Some mathematical models for flagellar activation mechanisms

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.