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ISSN:2164-6376 (print)
ISSN:2164-6414 (online)
Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA

Email: dr.volchenkov@gmail.com

Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania

Email: dumitru.baleanu@gmail.com

Breathing Instability in Biological Cells, Patterns of Membrane Proteins

Discontinuity, Nonlinearity, and Complexity 2(1) (2012) 75--84 | DOI:10.5890/DNC.2012.12.001

Marc Leonetti$^{1}$; Gwenn Boëdec$^{1}$; Marc Jaeger$^{2}$

$^{1}$ AixMarseille Universite, IRPHE,UMR CNRS 7342, CentraleMarseille, Technopôle de Château-Gombert, 13384 Marseille Cedex 13, France

$^{2}$ AixMarseille Universite, M2P2, UMR CNRS 7340, Centrale Marseille, Technopôle de Château-Gombert, 13451 Marseille Cedex 13, France

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Abstract

The activity of biological cells involves often the electric activity of its membranes which exhibit various spatiotemporal dynamics, from pulse, oscillatory bifurcation to stationary spatial modulation. This last kind of patterns appears on a typical diffusive time. A model has been proposed implying a coupling between the current flowing through membrane proteins and their electrophoretic motions in the case of mobile proteins. Here, we study the stability of the pattern in a 2D circular model cell versus the appearance of standing waves, the so-called breathing secondary instability.

Acknowledgments

This work has benefited of financial support from the ANR 11−BS09−013−02 and from CNES.

References

  1. [1]  Hodgkin, A.L. and Huxley, A.F. (1952), A quantitative description of membrane current and its application to conduction and excitation in nerve, The Journal of Physiology , 117, 500-544.
  2. [2]  Nagumo, J., Arimoto, S., and Yoshizawa, S. (1962), An active pulse transmission line stimulating nerve axon, Proceedings of the IRE, 50, 2061-2071.
  3. [3]  Fitzhugh, R. (1969), Mathematical models of excitation and propagation in nerve, In: Biological Engineering edited by H.P. Schwan, McGraw Hill N.Y., 1-85.
  4. [4]  Cole, K.S. and Curtis, H.J. (1938), Electrical impedance of nerve during activity, Nature, 142, 209-210.
  5. [5]  Heath, I.B. (1990), Tip Growth in Plant and Fungal Cells, Academic Press NY, San Diego.
  6. [6]  Gow, N.A.R. (1989), Circulating ionic currents in micro-organisms, Advances in Microbial Physiology , 30, 89- 124.
  7. [7]  Hoppe,W., Lohmann,W., Markl, H. and Ziegler, H. (1983),Biophysics, Springer-Verlag.
  8. [8]  Murray, J.D. (2002), Mathematical Biology, Springer, Berlin-Heidelberg.
  9. [9]  Leonetti, M., Dubois-Violette, E. and Homble, F. (2004), Pattern formation of stationary transcellular ionic currents in Fucus, PNAS, 101, 10243-10248.
  10. [10]  Homblé, F. and Leonetti, M. (2007), Emergence of symmetry breaking in fucoid zygotes, Trends in Plant Science, 12, 253-259.
  11. [11]  Larter, R. and Ortoleva, P. (1982), A study of instability to electrical symmetry breaking in unicellular systems, Journal of Theoretical Biology , 96, 175-200.
  12. [12]  Fromherz, P. and Zimmermann (1995), Stable spatially periodic patterns of ion channels in biomembranes, Physical Review E, 51, R1659-R1663.
  13. [13]  Fomherz, P. (1988), Spatiotemporal patterns in the fluid-mosaic model of membranes, PNAS, 85, 6353-6357.
  14. [14]  Leonetti, M. (2012), Pattern formation by electrostatic self-organization of membrane proteins, Chaos, Complexity and Transport, edited by X. Léoncini and M. Leonetti, World Scientific, 94-102.
  15. [15]  Jaffe, L.F. (1977), Electrophoresis along cell membranes, Nature, 265, 600-601.
  16. [16]  Poo, M-m. and Robinson, K.R. (1977), Electrophoresis of concanavalin A receptors along embryonic muscle cell membrane, Nature, 265, 602-605.
  17. [17]  Leonetti, M. and DuboisViolette, E. (1997), Pattern formation by electro-osmotic self-organization in flat biomembranes, Physical Review E, 56, 4521-4525.
  18. [18]  Tarama M., Ohta, T. and Pismen, L.M. (2011), Breathing instability versus drift instability in a two-component reaction-diffusion system, Physical Review E, 83, 017201.
  19. [19]  Hagberg, A. and Meron, E. (1994), Pattern formation in non-gradient reaction-diffusion systems : the effects of front bifurcations, Nonlinearity, 7, 805-835.
  20. [20]  Coombes, S., Schmidt, H. and Bojak, I. (2012), Interface dynamics in planar neural fields models, Journal of Mathematical Neuroscience , 2, 1-27.
  21. [21]  Misbah, C. and Valance, A. (1994), Secondary instabilities in the stabilized Kuramoto-Sivashinsky equation, Physical Review E, 49, 166-183.
  22. [22]  Dangelmayr, G. (1986), Steady-state mode interactions in the presence of O(2)-symmetry, Dynamics and Stability of Systems, 1, 159-185.
  23. [23]  Coullet, P. and Iooss, G. (1990), Instabilities of One-dimensional cellular patterns, Physical Review Letters, 64, 866-869.
  24. [24]  Cole, K.S. (1968), Membranes, Ions and Impulses, University of California Press, Berkeley.
  25. [25]  Leonetti, M. and Dubois-Violette, E. (1998), Theory of electrodynamic instabilities in biological cells, Physical Review Letters, 81, 1977-1980.
  26. [26]  Scott, A. C. (1975), The electrophysics of a nerve fiber, Reviews of Modern Physics, 47, 487-533.
  27. [27]  Leonetti, M. (1998), On biomembrane electrodiffusive models, European Physical Journal B, 2, 325-340.
  28. [28]  Koch, C. (2004),Biophysics of Computation, Oxford University Press, USA.
  29. [29]  Leonetti, M., Nuebler J., and Homble, F. (2006), Parity-breaking instability and global oscillation in patterns of ion channels, Physical Review Letters, 96, 218101.

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