Evolutionary emergent metabolic interactions in cell cultures: A statistical mechanics point of view

Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte Carlo simulations, we explore the equilibrium and dynamical properties of a population of cells arranged in a two-dimensional lattice, where each cell is characterized by fluxes of three reactions: glucose consumption (g), respiration (r), and waste production/absorption (w). The system minimizes an energy function influenced by competitive (J_{g}>0) and cooperative (J_{w}<0) couplings between cells. Our results reveal three distinct phases: a competitive phase dominated by glucose competition, a cooperative phase marked by ordered waste exchange, and a disordered phase with local-scale cooperation. By incorporating evolutionary dynamics, we demonstrate how initially noninteracting cells can develop effective metabolic interactions, leading to heterogeneous cultures sustained by cross feeding. These findings are further supported by analytical solutions derived using mean-field approximations. The model provides insights into how environmental constraints and stochastic fluctuations shape community structures, offering a versatile approach to study several emergent phenomena in biological systems.