Shah Rushina, Del Vecchio Domitilla
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, USA.
IEEE Trans Netw Sci Eng. 2020 Oct-Dec;7(4):2940-2951. doi: 10.1109/tnse.2020.3008135. Epub 2020 Jul 9.
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.
多稳定性是动态系统的一个关键属性，该动态系统用于对涉及细胞命运决定的细胞调节网络进行建模，在这种情况下，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调节网络中高度富集。在本文中，我们利用单调动态系统的性质来提供理论结果，以指导输入的选择，这些输入能够触发向期望的稳定稳态的转变，即对网络进行重编程。我们首先表明，具有有界轨迹的单调动态系统存在一个最小和一个最大稳定稳态。然后，我们提供了能够保证将系统重编程到这些极端稳态的输入选择。对于中间状态，我们提供了一个输入空间，该空间保证包含一个能将系统重编程到期望状态的输入。接着，我们为在该空间中搜索此类输入的有限时间过程提供了实现指南，以及在搜索过程中修剪部分空间的规则。我们在两个循环调节网络基序的模拟中展示了这些结果：相互拮抗中的自激活和相互合作中的自激活。我们的结果仅取决于网络的结构，而与特定的参数值无关。
