Molecular topology in crystals and fibers of hemoglobin S

Several lines of evidence indicate a close correspondence between the linear double filaments in the crystal form of hemoglobin S grown from solutions containing polyethylene glycol and the seven pairs of helical filaments that occur in the 14-filament fibers of hemoglobin S. An analysis of the adjustments to the intermolecular contacts required to convert the double filaments from crystals to fibers is presented here. In addition, postulated contacts between the helical double filaments, which are distinct from any of the contacts of the crystals, are specified for the first time. The movements from crystals to fibers are described in terms of three rotation angles: α, the inclination of the filaments with respect to the fiber axis; δ, the tilt of successive molecules along the filaments; and ω, the rotation of successive molecules along the filaments. On the basis of the fiber structure determined by three-dimensional reconstruction of electron micrographs and the assignment of filament pairs from data on incomplete fibers, the various angles have been evaluated. For the filaments at various radii in the fibers, a varies from 3 ° to 12 °, δ varies from 1 ° to 4 ° and ω is constant at 9 °. The effects of the rotations on the contacts between molecules of hemoglobin S at various positions in the fibers are characterized using surface maps based on polar coordinates. For each residue on the surface of hemoglobin the centroid position of its side-chain is located by a longitude, a latitude and an altitude. Locations on the maps are assigned for the contacts within the helical double filaments, as well as 11 classes of new contacts describing the potential interaction sites between double filaments. The resulting maps (1) deduce roles for the various α mutants of hemoglobin known to influence fiber formation that have been identified by the Benesches; (2) distinguish effects for the α chain mutants on the same (cis) or opposite (trans) α₁β₁ dimer as the β6 Val in asymmetric tetramers; (3) propose new sites where effects of mutations on fiber formation may be found; and (4) suggest why some mutants may inhibit, while others enhance, fiber formation. Concerning the last point, the possibility of certain mutants “correcting” the effects of other mutants is proposed as a test of contact assignments.     

Arrangement of myosin heads in relaxed thick filaments from frog skeletal muscle

The distribution of myosin heads on the surface of frog skeletal muscle thick filaments has been determined by computer processing of electron micrographs of isolated filaments stained with tannic acid and uranyl acetate. The heads are arranged in three strands but not in a strictly helical manner and so the structure has cylindrical symmetry. This accounts for the "forbidden" meridional reflections seen in diffraction patterns. Each layer-line therefore represents the sum of terms of Bessel orders 0, +/- 3, +/- 6, +/- 9 and so on. These terms interact so that, unlike a helical object without terms from overlapping Bessel orders, as the azimuth is changed, the amplitude on a layer-line at a particular radius varies substantially and its phase does not alter linearly. Consequently, a three-dimensional reconstruction cannot be produced from a single view. We have therefore used tilt series of three individual filaments to decompose the data on layer-lines 0 to 6 into terms of Bessel orders up to +/- 9 using a least-squares procedure. These data had a least-squares residual of 0.32 and enabled a three-dimensional reconstruction to be obtained at a nominal resolution of 6 nm. This showed, at a radius of about 10 nm, three strands of projecting morphological units with three units spaced along each strand every 42.9 nm axially. We have identified these units with pairs of myosin heads. Successive units along a strand are perturbed axially, azimuthally and radially from the positions expected if the structure was perfectly helical. This may simply be a consequence of steric restrictions in packing the heads on the thick filament surface, but could also reflect an underlying non-helical arrangement of myosin tails, which would be consistent with the thick filament shaft being constructed from three subfilaments in which the tails were arranged regularly. There was also material at a radius of about 6 nm spaced 42.9 nm axially, which we tentatively identified with accessory proteins. The filament shaft had a pronounced pattern of axial staining.     

Oblique section 3-D reconstruction of relaxed insect flight muscle reveals the cross-bridge lattice in helical registration.

