Inside living cells, chemical reactions form a large web of networks. Understanding the behavior of those complex reaction networks is an important and challenging problem. In many situations, it is hard to identify the details of the reactions, such as the reaction kinetics and parameter values. It would be good if we can clarify what we can say about the behavior of reaction systems, when we know the structure of reaction networks but reaction kinetics is unknown. In these talks, I plan to introduce two approaches in this spirit. Firstly, we will discuss the sensitivity analysis of reaction systems based on the structural information of reaction networks [1]. I will give an introduction to the method of identifying subnetworks inside which the effects of the perturbation of reaction parameters are confined. Secondly, I will introduce the reduction method that we developed recently [2]. In those two methods, an integer determined by the topology of a subnetwork, which we call an influence index, plays a crucial role.
[1] T. Okada, A. Mochizuki, “Law of Localization in Chemical Reaction Networks,” Phys. Rev. Lett. 117, 048101 (2016); T. Okada, A. Mochizuki, “Sensitivity and network topology in chemical reaction systems,” Phys. Rev. E 96, 022322 (2017).
[2] Y. Hirono, T. Okada, H. Miyazaki, Y. Hidaka, “Structural reduction of chemical reaction networks based on topology”, Phys. Rev. Research 3, 043123 (2021).
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