Mesoscopic modeling of bacterial flagellar microhydrodynamics

A particle-based hybrid method of elastic network model and smooth-particle hydrodynamics has been employed to describe the propulsion of bacterial flagella in a viscous hydrodynamic environment. The method explicitly models the two aspects of bacterial propulsion that involve flagellar flexibility and long-range hydrodynamic interaction of low-Reynolds-number flow. The model further incorporates the molecular organization of the flagellar filament at a coarse-grained level in terms of the 11 protofilaments. Each of these protofilaments is represented by a collection of material points that represent the flagellin proteins. A computational model of a single flexible helical segment representing the filament of a bacterial flagellum is presented. The propulsive dynamics and the flow fields generated by the motion of the model filament are examined. The nature of flagellar deformation and the influence of hydrodynamics in determining the shape of deformations are examined based on the helical filament.     

Bacterial flagellar microhydrodynamics: Laminar flow over complex flagellar filaments,analog archimedean screws and cylinders,and its perturbations

The flagellar filament, the bacterial organelle of motility, is the smallest rotary propeller known. It consists of 1), a basal body (part of which is the proton driven rotary motor), 2), a hook (universal joint-allowing for off-axial transmission of rotary motion), and 3), a filament (propeller-a long, rigid, supercoiled helical assembly allowing for the conversion of rotary motion into linear thrust). Helically perturbed (so-called "complex") filaments have a coarse surface composed of deep grooves and ridges following the three-start helical lines. These surface structures, reminiscent of a turbine or Archimedean screw, originate from symmetry reduction along the six-start helical lines due to dimerization of the flagellin monomers from which the filament self assembles. Using high-resolution electron microscopy and helical image reconstruction methods, we calculated three-dimensional density maps of the complex filament of Rhizobium lupini H13-3 and determined its surface pattern and boundaries. The helical symmetry of the filament allows viewing it as a stack of identical slices spaced axially and rotated by constant increments. Here we use the closed outlines of these slices to explore, in two dimensions, the hydrodynamic effect of the turbine-like boundaries of the flagellar filament. In particular, we try to determine if, and under what conditions, transitions from laminar to turbulent flow (or perturbations of the laminar flow) may occur on or near the surface of the bacterial propeller. To address these questions, we apply the boundary element method in a manner allowing the handling of convoluted boundaries. We tested the method on several simple, well-characterized cylindrical structures before applying it to real, highly convoluted biological surfaces and to simplified mechanical analogs. Our results indicate that under extreme structural and functional conditions, and at low Reynolds numbers, a deviation from laminar flow might occur on the flagellar surface. These transitions, and the conditions enabling them, may affect flagellar polymorphism and the formation and dispersion of flagellar bundles-factors important in the chemotactic response.     

Elastic properties of bacterial flagellar filaments: I. Free rotation case

Elongation of a helical bacterial flagellar filament in a fluid flow with one end attached to a slide glass is calculated. The flagellar filament is regarded as a coil spring. In this case, the spring constant is a function of the elastic constants of the flagellar filament. Relations between the elongation and the elastic constants are discussed.     

Refining the structure of the Halobacterium salinarum flagellar filament using the iterative helical real space reconstruction method: insights into polymorphism

The eubacterial flagellar filament is an external, self-assembling, helical polymer approximately 220 A in diameter constructed from a highly conserved monomer, flagellin, which polymerizes externally at the distal end. The archaeal filament is only approximately 100 A in diameter, assembles at the proximal end and is constructed from different, glycosylated flagellins. Although the phenomenology of swimming is similar to that of eubacteria, the symmetry of the archebacterial filament is entirely different. Here, we extend our previous study on the flagellar coiled filament structure of strain R1M1 of Halobacterium salinarum. We use strain M175 of H.salinarum, which forms poly-flagellar bundles at high yield which, under conditions of relatively low ionic-strength (0.8 M versus 5 M) and low pH ( approximately 2.5 versus approximately 6.8), form straight filaments. We demonstrated previously that a single-particle approach to helical reconstruction has many advantages over conventional Fourier-Bessel methods when dealing with variable helical symmetry and heterogeneity. We show here that when this method is applied to the ordered helical structure of the archebacterial uncoiled flagellar filament, significant extensions in resolution can be obtained readily when compared to applying traditional helical techniques. The filament population can be separated into classes of different morphologies, which may represent polymorphic states. Using cryo-negatively stained images, a resolution of approximately 10-15 A has been achieved. Single alpha-helices can be fit into the reconstruction, supporting the proposed similarity of the structure to that of type IV bacterial pili.     

