Statistical physics of multicellular systems

How does a system of communicating cells generate spatial organization in their gene expression levels? Various studies have addressed collective effects arising from a population of secrete-and-sense cells, which communicate by secreting and sensing the same signalling molecule. Yet a general theoretical framework for describing this collective behaviour remains lacking. We constructed a lattice model in which cells can have either a high or a low expression level. Each cell updates its state according to the concentration of signalling molecule it senses. The macroscopic behaviour can be described by two variables, the mean expression level and a “spatial order parameter”, together with a monotonically decreasing “Hamiltonian” that is a function of these variables. An effective Langevin equation based on the gradient of this Hamiltonian describes the macroscopic dynamics. We extend the framework to cells with a graded response and show that the main qualitative features are conserved. Moreover, the system exhibits a transition between an autonomous phase – where each cell determines its own fate - and a collective phase in which spatial organisation can arise. Further extensions of the model include addition of noise, multiple cell types and spatial inhomogeneity.