Polyhedral geometry and combinatorics of an autocatalytic ecosystem

IF 1.7 3区化学 Q3 CHEMISTRY, MULTIDISCIPLINARY

Journal of Mathematical Chemistry Pub Date : 2024-02-27 DOI:10.1007/s10910-024-01576-x

Praful Gagrani, Victor Blanco, Eric Smith, David Baum

引用次数: 0

Abstract

Developing a mathematical understanding of autocatalysis in reaction networks has both theoretical and practical implications. We review definitions of autocatalytic networks and prove some properties for minimal autocatalytic subnetworks (MASs). We show that it is possible to classify MASs in equivalence classes, and develop mathematical results about their behavior. We also provide linear-programming algorithms to exhaustively enumerate them and a scheme to visualize their polyhedral geometry and combinatorics. We then define cluster chemical reaction networks, a framework for coarse-graining real chemical reactions with positive integer conservation laws. We find that the size of the list of minimal autocatalytic subnetworks in a maximally connected cluster chemical reaction network with one conservation law grows exponentially in the number of species. We end our discussion with open questions concerning an ecosystem of autocatalytic subnetworks and multidisciplinary opportunities for future investigation.

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自催化生态系统的多面体几何和组合学

从数学角度理解反应网络中的自催化既有理论意义，也有实践意义。我们回顾了自催化网络的定义，并证明了最小自催化子网络（MAS）的一些特性。我们证明可以将 MAS 划分为等价类，并得出了有关其行为的数学结果。我们还提供了详尽列举 MAS 的线性编程算法，以及可视化其多面体几何和组合的方案。然后，我们定义了簇化学反应网络，这是一个对具有正整数守恒定律的真实化学反应进行粗粒化的框架。我们发现，在具有一个守恒定律的最大连接簇化学反应网络中，最小自催化子网络列表的大小会随着物种数量的增加而呈指数增长。最后，我们讨论了有关自催化子网络生态系统的开放性问题以及未来研究的多学科机会。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.