In this work we examined the arrangement of cross-bridges on the surface of myosin filaments in the A-band of Lethocerus flight muscle. Muscle fibers were fixed using the tannic-acid-uranyl-acetate, ("TAURAC") procedure. This new procedure provides remarkably good preservation of native features in relaxed insect flight muscle. We computed 3-D reconstructions from single images of oblique transverse sections. The reconstructions reveal a square profile of the averaged myosin filaments in cross section view, resulting from the symmetrical arrangement of four pairs of myosin heads in each 14.5-nm repeat along the filament. The square profiles form a very regular right-handed helical arrangement along the surface of the myosin filament. Furthermore, TAURAC fixation traps a near complete 38.7 nm labeling of the thin filaments in relaxed muscle marking the left-handed helix of actin targets surrounding the thick filaments. These features observed in an averaged reconstruction encompassing nearly an entire myofibril indicate that the myosin heads, even in relaxed muscle, are in excellent helical register in the A-band.     

Arrangement of the heads of myosin in relaxed thick filaments from tarantula muscle

Thick filaments from leg muscle of tarantula, maintained under relaxing conditions (Mg-ATP and EGTA), were negatively stained and photographed with minimal electron dose. Particles were selected for three-dimensional image reconstruction by general visual appearance and by the strength and symmetry of their optical diffraction patterns, the best of which extend to spacings of 1/5 nm-1. The helical symmetry is such that, on a given layer-line, Bessel function contributions of different orders start to overlap at fairly low resolution and must therefore be separated computationally by combining data from different views. Independent reconstructions agree well and show more detail than previous reconstructions of thick filaments from Limulus and scallop. The strongest feature is a set of four long-pitch right-handed helical ridges (pitch 4 X 43.5 nm) formed by the elongated myosin heads. The long-pitch helices are modulated to give ridges with an axial spacing of 14.5 nm, lying in planes roughly normal to the filament axis and running circumferentially. We suggest that the latter may be formed by the stacking of a subfragment 1 (S1) head from one myosin molecule on an S1 from an axially neighbouring molecule. Internal features in the map indicate an approximate local twofold axis relating the putative heads within a molecule. The heads appear to point in opposite directions along the filament axis and are located very close to the filament backbone. Thus, for the first time, the two heads of the myosin molecule appear to have been visualized in a native thick filament under relaxing conditions.     

Helical reconstruction of frozen-hydrated scallop myosin filaments.

Native myosin filaments from scallop striated muscle that have been rapidly frozen in relaxing solutions appear to be well preserved in vitreous ice. Electron micrographs of samples at -177 degrees C were recorded with an electron dose of 10 e/A2 at 1.5 microns defocus. After filament images were straightened by spline-fitting, several transforms showed well-defined layer-lines arising from the helical structure of the filament. A set of 17 near-meridional layer-lines has been collected and corrected for background and for phase and amplitude contrast functions. Preliminary helical reconstructions from this still incomplete data set reveal aspects of structure that were not apparent from earlier analysis of negatively stained filaments from scallop muscle. Individual pear-shaped myosin heads now appear to be well resolved from each other and from the filament backbone. The two heads of each myosin molecule appear to be splayed apart axially. The reconstructions also reveal that the filament backbone has a polygonal shape in cross-section, and that it appears to contain seven peripherally located subfilaments.     

An iterative Fourier-Bessel algorithm for reconstruction of helical structures with severe Bessel overlap

Classical Fourier-Bessel methodology fails when used to reconstruct helical structures with severe Bessel overlap on the layer lines. In the reconstruction of a peculiar type of double-layered helical tube of GDP-tubulin, we face the problem of Bessel overlap on all the layer lines due to the superposition of the Fourier components from the inner and outer layers of the tube. In order to decompose the Fourier terms of the inner and outer layers more than one image of the tubes must be combined and the orientations of their inner and outer layer helices must be determined. While there is no direct analytical method to determine these orientational parameters, we have devised an iterative Fourier-Bessel algorithm to calculate the correct orientations and thus allow us to obtain a reconstruction from multiple images of the double-layered tubes. The algorithm successfully works for the reconstruction of computer-modeled double-layered helical tubes as well as with real images obtained by cryo-electron microscopy. The algorithm has also been applied with very satisfactory results to the reconstruction of 13-protofilament microtubules, which is another helical structure that suffer Bessel overlap, suggesting its generality.     

Patterns in the quinary structures of proteins. Plasticity and inequivalence of individual molecules in helical arrays of sickle cell hemoglobin and tubulin.

