The Turing mechanism in vertebrate limb patterning

Newman, Stuart A.

doi:10.1038/nrm1830-c1

Correspondence
Published: June 2007

The Turing mechanism in vertebrate limb patterning

Stuart A. Newman¹

Nature Reviews Molecular Cell Biology volume 8, page 1 (2007)Cite this article

2111 Accesses
9 Citations
Metrics details

Access through your institution

Buy or subscribe

In the Review 'Making digit patterns in the vertebrate limb'¹, Cheryll Tickle discusses evidence that the long-standing concept of 'positional information' — which was formulated to account for differences in the appearance of distinct skeletal elements — is inadequate to explain the number and arrangement of such elements. As an alternative means for laying out the overall template for the limb skeleton, she briefly mentions an entirely different mechanism of pattern formation: the reaction–diffusion model, which was originally put forward by the mathematician A.M. Turing². As Tickle states, “The series of many unpatterned digits, which develop in the absence of GLI3 function in mouse mutants, is reminiscent of the digit pre-pattern that has been proposed to function in combination with the morphogen gradient³. According to this proposal, a series of digit condensations, a pre-pattern, is specified by a wave-like distribution of a morphogen that is generated by a reaction–diffusion mechanism, with the peaks corresponding to the condensations. A gradient of another morphogen ... then provides each peak with a positional value and a digit identity. The number of peaks that are generated by the reaction–diffusion mechanism depends on the width of the limb.”

The proposal that the limb skeleton is generated by a reaction–diffusion mechanism, with other morphogen gradients having a fine-tuning role, was first made not in the 1989 review³ that she cites, but a decade previously, in conjunction with a specific model for the production of patterns of pre-cartilage condensation through the interaction of mesenchymal cells with morphogens and with the extracellular matrix (ECM)⁴. More importantly, Tickle failed to describe research in the ensuing three decades that has seriously considered, tested and elaborated on the role of reaction–diffusion patterning in limb development. This includes a series of papers by Takashi Miura and his colleagues that provided evidence for a reaction–diffusion mechanism over a mechanochemical alternative in an in vitro model for pre-chondrogenic pattern formation⁵, and for the functionality of transforming growth factor-β2 (TGFβ2) as the activator in a reaction–diffusion scheme⁶. Later, it was demonstrated that lateral inhibition of limb pre-cartilage condensation (a necessary component of the reaction–diffusion framework) was induced by ectodermally produced fibroblast growth factors (FGFs)⁷. This was followed by a reaction–diffusion-based mathematical analysis⁸ that accounted for the coordinate effects of FGFs in laterally inhibiting and accelerating the rate of appearance of foci of pre-cartilage condensation. Miura and co-workers also showed that the peculiar 'thick–thin' morphology of limb skeletal elements that is observed in doublefoot-mutant mice could be understood by assuming that a reaction–diffusion mechanism underlies skeletal patterning⁹.

This is a preview of subscription content, access via your institution

Access options

Access through your institution

Buy this article

Purchase on SpringerLink
Instant access to the full article PDF.

USD 39.95

Prices may be subject to local taxes which are calculated during checkout

References

Tickle, C. Making digit patterns in the vertebrate limb. Nature Rev. Mol. Cell Biol. 7, 45–53 (2006).
Article CAS Google Scholar
Turing, A. The chemical basis of morphogenesis. Phil. Trans. R. Soc. Lond. B 237, 37–72 (1952).
Article Google Scholar
Wolpert, L. Positional information revisited. Development 107, 3–12 (1989).
PubMed Google Scholar
Newman, S. A. & Frisch, H. L. Dynamics of skeletal pattern formation in developing chick limb. Science 205, 662–668 (1979).
Article CAS Google Scholar
Miura, T. & Shiota, K. Extracellular matrix environment influences chondrogenic pattern formation in limb bud micromass culture: experimental verification of theoretical models. Anat. Rec. 258, 100–107 (2000).
Article CAS Google Scholar
Miura, T. & Shiota, K. TGFβ2 acts as an 'activator' molecule in reaction–diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture. Dev. Dyn. 217, 241–249 (2000).
Article CAS Google Scholar
Moftah, M. Z. et al. Ectodermal FGFs induce perinodular inhibition of limb chondrogenesis in vitro and in vivo via FGF receptor 2. Dev. Biol. 249, 270–282 (2002).
Article CAS Google Scholar
Miura, T. & Maini, P. K. Speed of pattern appearance in reaction–diffusion models: implications in the pattern formation of limb bud mesenchyme cells. Bull. Math. Biol. 66, 627–649 (2004).
Article Google Scholar
Miura, T., Shiota, K., Morriss-Kay, G. & Maini, P. K. Mixed-mode pattern in doublefoot mutant mouse limb — Turing reaction–diffusion model on a growing domain during limb development. J. Theor. Biol. 240, 562–573 (2006).
Article Google Scholar
Forgacs, G. & Newman, S. A. Biological Physics of the Developing Embryo (Cambridge Univ. Press, Cambridge, 2005).
Book Google Scholar
Hentschel, H. G., Glimm, T., Glazier, J. A. & Newman, S. A. Dynamical mechanisms for skeletal pattern formation in the vertebrate limb. Proc. R. Soc. Lond. B. 271, 1713–1722 (2004).
Article CAS Google Scholar
Chaturvedi, R. et al. On multiscale approaches to three-dimensional modelling of morphogenesis. J. R. Soc. Interface 2, 237–253 (2005).
Article CAS Google Scholar
Cickovski, T. et al. A framework for three-dimensional simulation of morphogenesis. IEEE/ACM Trans. Comput. Biol. Bioinform. 2, 273–288 (2005).
Article Google Scholar
Christley, S., Alber, M. S. and Newman, S. A. Patterns of mesenchymal condensation in a multiscale, discrete stochastic model. PLoS Comput. Biol. 3, e76 (2007).
Article Google Scholar
Alber, M., Hentschel, H. G. E., Kazmierczak, B. & Newman, S. A. Existence of solutions to a new model of biological pattern formation. J. Math. Anal. Appl. 308, 175–194 (2005).
Article Google Scholar
Maini, P. K., Baker, R. E. & Chuong, C. M. Developmental biology. The Turing model comes of molecular age. Science 314, 1397–1398 (2006).
Article CAS Google Scholar
Sick, S., Reinker, S., Timmer, J. & Schlake, T. WNT and DKK determine hair follicle spacing through a reaction–diffusion mechanism. Science 314, 1447–1450 (2006).
Article CAS Google Scholar
Jiang, T. X. et al. Integument pattern formation involves genetic and epigenetic controls: feather arrays simulated by digital hormone models. Int. J. Dev. Biol. 48, 117–135 (2004).
Article CAS Google Scholar
Salazar-Ciudad, I. & Jernvall, J. A gene network model accounting for development and evolution of mammalian teeth. Proc. Natl Acad. Sci. USA 99, 8116–8120 (2002).
Article CAS Google Scholar
Baker, R. E., Schnell, S. & Maini, P. K. A clock and wavefront mechanism for somite formation. Dev. Biol. 293, 116–126 (2006).
Article CAS Google Scholar