A Graph Partitioning Approach to Predict Patterns in Lateral Inhibition Systems

2012/12/07 by Ana Sofia Rufino Ferreira, Murat Arcak, Ferreira, Ana S. Rufino +1
Biochemistry, Genetics and Molecular Biology · Computer Science · Engineering · #Dynamical Systems (math.DS) #FOS: Electrical engineering #FOS: Mathematics #Gene Regulatory Network Analysis #Nonlinear Dynamics and Pattern Formation #Slime Mold and Myxomycetes Research #Systems and Control (eess.SY) #electronic engineering #information engineering

paper · pdf · doi:10.48550/arxiv.1212.1740

openalex publication_date 2012/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

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.

Citations

• Symmetry groups, semidefinite programs, and sums of squares

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