The four recognized levels of organization of protein structure (primary through quaternary) are extended to add the designation quinary structure for the interactions within helical arrays, such as found for sickle cell hemoglobin fibers or tubulin units in microtubules. For sickle cell hemoglobin the main quinary structure is a 14-filament fiber, with a number of other minor forms also encountered. Degenerate forms of the 14-filament fibers can be characterized that lack specific pairs of filaments; evidence is presented which suggests an overall organization of the 14 filaments in pairs, with particular pairs aligned in an antiparallel orientation. For tubulin, a range of quinary structures can be detected depending on the number of protofilaments and whether adjacent protofilaments composed of alternating alpha- and beta-subunits are aligned with contacts between like or unlike subunits and with parallel or antiparallel polarity. Thus, in contrast to quarternary structure, which generally involves a fixed number of subunits, the quinary structures of proteins can exhibit marked plasticity and inequivalence in the juxtaposition of constituent molecules.     

Three-dimensional reconstruction of the flagellar filament of Caulobacter crescentus. A flagellin lacking the outer domain and its amino acid sequence lacking an internal segment

We obtained a three-dimensional reconstruction of the flagellar filament of Caulobacter crescentus CB15 from electron micrographs of negatively stained preparations. The C. crescentus filament appears, both in negative stain and in the frozen-hydrated state, significantly smoother and narrower than other filaments. Its helical symmetry, and unit cell size, however, are similar to that of other filaments. Although the molecular weight of the C. crescentus flagellin is about half that of other plain flagellins, there is only one monomer per unit cell as indicated by diffraction studies and by linear mass density measurements with the scanning transmission electron microscope. Alignment of the primary amino acid sequences of Salmonella typhimurium (serotype i) and C. crescentus (29,000 Mr) flagellins shows that whereas there is homology at the amino and carboxyterminal ends of the two sequences, the central segment of the S. typhimurium sequence has no homology to that of C. crescentus. A correlated comparison between the three-dimensional reconstructions of the two filaments and primary amino acid sequences of the two flagellins suggests that: (1) the C. crescentus subunit is missing the outer molecular domain but is, otherwise, similar to that of S. typhimurium; (2) the outer molecular domain in S. typhimurium corresponds, therefore, to a central stretch of the primary amino acid sequence; and (3) the outer molecular domain, missing in C. crescentus, is not obligatory for flagellar motility.     

The structural basis for the intrinsic disorder of the actin filament: the "lateral slipping" model

Three-dimensional (3-D) helical reconstructions computed from electron micrographs of negatively stained dispersed F-actin filaments invariably revealed two uninterrupted columns of mass forming the "backbone" of the double-helical filament. The contact between neighboring subunits along the thus defined two long-pitch helical strands was spatially conserved and of high mass density, while the intersubunit contact between them was of lower mass density and varied among reconstructions. In contrast, phalloidinstabilized F-actin filaments displayed higher and spatially more conserved mass density between the two long-pitch helical strands, suggesting that this bicyclic hepta-peptide toxin strengthens the intersubunit contact between the two strands. Consistent with this distinct intersubunit bonding pattern, the two long-pitch helical strands of unstabilized filaments were sometimes observed separated from each other over a distance of two to six subunits, suggesting that the intrastrand intersubunit contact is also physically stronger than the interstrand contact. The resolution of the filament reconstructions, extending to 2.5 nm axially and radially, enabled us to reproducibly "cut out" the F-actin subunit which measured 5.5 nm axially by 6.0 nm tangentially by 3.2 nm radially. The subunit is distinctly polar with a massive "base" pointing towards the "barbed" end of the filament, and a slender "tip" defining its "pointed" end (i.e., relative to the "arrowhead" pattern revealed after stoichiometric decoration of the filaments with myosin subfragment 1). Concavities running approximately parallel to the filament axis both on the inner and outer face of the subunit define a distinct cleft separating the subunit into two domains of similar size: an inner domain confined to radii less than or equal to 2.5-nm forms the uninterrupted backbone of the two long-pitch helical strands, and an outer domain placed at radii of 2-5-nm protrudes radially and thus predominantly contributes to the outer part of the massive base. Quantitative evaluation of successive crossover spacings along individual F-actin filaments revealed the deviations from the mean repeat to be compensatory, i.e., short crossovers frequently followed long ones and vice versa. The variable crossover spacings and diameter of the F-actin filament together with the local unraveling of the two long-pitch helical strands are explained in terms of varying amounts of compensatory "lateral slipping" of the two strands past each other roughly perpendicular to the filament axis. This intrinsic disorder of the actin filament may enable the actin moiety to play a more active role in actin-myosin-based force generation than merely act as a rigid passive cable as has hitherto been assumed.     

