The equation of motion for sperm flagella.

Abstract:

:The equation of motion for sperm flagella, in which the elastic bending moment and the active contractile moment are balanced by the moment from the viscous resistance of the surrounding fluid, is solved for a wave solution that superimposes partial solutions. Substitution of the expression for the wave solution into the equation leads to an expression for the active contractile moment. This active moment can be decomposed into two parts. The first part describes an active moment that travels over the flagellum with the mechanical flagellar wave, the second part represents a moment in phase over the entire length of the flagellum, which decreases linearly towards the distal tip. The linear synchronous moment, to which an amount of traveling moment has been added as a perturbation, leads to wave solutions that closely resemble flagellar waves. Properties such as wavelength and wave amplitudes and also the shape of the waves in sea urchin sperm flagella at different frequencies are accurately described by the theory. The change in wave shape in sea urchin sperm flagella at raised viscosity is predicted well by the theory. The different wave properties caused in bull sperm flagella by different boundary conditions at the proximal junction are explained. When only a traveling active moment is present in a flagellum, the wave solutions describe waves of a small wave length in a long flagellum. Some properties of the wave motion of sperm flagella are derived from the theory and verified experimentally.

journal_name

Biophys J

journal_title

Biophysical journal

authors

Rikmenspoel R

doi

10.1016/S0006-3495(78)85442-3

subject

Has Abstract

pub_date

1978-08-01 00:00:00

pages

177-206

issue

2

eissn

0006-3495

issn

1542-0086

pii

S0006-3495(78)85442-3

journal_volume

23

pub_type

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