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 + 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.

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 remains 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 drive cells into three phenotypes -(high A, low B, low C) , (low A, high B, low C), and (low A, low B, high C). This network can also allow for hybrid or 'double positive' phenotypes -(high A, high B, low C), (low A, high B, high C) and (high A, low B, high C), especially upon including self-activation loops on A, B and C. Finally, we apply our results to understand the cellular decision-making in terms of differentiation of naïve CD4+ 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 multistable network topology and provides a framework for synthetic biology to design tristable systems.

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating 'master regulators' A and B, also called as toggle switch. Typically, it can allow for three stable states -(high A, low B), (low A, high B) and (medium A, medium B). A toggle triad -three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C) -can allow for six stable states: three 'single positive' and three 'double positive' ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The oddnumbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow 'circular permutation' patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.

Decoding the dynamics of cellular decision-making and cell differentiation is a central question in cell and developmental biology. A common network motif involved in many cell-fate decisions is a mutually inhibitory feedback loop between two self-activating ‘master regulators’ A and B, also called as toggle switch. Typically, it can allow for three stable states – (high A, low B), (low A, high B) and (medium A, medium B). A toggle triad – three mutually repressing regulators A, B and C, i.e. three toggle switches arranged circularly (between A and B, between B and C, and between A and C) – can allow for six stable states: three ‘single positive’ and three ‘double positive’ ones. However, the operating principles of larger toggle polygons, i.e. toggle switches arranged circularly to form a polygon, remain unclear. Here, we simulate using both discrete and continuous methods the dynamics of different sized toggle polygons. We observed a pattern in their steady state frequency depending on whether the polygon was an even or odd numbered one. The even-numbered toggle polygons result in two dominant states with consecutive components of the network expressing alternating high and low levels. The odd-numbered toggle polygons, on the other hand, enable more number of states, usually twice the number of components with the states that follow ‘circular permutation’ patterns in their composition. Incorporating self-activations preserved these trends while increasing the frequency of multistability in the corresponding network. Our results offer insights into design principles of circular arrangement of regulatory units involved in cell-fate decision making, and can offer design strategies for synthesizing genetic circuits.