Model of Morphogenesis with Repelling Signaling

The paper is devoted to a conceptual model of cell patterning, based on a generalized notion of the epigenetic code of a cell determining its state. We introduce the concept of signaling depending both upon the spatial distance between cells and the distance between their cell states (s-distance); signaling can repel cells in the space of cell states (s-space) or attract them. The influence of different types of repelling signaling on the evolution of cells is considered. Stabilizing signaling, namely a signaling monotonically decreasing with s-distance, causes the restoring of cell states after perturbations; destabilizing signaling, i.e., the one in which the signaling monotonically increases with s-distance, causes the appearance of pairs of cells with alternating cell states (one close to the state conventionally called "head", and another close to the "tail" state). Non-monotonic (in s-space) signaling splits the cells into groups. The model shows that different types of signaling may provide different types of cellular patterns. General principles for applying this model to complex cellular structures are discussed.