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Traveling Waves Emerging in a Diffusive Moving Filament System

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2014

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Freistühler, Heinrich
Fuhrmann, Jan
Stevens, Angela

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https://doi.org/10.1007/978-3-319-03759-2_10
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DELITALA, Marcello, ed., Giulia Ajmone MARSAN, ed.. Managing Complexity, Reducing Perplexity : Modeling Biological Systems. Cham: Springer, 2014, pp. 91-99. Springer Proceedings in Mathematics & Statistics. 67. ISBN 978-3-319-03758-5. Available under: doi: 10.1007/978-3-319-03759-2_10

Zusammenfassung

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.

Zusammenfassung in einer weiteren Sprache

Fachgebiet (DDC)
510 Mathematik

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Cytoskeleton, Nonlinear waves, Reaction diffusion advection equations

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ISO 690FREISTÜHLER, Heinrich, Jan FUHRMANN, Angela STEVENS, 2014. Traveling Waves Emerging in a Diffusive Moving Filament System. In: DELITALA, Marcello, ed., Giulia Ajmone MARSAN, ed.. Managing Complexity, Reducing Perplexity : Modeling Biological Systems. Cham: Springer, 2014, pp. 91-99. Springer Proceedings in Mathematics & Statistics. 67. ISBN 978-3-319-03758-5. Available under: doi: 10.1007/978-3-319-03759-2_10
BibTex
@incollection{Freistuhler2014Trave-55574,
  year={2014},
  doi={10.1007/978-3-319-03759-2_10},
  title={Traveling Waves Emerging in a Diffusive Moving Filament System},
  number={67},
  isbn={978-3-319-03758-5},
  publisher={Springer},
  address={Cham},
  series={Springer Proceedings in Mathematics & Statistics},
  booktitle={Managing Complexity, Reducing Perplexity : Modeling Biological Systems},
  pages={91--99},
  editor={Delitala, Marcello and Marsan, Giulia Ajmone},
  author={Freistühler, Heinrich and Fuhrmann, Jan and Stevens, Angela}
}
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