Beating Flagellum Research Articles

Intraflagellar transport speed is sensitive to genetic and mechanical perturbations to flagellar beating.

Two sets of motor proteins underpin motile cilia/flagella function. The axoneme-associated inner and outer dynein arms drive sliding of adjacent axoneme microtubule doublets to periodically bend the flagellum for beating, while intraflagellar transport (IFT) kinesins and dyneins carry IFT trains bidirectionally along the axoneme. Despite assembling motile cilia and flagella, IFT train speeds have only previously been quantified in immobilized flagella-mechanical immobilization or genetic paralysis. This has limited investigation of the interaction between IFT and flagellar beating. Here, in uniflagellate Leishmania parasites, we use high-frequency, dual-color fluorescence microscopy to visualize IFT train movement in beating flagella. We discovered that adhesion of flagella to a microscope slide is detrimental, reducing IFT train speed and increasing train stalling. In flagella free to move, IFT train speed is not strongly dependent on flagella beat type; however, permanent disruption of flagella beating by deletion of genes necessary for formation or regulation of beating showed an inverse correlation of beat frequency and IFT train speed.

Influence of vibrating wall on microswimmer migration in a channel

The migration of microorganisms or synthetic microscale robots is always affected by the local environment, such as the surrounding fluid or muscular contractions. This paper describes a numerical study and asymptotic analysis of the influence of a moving boundary on the migration of a microswimmer in a channel. The locomotion of a finite swimmer between vibrating walls is simulated with both a beating and motionless flagellum. The swimmer can be propelled by the wall vibration, and this propulsion is independent of the self-propulsion of the beating flagellum. To reveal the influence of the vibrating walls, asymptotic analysis is applied to two models, one with an infinitely long filament placed at the channel center and another with an infinitesimally small swimmer. The results show that the vibrating wall effect depends on the ratio of the distance between the walls to the wavelength. The wall effect functions for the two models are obtained for both two-dimensional and circular channels. The finite swimmer in the two-dimensional channel moves with the velocity of the flow induced by the vibrating wall, rather than the swimming speed of the infinite filament. However, in the circular channel, there is no difference between the migration speeds of the two models, and the range of the wall influence is much larger than in the two-dimensional case.

Intracellular coupling modulates biflagellar synchrony.

Beating flagella exhibit a variety of synchronization modes. This synchrony has long been attributed to hydrodynamic coupling between the flagella. However, recent work with flagellated algae indicates that a mechanism internal to the cell, through the contractile fibres connecting the flagella basal bodies, must be at play to actively modulate flagellar synchrony. Exactly how basal coupling mediates flagellar coordination remains unclear. Here, we examine the role of basal coupling in the synchronization of the model biflagellate Chlamydomonas reinhardtii using a series of mathematical models of decreasing levels of complexity. We report that basal coupling is sufficient to achieve inphase, antiphase and bistable synchrony, even in the absence of hydrodynamic coupling and flagellar compliance. These modes can be reached by modulating the activity level of the individual flagella or the strength of the basal coupling. We observe a slip mode when allowing for differential flagellar activity, just as in experiments with live cells. We introduce a dimensionless ratio of flagellar activity to basal coupling that is predictive of the mode of synchrony. This ratio allows us to query biological parameters which are not yet directly measurable experimentally. Our work shows a concrete route for cells to actively control the synchronization of their flagella.

Propulsion Mechanism of Flexible Microbead Swimmers in the Low Reynolds Number Regime.

A propulsion mechanism for a flexible microswimmer constructed from superparamagnetic microbeads with different diameters and subjected to an oscillating field was studied experimentally and theoretically herein. Various types of artificial swimmers with different bending patterns were fabricated to determine the flexibility and an effective waveform for a planar beating flagellum. Waveform evolutions for various swimmer configurations were studied to determine the flexible mechanism of the swimmers. A one-armed microswimmer can propel itself only if the friction of its wavelike body is anisotropic. A swimmer with a larger head and a stronger magnetic dipole moment with a flexible tail allows the bending wave to propagate from the head toward the tail to generate forward thrust. The oscillating head and tail do not simultaneously generate positive thrust all the time within a period of oscillation. To increase the propulsion for a bending swimmer, this study proposes a novel configuration for a microbead swimmer that ensures better swimming efficiency. The ratio of the oscillation amplitude of the head to the length of the swimmer (from 0.26 to 0.28) produces a faster swimmer. On the other hand, the swimmer is propelled more effectively if the ratio of the oscillation amplitude of the tail to the length of the swimmer is from 0.29 to 0.33. This study determined the optimal configuration for a flexible microbead swimmer that generates the greatest propulsion in a low Reynolds number environment.

