Distance between AER and ZPA is defined by feed-forward loop and is stabilized by their feedback loop in vertebrate limb bud

Tsuyoshi Hirashima, Yoh Iwasa, Yoshihiro Morishita

Research output: Contribution to journalArticle

19 Citations (Scopus)

Abstract

In the development of organs, multiple morphogen sources are often involved, and interact with each other. For example, the apical ectodermal ridge (AER) and the zone of polarizing activity (ZPA) are major morphogen sources in the limb bud formation of vertebrates. Fgf expression in the AER and Shh expression in the ZPA are maintained by their positive feedback regulation mediated by diffusible molecules, FGF and SHH. A recent experimental observation suggests that the FGF-signal regulates the Shh expression in a feed-forward manner with activation and repression regulatory pathways. We study the coupled dynamics of Shh expression in the ZPA and Fgf expression in the AER, and the relationship of the relative position between AER and ZPA. We first show that with the feed-forward regulation only, the peak of ZPA activity can be formed distant from the AER as observed experimentally. Then, we clarify that the robustness of the ZPA spatial pattern to changes in system parameters is enhanced by adding the feedback regulation between the AER and the ZPA. Furthermore, sensitivity analysis shows that there exists the optimal feedback strength where the robustness is the most improved.

Original languageEnglish
Pages (from-to)438-459
Number of pages22
JournalBulletin of Mathematical Biology
Volume70
Issue number2
DOIs
Publication statusPublished - Feb 1 2008

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limb bud
Limb Buds
food law
Feedback Loop
Ridge
Feedforward
bud
Vertebrates
limb
vertebrate
vertebrates
Feedback
Sensitivity analysis
Chemical activation
Observation
Molecules
Robustness
Positive Feedback
Spatial Pattern
sensitivity analysis

All Science Journal Classification (ASJC) codes

  • Neuroscience(all)
  • Immunology
  • Mathematics(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Pharmacology
  • Environmental Science(all)
  • Agricultural and Biological Sciences(all)
  • Computational Theory and Mathematics

Cite this

Distance between AER and ZPA is defined by feed-forward loop and is stabilized by their feedback loop in vertebrate limb bud. / Hirashima, Tsuyoshi; Iwasa, Yoh; Morishita, Yoshihiro.

In: Bulletin of Mathematical Biology, Vol. 70, No. 2, 01.02.2008, p. 438-459.

Research output: Contribution to journalArticle

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