Emergent properties of coupled bistable switches

Abstract

Understanding the dynamical hallmarks of network motifs is one of the fundamental aspects of systems biology. Positive feedback loops constituting one or two nodes, self-activation, toggle switch, and double activation loops, are commonly observed motifs in regulatory networks underlying cell-fate decision systems. Their individual dynamics are well-studied; they are capable of exhibiting bistability. However, studies across various biological systems suggest that such positive feedback loops are interconnected with one another, and design principles of coupled bistable motifs remain unclear. We wanted to ask what happens to bistability or multistability traits and the phenotypic space (collection of phenotypes exhibited by a system) due to the couplings. In this study, we explore a set of such interactions using discrete and continuous simulation methods. Our results suggest that couplings that do not connect the bistable switches in a way that contradicts the connections within individual bistable switches lead to a steady state space that is strictly a subset of the set of possible combinations of steady states of bistable switches. Furthermore, adding direct and indirect self-activations to these coupled networks can increase the frequency of multistability. Thus, our observations reveal specific dynamical traits exhibited by various coupled bistable motifs.

A Quantitative Evaluation of Topological Motifs and Their Coupling in Gene Circuit State Distributions

“…Third, it is still challenging to evaluate motif coupling, i.e., how one circuit motif interacts with another to produce the desired behaviors. The coupling of circuit motifs has been shown to play important roles to the overall behavior of gene circuits 21,22 . In particular, the role of circuit coupling may depend on the proportion of shared nodes between the two coupled circuit motifs 5 .…”

“…To model the dynamical behaviors of all these circuits in a high throughput way, we applied our recently developed method, random circuit perturbation (RACIPE) 24 , to simulate an ensemble of ODE models with randomly generated kinetic parameters and analyze the steady- state gene expression distribution from these models. RACIPE has been applied to elucidate the dynamics of synthetic gene circuits 10, 21, 25 , gene networks regulating stem cell differentiation 26 , cell cycle 27 , B-cell development 28 , and epithelial-mesenchymal transitions 29, 30 (EMT). These previous studies have shown that, despite having randomly sampled kinetic parameters and initial conditions, steady state solutions of models generally converge to distinct clusters of gene expression patterns representing the functional states of the circuit.…”

A quantitative evaluation of topological motifs and their coupling in gene circuit state distributions

“…The coupling of circuit motifs has been shown to play important roles in the overall behavior of gene circuits. 21 , 22 In particular, the role of circuit coupling may depend on the proportion of shared nodes between the two coupled circuit motifs. 5 Another recent study 23 developed a framework to identify over-represented connections of circuit motifs, termed hypermotifs, in existing biological, neuronal, social, linguistic, and electronic networks.…”

“…To model the dynamical behaviors of all these circuits in a high throughput way, we applied our recently developed method, random circuit perturbation (RACIPE), 25 to simulate an ensemble of ODE models with randomly generated kinetic parameters and analyze the steady-state gene expression distribution from these models. RACIPE has been applied to elucidate the dynamics of synthetic gene circuits, 10 , 21 , 26 gene networks regulating stem cell differentiation, 27 cell cycle, 28 B-cell development, 29 and epithelial-mesenchymal transitions 30 , 31 (EMTs). These previous studies have shown that despite having randomly sampled kinetic parameters and initial conditions steady state solutions of models generally converge to distinct clusters of gene expression patterns representing the functional states of the circuit.…”

Coupled Mutual Inhibition and Mutual Activation Motifs as Tools for Cell-Fate Control

“…While all three of these motifs can give rise to multistability, the presence of these motifs themselves is not sufficient for multistability. The appropriate sets of parameters that govern various interactions among these motifs are crucial for the emergence of multistability (32,7,27) . Furthermore, the noisy nature of biological systems can alter the likelihood of achieving multistability using these motifs (33,34,53) .…”