Correlation between Supercoiling and Conformational Motions of the Bacterial Flagellar Filament

The bacterial flagellar filament is a very large macromolecular assembly of a single protein, flagellin. Various supercoiled states of the filament exist, which are formed by two structurally different conformations of flagellin in different ratios. We investigated the correlation between supercoiling of the protofilaments and molecular dynamics in the flagellar filament using quasielastic and elastic incoherent neutron scattering on the picosecond and nanosecond timescales. Thermal fluctuations in the straight L- and R-type filaments were measured and compared to the resting state of the wild-type filament. Amplitudes of motion on the picosecond timescale were found to be similar in the different conformational states. Mean-square displacements and protein resilience on the 0.1 ns timescale demonstrate that the L-type state is more flexible and less resilient than the R-type, whereas the wild-type state lies in between. Our results provide strong support that supercoiling of the protofilaments in the flagellar filament is determined by the strength of molecular forces in and between the flagellin subunits.     

Polymorphic transition of the flagellar polyhook from Escherichia coli and Salmonella typhimurium

Bacterial flagellar polyhook fibers were reversibly transformed into a set of helical forms depending on pH, ionic strength and temperature. Electron microscopy with formalin fixation and freeze-drying was useful for observing three-dimensional shapes of various polyhook helices and determining their helical handedness. A Cartesian plot of curvature against twist for these polyhook helices gave a sinusoidal curve as in the case of the polymorphic forms of flagellar filament. In the study on the polymorphism of flagellar filaments. Calladine (1976, 1978) and Kamiya et al. (1979) pointed out that such a relation in the polymorphic forms could be derived from the assumption that the subunits on the near-longitudinal (11-start) helical lines should work as elastic fibers (protofilaments) having two distinct states of conformation. In contrast, the observed twist for the polyhook helices is too large to be explained by the same assumption. Instead, we must assume that subunits on the strongly twisted, 16-start helical line should work as the co-operative protofilament.     

Correlation between Supercoiling and Conformational Motions of the Bacterial Flagellar Filament

The bacterial flagellar filament is a very large macromolecular assembly of a single protein, flagellin. Various supercoiled states of the filament exist, which are formed by two structurally different conformations of flagellin in different ratios. We investigated the correlation between supercoiling of the protofilaments and molecular dynamics in the flagellar filament using quasielastic and elastic incoherent neutron scattering on the picosecond and nanosecond timescales. Thermal fluctuations in the straight L- and R-type filaments were measured and compared to the resting state of the wild-type filament. Amplitudes of motion on the picosecond timescale were found to be similar in the different conformational states. Mean-square displacements and protein resilience on the 0.1 ns timescale demonstrate that the L-type state is more flexible and less resilient than the R-type, whereas the wild-type state lies in between. Our results provide strong support that supercoiling of the protofilaments in the flagellar filament is determined by the strength of molecular forces in and between the flagellin subunits.     

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.     

Elastic properties of bacterial flagellar filaments. II. Determination of the modulus of rigidity

Elongation of a helical bacterial flagellar filament subjected to fluid flow was calculated on the assumption that one end of the filament is firmly attached to a substratum. It was found that the quantity [E(d/2 pi r)2 + 2 mu] could be determined by measuring the elongation at various flow rates, where E is Young's modulus, mu the modulus of rigidity, r the radius of the helix, and d the helical pitch. Experiments were carried out to determine the above quantity for Salmonella flagellar filaments assuming a close-coil form. Because the above quantity is almost equal to 2 mu for a helical form with a large radius/pitch ratio, we were able to determine the modulus of rigidity for this kind of flagellar filament from plots of elongation vs. flow rates. The modulus of rigidity was determined to be about 1 X 10(11) dyn/cm2, i.e., 2 orders of magnitude larger than the previously estimated value.     

Helical packing of needles from functionally altered Shigella type III secretion systems

Gram-negative bacteria commonly interact with eukaryotic host cells using type III secretion systems (TTSSs or secretons), which comprise cytoplasmic, transmembrane and extracellular domains. The extracellular domain is a hollow needle-like structure protruding 60 nm beyond the bacterial surface. The TTSS is activated to transfer bacterial proteins directly into a host cell only upon physical contact with the target cell. We showed previously that the monomer of the Shigella flexneri needle, MxiH, assembles into a helical structure with parameters similar to those defining the architecture of the extracellular components of bacterial flagella. By analogy with flagella, which are known to exist in different helical states, we proposed that changes in the helical packing of the needle might be used to sense host cell contact. Here, we show that, on the contrary, mutations within MxiH that lock the TTSS into altered secretion states do not detectably alter the helical packing of needles. This implies that either: (1) host cell contact is signalled through the TTSS via helical changes in the needle that are significantly smaller than those linked to structural changes in the flagellar filament and therefore too small to be detected by our analysis methods or (2) that signal transduction in this system occurs via a novel molecular mechanism.     

