Finding regulatory modules of chemical reaction systems

Within a cell, numerous chemical reactions form chemical reaction networks (CRNs), which are the origins of cellular functions. We previously developed a theoretical method called structural sensitivity analysis (SSA), which enables us to determine, solely from the network structure, the qualitative changes in the steady-state concentrations of chemicals resulting from the perturbations to a parameter. Notably, if a subnetwork satisfies specific topological conditions, it is referred to as a buffering structure, and the effects of perturbations to the parameter within the subnetwork are localized to the subnetwork (the law of localization). A buffering structure can be the origin of modularity in the regulation of cellular functions generated from CRNs. However, an efficient method to search for buffering structures in a large CRN has not yet been established. In this study, we prove the “inverse theorem” of the law of localization, which states that a certain subnetwork exhibiting a confined response range is always a buffering structure. In other words, we are able to identify buffering structures in terms of confined responses rather than the topological conditions. By leveraging this property, we develop an algorithm to enumerate all buffering structures for a given network by calculating responses. Additionally, we show that the hierarchy of perturbed response patterns corresponds to that of buffering structures, and present a method to illustrate the hierarchy. Our method will be a powerful tool for understanding the regulation of cellular functions generated from CRNs.