How do patterns develop in nature? How do digits develop on a limb? ~ Hox genes are the answer.

This article is based on the paper entitled “Hox genes regulate digit patterning by controlling the wavelength of a Turing-type mechanism” written by R. Sheth, L. Marcon, M.F. Bastida, M. Junco, L. Quintana, R. Dahn, M. Kmita, J. Sharpe and M. Ros and was published in Science, Vol 338 on December 14, 2012.

How do seashells acquire intricate patterns? How does a popper fish get spots?

Schematic drawing showing the mathematical analysis of the RD system and the patterns generated by the simulation. (A) Six stable states toward which the two-factor RD system can converge. (B) Two-dimensional patterns generated by the Turing model. These patterns were made by an identical equation with slightly different parameter values. These simulations were calculated by the software provided as supporting online material. (C) Reproduction of biological patterns created by modified RD mechanisms. With modification, the RD mechanism can generate more complex patterns such as those seen in the real organism. Image and caption from Kondo and Miura, 2010.

Turing-type model:

In 1952 Alan Turing proposed that natural patterns, like stripes on a tiger’s coat or spots on a fish, could be explained with a mathematical modeling system. He suggested that patterns arise from an interaction between two molecules that diffuse at different rates which he termed “morphogens”: one chemical acts as an activator to express a specific characteristic while the other chemical acts as an inhibitor and therefore has the ability to suppress the activator’s expression. A wave pattern results from the interactions between the two (or more) morphogens. When one morphogen is most concentrated, it not only is present but can also change the presence of another morphogen. Interactions between the activator and inhibitor determine the wavelength of the pattern (see Figure C for “Wave” in the picture below).

Much of Turing’s work was dismissed at first. In fact, until recently, it was thought that many morphological events during development occurred by a simple gradient of a single morphogen rather than by an interaction between two or more morphogens, as we will see later in Sheth et al. 2012. A gradient using a single morphogen can result in stripes (Figure A in the picture below), but not in more complex patterns such as spots.

Schematic drawing showing the difference between the morphogen gradient model and Turing model. (A) A morphogen molecule produced at one end of an embryo forms a gradient by diffusion. Cells “know” their position from the concentration of the molecule. The gradient is totally dependent on the prepattern of the morphogen source (boundary condition). (B) Adding a second morphogen produces a relatively complex pattern; but with no interactions between the morphogens, the system is not selfregulating. (C) With addition of the interactions between the morphogens, the system becomes selfregulating and can form a variety of patterns independent of the prepattern. Picture and caption taken from Kondo and Miura, 2010.

To clarify this example, let’s use a concrete example. To
achieve a leopard spot pattern, an activator produces a dark colored fur while an inhibitor prevents the dark color formation and results in the background gold color. The overall result is black spots on a gold background. A similar mechanism might explain the presence of spots on our Popper fish, or the labyrinth pattern on a seashell. The resulting pattern almost entirely depends on the interactions between two different morphogens, which Turing calls an activator and an inhibitor.

Evidence for Turing’s hypothesis:

Turing’s theories have been investigated recently, and evidence for his theories has been found in many systems including simple chemical systems, molecular signalling in developing embryos, fish scale coloring and even seashell coloring.

Turing Model Evidence in Mouse Digit Formation

Sonic hedgehog, Shh, is a morphogen that is thought to control digit patterning.  Shh is released from the ZPA, zone of polarizing activity, and establishes a gradient that is most concentrated at the posterior of the limb bud, the early stage of limb development in the embryo.

Gli3, another transcription factor, is processed into two forms in the limb bud: Gli3A is the activator form and Gli3R is the repressor form. Shh and Gli3 interact in that Shh prevents Gli3 from being processed to the repressor form, such that a gradient of Gli3R is established which is inverse to the Shh gradient.

