Computer Simulation of Flagellar Movement: I. Demonstration of Stable Bend Propagation and Bend Initiation by the Sliding Filament Model

A program has been developed for digital computer simulation of the movement of a flagellar model consisting of straight segments connected by joints at which bending occurs. The program finds values for the rate of bending at each joint by solving equations which balance active, viscous, and elastic bending moments at each joint. These bending rates are then used to compute the next position of the model. Stable swimming movements, similar to real flagellar movements, can be generated routinely with a 25-segment model using 16 time steps/beat cycle. These results depend on four assumptions about internal flagellar mechanisms: (a) Bending is generated by a sliding filament process. (b) The active process is controlled locally by the curvature of the flagellum. (c) Nonlinear elastic resistances stabilize the amplitude of the movement. (d) Internal viscous resistances stabilize the wavelength of the movement and explain the relatively low sensitivity of flagellar movement to changes in external viscosity.     

Morphological relationship between paraflagellar swelling and paraxial rod in Euglena Gracilis

euglena is a mobile photosynthetic and photosensitive cell which dwells in fresh water. Euglena has an important evolutionary role, therefore its morphology has been and still is a subject of interest. The structures in Euglena which are involved in photoreception and signal transduction and transmission have been well studied. In this paper morphological and ultrastructural evidence of a single stable structure formed by the photoreceptor (paraflagellar swelling) and the other specialized flagellar structures of Euglena gracilis (paraxial rod) is provided using conventional and non-conventional SEM and TEM, on detergent treated cells, and on isolated flagella retaining their photoreceptor.     

Coupling biochemistry and hydrodynamics captures hyperactivated sperm motility in a simple flagellar model

Hyperactivation in mammalian sperm is characterized by highly asymmetrical waveforms and an increase in the amplitude of flagellar bends. It is important for the sperm to be able to achieve hyperactivated motility in order to reach and fertilize the egg. Calcium (Ca²⁺) dynamics are known to play a large role in the initiation and maintenance of hyperactivated motility. Here we present an integrative model that couples the CatSper channel mediated Ca²⁺ dynamics of hyperactivation to a mechanical model of an idealized sperm flagellum in a 3-d viscous, incompressible fluid. The mechanical forces are due to passive stiffness properties and active bending moments that are a function of the local Ca²⁺ concentration along the length of the flagellum. By including an asymmetry in bending moments to reflect an asymmetry in the axoneme's response to Ca²⁺, we capture the transition from activated motility to hyperactivated motility. We examine the effects of elastic properties of the flagellum and the Ca²⁺ dynamics on the overall swimming patterns. The swimming velocities of the model flagellum compare well with data for hyperactivated mouse sperm.     

Effects of calcium on the longituindal flagellum of Oxyrrhis marina

Summary— 2–4 nm filaments represent a new class of cytoskeletal components. They are found in ciliary and flagellar roots and centrosomes of all eucaryotes. They are also the major components of paraflagellar rods (PFR) in Euglena, trypanosomes and dinoflagellates. Oxyrrhis marina, a marine dinoflagellate, possesses a transverse and a longitudinal flagellum. Only the longitudinal flagellum carries the PFR along the proximal two-thirds of its length. This flagellum is not only capable of the classic flagellar beat but is also able to retract and bend, a property mediated by external calcium. To determine if calcium has a direct role in the bending, experimental conditions were established to permeabilization and reactivation. Our conditions to reactivate the axoneme function (wave propagation) appear similar to those observed in the case of the sea urchin sperm. The results show that in vitro, an increase in calcium concentration induces a conformational change of the longitudinal flagellum in the absence of ATP with a half maximum effect at 0.1 μM. In the presence of ATP, this morphology modification causes a total inhibition of the wave propagation which is replaced by non-propulsive contractions of low amplitude. As these properties are not shared by reactivated sea urchin sperm flagella or the transverse flagellum of O marina devoid of PFR, we propose that PFR are responsible for the bending phenomenon. A calcium shock also induces flagellar excision with a half maximum effect at 0.3 μM, and immunofluorescence results suggest that a centrin-like protein is present in O marina and is responsible for this excision.     

