Department of Electrical Engineering and Computer Science, University of Liège, Liège, Belgium.
PLoS One. 2012;7(3):e33110. doi: 10.1371/journal.pone.0033110. Epub 2012 Mar 15.
Bistable dynamical switches are frequently encountered in mathematical modeling of biological systems because binary decisions are at the core of many cellular processes. Bistable switches present two stable steady-states, each of them corresponding to a distinct decision. In response to a transient signal, the system can flip back and forth between these two stable steady-states, switching between both decisions. Understanding which parameters and states affect this switch between stable states may shed light on the mechanisms underlying the decision-making process. Yet, answering such a question involves analyzing the global dynamical (i.e., transient) behavior of a nonlinear, possibly high dimensional model. In this paper, we show how a local analysis at a particular equilibrium point of bistable systems is highly relevant to understand the global properties of the switching system. The local analysis is performed at the saddle point, an often disregarded equilibrium point of bistable models but which is shown to be a key ruler of the decision-making process. Results are illustrated on three previously published models of biological switches: two models of apoptosis, the programmed cell death and one model of long-term potentiation, a phenomenon underlying synaptic plasticity.
双稳态动态开关在生物系统的数学建模中经常遇到，因为二进制决策是许多细胞过程的核心。双稳态开关具有两个稳定的稳态，每个稳态对应于一个不同的决策。在响应瞬态信号时，系统可以在这两个稳定的稳态之间来回翻转，在两个决策之间切换。了解哪些参数和状态会影响这种稳定状态之间的切换，可以揭示决策过程的潜在机制。然而，回答这样的问题需要分析非线性的、可能高维模型的全局动态（即瞬态）行为。在本文中，我们展示了如何在双稳态系统的特定平衡点进行局部分析，以便于理解开关系统的全局特性。局部分析是在鞍点处进行的，鞍点是双稳态模型中经常被忽视的平衡点，但它被证明是决策过程的关键决定因素。研究结果以三个先前发表的生物开关模型为例进行了说明：两个细胞凋亡模型，程序性细胞死亡和一个长时程增强模型，这是突触可塑性的基础。
