is the existence of a negative circuit

Methods

Results

Discussion

Conclusion