Beating patterns of filaments in viscoelastic fluids

Many swimming microorganisms, such as bacteria and sperm, use flexible flagella to move through viscoelastic media in their natural environments. In this paper we address the effects a viscoelastic fluid has on the motion and beating patterns of elastic filaments. We treat both a passive filament which is actuated at one end, and an active filament with bending forces arising from internal motors distributed along its length. We describe how viscoelasticity modifies the hydrodynamic forces exerted on the filaments, and how these modified forces affect the beating patterns. We show how high viscosity of purely viscous or viscoelastic solutions can lead to the experimentally observed beating patterns of sperm flagella, in which motion is concentrated at the distal end of the flagella

Physical Aspects of Axonemal Beating and Swimming

We discuss a two-dimensional model for the dynamics of axonemal deformations driven by internally generated forces of molecular motors. Our model consists of an elastic filament pair connected by active elements. We derive the dynamic equations for this system in presence of internal forces. In the limit of small deformations, a perturbative approach allows us to calculate filament shapes and the tension profile. We demonstrate that periodic filament motion can be generated via a self-organization of elastic filaments and molecular motors. Oscillatory motion and the propagation of bending waves can occur for an initially non-moving state via an instability termed Hopf bifurcation. Close to this instability, the behavior of the system is shown to be independent of microscopic details of the axoneme and the force-generating mechanism. The oscillation frequency however does depend on properties of the molecular motors. We calculate the oscillation frequency at the bifurcation point and show that a large frequency range is accessible by varying the axonemal length between 1 and 50$\mu$m. We calculate the velocity of swimming of a flagellum and discuss the effects of boundary conditions and externally applied forces on the axonemal oscillations.Comment: 14 pages, 8 figures, REVTE

Application of a numerical simulation to improve the separation efficiency of a sperm sorter

This paper describes a study in which numerical simulations were applied to improve the separation efficiency of a microfluidic-based sperm sorter. Initially, the motion of 31 sperm were modeled as a sinusoidal wave. The modeled sperm were expected to move while vibrating in the fluid within the microchannel. In this analysis, the number of sperm extracted at the outlet channel and the rate of movement of the highly motile sperm were obtained for a wide range of flow velocities within the microchannel. By varying the channel height, and the width and the position of the sperm-inlet channel, we confirmed that the separation efficiency was highly dependent on the fluid velocity within the channel. These results will be valuable for improving the device configuration, and might help to realize further improvements in efficiency in the future

Radiation damage to bull sperm motility. III. Further x-ray studies.

The results of previous radiation experiments, which indicated that the centriole serves as a control center for bull sperm motility, appear to be in conflict with experiments showing that the bull sperm flagellum is an autonomous oscillator. To resolve this conflict experiments were conducted to calibrate absolutely the dose-response curves for the radiation damage, and to measure the force production and the mechanochemical energy conversion after irradiation in bull sperm. The results indicate that the centriole acts as a mechanical anchor for the contractile fibers

The equation of motion for sperm flagella.

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

Contractile events in the cilia of Paramecium, Opalina, Mytilus, and Phragmatopoma.

The motion of the abnormal cilia of Opalina and Mytilus can be described by the recently developed model for ciliary motion, provided the activation of the contractility during the effective stroke is reduced by three- to fivefold compared with that in the recovery stroke. The stiffness of the Mytilus cilium during the effective stroke is found several hundred times larger than that predicted by the model, however. The stiffness of the cilia of Paramecium, Opalina, Phragmatopoma, and of Mytilus in the recovery phase, is predicted approximately correctly by the model. The activation of contractility in Mytilus and Phragmatopoma cilia increases with the viscosity of the medium, as the velocity of the ciliary motion slows down. This leads to the equivalent of a force-velocity relation. The velocity of propagation of the bend in the cilia during the recovery stroke is shown to be dependent only on the elastic properties of the ciliary shaft, and to be independent of the contractile activiey