Some mathematical models for flagellar activation mechanisms
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866916692272087040 |
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| author | Alouges, François Anello, Irene DeSimone, Antonio Lefebvre-Lepot, Aline Levillain, Jessie |
| author_facet | Alouges, François Anello, Irene DeSimone, Antonio Lefebvre-Lepot, Aline Levillain, Jessie |
| contents | This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by Jülicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_03506 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Some mathematical models for flagellar activation mechanisms Alouges, François Anello, Irene DeSimone, Antonio Lefebvre-Lepot, Aline Levillain, Jessie Numerical Analysis Dynamical Systems 92-10, 35B32, 35Q84 This paper focuses on studying a model for molecular motors responsible for the bending of the axoneme in the flagella of microorganisms. The model is a coupled system of partial differential equations inspired by Jülicher et al. or Camalet, incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution is proved, together with the presence of a supercritical Hopf bifurcation. Additionally, numerical simulations are provided to illustrate the theoretical results. A brief study on the generalization to N-rows is also included. |
| title | Some mathematical models for flagellar activation mechanisms |
| topic | Numerical Analysis Dynamical Systems 92-10, 35B32, 35Q84 |
| url | https://arxiv.org/abs/2409.03506 |