Functional role of a conserved aspartic acid residue in the motor of the Na-driven flagellum from Vibrio cholerae

The flagellar motor consists of a rotor and a stator and couples the flux of cations (H⁺ or Na⁺) to the generation of the torque necessary to drive flagellum rotation. The inner membrane proteins PomA and PomB are stator components of the Na⁺-driven flagellar motor from Vibrio cholerae. Affinity-tagged variants of PomA and PomB were co-expressed in trans in the non-motile V. cholerae pomAB deletion strain to study the role of the conserved D23 in the transmembrane helix of PomB. At pH 9, the D23E variant restored motility to 100% of that observed with wild type PomB, whereas the D23N variant resulted in a non-motile phenotype, indicating that a carboxylic group at position 23 in PomB is important for flagellum rotation. Motility tests at decreasing pH revealed a pronounced decline of flagellar function with a motor complex containing the PomB-D23E variant. It is suggested that the protonation state of the glutamate residue at position 23 determines the performance of the flagellar motor by altering the affinity of Na⁺ to PomB. The conserved aspartate residue in the transmembrane helix of PomB and its H⁺-dependent homologs might act as a ligand for the coupling cation in the flagellar motor.     

Control of flagellar motility in Euglena and Chlamydomonas. Microinjection of EDTA, EGTA, Mn(2)+, and Zn(2)+.

When a Euglena, in a medium containing ATP, is microinjected with 7 × 10^?14 l of 0.02 M EDTA, which binds Ca²⁺ and Mg²⁺, flagellar motility stops. Flagellar arrest in Chlamydomonas occurs with the injection of 2 × 10^?14 l of 0.02 M EDTA. The injection of similar amounts (7 × 10^?14 l in Euglena and 3 × 10^?14 l in Chlamydomonas) of 0.02 M EGTA, which preferentially binds Ca²⁺, did not significantly alter flagellar motility. This suggests that a decrease in the internal Ca²⁺ concentration in Euglena or Chlamydomonas did not stimulate flagellar beating. Further, flagellar motility decreased when internal Mg²⁺ was chelated. The microinjection of Zn²⁺ into these cells caused a decrease in flagellar frequency analogous to the decrease in frequency caused by the injection of Ca²⁺ and EDTA. The microinjection of 7 × 10^?14 l of 0.2 M Mn²⁺ caused an approx. 1.5-fold increase in Euglena flagellar motility. Chlamydomonas flagella, which cease to beat upon impalement in an Mg²⁺-free medium, resume a flagellar frequency of 18 Hz when injected with 3 × 10^?14 l of 0.2 M Mn²⁺. In the experiments reported here, Mn²⁺ acts as an analog of Mg²⁺.     

Simulating the Complex Cell Design of Trypanosoma brucei and Its Motility

The flagellate Trypanosoma brucei, which causes the sleeping sickness when infecting a mammalian host, goes through an intricate life cycle. It has a rather complex propulsion mechanism and swims in diverse microenvironments. These continuously exert selective pressure, to which the trypanosome adjusts with its architecture and behavior. As a result, the trypanosome assumes a diversity of complex morphotypes during its life cycle. However, although cell biology has detailed form and function of most of them, experimental data on the dynamic behavior and development of most morphotypes is lacking. Here we show that simulation science can predict intermediate cell designs by conducting specific and controlled modifications of an accurate, nature-inspired cell model, which we developed using information from live cell analyses. The cell models account for several important characteristics of the real trypanosomal morphotypes, such as the geometry and elastic properties of the cell body, and their swimming mechanism using an eukaryotic flagellum. We introduce an elastic network model for the cell body, including bending rigidity and simulate swimming in a fluid environment, using the mesoscale simulation technique called multi-particle collision dynamics. The in silico trypanosome of the bloodstream form displays the characteristic in vivo rotational and translational motility pattern that is crucial for survival and virulence in the vertebrate host. Moreover, our model accurately simulates the trypanosome''s tumbling and backward motion. We show that the distinctive course of the attached flagellum around the cell body is one important aspect to produce the observed swimming behavior in a viscous fluid, and also required to reach the maximal swimming velocity. Changing details of the flagellar attachment generates less efficient swimmers. We also simulate different morphotypes that occur during the parasite''s development in the tsetse fly, and predict a flagellar course we have not been able to measure in experiments so far.     

