cryo-EM Image Reconstruction Research Articles

Orientation estimation of cryo-EM images using projected gradient descent method

Orientation estimation is an important task in three-dimensional cryo-EM image reconstruction. By applying the common line method, the orientation estimation task can be formulated as a least squares (LS) problem or a least un-squared deviation (LUD) problem with orthogonality constraint. However, the non-convexity of the orthogonality constraint introduces numerical difficulties to the orientation estimation. The conventional approach is to reformulate the orthogonality constrained minimization problem into a semi-definite programming problem using convex relaxation strategies. In this paper, we consider a direct way to solve the constrained minimization problem without relaxation. We focus on the weighted LS problem because the LUD problem can be reformulated into a sequence of weighted LS problems using the iteratively re-weighted LS approach. As a classical approach, the projected gradient descent (PGD) method has been successfully applied to solve the convex constrained minimization problem. We apply the PGD method to the minimization problem with orthogonality constraint and show that the constraint set is a generalized prox-regular set, and it satisfies the norm compatibility condition. We also demonstrate that the objective function of the minimization problem satisfies the restricted strong convexity and the restricted strong smoothness over a constraint set. Therefore, the sequence generated by the PGD method converges when the initial conditions are satisfied. Experimental results show that the PGD method significantly outperforms the semi-definite relaxation methods from a computation standpoint, and the mean square error is almost the same or smaller.

Near-Atomic Resolution Cryo-EM Image Reconstruction of RNA.

The rapid development of cryogenic electron microscopy (cryo-EM) enables the structure determination of macromolecules without the need for crystallization. Protein, protein-lipid, and protein-nucleic acid complexes can now be routinely resolved by cryo-EM single-particle analysis (SPA) to near-atomic or atomic resolution. Here we describe the structure determination of pure RNAs by SPA, from cryo-specimen preparation to data collection and 3D reconstruction. This protocol is useful to yield many cryo-EM structures of RNA, here exemplified by the Tetrahymena L-21 ScaI ribozyme at 3.1-Å resolution.

Structural interpretation of cryo-EM image reconstructions

The productivity of single-particle cryo-EM as a structure determination method has rapidly increased as many novel biological structures are being elucidated. The ultimate result of the cryo-EM experiment is an atomic model that should faithfully represent the computed image reconstruction. Although the principal approach of atomic model building and refinement from maps resembles that of the X-ray crystallographic methods, there are important differences due to the unique properties resulting from the 3D image reconstructions. In this review, we discuss the practiced work-flow from the cryo-EM image reconstruction to the atomic model. We give an overview of (i) resolution determination methods in cryo-EM including local and directional resolution variation, (ii) cryo-EM map contrast optimization including complementary map types that can help in identifying ambiguous density features, (iii) atomic model building and (iv) refinement in various resolution regimes including (v) their validation and (vi) discuss differences between X-ray and cryo-EM maps. Based on the methods originally developed for X-ray crystallography, the path from 3D image reconstruction to atomic coordinates has become an integral and important part of the cryo-EM structure determination work-flow that routinely delivers atomic models.

The Integrity of the Intradimer Interface of the Hepatitis B Virus Capsid Protein Dimer Regulates Capsid Self-Assembly.

During the hepatitis B virus lifecycle, 120 copies of homodimeric capsid protein assemble around a copy of reverse transcriptase and viral RNA and go on to produce an infectious virion. Assembly needs to be tightly regulated by protein conformational change to ensure symmetry, fidelity, and reproducibility. Here, we show that structures at the intradimer interface regulate conformational changes at the distal interdimer interface and so regulate assembly. A pair of interacting charged residues, D78 from each monomer, conspicuously located at the top of a four-helix bundle that forms the intradimer interface, were mutated to serine to disrupt communication between the two monomers. The mutation slowed assembly and destabilized the dimer to thermal and chemical denaturation. Mutant dimers showed evidence of transient partial unfolding based on the appearance of new proteolytically sensitive sites. Though the mutant dimer was less stable, the resulting capsids were as stable as the wildtype, based on assembly and thermal denaturation studies. Cryo-EM image reconstructions of capsid indicated that the subunits adopted an "open" state more usually associated with a free dimer and that the spike tips were either disordered or highly flexible. Molecular dynamics simulations provide mechanistic explanations for these results, suggesting that D78 stabilizes helix 4a, which forms part of the intradimer interface, by capping its N-terminus and hydrogen-bonding to nearby residues, whereas the D78S mutation disrupts these interactions, leading to partial unwinding of helix 4a. This in turn weakens the connection from helix 4 and the intradimer interface to helix 5, which forms the interdimer interface.

