Abstract
Starting from a minimal model for the actin cytoskeleton of motile cells we derive a spatially one dimensional model describing populations of right and left moving filaments with intrinsic velocity, diffusion and mutual alignment. For this model we derive traveling wave solutions whose speed and shape depend on the model parameters and the type of alignment. We discuss possible wave profiles obtained from analytical investigations as well as waves emerging in numerical simulations. In particular, we will explicitly comment on the observed wave speeds and how they are related to the model parameters. Moreover, some particularly interesting patterns being composed of several wave profiles are discussed in some detail. Finally, we shall try to draw some conclusions for the full cytoskeleton model our system had emerged from.
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References
K. Doubrovinski, K. Kruse, Self-organization in systems of treadmilling filaments. Eur. Phys. J. E. 31, 95–104 (2010)
N. Fenichel, Geometric singular perturbation theory. J. Diff. Eq. 31, 53–98 (1979)
J. Fuhrmann, J. Käs, A. Stevens, Initiation of cytoskeletal asymmetry for cell polarization and movement. J. Theor. Biol. 249, 278–288 (2007)
P. Szmolyan, Transversal heteroclinic and homoclinic orbits in singular perturbation problems. J. Diff. Eq. 92(2), 252–281 (1991)
V. Volpert, S. Petrovskii, Reaction-diffusion waves in biology. Phys. Life Rev. 6, 267–310 (2009)
O.D. Weiner, An actin-based wave generator organizes cell motility. PLoS Biol. 5.9(e221), 1053–1063 (2007)
Acknowledgments
The work of H. Freistühler has been supported by the German Research Foundation (DFG) through its excellence grant to the University of Konstanz. The work of J. Fuhrmann has been supported by the German Federal Ministry of Education and Research through the Bernstein Center for Computational Neuroscience Heidelberg/Mannheim (BmBF, 01GQ1003A) and the DFG through the International Graduate College IGK 710. Part of the research by J.Fuhrmann and A. Stevens was done while they were working at the University of Heidelberg.
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© 2014 Springer International Publishing Switzerland
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Freistühler, H., Fuhrmann, J., Stevens, A. (2014). Traveling Waves Emerging in a Diffusive Moving Filament System. In: Delitala, M., Ajmone Marsan, G. (eds) Managing Complexity, Reducing Perplexity. Springer Proceedings in Mathematics & Statistics, vol 67. Springer, Cham. https://doi.org/10.1007/978-3-319-03759-2_10
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DOI: https://doi.org/10.1007/978-3-319-03759-2_10
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