Bending Waves of the Posterior Flagellum of Ceratium

Hydrodynamic evolution of sperm swimming: Optimal flagella by a genetic algorithm

Swimming performance of spermatozoa is an important index for the success of fertilization. For many years, numerous studies have reported the optimal swimming of flagellar organisms. Nevertheless, there is still a question as to which is optimal among planar, circular helical and ellipsoidal helical beating. In this paper, we use a genetic algorithm to investigate the beat pattern with the best swimming efficiency based on hydrodynamic dissipation and internal torque exertion. For the parameters considered, our results show that the planar beat is optimal for small heads and the helical flagellum is optimum for a larger heads, while the ellipsoidal beat is never optimal. Also, the genetic optimization reveals that the wavenumber and shape of wave envelope are relevant parameters, whereas the wave shape and head geometry have relatively minor effects on efficiency. The optimal beat with respect to the efficiency based on the internal torque exertion of an active elastic flagellum is characterized by a small-wavenumber and large-amplitude wave in a lower-viscosity medium. The obtained results on the optimal waveform are consistent with observations for planar waveforms, but in many respects, the results suggest the necessity of a detailed flagellar structure-fluid interaction to address whether real spermatozoa exhibit hydrodynamically efficient swimming. The evolutional optimization approach used in this study has distinguished biologically important parameters, and the methodology can potentially be applicable to various swimmers.

The Genus Neoceratium (Planktonic Dinoflagellates) as a Potential Indicator of Ocean Warming

Among the planktonic dinoflagellates, the species-rich genus Neoceratium has particularly remarkable features that include its easily recognizable outline and large size. This ubiquitous genus shows consistent presence in all plankton samples and has been a model for numerous studies since the end of the 19th century. It has already been described as a good candidate to monitor water masses and describe ocean circulation. We argue that the sensitivity displayed by Neoceratium to water temperature also makes it relevant as an indicator of ocean warming. The advantages and interests of using Neoceratium species to monitor climate change on a large scale are reassessed in view of recent advances in understanding their biology and ecology.

Stretch-activated calcium channels relay fast calcium waves propagated by calcium-induced calcium influx

For nearly 30 years, fast calcium waves have been attributed to a regenerative process propagated by CICR (calcium-induced calcium release) from the endoplasmic reticulum. Here, I propose a model containing a new subclass of fast calcium waves which is propagated by CICI (calcium-induced calcium influx) through the plasma membrane. They are called fast CICI waves. These move at the order of 100 to 1000 microm/s (at 20 degrees C), rather than the order of 3 to 30 microm/s found for CICR. Moreover, in this proposed subclass, the calcium influx which drives calcium waves is relayed by stretch-activated calcium channels. This model is based upon reports from approx. 60 various systems. In seven of these reports, calcium waves were imaged, and, in five of these, evidence was presented that these waves were regenerated by CICI. Much of this model involves waves that move along functioning flagella and cilia. In these systems, waves of local calcium influx are thought to cause waves of local contraction by inducing the sliding of dynein or of kinesin past tubulin microtubules. Other cells which are reported to exhibit waves, which move at speeds in the fast CICI range, include ones from a dozen protozoa, three polychaete worms, three molluscs, a bryozoan, two sea urchins, one arthropod, four insects, Amphioxus, frogs, two fish and a vascular plant (Equisetum), together with numerous healthy, as well as cancerous, mammalian cells, including ones from human. In two of these systems, very gentle local mechanical stimulation is reported to initiate waves. In these non-flagellar systems, the calcium influxes are thought to speed the sliding of actinomyosin filaments past each other. Finally, I propose that this mechanochemical model could be tested by seeing if gentle mechanical stimulation induces waves in more of these systems and, more importantly, by imaging the predicted calcium waves in more of them.

Biophysical aspects and modelling of ciliary motility

The dominance of viscous forces in the generation of propulsive thrust by cilia is emphasised. Fourier analysis indicates that ciliary bends consist of circular arcs joined by linear segments; this arc-line shape appears to be a property associated with the molecular mechanism responsible for bending the cilium and is unchanged by variations in the external viscous loading on the organelle. The flexibility of a computer-generated model of axonemal structure is demonstrated by the incorporation of recent data concerning the surface lattice of the microtubules. Computer simulations using the model show that predictions based on stochastic, rather than co-ordinated, dynein arm activity provide a qualitative match to experimental observations of microtubules gliding over fields of dynein molecules.

