Further Development 19.7: A Turing Model for Self-Organizing Digit Skeletogenesis

Development of the Tetrapod Limb

We have discussed the importance of Shh and Gli3 in regulating digit patterning along the anterior-to-posterior axis. However, we neglected to mention that Shh and Gli3 single- and double-null mutants still form digits; in fact, these mutants form a lot of digits—a polydactylous limb phenotype (see Litingtung et al. 2002; te Welscher et al. 2002). These data imply either that some other inductive system generates digits, or that digit formation is built on an intrinsic molecular prepattern of skeletogenesis. The anterior-to-posterior striped pattern of five digits in the mouse paw is reminiscent of Turing-type patterning (see Figure 19.15). If a Turing-type mechanism is enabling the distal mesenchyme to self-organize during chondrogenesis, what are the core factors representing the activating and inhibiting nodes of this pattern-generating system?

Knowing the essential roles that distal Hox genes play in the gene regulatory network of digit identity and their regulatory interactions with Shh/Gli3, Sheth and colleagues (2012) hypothesized that Hoxa13/Hoxd11–13 genes function through a Turing mechanism to control digit number. One way to theoretically increase the number of digits would be to narrow the wavelength of patterned chondrogenesis; that is, one could divide the distal mesenchyme into smaller stripes of precartilage development. Remarkably, Sheth and colleagues demonstrated that the progressive loss of distal Hox genes combined with similarly dosed reductions in Gli3 correlated with gradual increases in the number of digits (Figure 1). This collaborative work among the Ros, Sharpe, and Kmita labs used a reaction-diffusion simulation with assumed generic activator and inhibitor morphogens. This simulation showed that distal Hox genes in combination with AER-derived Fgf gradients were sufficient modulators of the wavelength of a Turing system to recapitulate the skeletogenic pattern of digits in normal mice and in Gli3-null backgrounds (Sheth et al.


This Turing model predicts that slight size changes of the distal limb bud will alter the number of digits. That was indeed found to be the case, and it may be a simple way of gaining or losing digits during evolution.1 In fact, comparison of the polydactyly in the combined hox/gli3 mutants with the limbs of early tetrapods and the fins of Sarcopterygian (lobe-finned) and Actinopterygian (ray-finned) fish strongly suggests that there may be a conserved, self-organizing, reaction-diffusion mechanism for digit skeletogenesis.

The assumptions built into this Turing model predict that morphogen activators and inhibitors should be present in the distal limb mesenchyme at the time of chondrogenesis. But what morphogens? The search was on. How might you identify the activators and inhibitors of this system?

The Sharpe lab approached this problem by first characterizing the temporal and spatial patterns of early precartilage formation in the distal limb, by looking at expression patterns of the precartilage marker Sox9. Meanwhile, Raspopovic and colleagues compared the transcriptomes of limb mesenchyme cells expressing Sox9 with those of cells not expressing Sox9 and found that developmental genes were expressed differently in the two populations. Namely, Wnt- and BMP-related genes were highly upregulated only in cells that were not expressing Sox9 (“out of phase”) (Figure 2A). In addition, it is known that loss of the Sox9 gene eliminates any periodic expression pattern of Wnt and BMP in the limb (Akiyama et al. 2002), suggesting that Sox9 is not only a marker for precartilage but also potentially a direct component of the regulatory gene network. Based on these results, Raspopovic created a “three-node” BMP-Sox9-Wnt (BSW) Turing-type network—in which BMP functions as the activator of Sox9 and Wnt as the inhibitor—to simulate the skeletogenesis of digits in the mouse (Figure 2B). It is interesting that only by including the wavelength modulating parameters of an FGF gradient for the timing of proximal-distal growth and the spatial restrictions of distal Hox genes did the BSW Turing model simulate accurately the self-organizing nature of digit development (Figure 2C).

In summary, it appears that the chondrogenic pattern of digit formation is governed by a self-organizing Turing system of molecular interactions (Figure 2D). BMP and Wnt morphogens differentially regulate the expression of Sox9, which functions under the tuning control of FGF and distal Hox genes. Last, the Sonic hedgehog morphogen provides an earlier polarization of the distal mesenchyme that influences the specification of digit identity along the anterior-posterior axis.


Figure 1 Gli3 and distal Hox gene expression. The loss of Gli3 combined with progressive reductions in distal Hox genes causes a concomitant increase in the number of digits. The pattern of supernumerary digits follows a Turing-type mechanism of formation (simulations [bottom row] match the expression pattern of Sox9 in the mouse forelimb [photos]). (After Sheth et al. 2012. Science 338: 1476–1480.)
Figure 2 A BMP-Sox9-Wnt Turing-type mechanism governs digit formation. (A) Sox9 gene expression is in alternating stripes with BMP and the Wnt pathway genes, Axin2 and Lef1. (B) Proper limb growth and digit formation are correctly simulated through a Turing mechanism of BMP/Wnt and Sox9 interactions (BSW) paired with distal expression of Hoxd13 and Fgf8. (C) These computer simulations of digit development under this model (top panel) match the endogenous in situ pattern of Sox9 gene expression (bottom panel) remarkably well. (D) Illustration of BMP-Sox9-Wnt expression in the limb bud with a representation of the quantitative differences among these genes along the anterior-posterior axis. (D after A. Zúñiga and R. Zeller. 2014. Science 345: 516–517.)


Literature Cited

Fondon, J. W. and H. R. Garner. 2004. Molecular origins of rapid and continuous morphological evolution. Proc. Natl. Acad. Sci. USA 101: 18058–18063.
PubMed Link

Litingtung, Y., R. D. Dahn, Y. Li, J. F. Fallon and C. Chiang. 2002. Shh and Gli3 are dispensable for limb skeleton formation but regulate digit number and identity. Nature 418: 979–983.
PubMed Link

Raspopovic, J., L. Marcon, L. Russo, and J. Sharpe. 2014. Modeling digits. Digit patterning is controlled by a BMP-Sox9-Wnt Turing network modulated by morphogen gradients. Science 345: 566–570.
PubMed Link

Sheth, R., L. Marcon, M. F. Bastida, M. Junco, L. Quintana, R. Dahn, M. Kmita, J. Sharpe and M. A. Ros. 2012. Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism. Science 338: 1476–1480.
PubMed Link

te Welscher, P., A. Zuniga, S. Kuijper, T. Drenth, H. J. Goedemans, F. Meijlink, and R. Zeller. 2002. Progression of vertebrate limb development through SHH-mediated counteraction of GLI3. Science 298: 827–830.
PubMed Link

Zúñiga, A. and R. Zeller. 2014. In Turing's hands: The making of digits. Science 345: 516–517.
PubMed Link


1. Thus, dogs with larger limb buds may generate enough cells that an additional cartilage condensation can fit into the autopod (Alberch 1985). Such appears to be the case with the St. Bernard and Great Pyrenees breeds. Fondon and Garner (2004) have shown that one allele of the Alx4 gene is homozygous in only one breed of dog, the Great Pyrenees. These dogs are characterized by polydactyly (an extra toe, the dew claw). Here, there is apparently more growth of the limb bud such that another condensation can emerge in the autopod.



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