Speed of pattern appearance in reaction-diffusion models

Implications in the pattern formation of limb bud mesenchyme cells

Takashi Miura, Philip K. Maini

Research output: Contribution to journalArticle

39 Citations (Scopus)

Abstract

It has been postulated that fibroblast growth factor (FGF) treatment of cultured limb bud mesenchyme cells reinforces the lateral inhibitory effect, but the cells also show accelerated pattern appearance. In the present study, we analyze how a small change in a specific parameter affects the speed of pattern appearance in a Turing reaction-diffusion system using linear stability analysis. It is shown that the sign of the change in appearance speed is qualitatively decided if the system is under the diffusion-driven instability condition, and this is confirmed by numerical simulations. Numerical simulations also show that a small change in parameter value induced easily detectable differences in the appearance speed of patterns. Analysis of the Gierer-Meinhardt model revealed that a change in a single parameter can explain two effects of FGF on limb mesenchyme cells - reinforcement of lateral inhibition and earlier appearance of pattern. These qualitative properties and easy detectability make this feature a promising tool to elucidate the underlying mechanisms of biological pattern formation where the quantitative parameters are difficult to obtain.

Original languageEnglish
Pages (from-to)627-649
Number of pages23
JournalBulletin of Mathematical Biology
Volume66
Issue number4
DOIs
Publication statusPublished - Jul 1 2004
Externally publishedYes

Fingerprint

limb bud
Limb Buds
Reaction-diffusion Model
Mesoderm
Pattern Formation
bud
limb
fibroblast growth factors
Fibroblast Growth Factors
Fibroblasts
Growth Factors
Cell
Lateral
Linear stability analysis
Computer simulation
cells
Numerical Simulation
Detectability
Qualitative Properties
Linear Stability Analysis

All Science Journal Classification (ASJC) codes

  • Agricultural and Biological Sciences(all)

Cite this

Speed of pattern appearance in reaction-diffusion models : Implications in the pattern formation of limb bud mesenchyme cells. / Miura, Takashi; Maini, Philip K.

In: Bulletin of Mathematical Biology, Vol. 66, No. 4, 01.07.2004, p. 627-649.

Research output: Contribution to journalArticle

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