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Related Experiment Videos

Oscillations and patterns in spatially discrete models for developmental intercellular signalling.

Steven D Webb1, Markus R Owen

  • 1Department of Mathematical Science, Loughborough University, Loughborough, LE11 3TU, UK. S.D.Webb@lboro.ac.uk

Journal of Mathematical Biology
|March 31, 2004
PubMed
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Lateral inhibition can create large-scale patterns in cell development by regulating ligand and receptor production. New dynamics, including spatiotemporal oscillations, were observed in different cell geometries.

Area of Science:

  • Cellular and developmental biology
  • Mathematical modeling
  • Systems biology

Background:

  • Previous models of ligand-receptor binding focused on simple geometries and lacked mechanisms for lateral induction/inhibition.
  • Understanding spatial pattern formation is crucial for cell differentiation and tissue development.

Purpose of the Study:

  • To extend existing models of ligand-receptor binding by incorporating lateral induction and inhibition of both ligand and receptor production.
  • To investigate pattern formation in various cellular geometries, including strings, square arrays, and hexagonal arrays.
  • To explore novel dynamics, such as spatiotemporal oscillations, arising from these extended models.

Main Methods:

  • Development of a mathematical model incorporating lateral induction and inhibition.

Related Experiment Videos

  • Analysis of different cellular geometries (strings, square, hexagonal arrays).
  • Analytical prediction and numerical simulation of pattern formation and dynamic behaviors.

    • Main Results:

    • Lateral inhibition, coupled with receptor production, can generate patterns spanning many cell diameters.
    • Lateral induction combined with receptor synthesis inhibition does not lead to patterning instability.
    • Spatiotemporal oscillations were analytically predicted and numerically observed, dependent on production terms and decay rates.
    • Hexagonal arrays require significant receptor production activation for lateral inhibition patterning, unlike previous analyses.

    Conclusions:

    • The extended model provides a more comprehensive framework for understanding cell-cell communication and pattern formation.
    • The findings highlight the critical role of receptor production in enabling large-scale pattern formation via lateral inhibition.
    • The study reveals new dynamic behaviors, including oscillations, offering insights into complex biological processes.