Generic properties of random gene regulatory networks

Abstract

Modeling gene regulatory networks (GRNs) is an important topic in systems biology. Although there has been much work focusing on various specific systems, the generic behavior of GRNs with continuous variables is still elusive. In particular, it is not clear typically how attractors partition among the three types of orbits: steady state, periodic and chaotic, and how the dynamical properties change with network’s topological characteristics. In this work, we first investigated these questions in random GRNs with different network sizes, connectivity, fraction of inhibitory links and transcription regulation rules. Then we searched for the core motifs that govern the dynamic behavior of large GRNs. We show that the stability of a random GRN is typically governed by a few embedding motifs of small sizes, and therefore can in general be understood in the context of these short motifs. Our results provide insights for the study and design of genetic networks.

Interrogating the Topological Robustness of Gene Regulatory Circuits

“…3A) and we observed that about 20% of models allow two coexisting stable steady states (bi-stability), while the remainder allow only one steady state (mono-stability). The observation that only a small fraction of TS models work as a bi-stable system is consistent with a previous study [39].…”

“…From the in silico generated data, we apply statistical analysis to identify the most probable features within all of the models, a process which can uncover the most robust functions of the core circuit. It is worth-noting that RACIPE is unique in the way it utilizes perturbation and the integration of statistical tools, compared to the traditional parameter sensitivity analysis [34][35][36][37][38] and the previous studies on random circuit topology [39,40].…”

Nonlinear delay differential equations and their application to modeling biological network motifs

“…Epilepsy has likewise been modeled as a chaotic disorder [101]. Much mathematical modeling has been done on gene networks that can give rise to chaos in both non-delayed [98,102,103] and delayed [82,104,105] In fact, none of the motifs analyzed so far can ever produce chaotic dynamics. This is because cyclic network topology (no more than one loop) and monotonic regulation guarantee that a system of delay equations will not have any chaotic solutions [42].…”

Uncovering the mechanisms of Caenorhabditis elegans ageing from global quantification of the underlying landscape

“…A total of 11 equations are used to describe the ageing network dynamics. We assumed that the regulatory interactions among ageing genes can be quantitatively modelled by the activations and repressions described by the sigmoid-shaped Hill function [29]. Variables x i and x j , respectively, represent the gene expression levels and the corresponding concentrations of gene production that activate or inhibit the expression of gene k. Parameter w k represents the relative strength of every regulation of gene k, which determines the maximum value of the corresponding Hill function.…”