Single particle analysis of relaxed and activated muscle thin filaments

The movement of tropomyosin from actin's outer to its inner domain plays a key role in sterically regulating muscle contraction. This movement, from a low Ca2+ to a Ca2+-induced position has been directly demonstrated by electron microscopy and helical reconstruction. Solution studies, however, suggest that tropomyosin oscillates dynamically between these positions at all Ca2+ levels, and that it is the position of this equilibrium that is controlled by Ca2+. Helical reconstruction reveals only the average position of tropomyosin on the filament, and not information on the local dynamics of tropomyosin in any one Ca2+ state. We have therefore used single particle analysis to analyze short filament segments to reveal local variations in tropomyosin behavior. Segments of Ca2+-free and Ca2+ treated thin filaments were sorted by cross-correlation to low and high Ca2+ models of the thin filament. Most segments from each data set produced reconstructions matching those previously obtained by helical reconstruction, showing low and high Ca2+ tropomyosin positions for low and high Ca2+ filaments. However, approximately 20% of segments from Ca2+-free filaments fitted best to the high Ca2+ model, yielding a corresponding high Ca2+ reconstruction. Conversely, approximately 20% of segments from Ca2+-treated filaments fitted best to the low Ca2+ model and produced a low Ca2+ reconstruction. Hence, tropomyosin position on actin is not fixed in either Ca2+ state. These findings provide direct structural evidence for the equilibration of tropomyosin position in both high and low Ca2+ states, and for the concept that Ca2+ controls the position of this equilibrium. This flexibility in the localization of tropomyosin may provide a means of sterically regulating contraction at low energy cost.     

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.     

Structure of short thick filaments from Limulus muscle

Shortened Limulus thick filaments, isolated from stimulated muscle, are structurally similar to long filaments, isolated from unstimulated muscle, except for length. Both have 3-fold screw symmetry with a helical repeat at approximately 43 nm, axial spacing of 14.5 nm between successive crowns of crossbridges and 4-fold rotational symmetry as estimated from the Bessel argument, by analysis of optical transforms of electron micrograph negatives of negatively stained samples. Both short and long filaments also have similar radii for the location of their crossbridges, thus similar diameters. Equal numbers of subunits/helical strand are also apparent on images of metal-shadowed long and short filaments. Since these data argue against molecular reorganization during filament shortening, it is suggested that the change in length of Limulus thick filaments may occur by reversible disaggregation of constituent protein molecules.     

Helical structure of unidirectionally shadowed metal replicas of cyanide hydratase from Gloeocercospora sorghi

The helical filaments of the cyanide hydratase from Gloeocercospora sorghi have been reconstructed in three dimensions from freeze dried, unidirectionally shadowed specimens using iterative real-space helical reconstruction. The average power spectrum of all selected images has three clear reflections on different layer lines. The reconstruction is complicated by the fact that three possible indexing schemes are possible and reconstructions using the starting symmetries based on each of these indexing schemes converge on three-dimensional volumes which appear plausible. Because only one side is visible in shadowed specimens, it is necessary to examine the phases from a single filament by cryo-electron microscopy in order to make an unequivocal assignment of the symmetry. Because of the novel nature of the reconstruction method used here, conventional cryo-EM methods were also used to determine a second reconstruction, allowing us to make comparisons between the two. The filament is shown to have a left-handed one-start helix with D(1) symmetry, 5.46 dimers per turn and a pitch of 7.15nm. The reconstruction suggests the presence of an interaction across the groove not previously seen in nitrilase helical fibres.     

