Oscillations and patterns in spatially discrete models for developmental intercellular signalling

S.D. Webb, M.R. Owen

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

We extend previous models for nearest neighbour ligand-receptor binding to include both lateral induction and inhibition of ligand and receptor production, and different geometries (strings of cells and hexagonal arrays, in addition to square arrays). We demonstrate the possibility of lateral inhibition giving patterns with a characteristic length scale of many cell diameters, when receptor production is included. In contrast, lateral induction combined with inhibition of receptor synthesis cannot give rise to a patterning instability under any circumstances. Interesting new dynamics include the analytical prediction and consequent numerical observation of spatiotemporal oscillations, this depends crucially on the production terms and on the relationship between the decay rates of ligand and free receptor. Our approach allows for a detailed comparison with the model for Delta-Notch interactions of Collier et al. [4], and we find that a formal reduction may be made only when the ligand receptor binding kinetics are very slow. Without such very slow receptor kinetics, spatial pattern formation via lateral inhibition in hexagonal cellular arrays requires significant activation of receptor production, a feature that is not apparent from previous analyses.
LanguageEnglish
Pages444-476
Number of pages32
JournalJournal of Mathematical Biology
Volume48
Issue number4
DOIs
Publication statusPublished - Apr 2004

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Discrete Model
Receptor
oscillation
Ligands
Oscillation
receptors
Lateral
Cellular arrays
Kinetics
Hexagon
Proof by induction
Chemical activation
Observation
kinetics
Geometry
Notch
Cell
Spatial Pattern
Patterning
Pattern Formation

Keywords

  • Delta-Notch
  • juxtacrine
  • lateral inhibition
  • morphogenesis

Cite this

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Oscillations and patterns in spatially discrete models for developmental intercellular signalling. / Webb, S.D.; Owen, M.R.

In: Journal of Mathematical Biology, Vol. 48, No. 4, 04.2004, p. 444-476.

Research output: Contribution to journalArticle

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AU - Webb, S.D.

AU - Owen, M.R.

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