Emergent properties of coupled bistable switches.

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 the 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. What happens to the 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 the most frequent states in coupled networks follow the 'rules' within a motif (double activation, toggle switch) and those across the two motifs in terms of how the two motifs have been coupled. Moreover, 'hybrid' states can be observed, too, where one of the above-mentioned 'rules' can be compromised, leading to a more diverse phenotypic repertoire. Furthermore, adding direct and indirect selfactivations to these coupled networks can increase the frequency of multistability. Thus, our observations revealed specific dynamical traits exhibited by various coupled bistable motifs.