Previous work found that Gli3 and Shh:Gli3 null mutants in mice both result in the same mutant polydactyly: they have too many digits. This evidence suggests that digit patterning is established by a Turing-type mechanism rather than by a simple morphogen gradient. (Litingtung et al., 2002; te Welscher et al. 2002) It has been hypothesized that wave patterns occurring during chondrogenesis define the distance between digits as well as the thickness of digits. (Miura et al., 2006)

Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism–Sheth et al.

In 2012, Sheth et al. hypothesized that Hox genes were good candidate molecules for regulating Shh and Gli3 because of interactions between these molecules. It is known that Hoxd12 binds to Gli3R and correspondingly decreases the repressor activity of Gli3R. (Litingtung et al., 2002) Previously, Sheth et al. showed that combined deletion of Hox genes 11-13 and Gli3 made mutations with more than 5 digits worse, which suggested a negative relationship between Hoxd genes, wave pattern (ultimately digit number). Additionally, in another study they found that Hoxd11-13; Gli3 mutants showed a gain of Hoxa13 expression in another study. They therefore examined various mutant phenotypes to look at the relationships between Hoxa13, Hoxd13, and digit number in the following experiments.

Figure 1:

Mouse limb Sox9 expression in various mutant genotypes for Hoxa13(Click on image for more information)

Figure 1: Mouse limb Sox9 expression in various mutant genotypes for Hoxa13. By knocking out Gli3 completely, they generated mouse mutants that were guaranteed to have more than 5 digits. Therefore, they could observe how changing the Hox gene expression altered the mutants without having a confounding factor (Gli3 present). In Fig. 1A, as the number of viable alleles of Hoxa13 decreases from the left to the right, the phenotype becomes more polydactylous and the digits are less defined. Fig. 1B shows the wavelength formed by measuring the distance between each point along a curve (the yellow line) with how far it is from marked chondrocytes. That is, the apex of each wave is the center of each digit and the trough is interdigitial tissue that is farthest from condrocyte tissue: this is also called the digit period.

By varying the types of Turing interactions between the activator and inhibitor that produce wavelengths, the authors were able to simulate the outcomes of different types of mutants in Fig. 1 D and E. More specific information of how exactly the authors completed these simulations can be found in the supplementary information.

Figure 2:

Skeletal phenotypes of mouse mutants. + indicates a normal allele and - , XtJ, or Del11-13 indicate an allele knockout or abnormal allele. Hox genes are indicated by column and Gli3 genes are indicated by row. (Click on image for more information)

Figure 2: As mentioned previously, Hoxa13; Gli3 double mutants showed ectopic anterior expression of Hoxd12 and Hoxd13 and the authors wanted to verify that polydactyly was not due increased expression of these genes. To do so, they generated triple mutants (for Hoxa13, Hoxd11-13, and Gli3). They observed that not only were polydactylous mutants observed, but also fused and shortened digits and absence of joints among other defects.

Then next question one should ask is, “In what way did the mutant alleles cause polydactyly?” It seems that the authors put forth two hypotheses to explain this occurrence: 1) There could be an increase in the distance from “mouse thumb” to “mouse pinkie” by having an overall wider (anterior to posterior) paw or 2) The width of the paw can remain the same, but the digits themselves can become narrower (compare WT to the homozygous double mutant in Figure 1A and 2) Interestingly, their experiment supports the second hypothesis because the digits and gaps between the digits were more narrow. This result supports the Turing-type model because a simple morphogen gradient system is not sufficient to explain the results in Figure 2. If digit development was guided by a simple morphogen gradient, then a single morphogen would be able to regulate proper digit formation: that is, Gli3 or a Hox gene would be sufficient as knockouts of either results in malformed digits.

Figure 3:

Manipulation of Gli3 and multiple Hox genes causes severe polydactyly. The Turing model correctly predicts phenotypes for various mutants. (Click on image for more information)

Figure 3: The top three rows are of mutants with decreasing numbers of viable Hoxa13 or Hoxd11-13 alleles. The bottom two rows show the most severe mutant phenotypes when Gli3 is completely knocked out. The bottom row is a reaction-diffusion computer simulation of the Turing model. Notice how the simulation parallels the experimentally manipulated embryos.

