Multistability is a key property of dynamical systems modeling cellular regulatory networks implicated in cell fate decisions, where, different stable steady states usually represent distinct cell phenotypes. Monotone network motifs are highly represented in these regulatory networks. In this paper, we leverage the properties of monotone dynamical systems to provide theoretical results that guide the selection of inputs that trigger a transition, i.e., reprogram the network, to a desired stable steady state. We first show that monotone dynamical systems with bounded trajectories admit a minimum and a maximum stable steady state. Then, we provide input choices that are guaranteed to reprogram the system to these extreme steady states. For intermediate states, we provide an input space that is guaranteed to contain an input that reprograms the system to the desired state. We then provide implementation guidelines for finite-time procedures that search this space for such an input, along with rules to prune parts of the space during search. We demonstrate these results on simulations of two recurrent regulatory network motifs: self-activation within mutual antagonism and self-activation within mutual cooperation. Our results depend uniquely on the structure of the network and are independent of specific parameter values.

中文翻译：

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重编程多稳态单调系统并应用于细胞命运控制

多重稳定性是动态系统建模涉及细胞命运决定的细胞调节网络的关键特性，其中，不同的稳定稳态通常代表不同的细胞表型。单调网络基序在这些监管网络中具有很高的代表性。在本文中，我们利用单调动力系统的特性来提供理论结果，指导选择触发转换的输入，即重新编程网络，以达到所需的稳定稳定状态。我们首先证明具有有界轨迹的单调动力系统允许最小和最大稳定状态。然后，我们提供保证将系统重新编程到这些极端稳定状态的输入选择。对于中间状态，我们提供了一个输入空间，保证包含将系统重新编程到所需状态的输入。然后，我们提供了有限时间过程的实现指南，这些过程在这个空间中搜索这样的输入，以及在搜索过程中修剪部分空间的规则。我们在两个反复出现的调节网络基序的模拟中证明了这些结果：相互对抗中的自我激活和相互合作中的自我激活。我们的结果唯一地取决于网络的结构，并且与特定的参数值无关。相互对抗中的自我激活和相互合作中的自我激活。我们的结果唯一地取决于网络的结构，并且与特定的参数值无关。相互对抗中的自我激活和相互合作中的自我激活。我们的结果唯一地取决于网络的结构，并且与特定的参数值无关。