[SS03] Cheimical reaction network theory

[SS03-03] Chemical Reaction Network’s Structures Prohibiting Turing’s Instability

*Devanand .¹, Minji Kang¹, Jinsu Kim¹ (1. Pohang University of Science and Technology, South Korea (Korea))

Keywords:

Chemical Reaction Networks,Reaction-Diffusion System,Turing Pattern Formation

The study of self-organized pattern formation through systems of reaction-diffusion equations is fundamental to many complex systems across various fields of science, such as biology, chemical reactions, mathematics, and more. Turing's theory of pattern formation has been at the forefront of this field. The interaction between two or more competing diffusive agents in a medium usually results in a uniform, homogenized stable state. However, under certain conditions, depending on the difference in the diffusivity between the competing agents (e.g., activator-inhibitor), there is a loss of stability of the uniform homogenized state (called Turing’s instability), leading to repetitive concentrations of these agents spatially that manifest as stable temporal patterns, known as Turing patterns. In recent years, scientists have been uncovering the ideas of Turing instability in chemical reaction networks through mass action kinetics. For example, [1] explored minimal reaction scheme models based on positive/negative feedback involving two reacting chemical species that are bimolecular at most, while [2], discussed Turing pattern formation in biochemical reaction networks without imposing the conditions of positive/negative feedback. Most of the previous studies have not discussed the idea of Turing instability depending on the structures of chemical reaction networks. Thus, in our study, we will discuss some of the important structures of chemical reaction networks with mass action kinetics that prohibit the occurrence of Turing instability through the absence of positive/negative feedback.

Reference:
[1] Fraser R. Waters, Christian A. Yates and Jonathan H.P. Dawes. "Minimal reaction schemes for pattern formation." Journal of Royal Society Interface, 2024.

[2] Shibashis Paul, Joy Adetunji and Tian Hong. "Widespread biochemical reaction networks enable Turing patterns without imposed feedback" Nature Communications, 2024