Importin β Can Bind Hepatitis B Virus Core Protein and Empty Core-Like Particles and Induce Structural Changes.

Hepatitis B virus (HBV) capsids are found in many forms: immature single-stranded RNA-filled cores, single-stranded DNA-filled replication intermediates, mature cores with relaxed circular double-stranded DNA, and empty capsids. A capsid, the protein shell of the core, is a complex of 240 copies of core protein. Mature cores are transported to the nucleus by a complex that includes both importin α and importin β (Impα and Impβ), which bind to the core protein’s C-terminal domains (CTDs). Here we have investigated the interactions of HBV core protein with importins in vitro. Strikingly, empty capsids and free core protein can bind Impβ without Impα. Cryo-EM image reconstructions show that the CTDs, which are located inside the capsid, can extrude through the capsid to be bound by Impβ. Impβ density localized on the capsid exterior near the quasi-sixfold vertices, suggested a maximum of 30 Impβ per capsid. However, examination of complexes using single molecule charge-detection mass spectrometry indicate that some complexes include over 90 Impβ molecules. Cryo-EM of capsids incubated with excess Impβ shows a population of damaged particles and a population of “dark” particles with internal density, suggesting that Impβ is effectively swallowed by the capsids, which implies that the capsids transiently open and close and can be destabilized by Impβ. Though the in vitro complexes with great excess of Impβ are not biological, these results have implications for trafficking of empty capsids and free core protein; activities that affect the basis of chronic HBV infection.

Self-Assembly of an Alphavirus Core-like Particle Is Distinguished by Strong Intersubunit Association Energy and Structural Defects.

Weak association energy can lead to uniform nanostructures: defects can anneal due to subunit lability. What happens when strong association energy leads to particles where defects are trapped? Alphaviruses are enveloped viruses whose icosahedral nucleocapsid core can assemble independently. We used a simplest case system to study Ross River virus (RRV) core-like particle (CLP) self-assembly using purified capsid protein and a short DNA oligomer. We find that capsid protein binds the oligomer with high affinity to form an assembly competent unit (U). Subsequently, U assembles with concentration dependence into CLPs. We determined that U-U pairwise interactions are very strong (ca. -6 kcal/mol) compared to other virus assembly systems. Assembled RRV CLPs appeared morphologically uniform and cryo-EM image reconstruction with imposed icosahedral symmetry yielded a T = 4 structure. However, 2D class averages of the CLPs show that virtually every class had disordered regions. These results suggested that irregular cores may be present in RRV virions. To test this hypothesis, we determined 2D class averages of RRV virions using authentic virions or only the core from intact virions isolated by computational masking. Virion-based class averages were symmetrical, geometric, and corresponded well to projections of image reconstructions. In core-based class averages, cores and envelope proteins in many classes were disordered. These results suggest that partly disordered components are common even in ostensibly well-ordered viruses, a biological realization of a patchy particle. Biological advantages of partly disordered complexes may arise from their ease of dissociation and asymmetry.

High-resolution 3D structures reveal the biological functions of reoviruses

Viruses in the family Reoviridae are non-enveloped particles comprising a segmented double-stranded RNA genome surrounded by a two-layered or multi-layered icosahedral protein capsid. These viruses are classified into two sub-families based on their particle structural organization. Recent studies have focused on high-resolution three-dimensional structures of reovirus particles by using cryo-electron microscopy (cryo-EM) to approach the resolutions seen in X-ray crystallographic structures. The results of cryo-EM image reconstructions allow tracing of most of the protein side chains, and thus permit integration of structural and functional information into a coherent mechanism for reovirus assembly and entry.

