  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.
