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.     

Structure of HIV-1 Capsid Assemblies by Cryo-electron Microscopy and Iterative Helical Real-space Reconstruction

Cryo-electron microscopy (cryo-EM), combined with image processing, is an increasingly powerful tool for structure determination of macromolecular protein complexes and assemblies. In fact, single particle electron microscopy¹ and two-dimensional (2D) electron crystallography² have become relatively routine methodologies and a large number of structures have been solved using these methods. At the same time, image processing and three-dimensional (3D) reconstruction of helical objects has rapidly developed, especially, the iterative helical real-space reconstruction (IHRSR) method³, which uses single particle analysis tools in conjunction with helical symmetry. Many biological entities function in filamentous or helical forms, including actin filaments⁴, microtubules⁵, amyloid fibers⁶, tobacco mosaic viruses⁷, and bacteria flagella⁸, and, because a 3D density map of a helical entity can be attained from a single projection image, compared to the many images required for 3D reconstruction of a non-helical object, with the IHRSR method, structural analysis of such flexible and disordered helical assemblies is now attainable.In this video article, we provide detailed protocols for obtaining a 3D density map of a helical protein assembly (HIV-1 capsid⁹ is our example), including protocols for cryo-EM specimen preparation, low dose data collection by cryo-EM, indexing of helical diffraction patterns, and image processing and 3D reconstruction using IHRSR. Compared to other techniques, cryo-EM offers optimal specimen preservation under near native conditions. Samples are embedded in a thin layer of vitreous ice, by rapid freezing, and imaged in electron microscopes at liquid nitrogen temperature, under low dose conditions to minimize the radiation damage. Sample images are obtained under near native conditions at the expense of low signal and low contrast in the recorded micrographs. Fortunately, the process of helical reconstruction has largely been automated, with the exception of indexing the helical diffraction pattern. Here, we describe an approach to index helical structure and determine helical symmetries (helical parameters) from digitized micrographs, an essential step for 3D helical reconstruction. Briefly, we obtain an initial 3D density map by applying the IHRSR method. This initial map is then iteratively refined by introducing constraints for the alignment parameters of each segment, thus controlling their degrees of freedom. Further improvement is achieved by correcting for the contrast transfer function (CTF) of the electron microscope (amplitude and phase correction) and by optimizing the helical symmetry of the assembly.     

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.     

The structure of a filamentous bacteriophage

Many thin helical polymers, including bacterial pili and filamentous bacteriophage, have been seen as refractory to high-resolution studies by electron microscopy. Studies of the quaternary structure of such filaments have depended upon techniques such as modeling or X-ray fiber diffraction, given that direct visualization of the subunit organization has not been possible. We report the first image reconstruction of a filamentous virus, bacteriophage fd, by cryoelectron microscopy. Although these thin ( approximately 70 A in diameter) rather featureless filaments scatter weakly, we have been able to achieve a nominal resolution of approximately 8 A using an iterative helical reconstruction procedure. We show that two different conformations of the virus exist, and that in both states the subunits are packed differently than in conflicting models previously proposed on the basis of X-ray fiber diffraction or solid-state NMR studies. A significant fraction of the population of wild-type fd is either disordered or in multiple conformational states, while in the presence of the Y21M mutation, this heterogeneity is greatly reduced, consistent with previous observations. These results show that new computational approaches to helical reconstruction can greatly extend the ability to visualize heterogeneous protein polymers at a reasonably high resolution.     

Ruby-Helix: an implementation of helical image processing based on object-oriented scripting language

Helical image analysis in combination with electron microscopy has been used to study three-dimensional structures of various biological filaments or tubes, such as microtubules, actin filaments, and bacterial flagella. A number of packages have been developed to carry out helical image analysis. Some biological specimens, however, have a symmetry break (seam) in their three-dimensional structure, even though their subunits are mostly arranged in a helical manner. We refer to these objects as "asymmetric helices". All the existing packages are designed for helically symmetric specimens, and do not allow analysis of asymmetric helical objects, such as microtubules with seams. Here, we describe Ruby-Helix, a new set of programs for the analysis of "helical" objects with or without a seam. Ruby-Helix is built on top of the Ruby programming language and is the first implementation of asymmetric helical reconstruction for practical image analysis. It also allows easier and semi-automated analysis, performing iterative unbending and accurate determination of the repeat length. As a result, Ruby-Helix enables us to analyze motor-microtubule complexes with higher throughput to higher resolution.     

