The polyhedral and differential geometry of chemical reaction networks

SEMINARIO DE JÓVENES INVESTIGADORES

Conferenciante: Praful Gagrani

Abstract: Chemical reaction networks (CRNs) play a central role in the mathematical modeling of chemistry and biology due to their capacity to capture a wide range of nonlinear phenomena. A CRN is a hypergraph and thus exhibits a rich topological structure. In particular, we will explore a particular feature termed autocatalysis that has many consequences for dynamical organization in CRNs for theoretical and practical reasons. I will define autocatalytic networks and explain the polyhedral geometry induced by the minimal autocatalytic subnetworks (MASs). (For details, see https://arxiv.org/abs/2303.14238.) A CRN, when equipped with the appropriate kinetics, also specifies a transition matrix for the stochastic dynamics of a population state in the positive orthant of the integer lattice. Analogous to the passage of classical mechanics from quantum mechanics, one can show that, to a first order approximation, the stochastic dynamics of the system are governed by solutions of the Hamilton-Jacobi equation. I will outline our functional gradient descent algorithm to estimate these solutions. (For details, see https://doi.org/10.1103/PhysRevE.107.034305.) I will conclude with a perspective on the applications of CRNs and mention open questions in the statistical learning of biochemical systems.