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Nonlinear amplitude dynamics in flagellar beating

The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein moto...

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Autores principales: Oriola, David, Gadêlha, Hermes, Casademunt, Jaume
Formato: Online Artículo Texto
Lenguaje:English
Publicado: The Royal Society Publishing 2017
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5383814/
https://www.ncbi.nlm.nih.gov/pubmed/28405357
http://dx.doi.org/10.1098/rsos.160698
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author Oriola, David
Gadêlha, Hermes
Casademunt, Jaume
author_facet Oriola, David
Gadêlha, Hermes
Casademunt, Jaume
author_sort Oriola, David
collection PubMed
description The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating.
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spelling pubmed-53838142017-04-12 Nonlinear amplitude dynamics in flagellar beating Oriola, David Gadêlha, Hermes Casademunt, Jaume R Soc Open Sci Biochemistry and Biophysics The physical basis of flagellar and ciliary beating is a major problem in biology which is still far from completely understood. The fundamental cytoskeleton structure of cilia and flagella is the axoneme, a cylindrical array of microtubule doublets connected by passive cross-linkers and dynein motor proteins. The complex interplay of these elements leads to the generation of self-organized bending waves. Although many mathematical models have been proposed to understand this process, few attempts have been made to assess the role of dyneins on the nonlinear nature of the axoneme. Here, we investigate the nonlinear dynamics of flagella by considering an axonemal sliding control mechanism for dynein activity. This approach unveils the nonlinear selection of the oscillation amplitudes, which are typically either missed or prescribed in mathematical models. The explicit set of nonlinear equations are derived and solved numerically. Our analysis reveals the spatio-temporal dynamics of dynein populations and flagellum shape for different regimes of motor activity, medium viscosity and flagellum elasticity. Unstable modes saturate via the coupling of dynein kinetics and flagellum shape without the need of invoking a nonlinear axonemal response. Hence, our work reveals a novel mechanism for the saturation of unstable modes in axonemal beating. The Royal Society Publishing 2017-03-08 /pmc/articles/PMC5383814/ /pubmed/28405357 http://dx.doi.org/10.1098/rsos.160698 Text en © 2017 The Authors. http://creativecommons.org/licenses/by/4.0/ Published by the Royal Society under the terms of the Creative Commons Attribution License http://creativecommons.org/licenses/by/4.0/, which permits unrestricted use, provided the original author and source are credited.
spellingShingle Biochemistry and Biophysics
Oriola, David
Gadêlha, Hermes
Casademunt, Jaume
Nonlinear amplitude dynamics in flagellar beating
title Nonlinear amplitude dynamics in flagellar beating
title_full Nonlinear amplitude dynamics in flagellar beating
title_fullStr Nonlinear amplitude dynamics in flagellar beating
title_full_unstemmed Nonlinear amplitude dynamics in flagellar beating
title_short Nonlinear amplitude dynamics in flagellar beating
title_sort nonlinear amplitude dynamics in flagellar beating
topic Biochemistry and Biophysics
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC5383814/
https://www.ncbi.nlm.nih.gov/pubmed/28405357
http://dx.doi.org/10.1098/rsos.160698
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