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A diffusion model for cell polarization with interactions on the membrane

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Abstract

We deal with a two-component system of linear diffusion equations in the bulk, under nonlinear interactions on the boundary. We give discussions on the existence and stability of equilibrium solutions. In particular, a stable non-uniform equilibrium solution is considered as representing a polarized state of a cell. Conditions for the stability of equilibrium solutions are given. To illustrate the results in concrete terms, we also analyze one dimensional problem in detail.

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Acknowledgements

The authors would like to thank the referees for useful comments for the revisions.

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Authors and Affiliations

  1. Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194, Japan

    Yoshihisa Morita

  2. Department of Mathematical and Life Sciences, Hiroshima University, 1-3-2 Kagamiyama, Higashihiroshima, 739-8526, Japan

    Kunimochi Sakamoto

Authors
  1. Yoshihisa Morita
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  2. Kunimochi Sakamoto
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Corresponding author

Correspondence to Yoshihisa Morita.

Additional information

Dedicated to Professor Masayasu Mimura on the occasion of his 75th birthday.

Yoshihisa Morita was partially supported by JSPS KAKENHI, (B) 26287025 and (A) 26247013. Kunimochi Sakamoto was partially supported by JSPS KAKENHI, (B) 26287025 and (C) 16K05231.

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Morita, Y., Sakamoto, K. A diffusion model for cell polarization with interactions on the membrane. Japan J. Indust. Appl. Math. 35, 261–276 (2018). https://doi.org/10.1007/s13160-017-0290-8

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  • DOI: https://doi.org/10.1007/s13160-017-0290-8

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