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.     

Flexural rigidity of microtubules and actin filaments measured from thermal fluctuations in shape

Microtubules are long, proteinaceous filaments that perform structural functions in eukaryotic cells by defining cellular shape and serving as tracks for intracellular motor proteins. We report the first accurate measurements of the flexural rigidity of microtubules. By analyzing the thermally driven fluctuations in their shape, we estimated the mean flexural rigidity of taxol-stabilized microtubules to be 2.2 x 10(-23) Nm2 (with 6.4% uncertainty) for seven unlabeled microtubules and 2.1 x 10(-23) Nm2 (with 4.7% uncertainty) for eight rhodamine-labeled microtubules. These values are similar to earlier, less precise estimates of microtubule bending stiffness obtained by modeling flagellar motion. A similar analysis on seven rhodamine-phalloidin- labeled actin filaments gave a flexural rigidity of 7.3 x 10(-26) Nm2 (with 6% uncertainty), consistent with previously reported results. The flexural rigidity of these microtubules corresponds to a persistence length of 5,200 microns showing that a microtubule is rigid over cellular dimensions. By contrast, the persistence length of an actin filament is only approximately 17.7 microns, perhaps explaining why actin filaments within cells are usually cross-linked into bundles. The greater flexural rigidity of a microtubule compared to an actin filament mainly derives from the former's larger cross-section. If tubulin were homogeneous and isotropic, then the microtubule's Young's modulus would be approximately 1.2 GPa, similar to Plexiglas and rigid plastics. Microtubules are expected to be almost inextensible: the compliance of cells is due primarily to filament bending or sliding between filaments rather than the stretching of the filaments themselves.     

The structure of the helically perturbed flagellar filament of Pseudomonas rhodos: implications for the absence of the outer domain in other complex flagellins and for the flexibility of the radial spokes

Bacterial flagella, the organelles of motility, are commonly divided into two classes: 'plain' and 'complex'. The complex filaments are pairwise, helically perturbed forms of the plain filaments and have been reported to occur only in Rhizobium and Pseudomonas. Previously, we reconstructed and analysed the structure of the complex filaments of Rhizobium lupini H13-3 and determined their unique symmetry and origin of the perturbations (Trachtenberg et al., 1986, J Mol Biol 190: 569-576; 1987, 195: 603-620; 1998, 276: 759-773; Cohen-Krausz and Trachtenberg, 1998, J Struct Biol 122: 267-282). Here, we analyse the structure of the flagellar filament of the other known complex filament, that of Pseudomonas rhodos, as reconstructed from electron microscope images. Compared with the filament of R. lupini, the filament of P. rhodos is more flexible, as implied from high-intensity darkfield light microscopy and, although constructed from flagellins of higher molecular weights (59 versus 41 kDa), has similar symmetry. Using cryonegative stained specimens and low-dose, field emission electron microscopy, we reconstructed and averaged 158 filaments each containing 170 statistically significant layer lines. The three-dimensional density maps of P. rhodos clearly suggest, when compared with those of R. lupini and the right-handed Salmonella typhimurium SJW1655, that R. lupini is missing the outer flagellin domain (D3), that the interior of the complex filament is rather similar to that of the plain filament and that the radial spokes (connecting domains D0 and D1), present in individual density maps, average out because of their variability and implied flexibility. Extending the three-start grooves and ridges on the propeller's surface, in the form of an Archimedean screw, may further improve the motility of the cell in viscous environments.     

Cofilin increases the bending flexibility of actin filaments: implications for severing and cell mechanics

We determined the flexural (bending) rigidities of actin and cofilactin filaments from a cosine correlation function analysis of their thermally driven, two-dimensional fluctuations in shape. The persistence length of actin filaments is 9.8 μm, corresponding to a flexural rigidity of 0.040 pN μm². Cofilin binding lowers the persistence length ∼5-fold to a value of 2.2 μm and the filament flexural rigidity to 0.0091 pN μm². That cofilin-decorated filaments are more flexible than native filaments despite an increased mass indicates that cofilin binding weakens and redistributes stabilizing subunit interactions of filaments. We favor a mechanism in which the increased flexibility of cofilin-decorated filaments results from the linked dissociation of filament-stabilizing ions and reorganization of actin subdomain 2 and as a consequence promotes severing due to a mechanical asymmetry. Knowledge of the effects of cofilin on actin filament bending mechanics, together with our previous analysis of torsional stiffness, provide a quantitative measure of the mechanical changes in actin filaments associated with cofilin binding, and suggest that the overall mechanical and force-producing properties of cells can be modulated by cofilin activity.     

