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arXiv · 1511.08626

Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles

Stefanie Hirsch·Dietmar Oelz·Christian Schmeiser
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Abstract

The model for disordered actomyosin bundles recently derived by Oelz, in the work 'A viscous two-phase model for contractile actomyosin bundles' (Math. Biol., 68 (2013), 1653--1676) includes the effects of cross-linking of parallel and anti-parallel actin filaments, their polymerization and depolymerization, and, most importantly, the interaction with the motor protein myosin, which leads to sliding of anti-parallel filaments relative to each other. The model relies on the assumption that actin filaments are short compared to the length of the bundle. It is a two-phase model which treats actin filaments of both orientations separately. It consists of quasi-stationary force balances determining the local velocities of the filament families and of transport equations for the filaments. Two types of initial-boundary value problems are considered, where either the bundle length or the total force on the bundle are prescribed. In the latter case, the bundle length is determined as a free boundary. Local in time existence and uniqueness results are proven. For the problem with given bundle length, a global solution exists for short enough bundles. For small prescribed force, a formal approximation can be computed explicitly, and the bundle length tends to a limiting value.

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Stefanie Hirsch, Dietmar Oelz, Christian Schmeiser. 2015-11-27. Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles. https://arxiv.org/abs/1511.08626

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