Identifying the design principles of complex regulatory networks driving cellular decision-making remains essential to decode embryonic development as well as enhance cellular reprogramming. A well-studied network motif involved in cellular decision-making is a toggle switch—a set of two opposing transcription factors A and B, each of which is a master regulator of a specific cell fate and can inhibit the activity of the other. A toggle switch can lead to two possible states—(high A, low B) and (low A, high B)—and drives the ‘either-or' choice between these two cell fates for a common progenitor cell. However, the principles of coupled toggle switches remain unclear. Here, we investigate the dynamics of three master regulators A, B and C inhibiting each other, thus forming three-coupled toggle switches to form a toggle triad. Our simulations show that this toggle triad can lead to co-existence of cells into three differentiated ‘single positive' phenotypes—(high A, low B, low C), (low A, high B, low C) and (low A, low B, high C). Moreover, the hybrid or ‘double positive' phenotypes—(high A, high B, low C), (low A, high B, high C) and (high A, low B, high C)—can coexist together with ‘single positive' phenotypes. Including self-activation loops on A, B and C can increase the frequency of ‘double positive' states. Finally, we apply our results to understand cellular decision-making in terms of differentiation of naive CD4
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T cells into Th1, Th2 and Th17 states, where hybrid Th1/Th2 and hybrid Th1/Th17 cells have been reported in addition to the Th1, Th2 and Th17 ones. Our results offer novel insights into the design principles of a multi-stable network topology and provide a framework for synthetic biology to design tristable systems.