Are the local adjustments of the relative spatial frequencies of the dynein arms and the beta-tubulin monomers involved in the regulation of the "9+2" axoneme?

The "9+2" axoneme is a highly specific cylindrical machine whose periodic bending is due to the cumulative shear of its 9 outer doublets of microtubules. Because of the discrete architecture of the tubulin monomers and the active appendices that the outer doublets carry (dynein arms, nexin links and radial spokes), this movement corresponds to the relative shear of these topological verniers, whose characteristics depend on the geometry of the wave train. When an axonemal segment bends, this induces the compressed and dilated conformations of the tubulin monomers and, consequently, the modification of the spatial frequencies of the appendages that the outer doublets carry. From a dynamic point of view, the adjustments of the spatial frequencies of the elements of the two facing verniers that must interact create different longitudinal periodic patterns of distribution of the joint probability of the molecular interaction as a function of the location of the doublet pairs around the axonemal cylinder and their spatial orientation within the axonemal cylinder. During the shear, these patterns move along the outer doublet intervals at a speed that ranges from one to more than a thousand times that of sliding, in two opposite directions along the two opposite halves of the axoneme separated by the bending plane, respecting the polarity of the dynein arms within the axoneme. Consequently, these waves might be involved in the regulation of the alternating activity of the dynein arms along the flagellum, because they induce the necessary intermolecular dialog along the axoneme since they could be an element of the local dynamic stability/instability equilibrium of the axoneme. This complements the geometric clutch model [Lindemann, C., 1994. A "geometric clutch" hypothesis to explain oscillations of the axoneme of cilia and flagella. J. Theor. Biol. 168, 175-189].