Abstract
Since the seminal paper “The chemical basis of morphogenesis” by Alan Turing, the temporal and spatial self-organization phenomena produced in chemically reacting and diffusing systems are often thought as paradigms for biological development. The basic theoretical principles on which the development of stationary concentration patterns (Turing structures) rely on are briefly presented. We review different aspects of our contribution to the experimental observation of reaction-diffusion patterns in iodine-oxychlorine systems. The experimental techniques are emphasized. Phase diagrams gathering different standing and travelling patterns are presented, analyzed and modeled. A special attention is also given to some peculiar pattern growth dynamics (spot division, finger splitting).
It has been suggested that a reaction-diffusion instability could be involved in the cell mitosis mechanism. In an attempt to test for such a contribution, we have performed a systematic study of the effect of geometric deformations (flattening) on the division of sea urchin eggs.
Preview
Unable to display preview. Download preview PDF.
References
A.M. Turing, Philos. Trans. R. S. London, B 327, 37 (1952).
G. Nicolis and I. Prigogine, “Self-organization in Nonequilibrium Chemical Systems” (Wiley, New York, 1977).
H. Meinhardt, “Models of Biological Pattern Formation” (Academic Press, New York, 1982).
A.J. Koch and H. Meinhardt, Reviews of modern physics, 66, 1481, (1994).
J.D. Murray, “Mathematical Biology” (Springer-Verlag, Berlin, 1989).
J.D. Murray and P.M. Kulesa, J. Chem. Soc. Faraday Trans., 92, 2927 (1996).
A. Hunding J. Theoret. Biol., 114, 571 (1985).
A. Hunding J. Theoret. Biol., 89, 353 (1981).
S.A. Newman and H.L. Firsh, Science 205, 662 (1979).
S.A. Newman and W.A. Cooper, Development 110, 1 (1990).
G.F Oster, J.D. Murray, A. K. Harris, J. Embryol. Exp Morphol. 78, 83 (1983).
B.C. Goodwin, J.D. Murray, D. Baldwin, Proc. 6th Intern. Symp. on Acetabularia, Pisa 1984. Belgian Nuclear Center, C.E.N.-S.C.K. Mol, Belgium, 101 (1985).
L.G. Harrisson, K.T. Graham, B.C. Lakowski, Development 104, 255 (1988).
V. Castets, E. Dulos, J. Boissonade, P. De Kepper, Phys. Rev. Lett. 64, 2953 (1990).
S. Chandrasekhar, “Hydrodynamic and Hydromagnetic Stability”, (Oxford Univ. Press, 1961); H.L. Swinney and J.P. Gollub Edts, “Hydrodynamic Instabilities and the Transition to Turbulence”, (Springer, 1981).
D. Walgraef, G. Dewel, P. Borckmans, Adv. Chem. Phys., 49, 311 (1982).
A. De Wit, G. Dewel, P. Borckmans, D. Walgraef, Physica D61, 289 (1992).
J.M. Mitchinson, J. Exp. Biol., 30, 515 (1953).
A.C. Scott Biol. Bull., 119, 246 (1960).
R. Oftebro and I. Wolf, Exp. Cell Res., 48, 39 (1967).
G. Keryer, H. Ris, G.G. Borisy, J. Cell Biol., 98, 2222 (1984).
R. Rappaport, Int. Rev. Cytology, 105, 245 (1986).
G.W. Conrad and T.E. Schroeder, (eds), “Cytokinesis”, Ann. New York Acad. Sci., 582 (1990).
C.F. Asnes and T.E. Schroeder, Exp. Cell Res., 122, 327 (1979).
L. Wordeman, K.L. McDonald, W.Z. Cande, J. Cell Biol., 102, 1688 (1986).
C.L. Rieder, A. Khodjakov, L.V. Paliulis, T.M. Fortier, R.W. Cole, G. Sluder Proc. Nat. Acad. Sci. US, 94, 5107 (1997).