Distinct regulation of two flagella by calcium during chemotaxis of male gametes in the brown alga Mutimo cylindricus (Cutleriaceae,Tilopteridales)

Brown algal male gametes show chemotaxis to the sex pheromone that is released from female gametes. The chemotactic behavior of the male gametes is controlled by the changes in the beating of two flagella known as the anterior and posterior flagellum. Our previous study using Mutimo cylindricus showed that the sex pheromone induced an increment in both the deflection angle of the anterior flagellum and sustained unilateral bend of the posterior flagellum, but the mechanisms regulating these two flagellar waveforms were not fully revealed. In this study, we analyzed the changes in swimming path and flagellar waveforms with a high-speed recording system under different calcium conditions. The extracellular Ca²⁺ concentration at 10⁻³ M caused an increment in the deflection angle of the anterior flagellum only when ionomycin was absent. No sustained unilateral bend of the posterior flagellum was induced either in the absence or presence of ionomycin in extracellular Ca²⁺ concentrations below 10⁻² M. Real-time Ca²⁺ imaging revealed that there is a spot near the basal part of anterior flagellum showing higher Ca²⁺ than in the other parts of the cell. The intensity of the spot slightly decreased when male gametes were treated with the sex pheromone. These results suggest that Ca²⁺-dependent changes in the anterior and posterior flagellum are regulated by distinct mechanisms and that the increase in the anterior flagellar deflection angle and sustained unilateral bend of the posterior flagellum may not be primarily induced by the Ca²⁺ concentration.     

Effect of Extracellular Ca2+ and Ca2+-Antagonists on the Movement and Chemoorientation of Male Gametes of Ectocarpus siliculosus (Phaeophyceae)

Chemoorientation in male gametes of Ectocarpus siliculosus in response to sexual pheromones is effected by two distinct mechanisms, chemokinesis and chemoklinotaxis. These are characterized by a strongly asymmetric bending pattern of the anteriorly-directed flagellum and transient unilateral bending of the hind flagellum, respectively. Removal of extracellular Ca²⁺ showed that normal flagellar movement and chemokinesis require millimolar concentrations of Ca²⁺ in the medium. The response to pheromones is strongly inhibited by La³⁺, whereas the Ca²⁺-channel drugs, verapamil and nifedipine, have only little effect. Nifedipine nethertheless effectively inhibited accumulation at pheromone sources. These results are interpreted as an indication for the involvement of two pharmacologically distinct Ca²⁺-channels in chemokinesis and chemoklinotaxis. The calmodulin-antagonist, trifluoperazine, induces, at low concentrations, the same flagellar response in chemokinesis as the pheromone, the mechanism of action remaining unknown.     

Serine 26 in the PomB Subunit of the Flagellar Motor Is Essential for Hypermotility of Vibrio cholerae

Vibrio cholerae is motile by means of its single polar flagellum which is driven by the sodium-motive force. In the motor driving rotation of the flagellar filament, a stator complex consisting of subunits PomA and PomB converts the electrochemical sodium ion gradient into torque. Charged or polar residues within the membrane part of PomB could act as ligands for Na⁺, or stabilize a hydrogen bond network by interacting with water within the putative channel between PomA and PomB. By analyzing a large data set of individual tracks of swimming cells, we show that S26 located within the transmembrane helix of PomB is required to promote very fast swimming of V. cholerae. Loss of hypermotility was observed with the S26T variant of PomB at pH 7.0, but fast swimming was restored by decreasing the H⁺ concentration of the external medium. Our study identifies S26 as a second important residue besides D23 in the PomB channel. It is proposed that S26, together with D23 located in close proximity, is important to perturb the hydration shell of Na⁺ before its passage through a constriction within the stator channel.     

