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

Hirsch, Stefanie, Oelz, Dietmar and Schmeiser, Christian (2016) Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles. Discrete and Continuous Dynamical Systems - Series A, 36 9: 4945-4962. doi:10.3934/dcds.2016014

Author Hirsch, Stefanie
Oelz, Dietmar
Schmeiser, Christian
Title Existence and uniqueness of solutions for a model of non-sarcomeric actomyosin bundles
Journal name Discrete and Continuous Dynamical Systems - Series A   Check publisher's open access policy
ISSN 1078-0947
Publication date 2016-09-01
Year available 2016
Sub-type Article (original research)
DOI 10.3934/dcds.2016014
Open Access Status Not yet assessed
Volume 36
Issue 9
Start page 4945
End page 4962
Total pages 18
Place of publication Springfield, MO United States
Publisher American Institute of Mathematical Sciences
Language eng
Abstract The model for disordered actomyosin bundles recently derived in [6] 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 equation 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.
Keyword Actomyosin bundles
(Free) boundary value problem
Fixed-point methods
Asymptotic methods
Long time behavior
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collections: School of Mathematics and Physics
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Created: Fri, 13 Jan 2017, 22:52:08 EST by Kay Mackie on behalf of School of Mathematics & Physics