Bending of the “9+2” axoneme analyzed by the finite element method

Many data demonstrate that the regulation of the bending polarity of the “9+2” axoneme is supported by the curvature itself, making the internal constraints central in this process, adjusting either the physical characteristics of the machinery or the activity of the enzymes involved in different pathways. Among them, the very integrated Geometric Clutch model founds this regulation on the convenient adjustments of the probability of interaction between the dynein arms and the β-tubulin monomers of the outer doublet pairs on which they walk. Taking into consideration (i) the deviated bending of the outer doublets pairs (Cibert, C., Heck, J.-V., 2004. Cell Motil. Cytoskeleton 59, 153–168), (ii) the internal tensions of the radial spokes and the tangential links (nexin links, dynein arms), (iii) a theoretical 5 μm long proximal segment of the axoneme and (iv) the short proximal segment of the axoneme, we have reevaluated the adjustments of these intervals using a finite element approach. The movements we have calculated within the axonemal cylinder are consistent with the basic hypothesis that found the Geometric Clutch model, except that the axonemal side where the dynein arms are active increases the intervals between the two neighbor outer doublet pairs. This result allows us to propose a mechanism of bending reversion of the axoneme, involving the concerted ignition of the molecular engines along the two opposite sides of the axoneme delineated by the bending plane.