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.     

Force-extension measurements on bacterial flagella: triggering polymorphic transformations

Bacterial flagella can adopt several different helical shapes in response to varying environmental conditions. A geometric model by Calladine ascribes these discrete shape changes to cooperative transitions between two stable tertiary structures of the constituent protein, flagellin, and predicts an ordered set of 12 helical states called polymorphic forms. Using long polymers of purified flagellin, we demonstrate controlled, reversible transformations between different polymorphic forms. While pulling on a single filament using an optical tweezer, we record the progressive transformation of the filament and also measure the force-extension curve. Both normal and coiled polymorphic forms stretch elastically with a bending stiffness of 3.5 pN x microm(2). At a force threshold of 4-7 pN or 3-5 pN (for normal and coiled forms, respectively), a fraction of the filament suddenly transforms to the next, longer, polymorphic form. This transformation is not deterministic because the force and amount of transformation vary from pull to pull. In addition, the force is highly dependent on stretching rate, suggesting that polymorphic transformation is associated with an activation energy.     

Modeling the bacterial flagellum by an elastic network of rigid bodies

Bacteria such as Escherichia coli propel themselves by rotating a bundle of helical filaments, each driven by a rotary motor embedded in the cell membrane. Each filament is an assembly of thousands of copies of the protein flagellin which assumes two different states. We model the filament by an elastic network of rigid bodies that form bonds with one another according to a scheme suggested by Namba and Vondervistz (1997 Q. Rev. Biophys. 30 1-65) and add additional binding sites at the inner part of the rigid body. Our model reproduces the helical parameters of the 12 possible polymorphic configurations very well. We demonstrate that its energetical ground state corresponds to the normal helical form, usually observed in nature, only when inner and outer binding sites of the rigid body have a large axial displacement. This finding correlates directly to the elongated shape of the flagellin molecule. An Ising Hamiltonian in our model directly addresses the two states of the flagellin protein. It contains an external field that represents external parameters which allow us to alter the ground state of the filament.     

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.     

Flagellin polymerisation control by a cytosolic export chaperone

Assembly of the long helical filament of the bacterial flagellum requires polymerisation of ca 20,000 flagellin (FliC) monomeric subunits into the growing structure extending from the cell surface. Here, we show that export of Salmonella flagellin is facilitated specifically by a cytosolic protein, FliS, and that FliS binds to the FliC C-terminal helical domain, which contributes to stabilisation of flagellin subunit interactions during polymerisation. Stable complexes of FliS with flagellin were assembled efficiently in vitro, apparently by FliS homodimers binding to FliC monomers. The data suggest that FliS acts as a substrate-specific chaperone, preventing premature interaction of newly synthesised flagellin subunits in the cytosol. Compatible with this view, FliS was able to prevent in vitro polymerisation of FliC into filaments.     

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.     

Oblique circle method for measuring the curvature and twist of mitotic spindle microtubule bundles

The highly ordered spatial organization of microtubule bundles in the mitotic spindle is crucial for its proper functioning. The recent discovery of twisted shapes of microtubule bundles and spindle chirality suggests that the bundles extend along curved paths in three dimensions, rather than being confined to a plane. This, in turn, implies that rotational forces, i.e., torques, exist in the spindle in addition to the widely studied linear forces. However, studies of spindle architecture and forces are impeded by a lack of a robust method for the geometric quantification of microtubule bundles in the spindle. In this work, we describe a simple method for measuring and evaluating the shapes of microtubule bundles by characterizing them in terms of their curvature and twist. By using confocal microscopy, we obtain three-dimensional images of spindles, which allows us to trace the entire microtubule bundle. For each traced bundle, we first fit a plane and then fit a circle lying in that plane. With this robust method, we extract the curvature and twist, which represent the geometric information characteristic for each bundle. As the bundle shapes reflect the forces within them, this method is valuable for the understanding of forces that act on chromosomes during mitosis.     

