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September  2016, 36(9): 4945-4962. doi: 10.3934/dcds.2016014

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

1. 

Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria

2. 

Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, N.Y. 10012-1185, United States, United States

Received  August 2015 Revised  October 2015 Published  May 2016

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

References:
[1]

Cell, 137 (2009), 926-937. doi: 10.1016/j.cell.2009.03.021.  Google Scholar

[2]

J. Biol. Chemistry, 285 (2010), 26350-26357. Google Scholar

[3]

J. Physiology, 243 (1974), 1-43. Google Scholar

[4]

Int. J. Biochem. Cell Biol., 42 (2010), 1614-1617. doi: 10.1016/j.biocel.2010.06.019.  Google Scholar

[5]

J. Math. Pures Appl., 96 (2011), 484-501. doi: 10.1016/j.matpur.2011.03.005.  Google Scholar

[6]

J. Math. Biol., 68 (2013), 1653-1676. doi: 10.1007/s00285-013-0682-6.  Google Scholar

[7]

Physica-D., 318 (2016), 70-83. doi: 10.1016/j.physd.2015.10.005.  Google Scholar

[8]

Discrete and Continuous Dynamical Systems - Series A, 36 (2016), 4553-4567. doi: 10.3934/dcds.2016.36.4553.  Google Scholar

[9]

Accepted for publication in Biophys. J., (2015). Google Scholar

[10]

Arch. Rational Mech. Anal., 198 (2010), 963-980. doi: 10.1007/s00205-010-0304-z.  Google Scholar

[11]

Biochimica et Biophysica Acta - Molecular Cell Research, 1404 (1998), 271-281. doi: 10.1016/S0167-4889(98)00080-9.  Google Scholar

[12]

J. Cell Biol., 139 (1997), 397-415. doi: 10.1083/jcb.139.2.397.  Google Scholar

[13]

Nature Rev. Mol. Cell Biol., 10 (2009), 778-790. doi: 10.1038/nrm2786.  Google Scholar

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