Speed and Diffusion of Kinesin-2 Are Competing Limiting Factors in Flagellar Length-Control Model

Flagellar length control in Chlamydomonas is a tractable model system for studying the general question of organelle size regulation. We have previously proposed that the diffusive return of the kinesin motor that powers intraflagellar transport can play a key role in length regulation. Here, we explore how the motor speed and diffusion coefficient for the return of kinesin-2 affect flagellar growth kinetics. We find that the system can exist in two distinct regimes, one dominated by motor speed and one by diffusion coefficient. Depending on length, a flagellum can switch between these regimes. Our results indicate that mutations can affect the length in distinct ways. We discuss our theory’s implication for flagellar growth influenced by beating and provide possible explanations for the experimental observation that a beating flagellum is usually longer than its immotile mutant. These results demonstrate how our simple model can suggest explanations for mutant phenotypes.

Characterization of Flagellar Propulsion of Soft Microrobotic Sperm in a Viscous Heterogeneous Medium.

Several microorganisms swim by a beating flagellum more rapidly in solutions with gel-like structure than they do in low-viscosity mediums. In this work, we aim to model and investigate this behavior in low Reynolds numbers viscous heterogeneous medium using soft microrobotic sperm samples. The microrobots are actuated using external magnetic fields and the influence of immersed obstacles on the flagellar propulsion is investigated. We use the resistive-force theory to predict the deformation of the beating flagellum, and the method of regularized Stokeslets for computing Stokes flows around the microrobot and the immersed obstacles. Our analysis and experiments show that obstacles in the medium improves the propulsion even when the Sperm number is not optimal (Sp ≠ 2.1). Experimental results also show propulsion enhancement for concentration range of 0−5% at relatively low actuation frequencies owing to the pressure gradient created by obstacles in close proximity to the beating flagellum. At relatively high actuation frequency, speed reduction is observed with the concentration of the obstacles.

Controllable switching between planar and helical flagellar swimming of a soft robotic sperm.

Sperm cells undergo a wide variety of swimming patterns by a beating flagellum to maintain high speed regardless of the rheological and physical properties of the background fluid. In this work, we develop and control a soft robotic sperm that undergoes controllable switching between swimming modes like biological sperm cells. The soft robotic sperm consists of a magnetic head and an ultra-thin flexible flagellum, and is actuated using external magnetic fields. We observe that out-of-plane wobbling of the head results in helical wave propagation along the flagellum, whereas in-plane wobbling achieves planar wave propagation. Our theoretical predictions and experimental results show the ability of the soft robotic sperm to change its swimming speed by tuning the beating frequency of its flagellum and the propulsion pattern. The average speed of the soft robotic sperm increases by factors of 2 and 1.2 in fluids with viscosity of 1 Pa.s and 5 Pa.s at relatively low actuation frequencies, respectively, when they switch between planar to helical flagellar propulsion.

Phase reduction approach to elastohydrodynamic synchronization of beating flagella.

We formulate a theory for the phase reduction of a beating flagellum. The theory enables us to describe the dynamics of a beating flagellum in a systematic manner using a single variable called the phase. The theory can also be considered as a phase reduction method for the limit-cycle solutions in infinite-dimensional dynamical systems, namely, the limit-cycle solutions to partial differential equations representing beating flagella. We derive the phase sensitivity function, which quantifies the phase response of a beating flagellum to weak perturbations applied at each point and at each time. Using the phase sensitivity function, we analyze the phase synchronization between a pair of beating flagella through hydrodynamic interactions at a low Reynolds number.