Scaffold Properties Are a Key Determinant of the Size and Shape of Self-Assembled Virus-Derived Particles

Controlling the geometry of self-assembly will enable a greater diversity of nanoparticles than now available. Viral capsid proteins, one starting point for investigating self-assembly, have evolved to form regular particles. The polyomavirus SV40 assembles from pentameric subunits and can encapsidate anionic cargos. On short ssRNA (≤814 nt), SV40 pentamers form 22 nm diameter capsids. On RNA too long to fit a T = 1 particle, pentamers forms strings of 22 nm particles and heterogeneous particles of 29-40 nm diameter. However, on dsDNA SV40 forms 50 nm particles composed of 72 pentamers. A 7.2-Å resolution cryo-EM image reconstruction of 22 nm particles shows that they are built of 12 pentamers arranged with T = 1 icosahedral symmetry. At 3-fold vertices, pentamers each contribute to a three-helix triangle. This geometry of interaction is not seen in crystal structures of T = 7 viruses and provides a structural basis for the smaller capsids. We propose that the heterogeneous particles are actually mosaics formed by combining different geometries of interaction from T = 1 capsids and virions. Assembly can be trapped in novel conformations because SV40 interpentamer contacts are relatively strong. The implication is that by virtue of their large catalog of interactions, SV40 pentamers have the ability to self-assemble on and conform to a broad range of shapes.

Cryoelectron Microscopy Analysis of Small Heat Shock Protein 16.5 (Hsp16.5) Complexes with T4 Lysozyme Reveals the Structural Basis of Multimode Binding

Small heat shock proteins (sHSPs) are ubiquitous chaperones that bind and sequester non-native proteins preventing their aggregation. Despite extensive studies of sHSPs chaperone activity, the location of the bound substrate within the sHSP oligomer has not been determined. In this paper, we used cryoelectron microscopy (cryoEM) to visualize destabilized mutants of T4 lysozyme (T4L) bound to engineered variants of the small heat shock protein Hsp16.5. In contrast to wild type Hsp16.5, binding of T4L to these variants does not induce oligomer heterogeneity enabling cryoEM analysis of the complexes. CryoEM image reconstruction reveals the sequestration of T4L in the interior of the Hsp16.5 oligomer primarily interacting with the buried N-terminal domain but also tethered by contacts with the α-crystallin domain shell. Analysis of Hsp16.5-WT/T4L complexes uncovers oligomer expansion as a requirement for high affinity binding. In contrast, a low affinity mode of binding is found to involve T4L binding on the outer surface of the oligomer bridging the formation of large complexes of Hsp16.5. These mechanistic principles were validated by cryoEM analysis of an expanded variant of Hsp16.5 in complex with T4L and Hsp16.5-R107G, which is equivalent to a mutant of human αB-crystallin linked to cardiomyopathy. In both cases, high affinity binding is found to involve conformational changes in the N-terminal region consistent with a central role of this region in substrate recognition.

Conformational changes in tubulin in GMPCPP and GDP-taxol microtubules observed by cryoelectron microscopy

Microtubules are dynamic polymers that stochastically switch between growing and shrinking phases. Microtubule dynamics are regulated by guanosine triphosphate (GTP) hydrolysis by β-tubulin, but the mechanism of this regulation remains elusive because high-resolution microtubule structures have only been revealed for the guanosine diphosphate (GDP) state. In this paper, we solved the cryoelectron microscopy (cryo-EM) structure of microtubule stabilized with a GTP analogue, guanylyl 5'-α,β-methylenediphosphonate (GMPCPP), at 8.8-Å resolution by developing a novel cryo-EM image reconstruction algorithm. In contrast to the crystal structures of GTP-bound tubulin relatives such as γ-tubulin and bacterial tubulins, significant changes were detected between GMPCPP and GDP-taxol microtubules at the contacts between tubulins both along the protofilament and between neighboring protofilaments, contributing to the stability of the microtubule. These findings are consistent with the structural plasticity or lattice model and suggest the structural basis not only for the regulatory mechanism of microtubule dynamics but also for the recognition of the nucleotide state of the microtubule by several microtubule-binding proteins, such as EB1 or kinesin.