Real-time imaging of fluorescent flagellar filaments of Rhizobium lupini H13-3: flagellar rotation and pH-induced polymorphic transitions

The soil bacterium Rhizobium lupini H13-3 has complex right-handed flagellar filaments with unusual ridged, grooved surfaces. Clockwise (CW) rotation propels the cells forward, and course changes (tumbling) result from changes in filament speed instead of the more common change in direction of rotation. In view of these novelties, fluorescence labeling was used to analyze the behavior of single flagellar filaments during swimming and tumbling, leading to a model for directional changes in R. lupini. Also, flagellar filaments were investigated for helical conformational changes, which have not been previously shown for complex filaments. During full-speed CW rotation, the flagellar filaments form a propulsive bundle that pushes the cell on a straight path. Tumbling is caused by asynchronous deceleration and stops of individual filaments, resulting in dissociation of the propulsive bundle. R. lupini tumbles were not accompanied by helical conformational changes as are tumbles in other organisms including enteric bacteria. However, when pH was experimentally changed, four different polymorphic forms were observed. At a physiological pH of 7, normal flagellar helices were characterized by a pitch angle of 30 degrees, a pitch of 1.36 micro m, and a helical diameter of 0.50 micro m. As pH increased from 9 to 11, the helices transformed from normal to semicoiled to straight. As pH decreased from 5 to 3, the helices transformed from normal to curly to straight. Transient conformational changes were also noted at high viscosity, suggesting that the R. lupini flagellar filament may adapt to high loads in viscous environments (soil) by assuming hydrodynamically favorable conformations.     

Structure and mobility of actin filaments as measured by quasielastic light scattering, viscometry, and electron microscopy

Actin filaments of different lengths were prepared by polymerizing actin in the presence of various concentrations of gelsolin, a protein which accelerates actin polymerization by stabilizing nuclei from which filaments grow and which binds to their fast growing ends. The lengths of the actin filaments following polymerization were measured by electron microscopy and showed that the number-average filament length agreed with the predicted length if each gelsolin molecule acted as a seed for the growth of an actin filament. The distribution of lengths was independent of the actin:gelsolin ratio and was similar to that of actin filaments polymerized in the absence of gelsolin (Lw/Ln = 1.8). The mobility of these filaments in solution was studied by quasielastic light scattering and by viscometry. The translational diffusion constant determined by quasielastic light scattering was in agreement with the infinite dilution values calculated from the dimensions and the distribution of lengths determined by electron microscopy for relatively short filament lengths. Under conditions where overlap of the rotational domains of the filaments would be expected to occur, the measured diffusion rates deviated from their predicted dilute solution values and the solution viscosity increased abruptly. The dependence of the diffusion constant and the solution viscosity on the length of the actin filaments can be explained in terms of a theory that describes the restraints on diffusion of independent rigid rods in semi-dilute solution. The results suggest that the rheology of actin filaments can be accounted for by steric restraints. The length of cytoplasmic actin filaments in some cell types is such that these steric constraints are significant and could produce large changes in physical properties with small changes in filament length.     

The axial alpha-helices and radial spokes in the core of the cryo-negatively stained complex flagellar filament of Pseudomonas rhodos: recovering high-resolution details from a flexible helical assembly

