Short- and long-range effects of Sonic hedgehog in limb development

Abstract

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-microm 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.

Fig. 1.

The kinetic model for the Shh-Ptc-Smo interactions. Solid lines denote primary steps, and dashed lines denote first-order decay.

Fig. 2.

A schematic of the growing limb and the processes involved in the limb. Ω, interior of the limb; Ω₁, AER region; Ω₂, ZPA region; Γ, boundary of the limb (from ref. 12).

Fig. 3.

Contours of the computed Ptc distribution for bead (a) and tissue (b) implants. Dimensionless distance from the posterior end is shown on the x axis, and the PI time in hours is shown on the y axis. Contour lines are equally spaced from 0.1 to 0.5 nM (a) and 0.05 to 0.5 nM (b). Here and in Figs. 4 and 5 white denotes the lowest concentration and black the highest. In a, the rightmost portion of the domain corresponds to the bead, where there is no ptc expression.

Fig. 4.

Shh profiles before and after bead (a) and tissue (b) implants as a function of distance from ZPA (x axis) and PI time (y axis). Contours range from 10 to 100 nM (a) and 2 to 12 nM (b).

Fig. 5.

1D simulation of Ptc concentration on application of a bead containing 100 nM (a) and 10 nM (b) Shh with a Shh diffusivity corresponding to N-Shh_p. Note the similarity of a to the bead-implant simulation (Fig. 3a) and the similarity of b to the tissue-implant simulation (Fig. 3b). Contours range from 0.1 to 0.5 nM (a) and 0.05 to 0.5 nM (b).

Fig. 6.

(Upper) Computational and experimental Ptc responses to bead implants. (Lower) Ptc response to tissue implants. (Upper) Numerical simulations of Ptc concentration 2, 6, and 18 h after bead implants (A, C, and E, respectively). (Lower) Ptc concentration 12, 16, and 20 h after tissue implant. (A, C, and E, respectively). Experimental results are from ref. for ptc transcript concentration 2, 6, and 16 h after bead implants PI and for tissue implants, 4, 8, and 16 h PI. (B, D, and F, respectively). [Reproduced with permission from Drossopoulou et al. (16) (Copyright 2000, Company of Biologists Ltd.).] The simulation shows the experimentally observed posterior-anterior ptc expression wave followed by restriction of expression near the implant site. Tissue implant simulations show the initial expression near the implant site followed by a decrease and subsequent reestablishment of ectopic ptc expression. The figures for numerical simulations have been rescaled. The unscaled length of the proximal boundary in each of the numerical simulations is identical. The rescaling with respect to A Upper is as follows: C Upper, 1.8:1; E Upper, 3:1; A Lower, 1.9:1; C Lower, 2.1:1; E Lower, 2.7:1. The unscaled version of C Upper, for example, is 1.8 times larger than shown.