自催化子网络上动力学 - 化学计量增长边界的优化
Optimization of Kinetic--Stoichiometric Growth Bounds over Autocatalytic Subnetworks
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- Institute of Mathematics (IMAG), Universidad de Granada（格拉纳达大学数学研究所）
- Instituto Tecnológico de Aeronáutica (ITA)（航空技术研究所）
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中文总结 AI 辅助
研究自催化子网络上动力学 - 化学计量增长边界的优化问题，核心方法是将其表述为混合整数双线性优化模型并开发精确参数算法，主要贡献是为识别高增长潜力反应子网络提供精确优化方法，揭示相关因素间相互作用。
中文摘要 AI 辅助
自催化子网络控制化学反应系统中的持续生产和平衡增长，可自然表示为联合编码化学计量结构和反应动力学的有向多超图。现有方法通过最大化结构放大（通常用最大放大因子MAF衡量）来识别此类子网络，但结构放大 alone 不能决定增长潜力，因为高放大子网络可能动力学效率低。受近期可扩展动力学下平衡增长的动力学 - 化学计量边界启发，研究选择使增长边界$(\alpha^*-1)\|\mathbb{S}|_{\mathcal A'}\|_\kappa$最大化的自催化子网络问题，其中$\alpha^*$是MAF，$\|\mathbb{S}|_{\mathcal A'}\|_\kappa$是动力学消耗范数。将问题表述为结合超图选择与广义分数放大约束的混合整数双线性优化模型，利用动力学范数的离散结构开发精确参数算法，每个子问题简化为MAF最大化并通过Dinkelbach型广义分数规划方法求解，建立了有限收敛和全局最优性。对俄勒冈ator、蚁醛反应、碳固定循环和合成基准网络的应用表明，最大化动力学 - 化学计量边界与单独最大化MAF的差异，揭示了化学计量放大、反应动力学和平衡增长之间的相互作用。所提出的框架为识别具有最高理论增长潜力的反应子网络提供了精确优化方法。
英文摘要
Autocatalytic subnetworks govern sustained production and balanced growth in chemical reaction systems and can be naturally represented as directed multihypergraphs that jointly encode stoichiometric structure and reaction kinetics. Existing optimization approaches identify such subnetworks by maximizing their structural amplification, typically measured through the Maximum Amplification Factor (MAF). However, structural amplification alone does not determine growth potential, since highly amplifying subnetworks may be kinetically inefficient. Motivated by recent kinetic--stoichiometric bounds on balanced growth under scalable dynamics, we study the problem of selecting the autocatalytic subnetwork maximizing the growth bound $(α^*-1)\|\mathbb{S}|_{\mathcal A'}\|_κ$, where $α^*$ is the MAF and $\|\mathbb{S}|_{\mathcal A'}\|_κ$ is a kinetic consumption norm. We formulate the problem as a mixed-integer bilinear optimization model combining hypergraph selection with generalized fractional amplification constraints. Exploiting the discrete structure of the kinetic norm, we develop an exact parametric algorithm in which each subproblem reduces to MAF maximization and is solved through a Dinkelbach-type generalized fractional programming method. Finite convergence and global optimality are established. Applications to the Oregonator, the formose reaction, carbon-fixation cycles, and synthetic benchmark networks show when maximizing the kinetic--stoichiometric bound differs from maximizing the MAF alone, revealing the interplay between stoichiometric amplification, reaction kinetics, and balanced growth. The proposed framework provides an exact optimization methodology for identifying reaction subnetworks with the highest theoretical growth potential.