Helical structure of the needle of the type III secretion system of Shigella flexneri

Gram-negative bacteria commonly interact with animal and plant hosts using type III secretion systems (TTSSs) for translocation of proteins into eukaryotic cells during infection. 10 of the 25 TTSS-encoding genes are homologous to components of the bacterial flagellar basal body, which the TTSS needle complex morphologically resembles. This indicates a common ancestry, although no TTSS sequence homologues for the genes encoding the flagellum are found. We here present an approximately 16-A structure of the central component, the needle, of the TTSS. Although the needle subunit is significantly smaller and shares no sequence homology with the flagellar hook and filament, it shares a common helical architecture ( approximately 5.6 subunits/turn, 24-A helical pitch). This common architecture implies that there will be further mechanistic analogies in the functioning of these two bacterial systems.     

Building the atomic model for the bacterial flagellar filament by electron cryomicroscopy and image analysis

The bacterial flagellar filament is a helical propeller for bacterial locomotion. It is a well-ordered helical assembly of a single protein, flagellin, and its tubular structure is formed by 11 protofilaments, each in either of the two distinct conformations, L- and R-type, for supercoiling. We have been studying the three-dimensional structures of the flagellar filaments by electron cryomicroscopy and recently obtained a density map of the R-type filament up to 4 angstroms resolution from an image data set containing only about 41,000 molecular images. The density map showed the features of the alpha-helical backbone and some large side chains, which allowed us to build the complete atomic model as one of the first atomic models of macromolecules obtained solely by electron microscopy image analysis (Yonekura et al., 2003a). We briefly review the structure and the structure analysis, and point out essential techniques that have made this analysis possible.     

Polarity of enteropathogenic Escherichia coli EspA filament assembly and protein secretion

Type III secretion systems (TTSS) are sophisticated macromolecular structures that play an imperative role in bacterial infections and human disease. The TTSS needle complex is conserved among bacterial pathogens and shows broad similarity to the flagellar basal body. However, the TTSS of enteropathogenic and enterohemorrhagic Escherichia coli, two important human enteric pathogens, is unique in that it has an approximately 12-nm-diameter filamentous extension to the needle that is composed of the secreted translocator protein EspA. EspA filaments and flagellar structures have very similar helical symmetry parameters. In this study we investigated EspA filament assembly and the delivery of effector proteins across the bacterial cell wall. We show that EspA filaments are elongated by addition of EspA subunits to the tip of the growing filament. Moreover, EspA filament length is modulated by the availability of intracellular EspA subunits. Finally, we provide direct evidence that EspA filaments are hollow conduits through which effector proteins are delivered to the extremity of the bacterial cell (and subsequently into the host cell).     

In vitro characterization of FlgB, FlgC, FlgF, FlgG, and FliE, flagellar basal body proteins of Salmonella

The bacterial flagellar basal body is a rotary motor. It spans the cytoplasmic and outer membranes and drives rapid rotation of a long helical filament in the cell exterior. The flagellar rod at its central axis is a drive shaft that transmits torque through the hook to the filament to propel the bacterial locomotion. To study the structure of the rod in detail, we have established purification procedures for Salmonella rod proteins, FlgB, FlgC, FlgF, FlgG, and also for FliE, a rod adapter protein, from an Escherichia coli expression system. While FlgF was highly soluble, FlgB, FlgC, FlgG and FliE tended to self or cross-aggregate into fibrils in solutions at neutral pH or below, at high ionic strength, or at high protein concentration. These aggregates were characterized to be beta-amyloid fibrils, unrelated to the rod structure formed in vivo. Under non-aggregative conditions, no protein-protein interactions were detected between any pairs of these five proteins, suggesting that their spontaneous, template-free polymerization is strongly suppressed. Limited proteolyses showed that FlgF and FlgG have natively unfolded N and C-terminal regions of about 100 residues in total just as flagellin does, whereas FlgB, FlgC and FliE, which are little over 100 residues long, are unfolded in their entire peptide chains. These results together with other data indicate that all of the ten flagellar axial proteins share structural characteristics and folding dynamics in relation to the mechanism of their self-assembly into the flagellar axial structure.     

