A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems
A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems
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DOI：
10.1007/s11538-014-0023-y
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发表时间：
2014-10-01
影响因子：
3.5
通讯作者：
Giordano, Giulia
中科院分区：
文献类型：
--
作者：
Blanchini, Franco;Franco, Elisa;Giordano, Giulia
分子系统是不确定的：反应参数的可变性和未知相互作用的存在会削弱固体数学模型的预测能力。然而，在没有详细了解其具体参数的情况下，通常可以得出关于模型可接受的动态行为的有力结论。例如，在具有符号确定雅可比矩阵的系统中，与著名的托马斯猜想相关的基于循环的准则已被大量用于表征振荡和多平稳动态结果。我们建立在丰富的文献集中在识别潜在的振荡和多平稳行为使用无参数准则。我们提出了一个分类符号确定的非自催化生化网络，总结了几个现有的文献结果。我们称弱（强）候选振子系统为可能（完全）由于存在复特征值对而过渡到不稳定的系统，而称弱（强）候选多平稳系统为可能（完全）由于存在实特征值而过渡到不稳定的系统。对于每个类别，我们提供了一个基于相关符号图中正循环和负循环的独占或同时存在的表征。大多数生化网络的现实例子落在系统的灰色地带，其中存在正循环和负循环：因此，振荡和双稳态行为原则上都是可能的。然而，许多表现出振荡或双稳性的典型示例电路属于强候选振荡器/多平稳系统的类别，与我们的结果一致。
Molecular systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid mathematical models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas' conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochemical networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of positive and negative cycles in the associated sign graph. Most realistic examples of biochemical networks fall in the gray area of systems in which both positive and negative cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.