A Model Describing Bending in Flagella

Abstract

In Part I of this paper, we present a modelto account for the force generationproducing bending, and the formation of awaveform in sperm flagella. The model isbased on the observation that dimers, andhence microtubules, possess dipole moments.The electric field these dipoles produce isthe source for storing mechanical work indynein arms. The mechanical work is thenreleased and act on the doublets to producea distally directed force with the resultthat bending occurs. The model described isconsistent with experimental observationsreported in the literature. The flexuralrigidity of a dynein arm is alsocalculated. In Part II of this paper, theconsequences of the bending mechanism arediscussed. It is shown that the sum offorces from dynein arms acting distallyalong doublet microtubules in a flagellumis essentially zero when all dyneins areattached thus resulting in the rigor state.The waveform in a flagellum occurs if oneof the sets of bending moments is zero,that is, a row of dyneins are detached oversome distance along the flagellum. Thedirection of the bend in the waveform isdetermined by which set of dynein arms aredetached with respect to the verticalmedian plane of the flagellum. Thepropagation of a bending wave is the resultof a moving region in which alternate sidesfrom the vertical median plane haveinactive dynein arms. The processes bywhich this moving region occurs and therelationship of the above results to thepropulsion of the flagellum are notconsidered.