FLAGELLAR REGENERATION IN PROTOZOAN FLAGELLATES

The flagella of populations of three protozoan species (Ochromonas, Euglena, and Astasia) were amputated and allowed to regenerate. The kinetics of regeneration in all species were characterized by a lag phase during which there was no apparent flagellar elongation; this phase was followed by elongation at a rate which constantly decelerated as the original length was regained. Inhibition by cycloheximide applied at the time of flagellar amputation showed that flagellar regeneration was dependent upon de novo protein synthesis. This was supported by evidence showing that a greater amount of leucine was incorporated into the proteins of regenerating than nonregenerating flagella. The degree of inhibition of flagellar elongation observed with cycloheximide depended on how soon after flagellar amputation it was applied: when applied to cells immediately following amputation, elongation was almost completely inhibited, but its application at various times thereafter permitted considerable elongation to occur prior to complete inhibition of flagellar elongation. Hence, a sufficient number of precursors were synthesized and accumulated prior to addition of cycloheximide so that their assembly (elongation) could occur for a time under conditions in which protein synthesis had been inhibited. Evidence that the site of this assembly may be at the tip of the elongating flagellum was obtained from radioautographic studies in which the flagella of Ochromonas were permitted to regenerate part way in the absence of labeled leucine and to complete their regeneration in the presence of the isotope. Possible mechanisms which may be operating to control flagellar regeneration are discussed in light of these and other observations.     

Photosensory transduction in the flagellated alga, Euglena gracilis. III. Induction of Ca2+-dependent responses by monovalent cation ionophores

(1) The effects of monovalent cation ionophores (valinomycin and gramicidin), a protonophore (nigericin) and extracellular pH change on the motility and blue light-induced photobehavior (step-down photophobic response) of Euglena were investigated. (2) Monovalent cation ionophores, but not the protonophore, can both partially suppress photobehavior and, under appropriate conditions, induce a change in flagellar activity (and thus cell movement) that appears identical to that associated with the photobehavior. (3) Valinomycin, at low extracellular KCl, delays the induction of photobehavior and also induces a light-independent elevation in the frequency of directional changes in the cells' swimming path. Both effects are suppressed by elevation in extracellular KCl. (4) Gramicidin, in the presence of the anion tetraphenylborate, suppresses photobehavior. The same combination, if applied in the presence of elevated extracellular NaCl, induces a light-independent cell tumbling and elevation in the frequency of directional changes in the cells' swimming path. The induced behavior is dependent on the extracellular Na concentration, requires the presence of extracellular Ca²⁺ and is blocked by La³⁺. (5) Photobehavior is observed over the pH range 3.5–8.2 and fluence/response relationships for photobehavior are not significantly different over the pH range 5.5–8.2. (6) The results provide a link between the previously reported effects of Ca²⁺ ionophores, and the effects of monovalent cations and monovalent cation-transport inhibitor on motility and photobehavior.     

Flagellar waveforms of gametes in the brown alga Ectocarpus siliculosus

Brown algae are members of the Stramenopiles and their gametes generally have two heterogeneous flagella: a long anterior flagellum (AF) with mastigonemes and a short posterior flagellum (PF). In this study, swimming paths and flagellar waveforms in free-swimming and thigmotactic-swimming male and female gametes and in male gametes during chemotaxis, were quantitatively analysed in the model brown alga Ectocarpus siliculosus. This analysis was performed using a high-speed video camera. It was revealed that the AF plays a role in changing the locomotion of male and female gametes from free-swimming to thigmotactic-swimming and also in changing the swimming path of male gametes from linear to circular during chemotaxis. In the presence of a sex pheromone, male gametes changed their swimming path from linear (swimming path curvature, 0–0.02 µm^–1) to middle and small circular path (swimming path curvature, 0.04–0.20 µm^–1). The flagellar asymmetry and the deflection angle of the AF became larger, whereas the oscillation pattern of the AF was stable. However, there was no correlation between the flagellar asymmetry and the deflection angle of the AF and the path curvature when the male gametes showed middle to small circular paths. The PF irregularly changed the deflection angle and the oscillation pattern was unstable depending on the gradient of the sex pheromone concentration. AF waveforms were independent of PF locomotion during chemotaxis. This means that the AF has the ability to change the swimming path of male gametes – for example, from a highly linear path to a circular path – while changes in locomotion from a middle circle path to a small circle path is the result of beating of the PF.     

