2018/08/28 by José Negrete, Jose Negrete Jr, Andrew C. Oates · 1 citation
Agricultural and Biological Sciences · Computer Science · Mathematics · Physics and Astronomy · #Nonlinear Dynamics and Pattern Formation #Plant Molecular Biology Research #Plant and Biological Electrophysiology Studies #math.DS #physics.bio-ph
paper · pdf · doi:10.1103/physreve.99.042417
published as Phys. Rev. E 99, 042417 (2019)
arxiv created 2018/08/28 · openalex publication_date 2019/04/25 · arxiv updated 2019/05/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Cellular checkerboard patterns are observed at many developmental stages of embryos. We study an analytically tractable model for lateral inhibition and show that a coupling coefficient with a negative value is sufficient to obtain noisy or periodic checkerboard patterns. We solve the case of a linear chain of cells explicitly and show that noisy anti-correlated patterns are available in a post-critical regime (εc < ε< 0). In the sub-critical regime (-∞ < ε≤ εc) a periodic and alternating steady state is available, where pattern selection is determined by making an analogy with the optical modes of phonons. For cells arranged in a hexagonal lattice, the sub-critical pattern can be driven into three different states: two of those states are periodic checkerboards and a third in which both periodic states coexist.