Abstract:

In living cells, chemical reactions are connected by sharing their products and substrates, and form complex network systems, e.g. metabolic network. It is considered that regulations of biological systems are realized by modulations of amount/activities of enzymes mediating reactions. However, due to the complexity of systems, relations between network structures and behaviors have been unclear. In this talk, we present novel mathematical theories to determine behaviors of chemical reaction systems to changes in amount/activity of enzymes from network structure alone. We found that (1) qualitative responses of chemical concentrations (and reaction fluxes) to enzymatic changes are determined from network structures alone, and the nonzero responses are localized in finite regions in networks. We found that (2) a general law, which we call "law of localization", directly governs the patterns of nonzero responses. Suppose a subnetwork of a reaction network satisfies the following equation: (#. chemical sp.) - (#. reactions) + (#. cycles) = 0, then the subnetwork is called "buffering structure". Any perturbation of reactions in a buffering structure does not change concentrations and fluxes outside the buffering structure, namely, perturbation effects are localized in the structure itself. In addition, we recently found that (3) buffering structures govern another aspect of chemical reaction networks: bifurcation behaviors, i.e. qualitative transition of behaviors. These results imply that network topology is an origin of biological adaptation, robustness and plasticity. The theories also show that such behaviors emerge modularly in reaction systems, and the modularity originates from network structures. These theorems are not only theoretically important, but also practically useful for examining real biological systems. We apply our method to several hypothetical and real chemical reaction networks, including the metabolic network of the E. coli.