Fine Structure of Spirochaeta stenostrepta, a Free-living, Anaerobic Spirochete

The fine structure of Spirochaeta stenostrepta strain Z1, a free-living anaerobic spirochete, was studied by electron microscopy. The organism possessed a coiled protoplasmic cylinder, an axial filament inserted subterminally, and a loosely fitting sheath which enclosed both the protoplasmic cylinder and the axial filament. The axial filament consisted of two fibrils partially overlapping in a 1-2-1 arrangement. The axial fibrils appeared to possess a sheath surrounding an inner core. Both inner core and sheath were apparently enclosed in a cross-striated tubular structure, which was itself surrounded by an outer sheath. The axial filament exhibited a basal hook. A disc- or mushroom-shaped structure, possibly consisting in part of cytoplasmic membrane, was observed at the insertion end of isolated filaments. The protoplasmic cylinder had a distinctive surface structure consisting of an array of tightly packed, longitudinally arranged helices measuring 2.0 to 2.5 nm in diameter. This layer of helices lay below the outer cell sheath and the axial filament. Ballistic disintegration loosened the helical array, causing individual helices or segments of helices to become separated from the cell. The function of this layer of helices is still obscure.     

Three-Dimensional Structure of the M-region (Bare Zone) of Vertebrate Striated Muscle Myosin Filaments by Single-Particle Analysis

The rods of anti-parallel myosin molecules overlap at the centre of bipolar myosin filaments to produce an M-region (bare zone) that is free of myosin heads. Beyond the M-region edges, myosin molecules aggregate in a parallel fashion to yield the bridge regions of the myosin filaments. Adjacent myosin filaments in striated muscle A-bands are cross-linked by the M-band. Vertebrate striated muscle myosin filaments have a 3-fold rotational symmetry around their long axes. In addition, at the centre of the M-region, there are three 2-fold axes perpendicular to the filament long axis, giving the whole filament dihedral 32-point group symmetry. Here we describe the three-dimensional structure obtained by a single-particle analysis of the M-region of myosin filaments from goldfish skeletal muscle under relaxing conditions and as viewed in negative stain. This is the first single-particle reconstruction of isolated M-regions. The resulting three-dimensional reconstruction reveals details to about 55 Å resolution of the density distribution in the five main nonmyosin densities in the M-band (M6′, M4′, M1, M4 and M6) and in the myosin head crowns (P1, P2 and P3) at the M-region edges. The outermost crowns in the reconstruction were identified specifically by their close similarity to the corresponding crown levels in our previously published bridge region reconstructions. The packing of myosin molecules into the M-region structure is discussed, and some unidentified densities are highlighted.     

Three-dimensional reconstruction of tarantula myosin filaments suggests how phosphorylation may regulate myosin activity

Muscle contraction involves the interaction of the myosin heads of the thick filaments with actin subunits of the thin filaments. Relaxation occurs when this interaction is blocked by molecular switches on these filaments. In many muscles, myosin-linked regulation involves phosphorylation of the myosin regulatory light chains (RLCs). Electron microscopy of vertebrate smooth muscle myosin molecules (regulated by phosphorylation) has provided insight into the relaxed structure, revealing that myosin is switched off by intramolecular interactions between its two heads, the free head and the blocked head. Three-dimensional reconstruction of frozen-hydrated specimens revealed that this asymmetric head interaction is also present in native thick filaments of tarantula striated muscle. Our goal in this study was to elucidate the structural features of the tarantula filament involved in phosphorylation-based regulation. A new reconstruction revealed intra- and intermolecular myosin interactions in addition to those seen previously. To help interpret the interactions, we sequenced the tarantula RLC and fitted an atomic model of the myosin head that included the predicted RLC atomic structure and an S2 (subfragment 2) crystal structure to the reconstruction. The fitting suggests one intramolecular interaction, between the cardiomyopathy loop of the free head and its own S2, and two intermolecular interactions, between the cardiac loop of the free head and the essential light chain of the blocked head and between the Leu305-Gln327 interaction loop of the free head and the N-terminal fragment of the RLC of the blocked head. These interactions, added to those previously described, would help switch off the thick filament. Molecular dynamics simulations suggest how phosphorylation could increase the helical content of the RLC N-terminus, weakening these interactions, thus releasing both heads and activating the thick filament.     

