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Global Analysis of Dynamical Decision-Making Models through Local Computation around the Hidden Saddle

机译：通过隐藏鞍周围的局部计算对动态决策模型进行全局分析

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摘要

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.
机译：由于二进制决策是许多细胞过程的核心，因此在生物系统的数学建模中经常会遇到双稳态动态切换。双稳态开关呈现两个稳定的稳态，每个稳态对应于一个不同的决策。响应于瞬态信号，系统可以在这两个稳定稳态之间来回翻转，从而在两个决策之间进行切换。了解哪些参数和状态会影响稳定状态之间的此切换，可能有助于阐明决策过程的基础机制。然而，回答这样的问题涉及分析非线性的，可能是高维模型的整体动力学（即，瞬态）行为。在本文中，我们显示了在双稳态系统的特定平衡点进行局部分析与理解开关系统的全局特性如何高度相关。局部分析是在鞍点进行的，鞍点是双稳态模型经常被忽略的平衡点，但事实证明它是决策过程的关键规则。结果在先前发表的三种生物开关模型中得到了说明：两种细胞凋亡模型，程序性细胞死亡和一种长期增强模型（一种突触可塑性的潜在现象）。

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