A Graph Partitioning Approach to Predict Patterns in Lateral Inhibition Systems

Abstract: We analyze pattern formation on a network of cells where each cell inhibits its neighbors through cell-to-cell contact signaling. The network is modeled as an interconnection of identical dynamical subsystems each of which represents the signaling reactions in a cell. We search for steady state patterns by partitioning the graph vertices into disjoint classes, where the cells in the same class have the same final fate. To prove the existence of steady states with this structure, we use results from monotone systems theory. Finally, we analyze the stability of these patterns with a block decomposition based on the graph partition.