Abstract:

Chemical reaction networks inherently possess algebraic constraints induced by stoichiometry and a gradient flow structure induced by thermodynamics. Mathematically, chemical reaction networks are dynamical systems of measures on graphs or hypergraphs with a thermodynamic structure. This resembles, yet significantly differs from, dynamical systems of probability measures defined on a continuous, finite-dimensional Euclidean space.  In this presentation, we show that these unique properties of chemical reaction networks can be unified by information geometry defined on homological algebra associated with the hypergraph structure [1,2]. We also demonstrate its application to the analysis of non-equilibrium reaction dynamics [1,2] and control of stochastic general reaction networks [3,4].

[1] Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, & Yuki Sughiyama, “Hessian geometry of nonequilibrium chemical reaction networks and entropy production decompositions”, Phys. Rev. Research 4, 033208 – Published 15 September 2022
[2] Tetsuya J. Kobayashi, Dimitri Loutchko, Atsushi Kamimura, Shuhei A. Horiguchi & Yuki Sughiyama, “Information geometry of dynamics on graphs and hypergraphs”, Volume 7, pages 97–166, (2024)
[3] Shuhei A. Horiguchi, Tetsuya J. Kobayashi, “Optimal control of stochastic reaction networks with entropic control cost and emergence of mode-switching strategies”, arXiv:2409.17488, (2024)
[4] Yusuke Himeoka, Shuhei A. Horiguchi, Tetsuya J. Kobayashi,  “A theoretical basis for cell deaths”, arXiv:2403.02169 (2024)