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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 |
References:
[1] |
A. Carvalho, A. Desai and K. Oegema, Structural memory in the contractile ring makes the duration of cytokinesis independent of cell size, Cell, 137 (2009), 926-937.
doi: 10.1016/j.cell.2009.03.021. |
[2] |
D. S. Courson and R. S. Rock, Actin cross-link assembly and disassembly mechanics for $\alpha$-actinin and fascin, J. Biol. Chemistry, 285 (2010), 26350-26357. |
[3] |
A. F. Huxley, Muscular contraction, J. Physiology, 243 (1974), 1-43. |
[4] |
A. Jayo and M. Parsons, Fascin: A key regulator of cytoskeletal dynamics, Int. J. Biochem. Cell Biol., 42 (2010), 1614-1617.
doi: 10.1016/j.biocel.2010.06.019. |
[5] |
V. Milisic and D. Ölz, On the asymptotic regime of a model for friction mediated by transient elastic linkages, J. Math. Pures Appl., 96 (2011), 484-501.
doi: 10.1016/j.matpur.2011.03.005. |
[6] |
D. Ölz, A viscous two-phase model for contractile actomyosin bundles, J. Math. Biol., 68 (2013), 1653-1676.
doi: 10.1007/s00285-013-0682-6. |
[7] |
D. Oelz and A. Mogilner, Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array, Physica-D., 318 (2016), 70-83.
doi: 10.1016/j.physd.2015.10.005. |
[8] |
D. Oelz and A. Mogilner, A drift-diffusion model for molecular motor transport in anisotropic filament bundles, Discrete and Continuous Dynamical Systems - Series A, 36 (2016), 4553-4567.
doi: 10.3934/dcds.2016.36.4553. |
[9] |
D. Oelz, B. Rubinstein and A. Mogilner, Contraction of random actomyosin arrays is enabled by the combined effect of actin treadmilling and crosslinking, Accepted for publication in Biophys. J., (2015). |
[10] |
D. Oelz and C. Schmeiser, Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover, Arch. Rational Mech. Anal., 198 (2010), 963-980.
doi: 10.1007/s00205-010-0304-z. |
[11] |
J. V. Small, K. Rottner, I. Kaverina and K. I. Anderson, Assembling an actin cytoskeleton for cell attachment and movement, Biochimica et Biophysica Acta - Molecular Cell Research, 1404 (1998), 271-281.
doi: 10.1016/S0167-4889(98)00080-9. |
[12] |
T. M. Svitkina, A. B. Verkhovsky, K. M. McQuade and G. G. Borisy, Analysis of the actin-myosin II system in fish epidermal keratocytes: mechanism of cell body translocation, J. Cell Biol., 139 (1997), 397-415.
doi: 10.1083/jcb.139.2.397. |
[13] |
M. Vicente-Manzanares, X. Ma, R. S. Adelstein and A. R. Horwitz, Non-muscle myosin II takes centre stage in cell adhesion and migration, Nature Rev. Mol. Cell Biol., 10 (2009), 778-790.
doi: 10.1038/nrm2786. |
show all references
References:
[1] |
A. Carvalho, A. Desai and K. Oegema, Structural memory in the contractile ring makes the duration of cytokinesis independent of cell size, Cell, 137 (2009), 926-937.
doi: 10.1016/j.cell.2009.03.021. |
[2] |
D. S. Courson and R. S. Rock, Actin cross-link assembly and disassembly mechanics for $\alpha$-actinin and fascin, J. Biol. Chemistry, 285 (2010), 26350-26357. |
[3] |
A. F. Huxley, Muscular contraction, J. Physiology, 243 (1974), 1-43. |
[4] |
A. Jayo and M. Parsons, Fascin: A key regulator of cytoskeletal dynamics, Int. J. Biochem. Cell Biol., 42 (2010), 1614-1617.
doi: 10.1016/j.biocel.2010.06.019. |
[5] |
V. Milisic and D. Ölz, On the asymptotic regime of a model for friction mediated by transient elastic linkages, J. Math. Pures Appl., 96 (2011), 484-501.
doi: 10.1016/j.matpur.2011.03.005. |
[6] |
D. Ölz, A viscous two-phase model for contractile actomyosin bundles, J. Math. Biol., 68 (2013), 1653-1676.
doi: 10.1007/s00285-013-0682-6. |
[7] |
D. Oelz and A. Mogilner, Actomyosin contraction, aggregation and traveling waves in a treadmilling actin array, Physica-D., 318 (2016), 70-83.
doi: 10.1016/j.physd.2015.10.005. |
[8] |
D. Oelz and A. Mogilner, A drift-diffusion model for molecular motor transport in anisotropic filament bundles, Discrete and Continuous Dynamical Systems - Series A, 36 (2016), 4553-4567.
doi: 10.3934/dcds.2016.36.4553. |
[9] |
D. Oelz, B. Rubinstein and A. Mogilner, Contraction of random actomyosin arrays is enabled by the combined effect of actin treadmilling and crosslinking, Accepted for publication in Biophys. J., (2015). |
[10] |
D. Oelz and C. Schmeiser, Derivation of a model for symmetric lamellipodia with instantaneous cross-link turnover, Arch. Rational Mech. Anal., 198 (2010), 963-980.
doi: 10.1007/s00205-010-0304-z. |
[11] |
J. V. Small, K. Rottner, I. Kaverina and K. I. Anderson, Assembling an actin cytoskeleton for cell attachment and movement, Biochimica et Biophysica Acta - Molecular Cell Research, 1404 (1998), 271-281.
doi: 10.1016/S0167-4889(98)00080-9. |
[12] |
T. M. Svitkina, A. B. Verkhovsky, K. M. McQuade and G. G. Borisy, Analysis of the actin-myosin II system in fish epidermal keratocytes: mechanism of cell body translocation, J. Cell Biol., 139 (1997), 397-415.
doi: 10.1083/jcb.139.2.397. |
[13] |
M. Vicente-Manzanares, X. Ma, R. S. Adelstein and A. R. Horwitz, Non-muscle myosin II takes centre stage in cell adhesion and migration, Nature Rev. Mol. Cell Biol., 10 (2009), 778-790.
doi: 10.1038/nrm2786. |
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