…
comment: The repository administrator has not yet configured an RDF license.
primary topic: On a Minimal Model for the Initiation of Cell Movement

On a Minimal Model for the Initiation of Cell Movement
type: Article
abstract: Actin-driven motility of eucaryotic cells plays a crucial role in many biological processes and has therefore been under intense experimental and theoretical investigation throughout several decades. In [10], we introduced a minimal model for the preparation of movement in a symmetric resting cell on a flat substrate. This system consists of at least four hyperbolic conservation laws describing the evolution of densities of actin filament tips and at least one parabolic equation for the actin monomer concentration. For this coupled hyperbolic-parabolic system, we shall now formulate a free boundary problem to allow for actual motion of the cell. For this model with some specific boundary conditions, we will show short time well posedness and present several mechanisms by which the solutions might break down for large times. In particular, possible blow-up phenomena are described and investigated, both analytically and numerically. Moreover, we discuss how the cease of existence of solutions can be interpreted physically as the emergence of actin polymerization fronts. Finally, different possible boundary conditions are presented, and their biological meanings are explained. We furthermore reformulate the model under certain assumptions and derive a system of two parabolic equations describing the motion of two interacting species of filaments moving in opposite directions. This simplified model is investigated in part II where we ask for stability of particular steady states and construct traveling wave solutions. The existence of the latter can also be found in simulations, and we will discuss the type and velocity of the evolving wave profiles. Particular attention will be paid to the remarkable differences between different types of nonlinearities describing the mutual interaction. Of special interest are the deviations from the predictions about stability and the traveling wave solutions obtained from the linearization of the model around its equilibria. These p…
date: 2012
status: published
author list: authors
type: EPrint
type: DoctoralThesisEPrint
is part of: repository
has document: On a Minimal Model for the Initiation of Cell Movement (PDF)
has document: On a Minimal Model for the Initiation of Cell Movement (Other)
subject: 510 Mathematik

On a Minimal Model for the Initiation of Cell Movement (PDF)
type: Document
has file: Dissertation_Fuhrmann.pdf
has part: Dissertation_Fuhrmann.pdf

Jan Fuhrmann
type: Person
given name: Jan
family name: Fuhrmann

On a Minimal Model for the Initiation of Cell Movement (Other)
type: Document
is version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is volatile version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is index codes version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
has file: indexcodes.txt
has part: indexcodes.txt

On a Minimal Model for the Initiation of Cell Movement (Other)
type: Document
is version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is volatile version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
islightbox thumbnail version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
has file: lightbox.jpg
has part: lightbox.jpg

On a Minimal Model for the Initiation of Cell Movement (Other)
type: Document
is version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is volatile version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
ispreview thumbnail version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
has file: preview.jpg
has part: preview.jpg

On a Minimal Model for the Initiation of Cell Movement (Other)
type: Document
is version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is volatile version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
ismedium thumbnail version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
has file: medium.jpg
has part: medium.jpg

On a Minimal Model for the Initiation of Cell Movement (Other)
type: Document
is version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
is volatile version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
issmall thumbnail version of: On a Minimal Model for the Initiation of Cell Movement (PDF)
has file: small.jpg
has part: small.jpg

HTML Summary of #13659 On a Minimal Model for the Initiation of Cell Movement
format: text/html
primary topic: On a Minimal Model for the Initiation of Cell Movement

510 Mathematik
type: Concept
preferred label: 510 Mathematics @en