This paper focuses on studying a model for dyneins, cytoskeletal motor proteins responsible for axonemal activity. The model is a coupled system of partial differential equations inspired by [F. Jülicher and J. Prost, Cooperative molecular motors, Phys. Rev. Lett. 75 (1995) 2618–2621; F. Jülicher and J. Prost, Molecular motors: From individual to collective behavior, Prog. Theor. Phys. Suppl. 130 (1998) 9–16] and incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution are 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.
Some mathematical models for flagellar activation mechanisms / Alouges, François; Anello, Irene; Desimone, Antonio; Lefebvre-Lepot, Aline; Levillain, Jessie. - In: MATHEMATICAL MODELS AND METHODS IN APPLIED SCIENCES. - ISSN 0218-2025. - 35:11(2025), pp. 2395-2424. [10.1142/S0218202525500423]
Some mathematical models for flagellar activation mechanisms
Irene Anello;Antonio DeSimone;
2025-01-01
Abstract
This paper focuses on studying a model for dyneins, cytoskeletal motor proteins responsible for axonemal activity. The model is a coupled system of partial differential equations inspired by [F. Jülicher and J. Prost, Cooperative molecular motors, Phys. Rev. Lett. 75 (1995) 2618–2621; F. Jülicher and J. Prost, Molecular motors: From individual to collective behavior, Prog. Theor. Phys. Suppl. 130 (1998) 9–16] and incorporating two rows of molecular motors between microtubules filaments. Existence and uniqueness of a solution are 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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
