A Graph Partitioning Approach to Predict Patterns in Lateral Inhibition Systems

TL;DR

This paper introduces a graph partitioning method to predict and analyze steady state patterns in cellular systems exhibiting lateral inhibition, combining dynamical systems theory and graph analysis.

Contribution

It presents a novel approach using graph partitioning and monotone systems theory to identify and analyze stable pattern formations in lateral inhibition networks.

Findings

Existence of steady state patterns proven using monotone systems theory.

Stable patterns can be characterized through block decomposition of the network.

Method provides a systematic way to predict cellular fate patterns.

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.