Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium

A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis–Menten type model...

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Autores principales: Manhart, Angelika, Schmeiser, Christian
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2016
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5206285/
https://www.ncbi.nlm.nih.gov/pubmed/27206776
http://dx.doi.org/10.1007/s00285-016-1027-z
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author Manhart, Angelika
Schmeiser, Christian
author_facet Manhart, Angelika
Schmeiser, Christian
author_sort Manhart, Angelika
collection PubMed
description A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis–Menten type modeling of the branching process. For branching rates large enough compared to capping rates, the existence and stability of nontrivial steady states is investigated. The main result is exponential convergence to nontrivial steady states, proven by investigating the decay of an appropriate Lyapunov functional.
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spelling pubmed-52062852017-01-18 Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium Manhart, Angelika Schmeiser, Christian J Math Biol Article A model for the dynamics of actin filament ends along the leading edge of the lamellipodium is analyzed. It contains accounts of nucleation by branching, of deactivation by capping, and of lateral flow along the leading edge by polymerization. A nonlinearity arises from a Michaelis–Menten type modeling of the branching process. For branching rates large enough compared to capping rates, the existence and stability of nontrivial steady states is investigated. The main result is exponential convergence to nontrivial steady states, proven by investigating the decay of an appropriate Lyapunov functional. Springer Berlin Heidelberg 2016-05-20 2017 /pmc/articles/PMC5206285/ /pubmed/27206776 http://dx.doi.org/10.1007/s00285-016-1027-z Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Manhart, Angelika
Schmeiser, Christian
Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title_full Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title_fullStr Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title_full_unstemmed Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title_short Existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
title_sort existence of and decay to equilibrium of the filament end density along the leading edge of the lamellipodium
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5206285/
https://www.ncbi.nlm.nih.gov/pubmed/27206776
http://dx.doi.org/10.1007/s00285-016-1027-z
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