Of the two known "complex" flagellar filaments, those of Pseudomonas are far more flexible than those of Rhizobium. Their diameter is larger and their outer three-start ridges and grooves are more prominent. Although the symmetry of both complex filaments is similar, the polymer's linear mass density and the flagellin molecular mass of the latter are lower. A recent comparison of a three-dimensional reconstruction of the filament of Pseudomonas rhodos to that of Rhizobium lupini indicates that the outer flagellin domain (D3) is missing in R.lupini. Here, we concentrate on the structure of the inner core of the filament of P.rhodos using field emission cryo-negative staining electron microscopy and a hybrid helical/single particle reconstruction technique. Averaging 158 filaments caused the density band corresponding to the radial spokes to nearly average out due to their variability and inferred flexibility. Treating the Z=0 cross-sections through the aligned individual three-dimensional density maps as images, classifying them by correspondence analysis (using a mask containing the radial spokes domain) and re-averaging the subclasses (using helical reconstruction techniques) allowed a recovery of the radial spokes and resolved the alpha-helices in domain D0 and the triple alpha-helical bundles in domain D1 at a resolution of 1/7A(-1). Although the perturbed components of the helical lattice are present along the entire filament's radius, the interior of the complex filament is similar to that of the plain one, whereas it's exterior is altered. Reconstructions of vitrified and cryo-negatively stained plain, right-handed filaments of Salmonella typhimurium SJW1655 prepared and imaged under conditions identical with those used for P.rhodos confirm the similarity of their inner cores and that the secondary structures in the interior of the flagellar filament can, under critical conditions of image recording and correction, be resolved in negative stain.     

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.     

Three-dimensional structure of the complex flagellar filament of Rhizobium lupini and its relation to the structure of the plain filament

Electron micrographs of negatively stained preparations were used to obtain a three-dimensional reconstruction of the complex flagellar filament of Rhizobium lupini H13-3. The complex filament has an organization similar to that of the more common plain filament, but the subunits are perturbed in a pairwise fashion to generate a very distinctive set of three continuous ridges of density along the outer surface of the filament. In the three-dimensional map, the design of the complex filament is similar to that of the plain filament described in the accompanying paper. The structures consist of 11 segmented rods of density lying at a radius of 65 to 70 A. The exterior surfaces of both kinds of filaments consist of features that protrude from the segmented rods. The interiors of both consist of arms that extend inwards from the rods. In the case of the complex filament, but not of the plain filament, the inner arms interact to generate three tubular features, which, together with the three outer ridges, may account for the more brittle and, by implication, stiffer nature of the complex filament.     

Cardiac Myosin Binding Protein-C Is Essential for Thick-Filament Stability and Flexural Rigidity

Using atomic force microscopy, we examined the contribution of cardiac myosin binding protein-C (cMyBP-C) to thick-filament length and flexural rigidity. Native thick filaments were isolated from the hearts of transgenic mice bearing a truncation mutation of cMyBP-C (t/t) that results in no detectable cMyBP-C and from age-matched wild-type controls (+/+). Atomic force microscopy images of these filaments were evaluated with an automated analysis algorithm that identified filament position and shape. The t/t thick-filament length (1.48 ± 0.02 μm) was significantly (P < 0.01) shorter than +/+ (1.56 ± 0.02 μm). This 5%-shorter thick-filament length in the t/t was reflected in 4% significantly shorter sarcomere lengths of relaxed isolated cardiomyocytes of the t/t (1.97 ± 0.01 μm) compared to +/+ (2.05 ± 0.01 μm). To determine if cMyBP-C contributes to the mechanical properties of thick filaments, we used statistical polymer chain mechanics to calculate a per-filament-specific persistence length, an index of flexural rigidity directly proportional to Young's modulus. Thick-filament-specific persistence length in the t/t (373 ± 62 μm) was significantly lower than in +/+ (639 ± 101 μm). Accordingly, Young's modulus of t/t thick filaments was ∼60% of +/+. These results provide what we consider a new understanding for the critical role of cMyBP-C in defining normal cardiac output by sustaining force and muscle stiffness.     

