Collective homeostasis in mean-field interacting systems

How should a collection of cells exchange information and regulate gene expression to maintain collective homeostasis? Here, we consider a model where single-cell dynamics are described by gradient flow in a dynamic 'seascape' that is modulated by the collective state of the population. The framework combines variational inference and optimal transport for finding signaling and regulatory strategies in systems where interactions are mediated by a few collective features that convey information about deviations from homeostasis. Our findings suggest signaling and regulatory strategies should be co-designed to sense and respond to the most relevant perturbations from homeostasis and prioritize accelerating the slowest-relaxing modes of the system. The theory offers a path towards designing systems that display self-organized robustness.