### Abstract

Angular self-organization of the actin cytoskeleton is modeled as a process of instant changing of filament orientation in the course of specific actin-actin interactions. These interactions are modified by cross-linking actin-binding proteins. This problem was raised first by Civelekoglu and Edelstein-Keshet [Bull. Math. Biol., 56 (1994), pp. 587-616]. When restricted to a two-dimensional configuration, the mathematical model consists of a single Boltzmann-like integrodifferential equation for the one-dimensional angular distribution. Linear stability analysis, asymptotic analysis, and numerical results reveal that at certain parameter values of actin-actin interactions, spontaneous alignment of filaments in the form of unipolar or bipolar bundles or orthogonal networks can be expected.

Original language | English (US) |
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Pages (from-to) | 787-809 |

Number of pages | 23 |

Journal | SIAM Journal on Applied Mathematics |

Volume | 59 |

Issue number | 3 |

State | Published - 1998 |

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

*SIAM Journal on Applied Mathematics*,

*59*(3), 787-809.