Logic-dependent emergence of multistability, hysteresis, and biphasic dynamics in a minimal positive feedback network with an autoloop

Cellular decision-making (CDM) is a dynamic phenomenon often controlled by regulatory networks defining interactions between genes and transcription factor proteins. Traditional studies have focussed on molecular switches such as positive feedback circuits that exhibit at most bistability. However, higher-order dynamics such as tristability is also prominent in many biological processes. It is thus imperative to identify a minimal circuit that can alone explain mono, bi, and tristable dynamics. In this work, we consider a two-component positive feedback network with an autoloop and explore these regimes of stability for different degrees of multimerization and the choice of Boolean logic functions. We report that this network can exhibit numerous dynamical scenarios such as bi-and tristability, hysteresis, and biphasic kinetics, explaining the possibilities of abrupt cell state transitions and the smooth state swap without a step-like switch. Specifically, while with monomeric regulation and competitive OR logic, the circuit exhibits mono-and bistability and biphasic dynamics, with non-competitive AND and OR logics only monostability can be achieved. To obtain bistability in the latter cases, we show that the autoloop must have (at least) dimeric regulation. In pursuit of higher-order stability, we show that tristability occurs with higher degrees of multimerization and with non-competitive OR logic only. Our results, backed by rigorous analytical calculations and numerical examples, thus explain the association between multistability, multimerization, and logic in this minimal circuit. Since this circuit underlies various biological processes, including epithelial-mesenchymal transition which often drives carcinoma metastasis, these results can thus offer crucial inputs to control cell state transition by manipulating multimerization and the logic of regulation in cells.