Modulation of actin mechanics by caldesmon and tropomyosin

The ability of cells to sense and respond to physiological forces relies on the actin cytoskeleton, a dynamic structure that can directly convert forces into biochemical signals. Because of the association of muscle actin-binding proteins (ABPs) may affect F-actin and hence cytoskeleton mechanics, we investigated the effects of several ABPs on the mechanical properties of the actin filaments. The structural interactions between ABPs and helical actin filaments can vary between interstrand interactions that bridge azimuthally adjacent actin monomers between filament strands (i.e. by molecular stapling as proposed for caldesmon) or, intrastrand interactions that reinforce axially adjacent actin monomers along strands (i.e. as in the interaction of tropomyosin with actin). Here, we analyzed thermally driven fluctuations in actin's shape to measure the flexural rigidity of actin filaments with different ABPs bound. We show that the binding of phalloidin increases the persistence length of actin by 1.9-fold. Similarly, the intrastrand reinforcement by smooth and skeletal muscle tropomyosins increases the persistence length 1.5- and 2- fold respectively. We also show that the interstrand crosslinking by the C-terminal actin-binding fragment of caldesmon, H32K, increases persistence length by 1.6-fold. While still remaining bound to actin, phosphorylation of H32K by ERK abolishes the molecular staple (Foster et al. 2004. J Biol Chem 279;53387-53394) and reduces filament rigidity to that of actin with no ABPs bound. Lastly, we show that the effect of binding both smooth muscle tropomyosin and H32K is not additive. The combination of structural and mechanical studies on ABP-actin interactions will help provide information about the biophysical mechanism of force transduction in cells.     

Distribution of mass within native thick filaments of vertebrate skeletal muscle

The distribution of mass within the vertebrate skeletal thick filament has been determined by scanning transmission electron microscopy. Thick and thin filaments from fresh rabbit muscle were mixed with tobacco mosaic virus (TMV), fixed with formaldehyde, dried onto thin carbon films and viewed in a computer-linked microscope. Electron scattering data from both TMV and thick filaments were analysed with reference to the long axis of the particles so that the distribution of mass within the particles could be determined. While TMV appeared to be a uniform rod at the resolution employed (4.3 nm), the thick filament was clearly differentiated along its length. M-line remnants at the centre of the filament were flanked by regions of low mass per unit length, corresponding to the bare zone of the filament, and then by the more massive cross-bridge regions. The mass per unit length was approximately constant through most of the cross-bridge zone and declined at the filament tips, in a manner consistent with a constant number of myosin molecules per 14.3 nm interval (crown) throughout the cross-bridge zone. Fourier analysis of the data failed to detect the expected 43 nm periodicity of C-protein. The total mass of the thick filament was 184 Mdalton (s.e.m., 1.6 X 10(6); n = 70). The mass of adhering M-line proteins was highly variable but, on average, was about 4 Mdalton. The total mass of the filament and the mass distribution in the cross-bridge zone are consistent with three myosin molecules per crown.     

Cytochalasin B and the structure of actin gels

We analyzed the structure of gels formed when macrophage actin-binding protein crosslinks skeletal muscle actin polymers and the effect of the fungal metabolite cytochalasin B on this structure. Measurement of the actin filament length distribution permitted calculation of the critical concentration of crosslinker theoretically required for gelation of actin polymer networks. The experimentally determined critical concentration of actin-binding protein agreed sufficiently with the theoretical to conclude that F-actin-actin-binding protein gels are networks composed of isotropically oriented filaments crosslinked at intervals. The effects of cytochalasin B on these actin networks fits this model. Cytochalasin B (1) bound to F-actin (but not to actin-binding protein), (2) decreased the length of actin filaments without increasing the quantity of monomeric actin, (3) decreased the rigidity of actin networks both in the presence and absence of crosslinking proteins and (4) increased the critical concentration of actin-binding protein required for incipient gelation by a magnitude predicted from network theory if filaments were divided and shortened by the extents observed. The effects of cytochalasin B on gelation were highly dependent on actin concentration and were inhibited by the actin-stabilizing agent phalloidin. Therefore, cytochalasin B diminishes actin gel structure by severing actin filaments at limited sites. The demonstration of gel-sol transformations in actin networks caused by limited actin filament cleavage suggests a new mechanism for the control of cytoplasmic structure.     

