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.

中文翻译：

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由三个相互抑制的主调节器网络实现的细胞分化的多重稳定性

确定驱动细胞决策的复杂调控网络的设计原则对于解码胚胎发育以及增强细胞重编程仍然至关重要。涉及细胞决策的一个经过充分研究的网络基序是拨动开关——一组两个相反的转录因子 A 和 B，每个都是特定细胞命运的主要调节因子，可以抑制另一个的活动。拨动开关可以导致两种可能的状态——（高 A，低 B）和（低 A，高 B）——并驱动共同祖细胞在这两种细胞命运之间的“非此即彼”选择。然而，耦合拨动开关的原理仍不清楚。在这里，我们研究了三个主调节器 A、B 和 C 相互抑制的动态，从而形成三耦合拨动开关以形成拨动三元组。我们的模拟表明，这种切换三联体可以导致细胞共存为三种分化的“单一阳性”表型——（高 A、低 B、低 C）、（低 A、高 B、低 C）和（低 A，低 B，高 C）。此外，混合型或“双阳性”表型——（高 A、高 B、低 C）、（低 A、高 B、高 C）和（高 A、低 B、高 C）——可以与“单阳性”共存。阳性”表型。在 A、B 和 C 上包括自激活循环可以增加“双正”状态的频率。最后，我们应用我们的结果来了解细胞在将初始 CD4+ T 细胞分化为 Th1、Th2 和 Th17 状态方面的决策，其中除了 Th1、Th2 之外，还报道了混合 Th1/Th2 和混合 Th1/Th17 细胞和 Th17 的。