S. Bornaccorsi, M.G. Giansanti, M. Gatti, J. Cell Biology, 142, 751 (1998).
P. De Kepper, V. Castets, E. Dulos, J. Boissonade, Physica D49, 161–169 (1991).
K. Agladze, E. Dulos, P. De Kepper, J. Phys. Chem. 96, 2400 (1992).
Q. Ouyang, and H.L. Swinney, Nature, 352, 610 (1991).
P. De Kepper, J.-J. Perraud, B. Rudovics, E. Dulos, Int. J. Bif. Chaos, 4, 1215 (1994).
P. De Kepper, I.R. Epstein, K. Kustin, M. Orbán, J. Phys. Chem., 86, 170 (1982).
Q. Ouyang Ph D Thesis, Bordeaux (1989).
I. Lengyel, G. Rabai, I.R. Epstein, J. Am. Chem. Soc., 112, 9104 (1990).
I. Lengyel and I.R. Epstein, Science, 251, 650 (1990).
I. Lengyel and I.R. Epstein, Proc. Nat. Sci. USA, 89, 3977 (1992).
B. Rudovics Ph D Thesis, Bordeaux (1995).
Zykov V.S., “Simulation of wave processes in excitable media” in Nonlinear Science Theory and Application, (Manchester University Press) (1987).
V.O. Pannbacker, O. Jensen, E. Mosekilde, G. Dewel, and P. Borckmans, in “Spatio-temporal Patterns in Nonequilibrium Complex Systems” Palffy-Muhoray and P. Cladis Eds. (Kluwer, Dordrech 1994).
B. Rudovics, E. Dulos, P. De Kepper, Physica Scripta, T67, 43 (1996).
A.De Wit Ph D Thesis, Bruxelles (1993). A. De Wit, G. Dewel, P. Borckmans, Phys. Rev. E48, R4191 (1993).
E. Dulos, P.W. Davies, B. Rudovics, P. De Kepper, Physica D98, 53 (1996).
J. Verdasca, A. De Wit, G. Dewel, P. Borckmans, Phys. Lett. A 179, 91 (1993).
J.E. Pearson and W.J. Bruno, Chaos, 2, 513 (1992).
J.E. Pearson, Physica A188, 178 (1992).
B. Rudovics, E. Barillot, P.W. Davies, E. Dulos, J. Boissonade, P. De Kepper, J. Phys. Chem., 103, 1790 (1999).
D. Horvàth, V. Petrov, S.K. Scott, and K. Showalter, J. Phys. Chem., 98, 6332 (1993).
A. Hagberg, E. Meron, I. Rubinstein, and B. Zaltman: Phys. Rev., E55, 4450 (1997).
P. Borckmans, G. Dewel, A. De Wit, Physica A188, 137 (1992).
T.C. Lacalli, D.A. Wilkinson, L.G. Harrisson, Development, 104, 105 (1988).
V. Dufiet and J. Boissonade, J. Phys. Rev., E53, 4883 (1996).
M. Bestehorn, Phys. Rev., 53, 4842 (1996).
A. Hagberg and E. Meron, Phys. Rev. Lett., 72, 2494 (1994).
A. Hagberg and E. Meron, Chaos, 4, 477 (1994).
K.J. Lee, W.D. Mc Cormick, J.E. Pearson, H.L. Swinney, Nature, 369 (1994).
K.J. Lee, W.D. Mc Cormick, Q. Ouyang, H.L. Swinney, Science, 261, 192 (1993).
K.J. Lee and H.L. Swinney, Phys. Rev. E51, 1899 (1995).
G. Li, Q. Ouyang, H.L. Swinney J. Chem. Phys., 105, 10830 (1995).
M. Watzl and A.F. Münster, Chem. Phys. Lett., 242, 273 (1995).
M. Glotzer Curr. Opin. Cell Biol., 9, 815 (1997).
D. Sept, Ph D Thesis, University of Alberta, Edmonton, (1997).
A.M. Zhabotinsky, Dokl. Akad. Nauk. USSR, 157, 392 (1964).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1999 Springer-Verlag
About this paper
Cite this paper
Dulos, E., Hunding, A., Boissonade, J., De Kepper, P. (1999). Reaction-diffusion patterns: From observations in halogene chemistry to a test for implication in mitosis. In: Müller, S.C., Parisi, J., Zimmermann, W. (eds) Transport and Structure. Lecture Notes in Physics, vol 532-532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0104236
Download citation
DOI: https://doi.org/10.1007/BFb0104236
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-66632-5
Online ISBN: 978-3-540-48070-9
eBook Packages: Springer Book Archive