Cooperative kinking at distant sites in mechanically stressed DNA

In cells, DNA is routinely subjected to significant levels of bending and twisting. In some cases, such as under physiological levels of supercoiling, DNA can be so highly strained, that it transitions into non-canonical structural conformations that are capable of relieving mechanical stress within the template. DNA minicircles offer a robust model system to study stress-induced DNA structures. Using DNA minicircles on the order of 100 bp in size, we have been able to control the bending and torsional stresses within a looped DNA construct. Through a combination of cryo-EM image reconstructions, Bal31 sensitivity assays and Brownian dynamics simulations, we have been able to analyze the effects of biologically relevant underwinding-induced kinks in DNA on the overall shape of DNA minicircles. Our results indicate that strongly underwound DNA minicircles, which mimic the physical behavior of small regulatory DNA loops, minimize their free energy by undergoing sequential, cooperative kinking at two sites that are located about 180° apart along the periphery of the minicircle. This novel form of structural cooperativity in DNA demonstrates that bending strain can localize hyperflexible kinks within the DNA template, which in turn reduces the energetic cost to tightly loop DNA.

The 2.3-Angstrom Structure of Porcine Circovirus 2

Porcine circovirus 2 (PCV2) is a T=1 nonenveloped icosahedral virus that has had severe impact on the swine industry. Here we report the crystal structure of an N-terminally truncated PCV2 virus-like particle at 2.3-Å resolution, and the cryo-electron microscopy (cryo-EM) image reconstruction of a full-length PCV2 virus-like particle at 9.6-Å resolution. This is the first atomic structure of a circovirus. The crystal structure revealed that the capsid protein fold is a canonical viral jelly roll. The loops connecting the strands of the jelly roll define the limited features of the surface. Sulfate ions interacting with the surface and electrostatic potential calculations strongly suggest a heparan sulfate binding site that allows PCV2 to gain entry into the cell. The crystal structure also allowed previously determined epitopes of the capsid to be visualized. The cryo-EM image reconstruction showed that the location of the N terminus, absent in the crystal structure, is inside the capsid. As the N terminus was previously shown to be antigenic, it may externalize through viral "breathing."

Atomic model of an infectious rotavirus particle

Non-enveloped viruses of different types have evolved distinct mechanisms for penetrating a cellular membrane during infection. Rotavirus penetration appears to occur by a process resembling enveloped-virus fusion: membrane distortion linked to conformational changes in a viral protein. Evidence for such a mechanism comes from crystallographic analyses of fragments of VP4, the rotavirus-penetration protein, and infectivity analyses of structure-based VP4 mutants. We describe here the structure of an infectious rotavirus particle determined by electron cryomicroscopy (cryoEM) and single-particle analysis at about 4.3 Å resolution. The cryoEM image reconstruction permits a nearly complete trace of the VP4 polypeptide chain, including the positions of most side chains. It shows how the two subfragments of VP4 (VP8(*) and VP5(*)) retain their association after proteolytic cleavage, reveals multiple structural roles for the β-barrel domain of VP5(*), and specifies interactions of VP4 with other capsid proteins. The virion model allows us to integrate structural and functional information into a coherent mechanism for rotavirus entry.

The role of subunit hinges and molecular “switches” in the control of viral capsid polymorphism

The coat protein (CP) of cowpea chlorotic mottle virus assembles exclusively into a T = 3 capsid in vivo and, under proper conditions, in vitro. The N-terminal domain of CP has been implicated in proper assembly and was viewed as a required switch for mediating hexamer and pentamer formation in T = 3 assembly. We observed that a mutant CP lacking most of the N-terminal domain, NΔ34, assembles, in vitro, into statistically predictable numbers of: native-like T = 3 capsids of 90 dimers; “ T = 2” capsids of 60 dimers; T = 1 capsids of 30 dimers. We generated cryo-EM image reconstructions of each form and built pseudo-atomic models based on the subunits from the crystal structure of plant-derived T = 3 virus allowing a detailed comparison of stabilizing interactions in the three assemblies. The statistical nature of the distribution of assembly products and the observed structures indicates that the N-terminus of CP is not a switch that is required to form the proper ratio of hexamers and pentamers for T = 3 assembly; rather, it biases the direction of assembly to T = 3 particles from the possibilities available to NΔ34 through flexible dimer hinges and variations in subunit contacts. Our results are consistent with a pentamer of dimers (PODs) nucleating assembly in all cases but subunit dimers can be added with different trajectories that favor specific T = 3 or T = 1 global particle geometries. Formation of the “ T = 2” particles appears to be fundamentally different in that they not only nucleate with PODs, but assembly propagates by the addition of mostly, if not exclusively PODs generating an entirely new subunit interface in the process. These results show that capsid geometry is flexible and may readily adapt to new requirements as the virus evolves.

