Mechanics of the eukaryotic flagellar axoneme: Evidence for structural distortion during bending

Abstract

The sliding doublet mechanism is the established explanation that allows us to understand the process of ciliary and flagellar bending. In this study, we apply the principles of the sliding doublet mechanism to analyze the mechanics of the counterbend phenomenon in sea urchin sperm flagella. When a passive, vanadate-treated, flagellum is forced into a bend with a glass microprobe, the portion of the flagellum distal to the probe exhibits a bend of opposite curvature (counterbend) to the imposed bend. This phenomenon was shown to be caused by the induction of inter-doublet shear and is dependent on the presence of an inter-doublet shear resistance. Here we report that in sea urchin flagella there is systematically less shear induced in the distal flagellum than is predicted by the sliding doublet mechanism, if we follow the assumption that the diameter of the flagellum is uniform. To account for the reduced shear that is observed, the likeliest and most direct interpretation is that the portion of the axoneme that is forced to bend undergoes substantial compression of the axoneme in the bending plane. A compression of 30-50 nm would be sufficient to account for the shear reduction from a bend of 2 radians. A compression of this magnitude would require considerable flexibility in the axoneme structure. This would necessitate that the radial spokes and/or the central pair apparatus are easily compressed by transverse stress. © 2016 Wiley Periodicals, Inc.

Basal bodies bend in response to ciliary forces

“…This is consistent with computer models proposing that the mechanical properties of BBs and coupling between BBs can regulate ciliary waveform ( Riedel-Kruse et al. , 2007 ; Lesich et al. , 2016 ; Lindemann and Lesich, 2016 ; Guo et al.…”

“…However, sperm that lack conserved BB structures (CWs and A-C linkers), deform at the connecting piece, and produce sperm head translocations during flagellar beating ( Vernon and Woolley, 2004 ; Lindemann and Mitchell, 2007 ; Khanal et al. , 2021 ), consistent with axonemal basal sliding force transmission to the sperm head ( Vernon and Woolley, 2004 ; Lesich et al. , 2016 ; Fishman et al.…”

“…Several models propose that the asymmetric ciliary waveform is established by asymmetric dynein activation, which spatially and temporally regulates doublet MT sliding of 25–100 nm along the axoneme ( Lindemann, 1994 ; Woolley and Bozkurt, 1995 ; Vernon and Woolley, 2004 ; Riedel-Kruse et al. , 2007 ; Satir et al ., 2014 ; Lesich et al. , 2016 ; Lin and Nicastro, 2018 ).…”

“…Resistance to basal sliding through variance in asymmetric elastic compliance and deformation of the connecting piece or basal region modulates flagellar beating ( Goldstein, 1981 ; Vernon and Woolley, 2002 , 2004; Lindemann and Mitchell, 2007 ; Lindemann and Lesich, 2016 ; Riedel-Kruse et al. , 2007 ; Lesich et al. , 2016 ).…”

Cilia oscillations

“…This sliding is resisted by cross-linker proteins that act as a linear spring of stiffness K. This sliding resistance is crucial to account for complex passive dynamics of the axoneme [49][50][51][52]. In other words, the internal force density f consists of active and passive parts, arising from both the motor activity and the passive response of the nexin cross-linkers [39,40] f(s, t)…”