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 language | English |
|---|---|
| Pages (from-to) | 627-649 |
| Number of pages | 23 |
| Journal | Bulletin of Mathematical Biology |
| Volume | 66 |
| Issue number | 4 |
| DOIs | |
| Publication status | Published - Jul 1 2004 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Speed of pattern appearance in reaction-diffusion models
T2 - Implications in the pattern formation of limb bud mesenchyme cells
AU - Miura, Takashi
AU - Maini, Philip K.
PY - 2004/7/1
Y1 - 2004/7/1
N2 - 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.
AB - 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.
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U2 - 10.1016/j.bulm.2003.09.009
DO - 10.1016/j.bulm.2003.09.009
M3 - Article
VL - 66
SP - 627
EP - 649
JO - Bulletin of Mathematical Biology
JF - Bulletin of Mathematical Biology
SN - 0092-8240
IS - 4
ER -