1952 scholarly article by Alan Turing
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] 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] 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 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] nonlinear partial differential equations , there are often possibilities for an analytical treatment.[ 7] [ 8] [ 9]
See also
References
^ 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 .^ Harrison, L.G. (1993). Kinetic Theory of Living Pattern . Cambridge University Press .
^ 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 . ^ 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
^ Meinhardt, H. (1982). Models of Biological Pattern Formation . Academic Press . ^ Murray, James D. (9 March 2013). Mathematical Biology 436– 450. ISBN 978-3-662-08539-4 ^ Grindrod, P. Patterns and Waves: The Theory and Applications of Reaction-Diffusion Equations, Clarendon Press (1991)
^ Smoller, J. Shock Waves and Reaction Diffusion Equations, Springer (1994)
^ Kerner, B. S. and Osipov, V. V. Autosolitons. A New Approach to Problems of Self-Organization and Turbulence, Kluwer Academic Publishers (1994).
