[POS] Biomathematics

[POS-53] Quantifying Relaxation Dynamics on Chemical Reaction Networks with Convexity

*Keisuke Sugie¹, Tetsuya J Kobayashi¹, Dimitri Loutchko¹ (1. The University of Tokyo (Japan))

Keywords:

Chemical Reaction Networks,Mass Action Kinetics,Slow Relaxation,Gradient Flows,Convex Optimization,Nonequilibrium Thermodynamics

Chemical reaction networks (CRNs) are a class of dynamical systems widely used to model and analyze a broad range of biochemical processes. Slow relaxation in CRNs is important to better understand living cells under limited resources, and its mechanisms and characteristics have been studied. However, it remains unclear how the relaxation rates of CRNs can be quantitatively characterized by stoichiometric and thermodynamic features, as previous studies have been limited to qualitative or simulation-based approaches. In this work, we explicitly calculate the general bounds of the KL divergence in mass-action CRN dynamics for the two dissipative formulations. We exploit the convex structure of equilibrium CRNs and use convergence analysis methods in convex optimization algorithms to quantify the relaxation process. The bounds are determined by the stoichiometric singular values, the convexity indicators, and the activities of the reactions. We numerically validate the divergence bounds on specific CRNs exhibiting slow relaxation, and identify the minimal and sufficient pairs of quantities for plateau formulation.