Dependence of thick filament structure in relaxed mammalian skeletal muscle on temperature and interfilament spacing

Contraction of skeletal muscle is regulated by structural changes in both actin-containing thin filaments and myosin-containing thick filaments, but myosin-based regulation is unlikely to be preserved after thick filament isolation, and its structural basis remains poorly characterized. Here, we describe the periodic features of the thick filament structure in situ by high-resolution small-angle x-ray diffraction and interference. We used both relaxed demembranated fibers and resting intact muscle preparations to assess whether thick filament regulation is preserved in demembranated fibers, which have been widely used for previous studies. We show that the thick filaments in both preparations exhibit two closely spaced axial periodicities, 43.1 nm and 45.5 nm, at near-physiological temperature. The shorter periodicity matches that of the myosin helix, and x-ray interference between the two arrays of myosin in the bipolar filament shows that all zones of the filament follow this periodicity. The 45.5-nm repeat has no helical component and originates from myosin layers closer to the filament midpoint associated with the titin super-repeat in that region. Cooling relaxed or resting muscle, which partially mimics the effects of calcium activation on thick filament structure, disrupts the helical order of the myosin motors, and they move out from the filament backbone. Compression of the filament lattice of demembranated fibers by 5% Dextran, which restores interfilament spacing to that in intact muscle, stabilizes the higher-temperature structure. The axial periodicity of the filament backbone increases on cooling, but in lattice-compressed fibers the periodicity of the myosin heads does not follow the extension of the backbone. Thick filament structure in lattice-compressed demembranated fibers at near-physiological temperature is similar to that in intact resting muscle, suggesting that the native structure of the thick filament is largely preserved after demembranation in these conditions, although not in the conditions used for most previous studies with this preparation.     

Triclinic crystals associated with fibers of deoxygenated sickle hemoglobin.

Triclinic crystals have been found in capillaries that initially contained deoxygenated sickled erythrocytes, and in solutions of sickle hemoglobin that were stirred during deoxygenation. In both cases these crystals occur as a phase transition from fibers. They have been observed only as twins; the a-axis of one member is related to that of its twin by 180 degrees rotation about the b* direction. The volume of the triclinic crystal unit cell is half that of the monoclinic crystals that have also transformed from fibers. Analysis of X-ray diffraction data indicates that the two molecules in the triclinic unit cell that repeat at an interval of 64 A form double filaments similar to those found in the monoclinic crystals and in the fiber. The existence of the triclinic crystals which contain only one double filament per unit cell removes a postulated requirement that antipolar double filament pairs be the sole unit of the fiber architecture.     

X-ray diffraction studies of 14-filament models of deoxygenated sickle cell hemoglobin fibers. Models based on electron micrograph reconstructions

The transforms of a large number of models of deoxygenated sickle hemoglobin fibers, related to that derived from image reconstruction of electron micrographs, have been calculated and compared with X-ray diffraction data of 15 A resolution. The model of the fiber, determined from the reconstructed image, is a helix consisting of 14 filaments that associate in a specific mode to form seven pairs, or protofilaments. Pairs were identified through the pattern of filament loss in partially disassembled fibers and by the separation between molecules, in adjacent filaments, of half a molecular diameter, along the fiber axis. An alternative mode of filament association can be derived also from the surface lattice of the reconstruction, which meets these criteria for the pairing of molecular filaments. Both pairing modes have been used in the search for structures whose transforms show the best agreement with the diffraction data. Models were generated by the systematic translation of six protofilaments, taken in symmetry related pairs, in steps of 3.5 A along the fiber axis relative to a fixed central protofilament. Each translation of a protofilament corresponds to a different fiber model, whose transform was compared with observed data. In all, over 11,000 transforms were calculated. Of all the models considered, three have been found whose residuals are minimal. At 30 A resolution, similar to that of electron micrographs, the model derived from image reconstruction and the three found through our search procedure are indistinguishable. At 15 A, however, the transforms of these models show better agreement with the observed data than the transform of the reconstructed image. Comparison of residuals shows that the model derived from the reconstructed image can be rejected with 99.5% probability relative to the model, with the same pairing scheme, found by our search procedures. The two other models, derived from the alternative pairing scheme, are also more credible than the reconstructed image, but at a lower confidence level. Each of our three models is equally acceptable. Their existence may reflect structural polymorphism of the fiber.