Positive equilibria of power law kinetic systems with kinetics-based decompositions

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-07-21 DOI:10.1007/s10910-024-01657-x

Jaysie Mher G. Tiongson, Dylan Antonio S. J. Talabis, Lauro L. Fontanil

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Abstract

The goal of this paper is to characterize the existence of positive equilibria of power law systems through their kinetics-based decompositions. To achieve this, we consider subclasses of power law systems: PL-RDK and PL-TIK systems. PL-RDK systems are those in which the kinetic order vectors are reactant-determined, that is, branching reactions have identical vectors. PL-TIK systems are characterized by having linearly independent kinetic order vectors per linkage class. We first introduced the notion of Zero Kinetic Deficiency Decomposition of cycle terminal power law systems. Then, by considering non-cycle terminal power law systems, we extend this by introducing the notion of PL-TIK decomposition. Through these novel decomposition classes, we showed that PL-RDK systems with weakly reversible decompositions admit positive equilibria. Moreover, to ensure the existence of PL-TIK decomposition, we developed an algorithm in which any power law system can generate a PL-TIK decomposition. Lastly, we applied the algorithm to Schmitz’ Global Carbon Cycle Model.

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幂律动力学系统的正平衡与基于动力学的分解

本文的目标是通过基于动力学的分解来描述幂律系统正平衡的存在性。为此，我们考虑了幂律系统的子类：PL-RDK 和 PL-TIK 系统。PL-RDK 系统是指动力学阶次向量由反应物决定的系统，即分支反应具有相同的向量。PL-TIK 系统的特点是每个连接类具有线性独立的动力学阶数向量。我们首先介绍了循环末端幂律系统的零动力学缺陷分解概念。然后，通过考虑非周期末端幂律系统，我们引入了 PL-TIK 分解的概念，从而扩展了这一概念。通过这些新颖的分解类，我们证明了具有弱可逆分解的 PL-RDK 系统承认正均衡。此外，为了确保 PL-TIK 分解的存在，我们开发了一种算法，其中任何幂律系统都能生成 PL-TIK 分解。最后，我们将该算法应用于 Schmitz 的全球碳循环模型。

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来源期刊

Journal of Mathematical Chemistry 化学-化学综合

CiteScore

3.70

自引率

17.60%

发文量

105

审稿时长

6 months

期刊介绍： The Journal of Mathematical Chemistry (JOMC) publishes original, chemically important mathematical results which use non-routine mathematical methodologies often unfamiliar to the usual audience of mainstream experimental and theoretical chemistry journals. Furthermore JOMC publishes papers on novel applications of more familiar mathematical techniques and analyses of chemical problems which indicate the need for new mathematical approaches. Mathematical chemistry is a truly interdisciplinary subject, a field of rapidly growing importance. As chemistry becomes more and more amenable to mathematically rigorous study, it is likely that chemistry will also become an alert and demanding consumer of new mathematical results. The level of complexity of chemical problems is often very high, and modeling molecular behaviour and chemical reactions does require new mathematical approaches. Chemistry is witnessing an important shift in emphasis: simplistic models are no longer satisfactory, and more detailed mathematical understanding of complex chemical properties and phenomena are required. From theoretical chemistry and quantum chemistry to applied fields such as molecular modeling, drug design, molecular engineering, and the development of supramolecular structures, mathematical chemistry is an important discipline providing both explanations and predictions. JOMC has an important role in advancing chemistry to an era of detailed understanding of molecules and reactions.