Axonemal activity relative to the 2D/3D-waveform conversion of the flagellum

The waveform of the flagellum of the sea urchin spermatozoon is mainly planar, but its 3D-properties were evoked for dynamic reasons and described as helical. In 1975, the apparent twisting pattern of the sea urchin axoneme was described [Gibbons I. 1975. The molecular basis of flagellar motility in sea urchin spermatozoa. In: Inoué S, Stephens R, editors. Molecular and cellular movement. New York: Raven Press, p. 207-232.] and was considered to be one of the main elements involved in axonemal behaviour. Recently, planar, quasi-planar, and helical waveforms were observed when the flagellum of sea urchin sperm cells was submitted to an increase in viscosity. The quasi-planar conformation seemed to be due to the alternating torsion of the inter-bend segments [Woolley D, Vernon G. 2001. A study of helical and planar waves on sea urchin sperm flagella, with a theory of how they are generated. J. Exp. Biol. 204:1333-1345]. These three waveforms, which are due to a change in axonemal activity, are possibly used by the sperm cells to adapt their movement to variations in the physico-chemical characteristics of the medium (seawater) in which the cells normally swim. We constructed a simple model to describe qualitatively the central shear (between the axonemal doublets and the central pair) and the tangential shear (between the doublets themselves). In this model, the 3D-bending is resolved into components in two perpendicular planes and each of the nine planes of inter-doublet interaction defines a potential bending plane that is independently regulated. These shears were calculated for the three waveforms and their inter-conversion. This allowed us to propose that axoneme is resolved in successive modules delineated by abscissas where the sliding is always nil. We discuss these data concerning the axonemal machinery, and especially the alternating activity of opposite sides of (two) neutral surface(s) that seem(s) to be responsible for this inter-conversion, and for the possible twist of the axoneme during the beating.