https://doi.org/10.1140/epjp/s13360-023-04606-w
Regular Article
Pattern formation in a one-dimensional MARCKS protein cyclic model with spatially inhomogeneous diffusion coefficients
1
Laboratory of Biophysics, Department of Physics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde, Cameroon
2
Botswana International University of Science and Technology, P/Bag 16, Palapye, Botswana
Received:
13
June
2023
Accepted:
9
October
2023
Published online:
6
November
2023
We analytically investigate the conditions for the wave instability in a reaction-diffusion system describing the nonlinear dynamics of the myristoylated alanine-rich C kinase substrate (MARCKS) between cytosol and cytoplasmic membrane. Taking into account the effect of spatial inhomogeneous diffusion coefficients, and by applying the discrete multiple scale expansion method, we show that the nonlinear generic model can be transformed into a one-dimensional discrete nonlinear Schrödinger equation. We perform a linear stability analysis on the plane wave solutions to derive the criterion of the modulational instability (MI) phenomenon. This analysis reveals that the critical amplitude of the plane wave is highly influenced by the phosphorylation rate and weakly influenced by the inhomogeneous diffusion coefficients. The exact analytical solutions show that the system exhibits traveling waves and periodic array of patterns. The results seem to indicate the features of synchronization in the collective dynamics. In homogenous state, we obtained a spatial pattern of horizontal stripes. By considering the spatial inhomogeneity effect, we obtain a spatial pattern of oblique stripes. We also notice that an increase in wavenumber induces the increase in the number of stripes in the model.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
