Abstract:
In this paper we study a four-species reaction-diffusion system where Turing patterns are stabilized by the presence of fast reversible reactions between the morphogens and two different mobile complexing agents (CAs) that are not necessarily in excess. We provide a quantitative explanation of how the interaction with the CA changes the size of the Turing space making it possible to observe patterns even in a region where the free diffusion coefficients of the relevant species are equal, as is usually the case in real systems. Our analytical treatment gives a series of mathematical relations that can be helpful for those designing experiments where Turing patterns are expected to appear. We also show how the mobility of CAs affect the characteristic size of the pattern. Finally, we provide an example of biological interest in order to illustrate the main procedures and results. © 2004 The American Physical Society.
Registro:
Documento: |
Artículo
|
Título: | Role of complexing agents in the appearance of Turing patterns |
Autor: | Strier, D.E.; Dawson, S.P. |
Filiación: | Departamento de Física, Facultad de Ciencias Exactas y Naturales, Ciudad Universitaria, Buenos Aires, 1428, Argentina
|
Año: | 2004
|
Volumen: | 69
|
Número: | 6
|
Página de inicio: | 10
|
DOI: |
http://dx.doi.org/10.1103/PhysRevE.69.066207 |
Título revista: | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
|
Título revista abreviado: | Phys Rev E.
|
ISSN: | 1063651X
|
Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_1063651X_v69_n6_p10_Strier |
Referencias:
- Glansdorff, P., Prigogine, I., (1971) Thermodynamic Theory of Structure, Stability and Fluctuations, , Wiley
- Nicolis, G., Prigogine, I., (1977) Self-Organization in NonEquilibrium Systems, , Wiley
- Turing, A.M., (1952) Philos. Trans. R. Soc. London, Ser. B, 237, p. 37
- Borckmans, P., Dewel, G., De Wit, A., Dulos, E., Boissonade, J., Gauffre, F., De Kepper, P., Int. J. Bifurcation Chaos Appl. Sci. Eng., 12, p. 2307
- Murray, J.D., (1989) Mathematical Biology, , Springer
- Noszticzius, Z., Horsthemke, W., McCormick, B., Swinney, H., Tam, W., (1987) Nature (London), 329, p. 619
- Castets, V., Dulos, E., Boissonade, J., De Kepper, P., (1990) Phys. Rev. Lett., 64, p. 2953
- De Kepper, P., Castets, V., Dulos, E., Boissonade, J., (1991) Physica D, 49, p. 161
- Boissonade, J., (1988) J. Phys. (Paris), 49, p. 541
- Dewel, G., Walgraef, D., Borckmans, P., (1987) J. Chim. Phys. Phys.-Chim. Biol., 84, p. 1335
- Lengyel, I., Epstein, I., (1991) Science, 251, p. 650
- Lengyel, AI., Rabai, G., Epstein, I., (1990) J. Am. Chem. Soc., 112, p. 4606
- Lengyel, AI., Rabai, G., Epstein, I., (1990) J. Am. Chem. Soc., 112, p. 9104
- Ouyang, Q., Swinney, H., (1991) Nature (London), 352, p. 610
- Ouyang, Q., Swinney, H., (1991) Chaos, 1, p. 411
- Lengyel, I., Epstein, I., (1992) Proc. Natl. Acad. Sci. U.S.A., 89, p. 3977
- Rudovics, B., Barillot, E., Davies, P.W., Dulos, E., Boissonade, J., De Kepper, P., (1999) J. Phys. Chem. A, 103, p. 1790
- Wagner, J., Keizer, J., (1994) Biophys. J., 67, p. 447
- Allbritton, N.L., Meyer, T., Stryer, L., (1992) Science, 258, p. 1812
- Hasslacher, B., Kapral, R., Lawniczak, A., (1993) Chaos, 3, p. 7
- Strier, D.E., Dawson, S.P., (2000) J. Chem. Phys., 112, p. 2
- Strier, D.E., Dawson, S.P., (2000) J. Chem. Phys., 112, p. 825
- Kondo, S., Asai, R., (1995) Nature (London), 376, p. 765
- Strier, D.E., Chernomoretz, A., Dawson, S.P., (2002) Phys. Rev. E, 65, p. 46233
- For example, in experiments where different types of exogenous calcium buffers are added into the cytoplasm of cells, there could be a dramatic difference in the spatiotemporal organization according to the buffer’s mobility. This fact has been clearly demonstrated in experiments done in oocytes, in which a transition from global calcium wave propagation to localized calcium release events (named puffs) could be induced by the addition of one type of mobile buffer (EGTA) but not of another one (BAPTA) c35; We will refer to the activator-inhibitor type in the rest of the paper, but exactly the same results hold for the other case; Sneyd, J., Dale, P., Duffy, A., (1998) SIAM (Soc. Ind. Appl. Math.) J. Appl. Math., 58, p. 4
- Smith, G., ; Strier, D.E., Dawson, S.P., ; This occurs, for example, in the case of cytosolic calcium dynamics, where, although the details of the interactions of calcium with specific membrane receptors are not fully known, yet it is known that buffers dramatically reduce the concentration of free calcium in the cytosol c29 and affect its diffusivity c15; This situation arises in biochemistry, where the same enzyme might bind, in different reaction steps, both, the inhibitor and the activator of a metabolic pathway c29; For example, the CIMA reaction is a particular case, where the starch molecules interact only with iodide c9. This case is also relevant in biochemistry, with the CA representing two different buffers or enzymes; Sec. 3 we analyze a particular example of this procedure. See Ref. for a general treatment; Keener, J., Sneyd, J., (1998) Mathematical Physiology, , Springer-Verlag
- Bruno, W., Pearson, J.E., (1992) Chaos, 2, p. 513
- This was first recognized in Ref; Goodwin, B.C., Murray, J.D., Baldwin, D., ; Michailova, A., DelPrincipe, F., Egger, M., Niggli, E., (2002) Biophys. J., 83, p. 3134
- Meinhardt, H., (1999) On Growth and Form: Spatio-temporal Pattern Formation in Biology, pp. 129-148. , M. A. J. Chaplain, G. D. Singh, and J. C. McLachlan, Wiley
- Callamaras, N., Parker, I., (2000) EMBO J., 19, p. 3608
- Marchant, J.S., Parker, I., (2001) EMBO J., 20, p. 65
- Schnackenberg, J., (1979) J. Theor. Biol., 81, p. 389
Citas:
---------- APA ----------
Strier, D.E. & Dawson, S.P.
(2004)
. Role of complexing agents in the appearance of Turing patterns. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, 69(6), 10.
http://dx.doi.org/10.1103/PhysRevE.69.066207---------- CHICAGO ----------
Strier, D.E., Dawson, S.P.
"Role of complexing agents in the appearance of Turing patterns"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics 69, no. 6
(2004) : 10.
http://dx.doi.org/10.1103/PhysRevE.69.066207---------- MLA ----------
Strier, D.E., Dawson, S.P.
"Role of complexing agents in the appearance of Turing patterns"
. Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, vol. 69, no. 6, 2004, pp. 10.
http://dx.doi.org/10.1103/PhysRevE.69.066207---------- VANCOUVER ----------
Strier, D.E., Dawson, S.P. Role of complexing agents in the appearance of Turing patterns. Phys Rev E. 2004;69(6):10.
http://dx.doi.org/10.1103/PhysRevE.69.066207