Caulobacter crescentus flagellar filament has a right-handed helical form

Caulobacter crescentus flagellar filaments were examined for their shape and handedness. Contour length, wavelength and height of the helical filaments were 1.34 +/- 0.14 micron, 1.08 +/- 0.05 micron and 0.27 +/- 0.04 micron, respectively. Together with the value of the filament diameter, 14 +/- 1.5 nm, the parameters of the curvature (alpha) and twist (phi) were calculated as 3.9(%) for alpha and 0.026 (rad) for phi, which are similar to those of the curly I filament of Salmonella typhimurium. Dark-field light microscopic analysis revealed that the C. crescentus wild-type filament possesses a right-handed helical form. Given the result that C. crescentus cells normally swim forward, in the opposite direction to a polar flagellum, it is likely that C. crescentus swims by rotation of a right-handed curly shaped flagellum in a clockwise sense, whereas S. typhimurium and Escherichia coli swim by rotation of left-handed normal type flagella in a counterclockwise sense.     

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.     

Intrinsic curvature of DNA influences LacR-mediated looping

Protein-mediated DNA looping is a common mechanism for regulating gene expression. Loops occur when a protein binds to two operators on the same DNA molecule. The probability of looping is controlled, in part, by the basepair sequence of inter-operator DNA, which influences its structural properties. One structural property is the intrinsic or stress-free curvature. In this article, we explore the influence of sequence-dependent intrinsic curvature by exercising a computational rod model for the inter-operator DNA as applied to looping of the LacR-DNA complex. Starting with known sequences for the inter-operator DNA, we first compute the intrinsic curvature of the helical axis as input to the rod model. The crystal structure of the LacR (with bound operators) then defines the requisite boundary conditions needed for the dynamic rod model that predicts the energetics and topology of the intervening DNA loop. A major contribution of this model is its ability to predict a broad range of published experimental data for highly bent (designed) sequences. The model successfully predicts the loop topologies known from fluorescence resonance energy transfer measurements, the linking number distribution known from cyclization assays with the LacR-DNA complex, the relative loop stability known from competition assays, and the relative loop size known from gel mobility assays. In addition, the computations reveal that highly curved sequences tend to lower the energetic cost of loop formation, widen the energy distribution among stable and meta-stable looped states, and substantially alter loop topology. The inclusion of sequence-dependent intrinsic curvature also leads to nonuniform twist and necessitates consideration of eight distinct binding topologies from the known crystal structure of the LacR-DNA complex.     

Pairwise perturbation of flagellin subunits. The structural basis for the differences between plain and complex bacterial flagellar filaments

Although plain and complex bacterial flagellar filaments differ in their physical properties and helical symmetry, they both appear to derive from a common underlying structure. Analysis of electron micrographs of complex filaments of Rhizobium lupini revealed that the unit cell has twice the length of that of plain filaments, with a corresponding reduction in helical symmetry whereby the six-start helical family present in plain filaments collapses into a three-start family. Mass per unit length measurements were made by scanning transmission electron microscopy. These, together with the unit cell dimensions and the molecular weight of the flagellin monomer, enabled the number of monomers per unit cell to be estimated. Whereas plain filaments have a single monomer per unit cell, complex filaments have two. These results suggest that complex filament structure differs from plain filament structure by a pairwise perturbation, or interaction, of the flagellin monomers. The additional bonding interactions involved in the perturbation in the complex filament may make it more rigid than the plain filament, which has no such perturbation.     

Z-curve: a computer program calculating DNA helical axis coordinates for three-dimensional graphic presentation of curvature.

