Maintenance of Constant Wave Parameters by Sperm Flagella at Reduced Frequencies of Beat

1. Treatment of Ciona spermatozoa with low concentrations of Triton X-100 (less than 0·01 %) causes them to beat at lower than normal frequencies. The wavelength of the flagellar bending waves remains constant over the range from 10 to 40 Hz. There is a small increase in wavelength at lower frequencies; in the range of 1·5-6·2 Hz, the wavelength averaged 114% of the normal value for Ciona spermatozoa. The angle of bend of the bent regions of the flagellar bending waves remained constant within ± 10% over this range of frequencies. 2. Decapitated sperm flagella from Lytechinus beat at a continually declining frequency as they exhaust their content of ATP. Both wavelength and bend angle retain normal values until the frequency falls below about 8 Hz. Both parameters increase at lower frequencies, with a sharp increase below 3 Hz. 3. ATP-reactivated spermatozoa from Lytechinus show relatively small changes in wavelength and bend angle as the frequency is varied over the range from 5 to 25 Hz by varying the ATP concentration. 4. Constancy of wavelength over a wide range of frequencies is consistent with the hypothesis that wavelength is determined by the relative values of viscous bending resistance within a flagellum and external viscosity. 5. No satisfactory explanation is available at present for the constancy of bend angle over a wide range of frequencies nor for the changes in wave parameters which are observed at low frequencies

Chemotactic Turning Behaviour of Tubularia Spermatozoa

1. The movements of Tubularia spermatozoa in the vicinity of micropipettes filled with extracts of female hydranths, which chemotactically attract the spermatozoa, have been recorded by multiple-flash photomicrography. 2. When a spermatozoon turns in response to a chemotactic stimulus, the flagellum continues to beat, with a highly asymmetrical pattern of bending, during the turn. 3. The magnitude of the turn, particularly the duration of the period of asymmetrical beating, is variable, but each spermatozoon is only able to make turns in one direction, relative to its own body. 4. Most of the behaviour of these spermatozoa may be explained if the turning mechanism is activated when the spermatozoon detects a decreasing concentration of the chemotactant

Localized Activation of Bending in Proximal, Medial and Distal Regions of Sea-Urchin Sperm Flagella

Spermatozoa from the sea urchin, Colobocentrotus atratus, were partially demembranated by extraction with solutions containing Triton X-100 at a concentration which was insufficient to solubilize the membranes completely. The resulting suspension was a mixture containing some spermatozoa in which a proximal, medial, or distal portion of the flagellum was membrane-covered, while the remaining portion was naked axoneme. In reactivating solutions containing 12 µM ATP, only the naked portions of the flagellum became motile. In reactivating solutions containing 0.8 mM ADP, the membrane-covered regions became motile and beat at 6-10 beats/s, while the naked regions remained immobile, or beat very slowly at about 0.3 beat/s. Activation of membrane-covered regions in ADP solutions probably results from the membrane restricting the diffusion of ATP which is formed from ADP by the axonemal adenylate kinase. The results indicate that any region of the flagellum has the capacity for autonomous beating, and that special properties of the basal end of the flagellum are not required for bend initiation. However, the beating of different regions of the flagellum is not completely independent, for in a fair number of spermatozoa the beating of the distal, membrane-covered region in 0.8 mM ADP was intermittent, and was turned on and off in phase with the much slower bending cycle in the proximal region of naked axoneme

Human sperm accumulation near surfaces: a simulation study

A hybrid boundary integral/slender body algorithm for modelling flagellar cell motility is presented. The algorithm uses the boundary element method to represent the ‘wedge-shaped’ head of the human sperm cell and a slender body theory representation of the flagellum. The head morphology is specified carefully due to its significant effect on the force and torque balance and hence movement of the free-swimming cell. The technique is used to investigate the mechanisms for the accumulation of human spermatozoa near surfaces. Sperm swimming in an infinite fluid, and near a plane boundary, with prescribed planar and three-dimensional flagellar waveforms are simulated. Both planar and ‘elliptical helicoid’ beating cells are predicted to accumulate at distances of approximately 8.5–22 μm from surfaces, for flagellar beating with angular wavenumber of 3π to 4π. Planar beating cells with wavenumber of approximately 2.4π or greater are predicted to accumulate at a finite distance, while cells with wavenumber of approximately 2π or less are predicted to escape from the surface, likely due to the breakdown of the stable swimming configuration. In the stable swimming trajectory the cell has a small angle of inclination away from the surface, no greater than approximately 0.5°. The trapping effect need not depend on specialized non-planar components of the flagellar beat but rather is a consequence of force and torque balance and the physical effect of the image systems in a no-slip plane boundary. The effect is relatively weak, so that a cell initially one body length from the surface and inclined at an angle of 4°–6° towards the surface will not be trapped but will rather be deflected from the surface. Cells performing rolling motility, where the flagellum sweeps out a ‘conical envelope’, are predicted to align with the surface provided that they approach with sufficiently steep angle. However simulation of cells swimming against a surface in such a configuration is not possible in the present framework. Simulated human sperm cells performing a planar beat with inclination between the beat plane and the plane-of-flattening of the head were not predicted to glide along surfaces, as has been observed in mouse sperm. Instead, cells initially with the head approximately 1.5–3 μm from the surface were predicted to turn away and escape. The simulation model was also used to examine rolling motility due to elliptical helicoid flagellar beating. The head was found to rotate by approximately 240° over one beat cycle and due to the time-varying torques associated with the flagellar beat was found to exhibit ‘looping’ as has been observed in cells swimming against coverslips

Self-organized Beating and Swimming of Internally Driven Filaments

We study a simple two-dimensional model for motion of an elastic filament subject to internally generated stresses and show that wave-like propagating shapes which can propel the filament can be induced by a self-organized mechanism via a dynamic instability. The resulting patterns of motion do not depend on the microscopic mechanism of the instability but only of the filament rigidity and hydrodynamic friction. Our results suggest that simplified systems, consisting only of molecular motors and filaments could be able to show beating motion and self-propulsion.Comment: 8 pages, 2 figures, REVTe

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

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