The Chemical Basis of Morphogenesis

Turing's paper explained how natural patterns, such as stripes, spots, and spirals, like those of the giant pufferfish, may arise.

"The Chemical Basis of Morphogenesis" is an article that the English mathematician Alan Turing wrote in 1952.[1] It describes how patterns in nature, such as stripes and spirals, can arise naturally from a homogeneous, uniform state. The theory, which can be called a reaction–diffusion theory of morphogenesis, has become a basic model in theoretical biology.[2] Such patterns have come to be known as Turing patterns. For example, it has been postulated that the protein VEGFC can form Turing patterns to govern the formation of lymphatic vessels in the zebrafish embryo.[3]

Reaction–diffusion systems

Main article: Reaction–diffusion system

Reaction–diffusion systems have attracted much interest as a prototype model for pattern formation. Patterns such as fronts, spirals, targets, hexagons, stripes and dissipative solitons are found in various types of reaction-diffusion systems in spite of large discrepancies e.g. in the local reaction terms. Such patterns have been dubbed "Turing patterns".[4]

Reaction–diffusion processes form one class of explanation for the embryonic development of animal coats and skin pigmentation.[5][6] Another reason for the interest in reaction-diffusion systems is that although they represent nonlinear partial differential equations, there are often possibilities for an analytical treatment.[7][8][9]

See also

References

  1. ^ Turing, Alan (1952). "The Chemical Basis of Morphogenesis" (PDF). Philosophical Transactions of the Royal Society of London B. 237 (641): 37–72. Bibcode:1952RSPTB.237...37T. doi:10.1098/rstb.1952.0012. JSTOR 92463. S2CID 120437796.
  2. ^ Harrison, L.G. (1993). Kinetic Theory of Living Pattern. Cambridge University Press.
  3. ^ Wertheim, Kenneth (2019). "Can VEGFC form turing patterns in the Zebrafish embryo?". Bulletin of Mathematical Biology. 81 (4): 1201–1237. doi:10.1007/s11538-018-00560-2. PMC 6397306. PMID 30607882.
  4. ^ Wooley, T. E., Baker, R. E., Maini, P. K., Chapter 34, Turing's theory of morphogenesis. In Copeland, B. Jack; Bowen, Jonathan P.; Wilson, Robin; Sprevak, Mark (2017). The Turing Guide. Oxford University Press. ISBN 978-0198747826.
  5. ^ Meinhardt, H. (1982). Models of Biological Pattern Formation. Academic Press.
  6. ^ Murray, James D. (9 March 2013). Mathematical Biology. Springer Science & Business Media. pp. 436–450. ISBN 978-3-662-08539-4.
  7. ^ Grindrod, P. Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
  8. ^ Smoller, J. Shock Waves and Reaction Diffusion Equations, Springer (1994)
  9. ^ Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers (1994).