Figure 4:

Figure 4: Schematic of the Turing model used in this study. Graphs showing the average digit period of different mutants. (Click on image for more information)

Figure 4 shows a schematic of the Turing model used in this study. Fig. 4B and C show the average digit period for different mutants. Notice how the average digit period decreases and the number of mutant alleles increases with the black line representing wild type. More clearly, the digits and interdigital spaces get more narrow as the mutant phenotype gets progressively more severe.

The authors conclude that these studies provide evidence supporting the hypothesis that distal Hox genes are necessary for correct digit formation and are parameters that complete Turing-type regulation of wavelength of digit formation. Additionally, they state that Hox genes are necessary for “an intrinsic self-organizing Turing-type mechanism responsible for digit patterning.”

Figure 5:

Figure 5: Phylogenetic tree of tetrapods and ancestors with images of limb similarities. (Click on image for more information)

The authors go on to discuss how Hox genes played a role in the fin-to-limb transition. Below, in Figure 5, they show how abnormalities in mouse limb development look remarkably similar to skeletons of early tetrapods, ray-finned fishes and cartilaginous fish like sharks. While these speculations have not been empirically studied in these organisms, the similarity does provide convincing visual evidence that an ancestral Turing-like mechanism was conserved in tetrapods and that regulation of conserved Hox genes played a very important role in the evolution of tetrapods from fish.


In conclusion, Sheth et al. provide pretty convincing evidence that a Turing mechanism is responsible for the regulation of Hox genes in mouse digit development because they could use Turing’s equations to predict the effects of eliminated Gli3 expression and decreased Hox gene expression on mouse digit formation.

Thoughts on the Paper:

Generally, I thought this paper was very strong. The authors successfully demonstrated that Turing’s hypothesized equations correctly predict the patterning occurring in digit development.  They left out the equations used and simulations performed of the main text of this work, but they can be found in the supplementary materials. If you are mathematically inclined, you will find this even more fascinating than the work itself as they provide detailed explanations of how they used Turing’s equations.

One of the only reservations about this work was the rather large leap they made in the tetrapod evolution comparison seen in Figure 5. I am not sure how much is known about Hox gene expression in extinct organisms, and I cannot imagine how one would go about studying this. It is clear that empirical studies need to be conducted to test the effects of varying Hox gene expression on other tetrapods and tetrapods extant ancestors such as the cartilaginous and ray-finned fishes they mention in Figure 5. I wonder what they have up their sleeves as a follow up to this experiment. Could they be studying the effects of altered Hox gene expression on fish? This is entirely speculation, but perhaps by increasing the Hox gene expression in a fish study system, they could produce a animal with a pentydactyl-like appendage? Intriguing!


Kondo, S. and Miura, T. Biological pattern formation reaction-diffusion model as a framework for understanding biological pattern formation. 2010. Science, 329, 1616-1620.

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

Miura, T., Shiota, K., Morriss-Kay, G., and Maini, P. K. Mixed-mode pattern in Doublefoot mutant mouse limb—Turing reaction-diffusion model on a growing domain during limb development. 2006. Journal of Theoretical Biology, 240, 562-573.

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

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

Tickle, C. Making digit pattern in the vertebrate limb. 2006. Nature Reviews, 7, 45-53.

Turing, A. M. The chemical basis of morphogenesis. 1952. Philos. Trans. R. Soc. London Ser. B. 237, 37-72.

Website References:

“Turing Mechanism And The Biology Of How We Generate Our Fingers And Toes.” Science 2.0 Join the Revolution. Ion Publications, 15 December 2012. Web. 22 April 2013.

Keim, Brandon. “Alan Turing’s Patterns in Nature, and Beyond.” Wired. Condé Nast Websites, 22 February 2011. Web. 22 April 2013.

Ouellette, Jennifer. “Biologists Home in on Turing Patterns.” Simons Foundation–Advancing Research in Basic Science and Mathematics.  N.P. 25 March 2013. Web. 22 April 2013.

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