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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


Dumitru Baleanu (editor)

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


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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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.


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


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