Generalized dynamics of cross-feeding bacteria

Bacterial cooperation involves the exchange of metabolites, which can range from costless byproducts of metabolism to intentionally produced and costly molecules. These interactions occur across spatial scales, from direct cell contact to the diffusion of metabolites in the environment. Due in part to this variety of interaction modes, the impacts of mutualism on bacterial community dynamics remain unclear. Using generalized models, we derive conditions for the onset of different dynamical behaviours in communities of interacting bacteria across these scenarios. These include exchanges of low-cost metabolites, costly cross-feeding and cases where bacteria produce either most or only a small fraction of available metabolites. Stability depends strongly on metabolite production costs and the balance between metabolite uptake and production. We further show that perturbations to bacteria have larger impacts than to metabolites. Finally, we demonstrate that spatial metabolite diffusion drives pattern formation, emphasizing the links between local stability and spatial structures in bacterial cooperation.