Structural and functional similarities between the capsid proteins of bacteriophages T4 and HK97 point to a common ancestry

Gene product (gp) 24 of bacteriophage T4 forms the pentameric vertices of the capsid. Using x-ray crystallography, we found the principal domain of gp24 to have a polypeptide fold similar to that of the HK97 phage capsid protein plus an additional insertion domain. Fitting gp24 monomers into a cryo-EM density map of the mature T4 capsid suggests that the insertion domain interacts with a neighboring subunit, effecting a stabilization analogous to the covalent crosslinking in the HK97 capsid. Sequence alignment and genetic data show that the folds of gp24 and the hexamer-forming capsid protein, gp23*, are similar. Accordingly, models of gp24* pentamers, gp23* hexamers, and the whole capsid were built, based on a cryo-EM image reconstruction of the capsid. Mutations in gene 23 that affect capsid shape map to the capsomer's periphery, whereas mutations that allow gp23 to substitute for gp24 at the vertices modify the interactions between monomers within capsomers. Structural data show that capsid proteins of most tailed phages, and some eukaryotic viruses, may have evolved from a common ancestor.

Postentry Neutralization of Adenovirus Type 5 by an Antihexon Antibody

Antibodies against hexon, the major coat protein of adenovirus (Ad), are an important component of the neutralizing activity in serum from naturally infected humans and experimentally infected animals. The mechanisms by which antihexon antibodies neutralize the virus have not been defined. As a model system, murine monoclonal antibodies raised against Ad type 5 (Ad5) were screened for antihexon binding and neutralization activity; one monoclonal antibody, designated 9C12, was selected for further characterization. The minimum ratio of 9C12 to Ad5 required for neutralization was 240 antibody molecules per virus particle, or 1 antibody per hexon trimer. Analysis of antibody-virus complexes by dynamic light scattering and negative-stain electron microscopy (EM) showed that the virus particles were coated with electron-dense material but not aggregated at neutralizing ratios. Cryo-EM image reconstruction of the antibody-virus complex showed that the surface of the virus particle was covered by a meshwork of 9C12 antibody density, consistent with bivalent binding at multiple sites. Confocal analysis revealed that viral attachment, cell entry, and intracellular transport to the nuclear periphery still occur in the presence of neutralizing levels of 9C12. A model is presented for neutralization of Ad by an antihexon antibody in which the hexon capsid is cross-linked by antibodies, thus preventing virus uncoating and nuclear entry of viral DNA.

DNA packaging intermediates of bacteriophage φX174

Like many viruses, bacteriophage phi X174 packages its DNA genome into a procapsid that is assembled from structural intermediates and scaffolding proteins. The procapsid contains the structural proteins F, G and H, as well as the scaffolding proteins B and D. Provirions are formed by packaging of DNA together with the small internal J proteins, while losing at least some of the B scaffolding proteins. Eventually, loss of the D scaffolding proteins and the remaining B proteins leads to the formation of mature virions. phi X174 108S 'procapsids' have been purified in milligram quantities by removing 114S (mature virion) and 70S (abortive capsid) particles from crude lysates by differential precipitation with polyethylene glycol. 132S 'provirions' were purified on sucrose gradients in the presence of EDTA. Cryo-electron microscopy (cryo-EM) was used to obtain reconstructions of procapsids and provirions. Although these are very similar to each other, their structures differ greatly from that of the virion. The F and G proteins, whose atomic structures in virions were previously determined from X-ray crystallography, were fitted into the cryo-EM reconstructions. This showed that the pentamer of G proteins on each five-fold vertex changes its conformation only slightly during DNA packaging and maturation, whereas major tertiary and quaternary structural changes occur in the F protein. The procapsids and provirions were found to contain 120 copies of the D protein arranged as tetramers on the two-fold axes. DNA might enter procapsids through one of the 30 A diameter holes on the icosahedral three-fold axes. Combining cryo-EM image reconstruction and X-ray crystallography has revealed the major conformational changes that can occur in viral assembly. The function of the scaffolding proteins may be, in part, to support weak interactions between the structural proteins in the procapsids and to cover surfaces that are subsequently required for subunit-subunit interaction in the virion. The structures presented here are, therefore, analogous to chaperone proteins complexed with folding intermediates of a substrate.