Geometry drives the "deviated-bending" of the bi-tubular structures of the 9 + 2 axoneme in the flagellum.
The axoneme "9 + 2" is basically a system constituted of a cylinder of 9 microtubule doublets surrounding a central pair of microtubules. These bi-tubular structures are considered as the support system of the active molecular complexes that generate and regulate the axonemal movement. Schoutens has calculated their moments of inertia [Schoutens, 1994: Journal of Theoretical Biology 171:163-177]. The results obtained allowed us to assume that these bi-tubular systems are endowed with dynamic properties that could be involved in the regulation of the axonemal machinery. For the first time, using the finite elements methods and the resistance of material principles, we have now calculated that the curvature of the axoneme induces the deviated-bending of the bi-tubular structures of the axoneme, because of their geometry only; they behave as beams in a framework. This approach is similar to the one used to measure the deflection of a single microtubule [Kasas et al., 2004: Chem Phys Chem 5:252-257]. These behaviors induce internal movement or constraints of either couples or triplets of doublets within the axonemal cylinder that could be directly involved in a constrained or a spontaneous "convergence/divergence" equilibrium of the cylindrical generatrices that they draw along the axonemal cylinder, which could apparently regulate the activity of the axonemal motors (the dynein arms). These results are discussed here, taking into consideration the dynamic propagation of the wave train along the flagellar axoneme, and the regulated balance between the activities of the two opposite sides of the axoneme during the beat. This study raises a few questions about the architecture-activity duo of the axonemal doublets.
Cibert
Christian
C
Groupe de Morphométrie et Modélisation Cellulaire, Institut Jacques Monod, CNRS, Universités Paris 6 et Paris 7, 2, place Jussieu, F-75251 Paris Cedex 05, France. cibert@ijm.jussieu.fr
Heck
Jean-Vivien
JV
D001696:Biomechanical Phenomena; D002465:Cell Movement; D003198:Computer Simulation; D004548:Elasticity; D005407:Flagella / Q000378:metabolism* / Q000648:ultrastructure*; D008870:Microtubules / Q000378:metabolism*; D008954:Models, Biological