Understanding the relationship between the structure of chemical reaction networks and their reaction dynamics is essential for unveiling the design principles of living organisms. However, while some network-structural features are known to relate to the steady-state characteristics of chemical reaction networks, mathematical frameworks describing the links between out-of-steady-state dynamics and network structure are still underdeveloped. Here, we characterize the out-of-steady-state behavior of a class of artificial chemical reaction networks consisting of the ligation and splitting reactions of polymers. Within this class, we examine minimal networks that can convert a given set of sources (e.g., nutrients) to a specified set of targets (e.g., biomass precursors). By exploring the dynamics of the models with a simple setup, we find three distinct types of relaxation dynamics after perturbation from a steady-state: exponential-, power-law-, and plateau-dominated. We computationally show that we can predict this out-of-steady-state dynamical behavior from just three features computed from the network’s stoichiometric matrix, namely, (1) the rank gap, determining the existence of a steady-state; (2) the left null-space, being related to conserved quantities in the dynamics; and (3) the stoichiometric cone, dictating the range of achievable chemical concentrations. We further demonstrate that these three quantities relates to the type of relaxation dynamics of combinations of our minimal networks, larger networks with many redundant pathways, and a real example of a metabolic network. The relationship between the topological features of reaction networks and the relaxation dynamics presented here are useful clues for understanding the design of metabolic reaction networks as well as industrially useful chemical production pathways.

了解化学反应网络的结构及其反应动力学之间的关系对于揭示生物体的设计原理至关重要。然而，虽然已知一些网络结构特征与化学反应网络的稳态特征有关，但描述非稳态动力学和网络结构之间联系的数学框架仍然不发达。在这里，我们描述了一类由聚合物的连接和分裂反应组成的人工化学反应网络的非稳态行为。在这一类中，我们研究了可以将一组给定来源（例如，营养物质）转换为一组指定目标（例如，生物质前体）的最小网络。通过使用简单的设置探索模型的动力学，我们发现了稳态扰动后三种不同类型的松弛动力学：指数主导、幂律主导和平稳主导。我们通过计算表明，我们可以仅根据网络化学计量矩阵计算出的三个特征来预测这种非稳态动态行为，即（1）等级差距，确定稳态的存在； (2) 左零空间，与动力学中的守恒量相关； (3) 化学计量锥，规定可达到的化学浓度范围。我们进一步证明，这三个量与我们的最小网络、具有许多冗余路径的较大网络以及代谢网络的真实示例的组合的松弛动力学类型有关。 这里提出的反应网络的拓扑特征和松弛动力学之间的关系是理解代谢反应网络的设计以及工业上有用的化学生产途径的有用线索。