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Multiscale analysis of pattern formation via intercellular signalling.

R D O'Dea1, J R King

  • 1School of Science and Technology, Nottingham Trent University, Nottingham NG11 8NS, UK. reuben.odea@ntu.ac.uk

Mathematical Biosciences
|March 10, 2011
PubMed
Summary
This summary is machine-generated.

Lateral inhibition, a cell communication process, forms fine-grained spatial patterns. A new multiscale method enables continuum modeling of this process, revealing linear diffusion and matching discrete model predictions.

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Area of Science:

  • Developmental biology
  • Mathematical modeling
  • Cell signaling

Background:

  • Lateral inhibition is a cell communication mechanism crucial for spatial pattern formation in developing tissues.
  • Discrete methods are typically used for analyzing fine-grained patterns due to limitations of continuum approaches.
  • The Delta-Notch signaling pathway is a key example of lateral inhibition.

Purpose of the Study:

  • To derive a continuum model from a discrete Delta-Notch signaling model using a multiscale method.
  • To analyze the generation of fine-grained spatial patterns using the derived continuum model.
  • To investigate the manifestation of juxtacrine signaling as diffusion and analyze traveling-wave behavior.

Main Methods:

  • Application of a multiscale method to a discrete Delta-Notch signaling model.
  • Systematic derivation of a continuum model from a discrete model.
  • Analysis of the derived continuum model for pattern formation and traveling-wave dynamics.

Main Results:

  • Successfully derived a continuum model from the discrete Delta-Notch model.
  • Demonstrated that juxtacrine signaling manifests as linear diffusion on the macroscale.
  • Achieved good quantitative agreement between the continuum model and the discrete system for traveling-wave behavior.

Conclusions:

  • The multiscale method provides a valid approach to model fine-grained patterns using continuum methods.
  • Reaction-diffusion models are suitable for cell-signaling systems exhibiting contact-dependent juxtacrine signaling.
  • The derived continuum model accurately captures key behaviors of the discrete system, including traveling waves.