幂律动力系统多平稳性的计算方法
A Computational Approach to Multistationarity of Power-Law Kinetic Systems
摘要：
本文提出了一种计算方法来确定具有幂律动力学的化学反应网络（PLK系统）是否具有多稳态能力，即，是否存在正的速率常数，使得相应的微分方程在化学计量类内允许多个正的稳态。该方法被称为“PLK系统的多稳态算法”（MSA），结合了（i）Ji和Feinberg的质量作用量的“高等亏格算法”到具有反应决定相互作用的PLK系统的扩展，以及（ii）将任何PLK系统转换为具有反应决定相互作用的动态等价系统的方法。使用该算法，我们得到了两个新的结果：一个流行的模型的厌氧酵母发酵途径的单平稳性，和气候工程的全球碳循环模型的多平稳性，无论是在广义质量作用形式的生化系统理论。我们还提供了更广泛的范围内，我们的方法相比，范伯格的“缺陷一算法”，这样的系统的扩展的不足之一PLK系统的例子。
英文摘要：
This paper presents a computational solution to determine if a chemical reaction network endowed with power-law kinetics (PLK system) has the capacity for multistationarity, i.e., whether there exist positive rate constants such that the corresponding differential equations admit multiple positive steady states within a stoichiometric class. The approach, which is called the "Multistationarity Algorithm for PLK systems" (MSA), combines (i) the extension of the "higher deficiency algorithm" of Ji and Feinberg for mass action to PLK systems with reactant-determined interactions, and (ii) a method that transforms any PLK system to a dynamically equivalent one with reactant-determined interactions. Using this algorithm, we obtain two new results: the monostationarity of a popular model of anaerobic yeast fermentation pathway, and the multistationarity of a global carbon cycle model with climate engineering, both in the generalized mass action format of biochemical systems theory. We also provide examples of the broader scope of our approach for deficiency one PLK systems in comparison to the extension of Feinberg's "deficiency one algorithm" to such systems.
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