Ultrastructural analysis of flagellar development in plurilocular sporangia of Ectocarpus siliculosus (Phaeophyceae)

Flagellar development in the plurilocular zoidangia of sporophytes of the brown alga Ectocarpus siliculosus was analyzed in detail using transmission electron microscopy and electron tomography. A series of cell divisions in the plurilocular zoidangia produced the spore-mother cells. In these cells, the centrioles differentiated into flagellar basal bodies with basal plates at their distal ends and attached to the plasma membrane. The plasma membrane formed a depression (flagellar pocket) into where the flagella elongated and in which variously sized vesicles and cytoplasmic fragments accumulated. The anterior and posterior flagella started elongating simultaneously, and the vesicles and cytoplasmic fragments in the flagellar pocket fused to the flagellar membranes. The two flagella (anterior and posterior) could be clearly distinguished from each other at the initial stage of their development by differences in length, diameter and the appendage flagellar rootlets. Flagella continued to elongate in the flagellar pocket and maintained their mutually parallel arrangement as the flagellar pocket gradually changed position. In mature zoids, the basal part of the posterior flagellum (paraflagellar body) characteristically became swollen and faced the eyespot region. Electron dense materials accumulated between the axoneme and the flagellar membrane, and crystallized materials could also be observed in the swollen region. Before liberation of the zoospores from the plurilocular zoidangia, mastigoneme attachment was restricted to the distal region of the anterior flagellum. Structures just below the flagellar membrane that connected to the mastigonemes were clearly visible by electron tomography.     

Protein kinase involved in flagellar-length control

During its life cycle, the parasitic protozoon Leishmania mexicana differentiates from a flagellated form, the promastigote, to an amastigote form carrying a rudimentary flagellum. Besides biochemical changes, this process involves a change in overall cell morphology including flagellar shortening. A mitogen-activated protein kinase kinase homologue designated LmxMKK was identified in a homology screening and found to be critically involved in the regulation of flagellar assembly and cell size. LmxMKK is exclusively expressed in the promastigote stage and is likely to be regulated by posttranslational mechanisms such as phosphorylation. A deletion mutant for the single-copy gene revealed motile flagella dramatically reduced in length and lacking the paraflagellar rod, a structure adjacent to the axoneme in kinetoplastid flagella. Moreover, a fraction of the cells showed perturbance of the axonemal structure. Complementation of the deletion mutant with the wild-type gene restored typical promastigote morphology. We propose that LmxMKK influences anterograde intraflagellar transport to maintain flagellar length in Leishmania promastigotes; as such, it is the first protein kinase known to be involved in organellar assembly.     

Structural Changes of the Paraflagellar Rod during Flagellar Beating in Trypanosoma cruzi

Background

Trypanosoma cruzi, the agent of Chagas disease, is a protozoan member of the Kinetoplastidae family characterized for the presence of specific and unique structures that are involved in different cell activities. One of them is the paraflagellar rod (PFR), a complex array of filaments connected to the flagellar axoneme. Although the function played by the PFR is not well established, it has been shown that silencing of the synthesis of its major proteins by either knockout of RNAi impairs and/or modifies the flagellar motility.

Methodology/Principal Findings

Here, we present results obtained by atomic force microscopy (AFM) and transmission electron microscopy (TEM) of replicas of quick-frozen, freeze-fractured, deep-etched and rotary-replicated cells to obtain detailed information of the PFR structures in regions of the flagellum in straight and in bent state. The images obtained show that the PFR is not a fixed and static structure. The pattern of organization of the PFR filament network differs between regions of the flagellum in a straight state and those in a bent state. Measurements of the distances between the PFR filaments and the filaments that connect the PFR to the axoneme as well as of the angles between the intercrossed filaments supported this idea.

