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Applied Mathematics
Short- and long-range effects of Sonic hedgehog in limb development
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Department of Mathematics, Washington State University, Pullman, WA 99164; and ¶School of Mathematics, University of Minnesota, Minneapolis, MN 55455
Edited by Charles S. Peskin, New York University, New York, NY, and approved June 30, 2003 (received for review January 27, 2003)
The secreted protein Sonic hedgehog (Shh) and its transmembrane receptor Patched (Ptc) control a major signal transduction pathway in early vertebrate limb development. Ligand-free Ptc interacts with the transmembrane protein Smoothened (Smo) and blocks expression of Smo-controlled genes including ptc. Ligand-bound Ptc removes the block and leads to further expression of ptc, which in turn restricts the range of Shh transport. Currently it is not certain that Shh functions as a morphogen on the 300-µm scale of early chick limb development, because it has been difficult to determine how far different forms of Shh are transported. We develop a model to study the effects of two forms of Shh used experimentally and propose a mechanism for Shh signal transduction based on a two-state model for the Ptc-Smo interaction. Recent bead- and tissue-implant experiments can be explained by using this model without postulating different diffusivities for the two forms of Shh; a difference in other parameters such as the rate of release of Shh from the bead or transplant can explain the results equally well. The model also predicts that lower concentrations of Shh in a bead will produce a response similar to that after a tissue transplant. Our results provide an explanation for the counterintuitive experimental results and show that the same signal transduction mechanism can explain both short- and long-range Shh signaling. We conclude that Shh can function as a long-range morphogen.
Abbreviations: AP, anterior-posterior; AER, apical ectodermal ridge; ZPA, zone of polarizing activity; FGF, fibroblast growth factor; Shh, Sonic hedgehog; N-Shh, N-terminal peptide of Shh; N-Shhp, native form of N-Shh with cholesterol attached; Ptc, Patched; PI, postimplant; Smo, Smoothened.
R.D. and C.G. contributed equally to this work.
|| This is 0.1% of the concentration of the N-Shh solution in which the bead is soaked (as reported in ref. 16).
To whom correspondence should be addressed. E-mail: dillon{at}math.wsu.edu.
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