Tomography of Reaction-Diffusion Microemulsions Reveals Three-Dimensional Turing Patterns
Abstract
Spatially periodic, temporally stationary patterns that emerge from instability of a homogeneous steady state were proposed by Alan Turing in 1952 as a mechanism for morphogenesis in living systems and have attracted increasing attention in biology, chemistry, and physics. Patterns found to date have been confined to one or two spatial dimensions. We used tomography to study the Belousov-Zhabotinsky reaction in a microemulsion in which the polar reactants are confined to aqueous nanodroplets much smaller than the scale of the stationary patterns. We demonstrate the existence of Turing patterns that can exist only in three dimensions, including curved surfaces, hexagonally packed cylinders, spots, and labyrinthine and lamellar patterns.
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References and Notes
1
Turing A. M., The chemical basis of morphogenesis. Philos. Trans. R. Soc. London. Ser. B 237, 37 (1952).
2
Castets V., Dulos E., Boissonade J., De Kepper P., Experimental evidence of a sustained standing Turing-type nonequilibrium chemical pattern. Phys. Rev. Lett. 64, 2953 (1990).
3
Ouyang Q., Swinney H. L., Transition from a uniform state to hexagonal and striped Turing patterns. Nature 352, 610 (1991).
4
De Kepper P., Epstein I. R., Kustin K., Orbán M., Systematic design of chemical oscillators. Part 8. Batch oscillations and spatial wave patterns in chlorite oscillating systems. J. Phys. Chem. 86, 170 (1982).
5
Jiang T. X., Jung H. S., Widelitz R. B., Chuong C. M., Self-organization of periodic patterns by dissociated feather mesenchymal cells and the regulation of size, number and spacing of primordia. Development 126, 4997 (1999).
6
Jung H. S., et al., Local inhibitory action of BMPs and their relationships with activators in feather formation: Implications for periodic patterning. Dev. Biol. 196, 11 (1998).
7
Sick S., Reinker S., Timmer J., Schlake T., WNT and DKK determine hair follicle spacing through a reaction-diffusion mechanism. Science 314, 1447 (2006); .
8
Maini P. K., Baker R. E., Chuong C.-M., The Turing model comes of molecular age. Science 314, 1397 (2006).
9
Kondo S., Miura T., Reaction-diffusion model as a framework for understanding biological pattern formation. Science 329, 1616 (2010).
10
Liu R. T., Liaw S. S., Maini P. K., Two-stage Turing model for generating pigment patterns on the leopard and the jaguar. Phys. Rev. E 74, 011914 (2006).
11
Callahan T. K., Turing patterns with O(3) symmetry. Physica D 188, 65 (2004).
12
De Wit A., Borckmans P., Dewel G., Twist grain boundaries in three-dimensional lamellar Turing structures. Proc. Natl. Acad. Sci. U.S.A. 94, 12765 (1997).
13
Leppänen T., Karttunen M., Kaski K., Dimensionality effects in Turing pattern formation. Int. J. Mod. Phys. B 17, 5541 (2003).
14
Horváth J., Szalai I., De Kepper P., An experimental design method leading to chemical Turing patterns. Science 324, 772 (2009).
15
Dulos E., Davies P., Rudovics B., De Kepper P., From quasi-2D to 3D Turing patterns in ramped systems. Physica D 98, 53 (1996).
16
Moore P. K., Horsthemke W., Three-dimensional patterns in the Lengyel-R′bai-Epstein model of the chlorine dioxide-iodine-malonic acid reaction. Chaos 19, 043116 (2009).
17
Winfree A. T., Caudle S., Chen G., McGuire P., Szilagyi Z., Quantitative optical tomography of chemical waves and their organizing centers. Chaos 6, 617 (1996).
18
Storb U., Neto C. R., Bär M., Müller S. C., A tomographic study of desynchronization and complex dynamics of scroll waves in an excitable chemical reaction with a gradient. Phys. Chem. Chem. Phys. 5, 2344 (2003).
19
Bánsági T., Steinbock O., Three-dimensional spiral waves in an excitable reaction system: Initiation and dynamics of scroll rings and scroll ring pairs. Chaos 18, 026102 (2008).
20
Vanag V. K., Boulanov D. V., Behavior of the Belousov-Zhabotinskii oscillator in reverse micelles of AOT in octane. J. Phys. Chem. 98, 1449 (1994).
21
Vanag V. K., Epstein I. R., Inwardly rotating spiral waves in a reaction-diffusion system. Science 294, 835 (2001).
22
Vanag V. K., Epstein I. R., Pattern formation in a tunable medium: The Belousov-Zhabotinsky reaction in an aerosol OT microemulsion. Phys. Rev. Lett. 87, 228301 (2001).
23
A. S. Kak, M. Slaney, Principles of Computerized Tomographic Imaging (IEEE Press, New York, 1988).
24
Kaminaga A., Vanag V. K., Epstein I. R., “Black spots” in a surfactant-rich Belousov-Zhabotinsky reaction dispersed in a water-in-oil microemulsion system. J. Chem. Phys. 122, 174706 (2005).
25
Shoji H., Yamada K., Ueyama D., Ohta T., Turing patterns in three dimensions. Phys. Rev. E 75, 046212 (2007).
26
Newman S. A., Frisch H. L., Dynamics of skeletal pattern formation in developing chick limb. Science 205, 662 (1979).
27
Augustin R., et al., Dickkopf related genes are components of the positional value gradient in Hydra. Dev. Biol. 296, 62 (2006).
28
Leda M., Vanag V. K., Epstein I. R., Instabilities of a three-dimensional localized spot. Phys. Rev. E 80, 066204 (2009).
29
Coullet P., Riera C., Tresser C., A new approach to data storage using localized structures. Chaos 14, 193 (2004).
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Published In
Science
Volume 331 | Issue 6022
11 March 2011
11 March 2011
Copyright
Copyright © 2011, American Association for the Advancement of Science.
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Submission history
Received: 23 November 2010
Accepted: 26 January 2011
Published in print: 11 March 2011
Acknowledgments
We thank M. Hauser for helpful discussions, J. Carballido-Landeira for preliminary experiments, and F. Mello for assistance in constructing the tomography apparatus. This work was funded by the NSF under grants CHE-0615507, CHE-0526866, and NSF Materials Research Science and Engineering Center grant DMR-0820492 and a U.S.-Hungarian Cooperative Grant. I.R.E. thanks the Radcliffe Institute for a fellowship.
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