Mathematical biology and related mathematical subjects

Chemical reaction network theory and continuous-time Markov chain

A biochemical system can be described with a graphical configuration called chemical reaction network (CRN), a directed graph whose edges are reactions and the vertices are complex of chemical species. Chemical reaction network theory allows us to analyze the dynamical properties of CRN solely based on the network structure. Some of my questions are : How does biochemical system maintains homeostasis? How does the structure of CRN affects the homeostasis? Can we construct a new network structure to obtain some properties?

CRN can be mathematically described by the deterministic model (ODEs) and the stochastic model (continuous-time Markov chain), and the homeostasis of stochastic CRN corresponds to the ergodicity of continuous-time Markov chain. In this sense, the ergodicity and exponential ergodicity of CTMC, and the properties at the stationary distribution are my current interest.

Biological pattern formation and partial derivative equations

One problem of CRN is the well-mixed assumption. In real life, many environments are not well-mixed. To consider the spatiality, it is crucial to describe dynamics using PDE.

In this aspect, I'm interested in the biological pattern formation, especially the relationship between evolutionary game theory (EGT) and spatial patterns. Some of my questions are : When the evolutionary game could generate the spatial pattern? What does the spatial pattern and its generating condition biologically means? At the end, I believe that CRN-based description, EGT-based description, and PDE-based description could be merged.

---

- Hyukpyo Hong*, Seokhwan Moon*, Yuji Hirono*, and Jae Kyoung Kim. Topological Criterion for Robust Perfect Adaptation of Reaction Fluxes in Biological Networks, iScience (2025)

- Minjoon Kim*, Seokhwan Moon*, and Jinsu Kim. Exponential ergodicity of one-dimensional stochastic reaction networks, In Preperation.

- Dongju Lim*, Seokhwan Moon*, Yun Min Song, Jinsu Kim, and Jinsu Kim. Toward Single-Cell Control: Noise-Robust Perfect Adaptation in Biomolecular Systems, In Preperation.