Dimer ribbons in the three-dimensional structure of sarcoplasmic reticulum

The three-dimensional structure of scallop sarcoplasmic reticulum membranes has been determined from electron micrographs of two classes of stain-filled tubules by helical reconstruction methods. These structures are characterized by dimer ribbons of Ca2+-ATPase molecules running diagonally around the tube wall. Deep right-handed grooves separate the ribbons. The elongated, curved units of the dimer (approximately 95 A long in the radial direction; 60 to 70 A axially, and about 30 A wide) are displaced axially by approximately 34 A and are connected at their outer ends by a bridge running nearly parallel to the tube axis. The monomers make a second contact at their inner ends. Adjacent units with the same orientation form a strong contact that is responsible for the ribbon appearance. Comparison of tubules of different diameter shows that one set of connections between the dimer ribbons is conserved: the inner ends of axially displaced dimers appear to make contact along a left-handed path almost perpendicular to the major grooves. The lipid bilayer cannot be clearly identified. The two-dimensional map obtained from flattened tubules is consistent with the three-dimensional reconstruction in showing dimer ribbons connected by a weak contact across the grooves, strongly resembling the inter-dimer bond observed in three dimensions. The two-dimensional map shows a 2-fold axis relating units of the dimer, but the three-dimensional tubes show a slight axial polarity that may arise from the presence of proteins other than the Ca2+-ATPase.     

The iterative helical real space reconstruction method: surmounting the problems posed by real polymers

Many important biological macromolecules exist as helical polymers. Examples are actin, tubulin, myosin, RecA, Rad51, flagellin, pili, and filamentous bacteriophage. The first application of three-dimensional reconstruction from electron microscopic images was to a helical polymer, and a number of laboratories today are using helical tubes of integral membrane proteins for solving the structure of these proteins in the electron microscope at near atomic resolution. We have developed a method to analyze and reconstruct electron microscopic images of macromolecular helical polymers, the iterative helical real space reconstruction (IHRSR) algorithm. We can show that when there is disorder or heterogeneity, when the specimens diffract weakly, or when Bessel functions overlap, we can do far better with our method than can be done using traditional Fourier-Bessel approaches. In many cases, structures that were not even amenable to analysis can be solved at fairly high resolution using our method. The problems inherent in the traditional approach are discussed, and examples are presented illustrating how the IHRSR approach surmounts these problems.     

Phloem ultrastructure and pressure flow: Sieve-Element-Occlusion-Related agglomerations do not affect translocation

Since the first ultrastructural investigations of sieve tubes in the early 1960s, their structure has been a matter of debate. Because sieve tube structure defines frictional interactions in the tube system, the presence of P protein obstructions shown in many transmission electron micrographs led to a discussion about the mode of phloem transport. At present, it is generally agreed that P protein agglomerations are preparation artifacts due to injury, the lumen of sieve tubes is free of obstructions, and phloem flow is driven by an osmotically generated pressure differential according to Münch's classical hypothesis. Here, we show that the phloem contains a distinctive network of protein filaments. Stable transgenic lines expressing Arabidopsis thaliana Sieve-Element-Occlusion-Related1 (SEOR1)-yellow fluorescent protein fusions show that At SEOR1 meshworks at the margins and clots in the lumen are a general feature of living sieve tubes. Live imaging of phloem flow and flow velocity measurements in individual tubes indicate that At SEOR1 agglomerations do not markedly affect or alter flow. A transmission electron microscopy preparation protocol has been generated showing sieve tube ultrastructure of unprecedented quality. A reconstruction of sieve tube ultrastructure served as basis for tube resistance calculations. The impact of agglomerations on phloem flow is discussed.     

Tube morphogenesis: making and shaping biological tubes

Many organs are composed of epithelial tubes that transport vital fluids. Such tubular organs develop in many different ways and generate tubes of widely varying sizes and structures, but always with the apical epithelial surface lining the lumen. We describe recent progress in several diverse cell culture and genetic models of tube morphogenesis, which suggest apical membrane biogenesis, vesicle fusion, and secretion play central roles in tube formation and growth. We propose a unifying mechanism of tube morphogenesis that has been modified to create tube diversity and describe how defects in the tube size-sensing step can lead to polycystic kidney disease.     

