Bistable biological systems:: A characterization through local compact input-to-state stability
Bistable biological systems:: A characterization through local compact input-to-state stability
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DOI：
10.1109/tac.2007.911328
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发表时间：
2008-01-01
影响因子：
6.8
通讯作者：
Allgoewer, Frank
中科院分区：
文献类型：
--
作者：
Chaves, Madalena;Eissing, Thomas;Allgoewer, Frank
许多生物系统有能力以稳定的方式以两种不同的模式运作。系统可以根据特定的外部输入从一种稳定模式切换到另一种稳定模式。在数学上，这些双稳态系统通常用表现出（至少）两种不同稳定状态的模型来描述。另一方面，为了捕捉生物可变性，似乎更自然的是将每个稳定的操作模式与状态空间中适当的不变量集联系起来，而不是单个固定点。本文提出了一个一般的公式，它允许动力学相互作用形式的自由，并且适合于建立给定系统存在一个或多个不相交的正不变量集的条件。利用紧集的输入到状态稳定性的局部概念研究了每个集合的稳定性。在这个框架中分析了两个众所周知的双稳定性系统：lac操纵子和细胞凋亡网络。对于第一个例子，还考虑了设计驱动系统在模式之间切换的输入的问题。
Many biological systems have the capacity to operate in two distinct modes, in a stable manner. Topically, the system can switch from one stable mode to the other in response to a specific external input. Mathematically, these bistable systems are usually described by models that exhibit (at least) two distinct stable steady states. On the other hand, to capture biological variability, it seems more natural to associate to each stable mode of operation an appropriate invariant set in the state space rather than a single fixed point. A general formulation is proposed in this paper, which allows freedom in the form of kinetic interactions, and is suitable for establishing conditions on the existence of one or more disjoint forward-invariant sets for the given system. Stability with respect to each set is studied in terms of a local notion of input-to-state stability with respect to compact sets. Two well known systems that exhibit bistability are analyzed in this framework: the lac operon and an apoptosis network. For the first example, the question of designing an input that drives the system to switch between modes is also considered.