A Model Describing Bending in Flagella

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In Part I of this paper, we present a model to account for the force generation producing bending, and the formation of a waveform in sperm flagella. The model is based on the observation that dimers, and hence microtubules, possess dipole moments. The electric field these dipoles produce is the source for storing mechanical work in dynein arms. The mechanical work is then released and act on the doublets to produce a distally directed force with the result that bending occurs. The model described is consistent with experimental observations reported in the literature. The flexural rigidity of a dynein arm is also calculated. In Part II of this paper, the consequences of the bending mechanism are discussed. It is shown that the sum of forces from dynein arms acting distally along doublet microtubules in a flagellum is essentially zero when all dyneins are attached thus resulting in the rigor state. The waveform in a flagellum occurs if one of the sets of bending moments is zero, that is, a row of dyneins are detached over some distance along the flagellum. The direction of the bend in the waveform is determined by which set of dynein arms are detached with respect to the vertical median plane of the flagellum. The propagation of a bending wave is the result of a moving region in which alternate sides from the vertical median plane have inactive dynein arms. The processes by which this moving region occurs and the relationship of the above results to the propulsion of the flagellum are not considered.

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