GUI programs for processing individual images in early stages of helical image reconstruction--for high-resolution structure analysis

A set of programs equipped with graphical user interface has been developed for processing individual images in early stages of the three-dimensional helical image reconstruction procedure. These programs can be used for initial screening of suitable image area, straightening the object image, determination of box parameters including the repeat distance, determination of the out-of-plane tilt and initial editing of the layer-line data. These tasks are difficult to automate and therefore very time-consuming. The programs, developed by adopting the concept of the layer-line indexing [Ultramicroscopy 84 (2000) 1-14], are effective for processing many images of filamentous molecular assemblies and especially tubular crystals having various helical classes. Using these programs, higher-resolution signals can be extracted more reliably and quickly, and the time required for processing each image can be reduced to 1/2-1/10. Here also presented is an overview on helical image reconstruction for high-resolution structure analysis.     

Structural polymorphism in bacterial EspA filaments revealed by cryo-EM and an improved approach to helical reconstruction

The traditional Fourier-Bessel approach to three-dimensional reconstruction from electron microscopic (EM) images of helical polymers involves averaging over filaments, assuming a homogeneous structure and symmetry. We have used a real-space reconstruction approach to study the EspA filaments formed by enteropathogenic E. coli. In negative stain, the symmetry of these filaments is ambiguous, and we suggest that such ambiguities may be more prevalent than realized. Using cryo-EM of frozen-hydrated filaments, we find that these filaments have a fixed twist with 5.6 subunits per turn but an axial rise per subunit that varies from about 3.6 A to 5.6 A. Reconstructions at approximately 15 A resolution show a switching between the more compressed and extended filaments in the packing of putative alpha helices around the hollow lumen. Outside of a crystal, where there is nothing to maintain long-range order, the structural polymorphism in helical polymers may be much greater than has been assumed.     

Characterization of the In Vitro HIV-1 Capsid Assembly Pathway

During the morphogenesis of mature human immunodeficiency virus-1 cores, viral capsid proteins assemble conical or tubular shells around viral ribonucleoprotein complexes. This assembly step is mimicked in vitro through reactions in which capsid proteins oligomerize to form long tubes, and this process can be modeled as consisting of a slow nucleation period, followed by a rapid phase of tube growth. We have developed a novel fluorescence microscopy approach to monitor in vitro assembly reactions and have employed it, along with electron microscopy analysis, to characterize the assembly process. Our results indicate that temperature, salt concentration, and pH changes have differential effects on tube nucleation and growth steps. We also demonstrate that assembly can be unidirectional or bidirectional, that growth can be capped, and that proteins can assemble onto the surfaces of tubes, yielding multiwalled or nested structures. Finally, experiments show that a peptide inhibitor of in vitro assembly also can dismantle preexisting tubes, suggesting that such reagents may possess antiviral effects against both viral assembly and uncoating. Our investigations help establish a basis for understanding the mechanism of mature human immunodeficiency virus-1 core assembly and avenues for antiviral inhibition.     

The Chiral Looping of the Embryonic Heart Is Formed by the Combination of Three Axial Asymmetries

In mammals and birds, embryonic development of the heart involves conversion of a straight tubular structure into a three-dimensional helical loop, which is a chiral structure. We investigated theoretically the mechanism of helical loop formation of the mouse embryonic heart, especially focusing on determination of left-/right-handedness of the helical loop. In geometrical terms, chirality is the result of the combination of three axial asymmetries in three-dimensional space. We hypothesized the following correspondences between axial asymmetries and morphogenesis (bending and displacement): the dorsal-ventral asymmetry by ventral bending of a straight tube of the initial heart and the left-right and anterior-posterior asymmetries, the left-right asymmetry by rightward displacement of the heart tube, which is confined to the anterior region of the tube. Morphogenesis of chiral looping of the embryonic heart is a large-scaled event of the multicellular system in which substantial physical force operates dynamically. Using computer simulations with a cell-based physico-mechanical model and experiments with mouse embryos, we confirmed the hypothesis. We conclude that rightward displacement of the tube determines the left-handed screw of the loop. The process of helix loop formation consists of three steps: 1) the left-right biasing system involving Nodal-related signals that leads to left-right asymmetry in the embryonic body; 2) the rightward displacement of the tube; and finally 3) the left-handed helical looping. Step 1 is already established. Step 3 is elucidated by our study, which highlights the need for step 2 to be clarified; namely, we explore how the left-right asymmetry in the embryonic body leads to the rightward displacement of the heart tube.     