Hydrodynamics of microbial filter feeding

Microbial filter feeders are an important group of grazers, significant to the microbial loop, aquatic food webs, and biogeochemical cycling. Our understanding of microbial filter feeding is poor, and, importantly, it is unknown what force microbial filter feeders must generate to process adequate amounts of water. Also, the trade-off in the filter spacing remains unexplored, despite its simple formulation: A filter too coarse will allow suitably sized prey to pass unintercepted, whereas a filter too fine will cause strong flow resistance. We quantify the feeding flow of the filter-feeding choanoflagellate Diaphanoeca grandis using particle tracking, and demonstrate that the current understanding of microbial filter feeding is inconsistent with computational fluid dynamics (CFD) and analytical estimates. Both approaches underestimate observed filtration rates by more than an order of magnitude; the beating flagellum is simply unable to draw enough water through the fine filter. We find similar discrepancies for other choanoflagellate species, highlighting an apparent paradox. Our observations motivate us to suggest a radically different filtration mechanism that requires a flagellar vane (sheet), something notoriously difficult to visualize but sporadically observed in the related choanocytes (sponges). A CFD model with a flagellar vane correctly predicts the filtration rate of D. grandis, and using a simple model we can account for the filtration rates of other microbial filter feeders. We finally predict how optimum filter mesh size increases with cell size in microbial filter feeders, a prediction that accords very well with observations. We expect our results to be of significance for small-scale biophysics and trait-based ecological modeling.

Cryo-Electron Tomography Provides a New Window into Ciliary Structure and Function

Cilia and flagella are conserved and ubiquitous eukaryotic organelles that are composed of more than 600 different proteins and have important biological roles in motility and sensation. The beating of motile cilia and flagella is driven by conformational changes of dynein motors that are coordinated by regulatory complexes. However, the mechanism(s) by which flagellar motility is generated and regulated are largely unknown. We use cryo-electron tomography, subtomogram averaging, molecular tagging and classification analyses to visualize the three-dimensional structures of intact wild-type and mutant flagella, and dissect the organization of key macromolecular complexes. We also study active (beating) flagella that were rapidly frozen to resolve the different conformations of these complexes and identify distinct conformations for different axonemal dyneins and other structures, many of which showing bend direction dependent distributions. Our comprehensive analyses combined with biochemical investigations provides a new understanding of the distinct roles played by various dyneins and regulatory complexes in the motility of cilia and flagella, and suggests critical modifications to previous hypotheses for the molecular mechanisms underlying their motility.

Genetics of male fertility.

Early in embryogenesis, cells that are destined to become germ cells take on a different destiny from other cells in the embryo. The germ cells are not programmed to perform "vital" functions but to perpetuate the species through the transfer of genetic materials to the next generation. To fulfill their destiny, male germ cells undergo meiosis and extensive morphogenesis that transforms the round-shaped cells into freely motile sperm propelled by a beating flagellum to seek out their missing half. Apparently, extra genes and additional regulatory mechanisms are required to achieve all these unique features, and an estimated 11 % of genes are involved in fertility in Drosophila (Hackstein et al., Trends Genet 16(12):565-572, 2000). If comparative numbers of male fertility genes are needed in mammals, extra risks of male fertility problems are associated with disruptive mutations in those genes. Among human male infertility cases, approximately 22 % were classified as "idiopathic," a term used to describe diseases of unknown causes, with idiopathic oligozoospermia being the most common semen abnormality (11.2 %) (Comhaire et al., Int J Androl (Suppl 7):1-53, 1987). "Idiopathic" is a widely used adjective that is used to reflect our lack of understanding of the genetics of male fertility. Fortunately, after more than two decades of phenotypic studies using knockout mice and identifying genes disrupted in spontaneous mutant mice, we have unveiled new and unexpected aspects of crucial gene functions for fertility. Other efforts to categorize genes involved in male fertility in mammals have suggested a total of 1,188 genes (Hermo et al., Microsc Res Tech 73(4):241-494, 2010). Although intracytoplasmic sperm injection (ICSI) can be used to bypass many fertilization obstacles to achieve fertilization with only a few extracted sperm, the widespread use of ICSI without proper knowledge for genetic testing and counseling could still potentially propagate pleiotropic gene mutations associated with male infertility and other genetic diseases (Alukal and Lamb, Urol Clin North Am 35(2):277-288, 2008). In this chapter, we give a brief account of major events during the development of male germ cells and focus on the functions of several crucial genes that have been studied in mutant mouse models and are potential causes of human male infertility.