In order to predict curvature of DNA fragments, we previously developed a computer program for simply calculating a vectorial sum of all individual roll, tilt and twist wedge angles between the nearest base pairs for a given DNA fragment [Lee et al., (1991)]. Now, a new program, called Z-curve, was developed to calculate three-dimensional coordinates of the helical center of each base pair along the DNA, using helical axis deviations from B-form DNA by wedge angles. The output file of the new program was designed to become an input file for a graphics program, Insight II. Thus, we were able to obtain three-dimensional graphic presentations of DNA helical axis curvatures of any length. It visualized spatial details of the DNA curvature, where and how much it curves, and to which direction. It also allowed calculation of the three-dimensional distance between two ends of a DNA fragment, which could provide a measure of its curvature. Here, three DNA fragments, both curved and straight, were subjected to the Z-curve and Insight II programs. The results showed that their curvature details could be visualized to the level of the base pair, whether the DNA fragments contained an oligo(A) track or not. Their estimated curvatures were consistent with the experimental results of permutation gel mobility assay.     

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.     

Molecular determination by electron microscopy of the actin filament end structure

In eukaryotic cells, actin filaments play various crucial roles by altering their spatial and temporal distributions in the cell. The distribution of actin filaments is regulated by the binding of end-binding proteins, including capping protein (CapZ in muscle), the Arp2/3 complex, gelsolin, formin and tropomodulin, to the end of the actin filament. In order to determine the nature of these regulations, structural elucidations of actin filament-end-binding protein complexes are crucially important. Here, we have developed new procedures on the basis of single-particle analysis to determine the structure of the end of actin filaments from electron micrographs. In these procedures, the polarity of the actin filament image, as well as the azimuth orientation and the axial position of each actin protomer within a short stretch near the filament end, were determined accurately. This improved both the stability and accuracy of the structural determination dramatically. We tested our procedures by reconstructing structures from simulated filament images, which were obtained from 24 model structures for the actin-CapZ complex. These model structures were generated by random docking of the atomic structure of CapZ to the barbed end of an atomic model of the actin filament. Of the 24 model structures, 23 were recovered correctly by the present procedures. We found that our analysis was robust against local aberrations of the helical twist near the end of the actin filament. Finally, the procedures were applied successfully to determine the structure of the actin-CapZ complex from real cryo-electron micrographs of the complex. This is the first method for elucidating the detailed 3D structures at the end of the actin filament.     

Coarse-grained molecular dynamics simulations of a rotating bacterial flagellum

Many types of bacteria propel themselves using elongated structures known as flagella. The bacterial flagellar filament is a relatively simple and well-studied macromolecular assembly, which assumes different helical shapes when rotated in different directions. This polymorphism enables a bacterium to switch between running and tumbling modes; however, the mechanism governing the filament polymorphism is not completely understood. Here we report a study of the bacterial flagellar filament using numerical simulations that employ a novel coarse-grained molecular dynamics method. The simulations reveal the dynamics of a half-micrometer-long flagellum segment on a timescale of tens of microseconds. Depending on the rotation direction, specific modes of filament coiling and arrangement of monomers are observed, in qualitative agreement with experimental observations of flagellar polymorphism. We find that solvent-protein interactions are likely to contribute to the polymorphic helical shapes of the filament.     

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.     

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.     

Structure Analysis of the Flagellar Cap–Filament Complex by Electron Cryomicroscopy and Single-Particle Image Analysis

The cap of the bacterial flagellum plays an essential role in the growth of the long helical filament by promoting the efficient self-assembly of flagellin transported to the distal end through the narrow central channel of the flagellum. The structure of the cap–filament complex was analyzed by electron cryomicroscopy and single-particle image analysis to understand how the cap stays attached while allowing the flagellin insertion between the cap and the filament end and also allowing the HAP proteins to pass through. In the images of the complex, the projection pattern of the helical subunit array in the filament portion occupied the major fraction but was variable depending on the azimuthal orientation of the filament; therefore the images showed a strong tendency to be misaligned. Various methods had to be newly developed to correctly align the images by overcoming this misalignment problem. The structure thus obtained clearly demonstrated the pentameric structure of the cap and how the cap operates. The new methods of analysis presented here would be generally applicable to cap structures of various filaments that play biologically important roles in cellular activities.     

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.