Amino acids responsible for flagellar shape are distributed in terminal regions of flagellin

The shape of the flagellar filaments of the bacterium Salmonella typhimurium under ordinary conditions is a left-handed helix. In addition to the normal wild-type filament, non-helical (i.e. straight), right-handed helical (early), or circular (semi-coiled and coiled) filaments and filament with small amplitude (fl-type) have been found in mutants or in filaments reconstituted in vitro. We analysed wild-type flagellin and flagellins from 17 flagellar-shape mutants (6 with straight filaments, 6 with curly filaments, 4 with coiled filaments and 1 with fl-type filament) by amino acid sequencing to identify the mutational sites. All mutant flagellins except that of the fl-type filament had single mutations; the fl-type flagellin had two mutations in the molecule. The sites of these mutations were localized in alpha-helical segments of the terminal regions of flagellin. A possible mechanism of the polymorphism of the flagellar filament is discussed.     

Various mechanisms of flagella helicity formation in haloarchaea

The genome of a halophilic archaeon Haloarcula marismortui carries two flagellin genes, flaA2 and flaB. Previously, we demonstrated that the helical flagellar filaments of H. marismortui were composed primarily of flagellin FlaB molecules, while the other flagellin (FlaA2) was present in minor amounts. Mutant H. marismortui strains with either flagellin gene inactivated were obtained. It was shown that inactivation of the flaA2 gene did not lead to changes in cell motility and helicity of the filaments, while the cells with inactivated flaB lost their motility and flagella synthesis was stopped. Two FlaB flagellin forms having different sensitivities to proteolysis were found in the flagellar filament structure. It is speculated that these flagellin forms may ensure the helical filament formation. Moreover, the flagella of a psychrotrophic haloarchaeon Halorubrum lacusprofundi were isolated and characterized for the first time. H. lacusprofundi filaments were helical and exhibited morphological polymorphism, although the genome contained a single flagellin gene. These results suggest that the mechanisms of flagellar helicity may differ in different halophilic archaea, and sometimes the presence of two flagellin genes, in contrast to Halobacterium salinarum, is not necessary for the formation of a functional helical flagellum.     

Role of flagellar hydrogen bonding in Salmonella motility and flagellar polymorphic transition

Bacterial flagellar filaments are assembled by tens of thousands flagellin subunits, forming 11 helically arranged protofilaments. Each protofilament can take either of the two bistable forms L‐type or R‐type, having slightly different conformations and inter‐protofilaments interactions. By mixing different ratios of L‐type and R‐type protofilaments, flagella adopt multiple filament polymorphs and promote bacterial motility. In this study, we investigated the hydrogen bonding networks at the flagellin crystal packing interface in Salmonella enterica serovar typhimurium (S. typhimurium) by site‐directed mutagenesis of each hydrogen bonded residue. We identified three flagellin mutants D108A, N133A and D152A that were non‐motile despite their fully assembled flagella. Mutants D108A and D152A trapped their flagellar filament into inflexible right‐handed polymorphs, which resemble the previously predicted 3L/8R and 4L/7R helical forms in Calladine’s model but have never been reported in vivo. Mutant N133A produces floppy flagella that transform flagellar polymorphs in a disordered manner, preventing the formation of flagellar bundles. Further, we found that the hydrogen bonding interactions around these residues are conserved and coupled to flagellin L/R transition. Therefore, we demonstrate that the hydrogen bonding networks formed around flagellin residues D108, N133 and D152 greatly contribute to flagellar bending, flexibility, polymorphisms and bacterial motility.     

Alternative flagellar filament types in the haloarchaeon Haloarcula marismortui

Many Archaea use rotation of helical flagellar filaments for swimming motility. We isolated and characterized the flagellar filaments of Haloarcula marismortui, an archaeal species previously considered to be nonmotile. Two Haloarcula marismortui phenotypes were discriminated--their filaments are composed predominantly of either FlaB or FlaA2 flagellin, and the corresponding genes are located on different replicons. FlaB and FlaA2 filaments differ in antigenicity and thermostability. FlaA2 filaments are distinctly thicker (20-22 nm) than FlaB filaments (16-18 nm). The observed filaments are nearly twice as thick as those of other characterized euryarchaeal filaments. The results suggest that the helicity of Haloarcula marismortui filaments is provided by a mechanism different from that in the related haloarchaeon Halobacterium salinarum, where 2 different flagellin molecules present in comparable quantities are required to form a helical filament.     

The stall torque of the bacterial flagellar motor.

The bacterial flagellar motor couples the flow of protons across the cytoplasmic membrane to the rotation of a helical flagellar filament. Using tethered cells, we have measured the stall torque required to block this rotation and compared it with the torque of the running motor over a wide range of values of proton-motive force and pH. The stall torque and the running torque vary identically: both appear to saturate at large values of the proton-motive force and both decrease at low or high pH. This suggests that up to speeds of approximately 5 Hz the operation of the motor is not limited by the mobility of its internal components or the rates of proton transfer reactions coupled to flagellar rotation.