SPERM SWIMMING THEORY STANDS THE TEST OF TIME

When sperm cells are released, they have a simple objective: find the egg and do it fast. Benjamin Friedrich is a physicist who is fascinated by the relationship between the sperm's beating flagellum and the path it takes. ‘How you get from the beat of the tail to the swimming path is pure physics of hydrodynamic forces,’ says Friedrich. Friedrich explains that James Gray and G. J. Hancock proposed a theory of sperm motility, known as resistive force theory, which could predict a sperm's speed in The Journal of Experimental Biology in 1955. However, no one had successfully tested the theory by comparing it with an extensive data set and there had been some debate about the reliability of Gray's simple approach. Working with Frank Jülicher at the Max Planck Institute for the Physics of Complex Systems in Dresden, Germany, Friedrich realised that he and his collaborators, biologists Ingmar Riedel-Kruse and Jonathon Howard, were collecting the ideal data on sperm swimming to test the 50-year-old theory (p. 1226).Filming bull sperm swimming in circles at 250 frames s−1 through a phase contrast microscope, Riedel-Kruse accurately measured the position of the beating flagellum and sperm head within less than 1 μm. ‘Of course this cannot be done accurately by hand,’ explains Friedrich, so Riedel-Kruse developed accurate computer algorithms to determine the position of the flagellum.With 1 million datapoints for the flagellum's position in hand, it was time for Friedrich to begin testing the theory. Knowing the position of the flagellum and its instantaneous speed, Friedrich plugged these values into Gray and Hancock's theory to calculate the way in which the sperm head wiggled as it moved along its circular path. Amazingly, Friedrich's calculations agreed remarkably well with the movies: his calculated sperm movements were identical to the sperm's movements in the movies.Having used the theory to calculate the sperm's trajectory, Friedrich was also able to calculate a key parameter in Gray and Hancock's equations called the drag anisotropy ratio. According to Friedrich, whenever we move we push against something solid, like the earth, but sperm swimming in fluids have nothing solid to push against, so they have to rely on an imbalance between the friction forces that the flagellum experiences as it moves sideways and forward. The ratio of the two friction coefficients is the drag anisotropy factor and it must be greater than 1 for the sperm to move forward. Comparing his calculations with the movies of swimming sperm, Friedrich found that the perpendicular friction coefficient is 80% higher than the parallel friction coefficient, giving him a drag anisotropy factor of 1.8. Using this value, he was then able to calculate the radius of curvature of the sperm's circular path and found that it agreed perfectly with the movies. Gray and Hancock's theory had stood the test of time remarkably well.Friedrich says, ‘It is exciting that we can use physics to better understand biological questions. Of course sometimes physicists are ignorant of the nice details of a study and there can be clashes between the two cultures, but it is well worth the joint efforts of biologists and physicists to find out how biological phenomena work.’

On Allen's suggestion for long-distance translocation in phloem of plants

N. S. ALLEN has made a film of the streaming of cytoplasm in Nitella, in which she used laser light through chloroplast-free ‘windows’ in the walls of the giant alga cell to take a cine film under Nomarski optics. This film shows that the cytoplasm, which seems to flow steadily and spirally along the axis of the cell, contains undulating filaments that apparently provide the motive force for streaming. It is postulated1 that endoplasmic filaments undulate in a sinusoidal fashion and thereby drive the cytoplasm. There is some supporting evidence that these filaments are branches originating from microfilament bundles which in turn are normally anchored and parallel to the fixed chloroplast rows. The waves passing along the semi-free microfilament branches cause them to act somewhat like beating flagella in other organisms.

Hydrodynamic analysis of non-uniform flagellar undulations

The velocity of translation and power expenditure against viscous resistance of non-uniformly beating flagella are calculated. If the mean wave parameters of flagella bearing waves of varying amplitude and wavelength are used, reasonable approximations to the true propulsive speed can be obtained by using equations developed by earlier workers. The power expenditure against viscous resistance may, however, be significantly greater than that calculated on the basis of the mean wave parameter assumption.