Abstract
Patterns resulting from the sole interplay between reaction and diffusion are probably involved in certain stages of morphogenesis in biological systems, as initially proposed by Alan Turing. Self-organization phenomena of this type can only develop in nonlinear systems (i.e. involving positive and negative feedback loops) maintained far from equilibrium. We present Turing patterns experimentally observed in a chemical system. An oscillating chemical reaction, the CIMA reaction, is operated in an open spatial reactor designed in order to obtain a pure reaction-diffusion system. The two types of Turing patterns observed, hexagonal arrays of spots and parallel stripes, are characterized by an intrinsic wavelength. We identify the origin of the necessary difference of diffusivity between activator and inhibitor. We also describe a pattern growth mechanism by spot splitting that recalls cell division.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Agladze, K., E. Dulos and P. De Kepper (1992). Turing patterns in confined gel and gel-free media. J. Phys. Chem 96: 2400–2403.
Babloyantz, A. (1987). Molecules, Dynamics and Life. New York, Wiley.
Boissonade, J. (1988). Stationary structure induced along a reaction-diffusion front by a Turing symmetry breaking instability. J. Phys. (France). 49: 541–546.
Boissonade, J., E. Dulos and P. De Kepper (1995). Turing patterns: From myth to reality. In: R. Kapral and K. Showalter, eds, Chemical Waves and Patterns, p. 222–268. Amsterdam, Kluwer.
Castets, V., E. Dulos, J. Boissonade and P. De Kepper (1990). Experimental evidence of a sustained standing turing-type nonequilibrium chemical pattern. Phys. Rev. Lett. 64: 2953–2956.
De Kepper, P., I.R. Epstein, K. Kustin and M. Orbán (1982). Batch oscillations and spatial wave patterns in chlorite oscillating systems. J. Phys. Chem. 86: 170–171.
De Kepper, P., V. Castets, E. Dulos and J. Boissonade (1991). Turing-type chemical patterns in the chlorite-iodide-malonic acid reaction. Physica D 46: 161–169.
Dewel, G., D. Walgraef and P. Borckmans (1987). Turing instability in anisotropic systems. J. Chim. Phys. Phys. Chim. Biol. 84: 1335.
Dufiet, V. and J. Boissonade (1996). Dynamics of Turing pattern monolayers close to onset. Phys. Rev. E., submitted.
Dulos, E., J. Boissonade and P. De Kepper (1992). Dynamics and morphology of sustained two-dimensional wavetrains. Physica A 188: 120–131.
Field, R.J. and M. Burger, eds. (1985). Oscillations and Travelling Waves in Chemical Systems. New York, Wiley.
Goodwin, B.C., J.D. Murray and D. Baldwin (1985). Calcium, the elusive morphogen in Acetabularia, In: S. Bonotto, F. Cinelli and R. Billiau, eds, Proc. 6th Intern. Symp. on Acetabularia. Pisa 1984. Belgian Nuclear Center, C.E.N.-S.C.K. Mol, Belgium, 101–108.
Haken, H. (1978). Synergetics, an Introduction. Berlin, Springer-Verlag.
Harrison, L.G., K.T. Graham and B.C. Lakowski (1988). Calcium localization during Acetabularia whorl formation: evidence supporting a two-stage hierarchical mechanism. Development 104: 255–262.
Harrison, L.G. (1993). Kinetic Theory of Living Pattern. Cambridge Univ.Press.
Herschkowitz-Kaufman, M. (1975). Bifurcation analysis of nonlinear reaction-diffusion equations II: steady state solutions and comparison with numerical simulations. Bull. Math. Soc. 37: 589–636.
Hunding, A. (1981). Possible prepatterns governing mitosis: the mechanism of spindle-free chromosome movement in Aulacantha Scolymantha. J. Theor. Biol. 89: 353–385.
Hunding, A. and P.G. Sorensen (1988). Size adaptation of Turing prepattern. J. Math. Biol. 26: 27–39.
Hunding, A., S.A. Kaufman and B.C. Goodwin (1990). Drosophila segmentation: supercomputer simulation of prepattern hierarchy. J.Theor. Biol. 145: 369–384.
Koch A.J. and H. Meinhardt (1994). Biological pattern formation: from basic mechanisms to complex structures. Reviews of modern Physics 66: 1481–1507.
Lacalli, T.C., D. Wilkinson and L.G. Harrison (1988). Theoretical aspects of stripe formation in relation to drosophila segmentation. Development 104: 105–113.
Lee, K.J., W.D. McCormick, J.E. Pearson and H.L. Swinney (1994). Experimental observation of self-replicating spots in a reaction-diffusion system. Nature 369: 215.
Lengyel, L., G. Rabai and I.R. Epstein (1990). Experimental and modeling study of oscillations in the chlorine dioxide-iodin-acid reaction. J. Am. Chem. Soc. 112: 9104–9110.
Lengyel, L. and I.R. Epstein (1992). A chemical approach to designing Turing patterns in reaction-diffusion systems. Proc. Nat Acad. Sci. USA 89: 3977–3979.
Meinhardt, H. (1982). Models of Biological Pattern Formation. New York, Academic Press.
Murray, J.D. (1989). Mathematical Biology. Berlin, Springer-Verlag.
Newman S.A. and H.L. Firsch (1979). Dynamics of squeletal pattern formation in developing chick limb. Science 205: 662–668.
Newman, S.A. and W.A. Comper (1990). ‘Generic’ physical mechanisms of morphogenesis and pattern formation. Development 110: 1–18.
Nicolis, G. and I. Prigogine (1977). Self-Organization in Nonequilibrium Chemical Systems. New York, Wiley.
Noszticzius Z., W. Horsthemke, W.D. McCormick, H.L. Swinney and W.Y. Tam (1987). Sustained chemical waves in an annular gel reactor: a chemical pinwheel. Nature 329: 619–621.
Oster, G.F., J.D. Murray and A.K. Harris (1983). Mechanical aspects of mesenchymal morphogenesis. J. Embryol. exp. Morphol. 78: 83–125.
Ouyang, Q. and H.L. Swinney (1991). Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352: 610–612.
Ouyang, Q. and H.L. Swinney (1991). Transition to chemical turbulence. Chaos 1: 411–420.
Pearson, J.E. and W.J. Bruno (1992). Pattern formation in an N+Q component reaction-diffusion system. Chaos 2: 513.
Pearson, J.E. (1993). Complex pattern in a simple system. Science 261: 189–191.
Prigogine, I. and G. Nicolis (1967). On symmetry-breaking instabilities in dissipative systems. J. Chem. Phys. 46: 3542–3550.
Turing A.M. (1952). The chemical basis of morphogenesis. Philos.Trans. R. Acad. Sci., London, B327: 37–72.
Zeldovich, Y.B. (1944). The Theory of Combustion and Detonation of Gases. Moscou, AN-SSSR.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dulos, E., Boissonade, J., Perraud, J.J. et al. Chemical morphogenesis: Turing patterns in an experimental chemical system. Acta Biotheor 44, 249–261 (1996). https://doi.org/10.1007/BF00046531
Published:
Issue Date:
DOI: https://doi.org/10.1007/BF00046531