Mapping thermodynamically feasible metabolic states

Thermodynamically, living cells are open systems, driven out of equilibrium by input fluxes (resources) and output fluxes (products, work, waste). A central question of systems biology is to understand the possible internal states of a cell from the knowledge of input/output fluxes and other biological bounds. Chemical reaction networks (CRNs) are now widely known for many cells and offer a quantitative framework to tackle it. A Physicist’s take of the problem consists in mapping the allowed values of internal reaction currents given the known constraints. At stationarity, the relation between internal reaction currents and external ones would be purely affine if it were not for an essential feature of biological CRNs: inside a cell, conservation of energy implies that reaction rates must satisfy detailed balance. The corresponding constraint on currents, named thermodynamic feasibility, renders the internal/external currents' relation non-linear.
In this work, we fully characterize the space of thermodynamically feasible currents by showing that they constitute the bounded chambers of a well-defined hyperplane arrangement. To achieve this, we make use «geometric» concepts of (hyper)graph theory (such as cycles and cocycles), that generalize the notion of Kirchoff laws to CRNs.

Joint work with Sara Dal Cengio and Delphine Ropers