Geometrical and Mechanical Properties Control Actin Filament Organization

The different actin structures governing eukaryotic cell shape and movement are not only determined by the properties of the actin filaments and associated proteins, but also by geometrical constraints. We recently demonstrated that limiting nucleation to specific regions was sufficient to obtain actin networks with different organization. To further investigate how spatially constrained actin nucleation determines the emergent actin organization, we performed detailed simulations of the actin filament system using Cytosim. We first calibrated the steric interaction between filaments, by matching, in simulations and experiments, the bundled actin organization observed with a rectangular bar of nucleating factor. We then studied the overall organization of actin filaments generated by more complex pattern geometries used experimentally. We found that the fraction of parallel versus antiparallel bundles is determined by the mechanical properties of actin filament or bundles and the efficiency of nucleation. Thus nucleation geometry, actin filaments local interactions, bundle rigidity, and nucleation efficiency are the key parameters controlling the emergent actin architecture. We finally simulated more complex nucleation patterns and performed the corresponding experiments to confirm the predictive capabilities of the model.     

Purification and biochemical properties of complex flagella isolated from Rhizobium lupini H13-3

1. The complex flagella of Rhizobium lupini H13-3 differ from plain bacterial flagella in the fine structure of their filaments dominated by conspicuous helical bands, in their fragility and their resistance against heat decomposition. To elucidate the basis of these differences, the composition of complex filaments and their subunits was analysed. 2. Isolated complex flagella containing the filament and hook protions were purified by differential centrifugation. Hooks were separated by ultracentrifugation after acid degradation of filaments at pH 2. The complex filaments consist of 43 000 dalton monomers (cx-flagellin), the hooks are composed of 41 000 dalton subunits. 3. Amino acid analysis of cx-flagellin indicated the presence of approx. 417 amino acid residues. These comprise 47% hydrophobic residues and 21% Asp and Glu (or amides), but no Cys, His, Pro and Trp. No carbohydrate, phosphate or lipid moieties have been detected. Fingerprint analysis after tryptic digestion yields approx. 36 peptides, about half of them clustered in the neutral region. A comparison with the composition of varous known flagellins from plain flagella indicates a 7% higher content of hydrophobic amino acid residues in complex filaments; this is largely compensated for by the higher content of Glu and Asp (presumably as Gln and Asn) in plain filaments. 4. Immunodiffusion and immunoelectrophoresis of cx-flagellin yield single precipitin bands indicating homogeneity. In contrast, isoelectric focusing lead to three close-running bands around pH4.7. When isolated, the two major bands again produced an "isoelectric spectrum" suggesting that it reflects an allomorphism of cx-flagellin. 5. Self-assembly experiments with cx-flagellin lead to coiled fibres including helical regions, but not to intact filaments. The products resemble heat-denatured complex filaments and may represent intermediates between monomers and complete polymers.     

Tracer diffusion through F-actin: effect of filament length and cross-linking.

We have determined diffusion coefficients for small (50- to 70-nm diameter) fluorescein-thiocarbamoyl-labeled Ficoll tracers through F-actin as a function of filament length and cross-linking. fx45 was used to regulate filament length and avidin/biotinylated actin or ABP-280 was used to prepare cross-linked actin gels. We found that tracer diffusion was generally independent of filament length in agreement with theoretical predictions for diffusion through solutions of rods. However, in some experiments diffusion was slower through short (< or = 1.0 micron) filaments, although this result was not consistently reproducible. Measured diffusion coefficients through unregulated F-actin and filaments of lengths > 1.0 micron were more rapid than predicted by theory for tracer diffusion through rigid, random networks, which was consistent with some degree of actin bundling. Avidin-induced cross-linking of biotinylated F-actin did not affect diffusion through unregulated F-actin, but in cases where diffusion was slower through short filaments this cross-linking method resulted in enhanced tracer diffusion rates indistinguishable from unregulated F-actin. This finding, in conjunction with increased turbidity of 1.0-micron filaments upon avidin cross-linking, indicated that this cross-linking method induces F-actin bundling. By contrast, ABP-280 cross-linking retarded diffusion through unregulated F-actin and decreased turbidity. Tracer diffusion under these conditions was well approximated by the diffusion theory. Both cross-linking procedures resulted in gel formation as determined by falling ball viscometry. These results demonstrate that network microscopic geometry is dependent on the cross-linking method, although both methods markedly increase F-actin macroscopic viscosity.     

