page_title: Turing pattern
section_title: Biological application
hierarchical_section_title: Turing pattern / Biological application
caption_attribution_description: English: (Simulations of effect of limb bud distal expansion. ZPA graft (left) expanded chicken wing bud that results from anterior graft of an ectopic zone of polarizing activity from the proximal posterior region of another wing bud (normal limb profile at this stage shown in red); (center) resulting cartilage skeleton, with mirror-image duplication; (right) end-stage of simulation with distal expansion corresponding to that shown on left. Shh2/2, Gli32/2 (left) expanded mouse forelimb bud in embryos null for both Shh and Gli3 (normal limb profile at this stage shown in red); (center) resulting skeleton, with supernumerary digits [61]; (right) end-stage of simulation with distal expansion corresponding to that shown on left. talpid2 (left) expanded wing bud of chicken embryo homozygous for talpid2 mutation; (center) cartilage skeleton formed from such a limb bud later during development; (right) end-stage of simulation with distal expansion corresponding to that shown on left. Dogfish (left) shape of the pectoral fin-bud in an embryo of the dogfish Scyliorhinus torazame; (center) cartilaginous fin skeleton formed from such a limb bud [5]; (right) end-stage of simulation using a limb bud contour like that shown on left. In each of these simulations reaction parameter values different from the standard ones were used
context_page_description: The English mathematician Alan Turing introduced a concept, which came to be known as a Turing pattern, in a 1952 paper entitled "The Chemical Basis of Morphogenesis". This foundational paper describes how patterns in nature, such as stripes and spots, can arise naturally and autonomously from a homogeneous, uniform state. In his classic paper, Turing examined the behaviour of a system in which two diffusible substances interact with each other, and found that such a system is able to generate a spatially periodic pattern even from a random or almost uniform initial condition. Turing hypothesized that the resulting wavelike patterns are the chemical basis of morphogenesis.
context_section_description: A mechanism that has gained increasing attention as a generator of spot- and stripe-like patterns in developmental systems is related to the chemical reaction-diffusion process described by Turing in 1952. This has been schematized in a biological "local autoactivation-lateral inhibition" (LALI) framework by Meinhardt and Gierer. LALI systems, while formally similar to reaction-diffusion systems, are more suitable to biological applications, since they include cases where the activator and inhibitor terms are mediated by cellular ‘‘reactors’’ rather than simple chemical reactions, and spatial transport can be mediated by mechanisms in addition to simple diffusion. This models can be applied to limb formation and teeth development among other examples.
  
  Reaction-diffusion models can be use to forecast the exact location of the tooth cusps in mice and voles based on differences in gene expression patterns. The model can be use to explain the differences in gene expression between mica and voles tooth, the signaling center of the tooth, enamel knot, secrets BMPs, FGFs and Shh. Shh and FGF inhibits BMP production, while BMP stimulates both the production of more BMPs and the synthesis of their own inhibitors. BMPs also induce epithelial differentiation, while FGFs induce epithelial growth. The result is a pattern of gene activity that changes as the shape of the tooth changes, and vice versa. Under this model, the large differences between mouse and vole molars can be generated by small changes in the binding constants and diffusion rates of the BMP and Shh proteins. A small increase in the diffusion rate of BMP4 and a stronger binding constant of its inhibitor is sufficient to change the vole pattern of tooth growth into that of the mouse.
caption: Simulations of effect of limb bud distal expansion [18]
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