Spatial separation of bistable cell types in heterogeneous populations*

Cellular differentiation is commonly modeled by bistable switches under the influence of a diffusive morphogen. In higher organisms, differentiation is relevant for the formation of different tissue types, which require a clear spatial separation. Cellular heterogeneity in the sensitivity to the morphogen impairs the formation of a clear boundary. We are investigating the role of intercellular communication and synchronized switching for tissue separation. We construct a spatially distributed model that combines a cellular population of bistable switches with the diffusion of a morphogen in the extracellular medium. The model is able to predict a clear separation in different tissue types despite cellular heterogeneity. Based on that model, we formulate an objective function that measures the quality of the spatial separation, and use numerical optimization to determine parameter values that yield a clear tissue boundary.