Ordered hexagonal patterns via notch–delta signaling
| Autor: | David A. Kessler, Herbert Levine, Eial Teomy |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Delta
Molecular Networks (q-bio.MN) Cellular differentiation Biophysics FOS: Physical sciences Pattern formation Pattern Formation and Solitons (nlin.PS) Ligands Topology Structural Biology Quantitative Biology - Molecular Networks Molecular Biology Condensed Matter - Statistical Mechanics Body Patterning Statistical Mechanics (cond-mat.stat-mech) Hexagonal crystal system Mechanism (biology) Intracellular Signaling Peptides and Proteins Membrane Proteins Cell Biology Nonlinear Sciences - Pattern Formation and Solitons Range (mathematics) Pitchfork bifurcation Signalling FOS: Biological sciences Ordinary differential equation Biological system Signal Transduction |
| Zdroj: | Physical Biology. 18:066006 |
| ISSN: | 1478-3975 1478-3967 |
| DOI: | 10.1088/1478-3975/ac28a4 |
| Popis: | Many developmental processes in biology utilize Notch-Delta signaling to construct an ordered pattern of cellular differentiation. This signaling modality is based on nearest-neighbor contact, as opposed to the more familiar mechanism driven by the release of diffusible ligands. Here, exploiting this ``juxtacrine" property, we present an exact treatment of the pattern formation problem via a system of nine coupled ordinary differential equations. The possible patterns that are realized for realistic parameters can be analyzed by considering a co-dimension 2 pitchfork bifurcation of this system. This analysis explains the observed prevalence of hexagonal patterns with high Delta at their center, as opposed to those with central high Notch levels. We show that outside this range of parameters, in particular for low cis-coupling, a novel kind of pattern is produced, where high Delta cells have high Notch as well. It also suggests that the biological system is only weakly first order, so that an additional mechanism is required to generate the observed defect-free patterns. We construct a simple strategy for producing such defect-free patterns. |
| Databáze: | OpenAIRE |
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