Cartilage proteoglycan aggregates. Electronmicroscopic studies of native and fragmented molecules

1. Proteoglycan aggregates from bovine nasal cartilage were studied by using electron microscopy of proteoglycan/cytochrome c monolayers. 2. The aggregates contained a variably long central filament of hyaluronic acid with an average length of 1037nm. The proteoglycan monomers attached to the hyaluronic acid appeared as side chain filaments varying in length (averaging 249nm). They were distributed along the central filament at an average distance of about 36nm. 3. Chondroitin sulphate side chains were removed from the proteoglycan monomers of the aggregates by partial chondroitinase digestion. The molecules obtained had the same general appearance as intact aggregates. 4. Proteoglycan aggregates were treated with trypsin and the largest fragment, which contains the hyaluronic acid, link protein and hyaluronic acid-binding region, was recovered and studied with electron microscopy. Filaments that lacked the side chain extensions and had the same length as the central filament in the intact aggregate were observed. 5. Hyaluronic acid isolated after papain digestion of cartilage extracts gave filaments with similar length and size distribution as observed for the central filament both in the intact aggregate and in the trypsin digests. 6. Umbilical-cord hyaluronic acid was also studied and gave electron micrographs similar to those described for hyaluronic acid from cartilage. However, the length of the filament was somewhat shorter. 7. The electron micrographs of both intact and selectively degraded proteoglycans corroborate the current model of cartilage proteoglycan structure.     

Compliance of bacterial polyhooks measured with optical tweezers.

In earlier work, a single-beam gradient force optical trap ("optical tweezers") was used to measure the torsional compliance of flagella in wild-type cells of Escherichia coli that had been tethered to glass by a single flagellum. This compliance was nonlinear, exhibiting a torsionally soft phase up to 180 degrees, followed by a torsionally rigid phase for larger angles. Values for the torsional spring constant in the soft phase were substantially less than estimates based on the rigidity determined for isolated flagellar filaments. It was suggested that the soft phase might correspond to wind-up of the flagellar hook, and the rigid phase to wind-up of the stiffer filament. Here, we have measured the torsional compliance of flagella on cells of an E. coli strain that produces abnormally long hooks but no filaments. The small-angle compliance of these cells, as determined from the elastic rebound of the cell body after wind-up and release, was found to be the same as for wild-type cells. This confirms that the small-angle compliance of wild-type cells is dominated by the response of the hook. Hook flexibility is likely to play a useful role in stabilizing the flagellar bundle.     

The myosin filament: V. Intermediate voltage electron microscopy and optical diffraction studies of the substructure

Using a 200 kV electron microscope (JEM 200 A), thick (up to 0.4 μm) crosssections of the myosin filaments of vertebrate striated muscle were studied. It was found that: (a) with increasing section thickness the cross-sectional profiles of the shaft of the filament were increasingly more triangular and in sections 0.4 μm thick each apex of the triangle was clearly blunted. This unique cross-sectional profile is predicted by the model proposed by Pepe (1966,1967) in which 12 parallel structural units are packed to form a triangular profile with a structural unit missing at each apex of the triangle. (b) With increasing section thickness the substructure of the myosin filament was enhanced, with the best substructure visible in sections 0.2 μm to 0.3 μm thick. This strongly supports parallel alignment of structural units in the shaft of the filament as proposed by Pepe (1966,1967). (c) The substructure spacing, determined by optical diffraction from electron micrographs of cross-sections of individual myosin filaments or groups of filaments is about 4 nm. (d) The different optical diffraction patterns observed from individual myosin filaments can be explained if the projection of each structural unit in the plane of the section has an elongated profile. With a substructure spacing of 4 nm an elongated cross-sectional profile could be produced by having two myosin molecules per structural unit. Models drawn with two myosin molecules per structural unit in the model proposed by Pepe (1966,1967) gave optical diffraction patterns similar to those observed from individual filaments. (e) The different optical diffraction patterns observed from individual myosin filaments can be explained if the elongated profiles in each structural unit are similarly oriented but with the orientation changing along the length of the filament. The change in orientation per unit length of the filament must be small enough to maintain an elongated profile for the projection of the structural unit in the plane of the sections 0.3 μm thick. All of these observations and conclusions strongly support the model for the myosin filament proposed by Pepe (1966,1967).