Three-dimensional structure of the acetylcholine receptor by cryoelectron microscopy and helical image reconstruction

Long tubular vesicles have been grown from isolated Torpedo postsynaptic membranes, in which the receptors are arranged helically on the vesicle surface. The structures of these tubes have been analyzed by cryoelectron microscopy of specimens embedded in thin films of ice, combined with helical image reconstruction. Complete data sets from tubes belonging to several helical families have been obtained to a resolution of 17 A in all directions. Confirming a preliminary study (Toyoshima, C., and N. Unwin. 1988. Nature (Lond.). 336:247-250), the central ion channel has an almost constant diameter throughout the molecule except for the portion extending through the hydrophobic part of the lipid bilayer, where the pore is too small to be resolved. However, the density on the pseudo fivefold axis running through the pore is consistently highest in the cytoplasmic half of the bilayer, suggesting the gate is located in that region. The path followed by each subunit has been identified throughout the length of the receptor. The two alpha subunits follow equivalent paths. All subunits have similar features which change in character at the same level relative to the membrane.     

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.     

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.     

Intercarpellary growth of pollen tubes in the extragynoecial compitum and its contribution to fruit set in an apocarpous species, Schisandra sphenanthera (Schisandraceae)

? Premise of the study: Apocarpous plants possess carpels that are separated in the gynoecium. Extragynoecial compita, commonly occurring in basal angiosperms, have been proposed to have the potential to increase offspring quantity in apocarpous species through the intercarpellary growth of pollen tubes. To date, the impact of an extragynoecial compitum on fruit or seed set has not been studied in any species. This study investigated the pollen tube pathway between adjacent carpels and its contribution to fruit set in Schisandra sphenanthera. ? Methods: We investigated the fruit set ratio in the field and collected hundreds of gynoecia at their full flowering stage. Pollinated carpel ratio and pollen tube pathway observations were performed using fluorescence optics. ? Key results: Pollen grains germinated and tubes extended along the pseudostyle surface. Some of them turned and entered the ovules at the end of the stigmatic crest, whereas others subsequently grew into neighboring carpels through promontory connections located at the base of the unfused carpels. No tubes were found growing on the surface of the receptacle. More than 24 carpels could be fertilized by pollen tubes from one carpel through hand pollination. The pollinated carpel ratio was significantly lower than the fruit set ratio under natural conditions. ? Conclusions: Pollen tubes from one carpel can easily cross in the extragynoecial compitum between the adjacent carpels of S. sphenanthera, and this intercarpellary growth of pollen tubes can significantly increase the fruit set of apocarpous species, at least in S. sphenanthera.     

Diffraction imaging of single particles and biomolecules

Theory predicts that with a very short and very intense X-ray pulse, the image of a single diffraction pattern may be recorded from a large macromolecule, a virus, or a nanocluster of proteins without the need for a crystal. A three-dimensional data set can be assembled from such images when many copies of the molecule are exposed to the beam one by one in random orientations. We outline a method for structure reconstruction from such a data set in which no independent information is available about the orientation of the images. The basic requirement for reconstruction and/or signal averaging is the ability to tell whether two noisy diffraction patterns represent the same view of the sample or two different views. With this knowledge, averaging techniques can be used to enhance the signal and extend the resolution in a redundant data set. Based on statistical properties of the diffraction pattern, we present an analytical solution to the classification problem. The solution connects the number of incident X-ray photons with the particle size and the achievable resolution. The results are surprising in that they show that classification can be done with less than one photon per pixel in the limiting resolution shell, assuming Poisson-type photon noise in the image. The results can also be used to provide criteria for improvements in other image classification procedures, e.g., those used in electron tomography or diffraction.     

Electron microscopy of muscle phosphorylase a

Electron microscopy of negatively stained preparations of phosphorylase a (tetrameric form) from solutions with and without added protamine revealed three characteristic types of particle images. In preparations with added protamine several types of crystalline formation were observed: three types of plane monolayers, tubes and small three-dimensional crystals. The tubes have been studied by optical diffraction and filtering. In the main class of tubes the particles form $\text{26}\text{9}$ three-start helices (it may well be that narrow tubes with different parameters exist). Now and again, one can observe tubes twice as large in diameter, and tubes with two-layer walls. Analysis of the images of particles in solution and in crystalline formations showed that their structure can be characterized in terms of one model consisting of four elongated bent subunits arranged with the point-group symmetry 222 at the vertices of a tetrahedron. The structure of phosphorylase b particles, previously studied (Kiselev et al., 1971), can also be characterized satisfactorily by the same model. The difference in the structure of these two forms expresses itself in a different character of mutual aggregation of the molecules in plane layers, and in the parameters of the helical packing of the molecules in tubes.