Cellular gradient flow structure linking single-cell-level rules and population-level dynamics

Abstract

In multicellular systems, single-cell behaviors should be coordinated consistently with the overall population dynamics and functions. However, the interrelation between single-cell rules and the population-level goal is still elusive. In this work, we reveal that these two levels are naturally connected via a gradient flow structure of heterogeneous cellular populations and that biologically prevalent single-cell rules, such as unidirectional type switching and hierarchical order in types, emerge from this structure. We also demonstrate the gradient flow structure in a standard model of the T-cell immune response. This theoretical framework works as a basis for understanding multicellular dynamics and functions.