Borrelia burgdorferi swims with a planar waveform similar to that of eukaryotic flagella

Borrelia burgdorferi is a motile spirochete with multiple internal periplasmic flagella (PFs) attached near each end of the cell cylinder; these PFs overlap in the cell center. We analyzed the shape and motion of wild type and PF-deficient mutants using both photomicrography and video microscopy. We found that swimming cells resembled the dynamic movements of eukaryotic flagella. In contrast to helically shaped spirochetes, which propagate spiral waves, translating B. burgdorferi swam with a planar waveform with occasional axial twists; waves had a peak-to-peak amplitude of 0.85 micron and a wavelength of 3.19 microns. Planar waves began full-sized at the anterior end and propagated toward the back end of the cell. Concomitantly, these waves gyrated counter-clockwise as viewed from the posterior end along the cell axis. In nontranslating cells, wave propagation ceased. Either the waveform of nontranslating cells resembled the translating form, or the cells became markedly contorted. Cells of the PF-deficient mutant isolated by Sadziene et al. [Sadziene, A., Thomas, D. D., Bundoc, V. G., Holt, S. C. & Barbour, A. G. (1991) J. Clin. Invest. 88, 82-92] were found to be relatively straight. The results suggest that the shape of B. burgdorferi is dictated by interactions between the cell body and the PFs. In addition, the PFs from opposite ends of the cell are believed to interact with one another so that during the markedly distorted nontranslational form, the PFs from opposite ends rotate in opposing directions around one another, causing the cell to bend.

Determination of the average shape of flagellar bends: a gradient curvature model

Data obtained by manual digitization of photographs of flagellar bending waves have been analyzed by determining size parameters for the bends by least-squares fitting of a model waveform. These parameters were then used to normalize the data so that the average shape of the bends could be determined. Best fits were obtained with a model waveform derived from the constant curvature waveforms used previously but with provision for a linear change in curvature across the central region of the bend-the gradient curvature model (GCM). The central regions of the GCM bending waves are separated by transition regions with length determined by a parameter called the truncation factor (FT). Fitting the GCM to sine-generated bending waves give optimal fit when FT = 0.34. Fitting the GCM to four different samples of flagellar bending waves gave best fits with values of FT ranging from 0.17 for ATP-reactivated Lytechinus spermatozoa beating at approximately 10 Hz to 0.32 for live spermatozoa of Arbacia. The difference between the Arbacia waveforms and a sine-generated waveform is therefore very small, but a sine-generated waveform lacks the degree of freedom represented by FT that is required to fit other waveforms optimally. The residual differences between the waveform data and optimal GCM waveforms were averaged and found to be small. In most cases, the curvature in the central region of the optimal GCM decreased in magnitude towards the tip of the flagellum; however, this slope was highly variable and sometimes positive. Significant variations in both this slope and FT were found in individual bends as they propagated along a flagellum.

Morphological aspects of ciliary motility

In Elliptio complanatus lateral cilia, two distinct patterns of filament termination can be discerned. In one case, all nine filaments are present and all are single; in the second, at least one filament is missing but doublets are still present. These probably represent different configurations within one cilium in different stroke positions; to get from one to the other, some peripheral filaments must move with respect to others. The data are consistent with the hypothesis that the filaments themselves do not change length, but rather slide past one another to accommodate increasing curvature. The bent regions of the cilium are in the form of circular arcs. In a few cases, apparent displacement of filaments at the tip (Deltal) can be shown to be accounted for if we assume that all differences are generated within these arcs. The displacement per degree of bend is 35 A. Regions of bent arc are initially confined to the base of the cilium but move up the shaft as straight regions appear below them. From the relationship between arc length and radius of curvature, a shaft length that is the unit that initially bends and slides may be defined. Quantal displacements of the length of one 14S dynein may perhaps occur at sites between filaments at opposite sides of such a unit as sliding occurs.

Adenosine triphosphate usage by flagella

Comparison of beat frequencies with rates of dephosphorylation of adenosine triphosphate by glycerinated sea urchin spermatozoa as functions of adenosine triphosphate concentration suggests that each molecule of the flagellar adenosine triphosphatase, dynein, dephosphorylates one adenosine triphosphate molecule during each beat cycle.