Chemical reaction networks (CRNs) are essential for modeling and analyzing complex systems across fields, from biochemistry to economics. Autocatalytic reaction network -- networks where certain species catalyze their own production -- are particularly significant for understanding self-replication dynamics in biological systems and serve as foundational elements in formalizing the concept of a circular economy. In a previous study, we developed a mixed-integer linear optimization-based procedure to enumerate all minimal autocatalytic subnetworks within a network. In this work, we define the maximum growth factor (MGF) of an autocatalytic subnetwork, develop mathematical optimization approaches to compute this metric, and explore its implications in the field of economics and dynamical systems. We develop exact approaches to determine the MGF of any subnetwork based on an iterative procedure with guaranteed convergence, which allows for identifying autocatalytic subnetworks with the highest MGF. We report the results of computational experiments on synthetic CRNs and two well-known datasets, namely the Formose and E. coli reaction networks, identifying their autocatalytic subnetworks and exploring their scientific ramifications. Using advanced optimization techniques and interdisciplinary applications, our framework adds an essential resource to analyze complex systems modeled as reaction networks.

翻译：化学反应网络（CRN）对于从生物化学到经济学等多个领域复杂系统的建模与分析至关重要。自催化反应网络——即某些物种催化其自身生成的网络——对于理解生物系统中的自我复制动态尤为重要，并作为形式化循环经济概念的基础要素。在先前的研究中，我们开发了一种基于混合整数线性优化的程序，用于枚举网络内所有最小自催化子网络。在本工作中，我们定义了自催化子网络的最大增长因子（MGF），开发了计算该指标的数学优化方法，并探讨了其在经济学和动力系统领域中的意义。我们基于一种保证收敛的迭代过程，开发了确定任意子网络MGF的精确方法，从而能够识别具有最高MGF的自催化子网络。我们报告了在合成CRN以及两个著名数据集（即Formose和大肠杆菌反应网络）上的计算实验结果，识别了它们的自催化子网络并探讨了其科学意义。通过运用先进的优化技术和跨学科应用，我们的框架为分析以反应网络建模的复杂系统增添了一项重要资源。