Conclusions/Significance

Graphic computation based on the information obtained allowed the proposal of an animated model for the PFR structure during flagellar beating and provided a new way of observing PFR filaments during flagellar beating.     

Polarotaxis,gravitaxis and vertical phototaxis in the green flagellate,Euglena gracilis

A fully automatic computer-controlled video analysis system has been used to study the movement of the green unicellular flagellate, Euglena gracilis in a horizontal or vertical cuvette. In darkness, in the absence of gaseous gradients, most cells swim straight upwards. While in a horizontal cuvette the transition between positive and negative phototaxis is found at about 1.5 W m^-2, an excess of 30 W m^-2 is required to reverse the upward swimming (due to the combined stimulus of negative gravitaxis and positive phototaxis) in a vertical cuvette. By studying the swimming direction in horizontal and vertical cuvettes in polarized light irradiated from above or from the side, respectively, the dichroic orientation of the photoreceptor molecules can be determined in three dimensions with respect to the axes of the cell: In a horizontal cuvette, in a linearly polarized beam from above, the cells orient predominantly at an angle of about 30° clockwise off the electric dipole transition moment as seen from above. The behavior in a vertical cuvette with polarized light entering from above indicates that the photoreceptor pigments are dichroically oriented 60° counterclockwise from the flagellar plane (seen from the front end of the cell). Experiments with horizontal polarized light indicate that the photoreceptor transition moment deviates 25° clockwise off the long axis of the cell.Abbreviation PFB paraflagellar body Dedicated to Prof. Dr. W. Nultsch on the occasion of his 60th birthday     

A 3D Motile Rod-Shaped Monotrichous Bacterial Model

We introduce a 3D model for a motile rod-shaped bacterial cell with a single polar flagellum which is based on the configuration of a monotrichous type of bacteria such as Pseudomonas aeruginosa. The structure of the model bacterial cell consists of a cylindrical body together with the flagellar forces produced by the rotation of a helical flagellum. The rod-shaped cell body is composed of a set of immersed boundary points and elastic links. The helical flagellum is assumed to be rigid and modeled as a set of discrete points along the helical flagellum and flagellar hook. A set of flagellar forces are applied along this helical curve as the flagellum rotates. An additional set of torque balance forces are applied on the cell body to induce counter-rotation of the body and provide torque balance. The three-dimensional Navier–Stokes equations for incompressible fluid are used to describe the fluid dynamics of the coupled fluid–microorganism system using Peskin’s immersed boundary method. A study of numerical convergence is presented along with simulations of a single swimming cell, the hydrodynamic interaction of two cells, and the interaction of a small cluster of cells.     

ULTRASTRUCTURAL OBSERVATIONS OF A COLACIUM PALMELLA: THE RESERVOIR,EYESPOT, AND FLAGELLA1

A recently described euglenoid of the genus Colacium inhabits the rectums of damselfly larvae during the winter as a nonflagellated, stalkless palmella stage. Contrary to previous reports, which were based on light microscope observations, ultrastructural observations establish that the reservoir and canal with its nonemergent flagella remain structurally intact in the palmella condition. The 2 non-emergent flagella are structurally distinct. The larger flagellum, which probably gives rise to the single, emergent flagellant of the swimming euglenoid, has the typical 9 + 2 microtubular arrangement, together with a paraflagellar rod throughout most of its length. The crystalline paraflagellar body, typical of swimming euglenoids, is absent. The smaller flagellum has a 9 + 0 arrangement of the axonemal microtubules. This flagellum appears to terminate within the reservoir with a successive loss of number and arrangement of microtubules near its distal end. Hair-like structures lining the reservoir membrane may represent preformed nontubular mastigonemes. The eyespot granules are clustered around the cytostome and do not display the compact organization or position typical of the flagellated stage or the stalked stage of Colacium.