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While classic studies proved that wide networks allow universal approximation, recent research and successes of deep learning demonstrate the power of deep networks. Based on a symmetric consideration, we investigate if the design of artificial neural networks should have a directional preference, and what the mechanism of interaction is between the width and depth of a network. Inspired by the De Morgan law, we address this fundamental question by establishing a quasi-equivalence between the width and depth of ReLU networks. We formulate two transforms for mapping an arbitrary ReLU network to a wide ReLU network and a deep ReLU network respectively, so that the essentially same capability of the original network can be implemented. Based on our findings, a deep network has a wide equivalent, and vice versa, subject to an arbitrarily small error. [ABSTRACT FROM AUTHOR]

Alphaviruses are spherical, enveloped RNA viruses primarily transmitted by mosquitoes, and cause significant arthritogenic and neurotropic disease in humans and livestock. Previous reports have shown that—in contrast to prototypical icosahedral viruses—alphaviruses incorporate frequent defects, and these may serve important functions in the viral life cycle. We confirm the genus-wide pleomorphism in live viral particles and extend our understanding of alphavirus assembly through the discovery of an alternate architecture of Eastern equine encephalitis virus (EEEV) particles. The alternate T = 3 icosahedral architecture differs in triangulation number from the classic T = 4 icosahedral organization that typifies alphaviruses, but the alternate architecture maintains the quasi-equivalence relationship of asymmetric units. The fusion spike glycoproteins are more loosely apposed in the T = 3 form with corresponding changes in the underlying capsid protein lattice. This alternate architecture could potentially be exploited in engineering alphavirus-based particles for delivery of alphaviral or other RNA. [ABSTRACT FROM AUTHOR]

Foamy viruses (FVs) are an ancient lineage of retroviruses, with an evolutionary history spanning over 450 million years. Vector systems based on Prototype Foamy Virus (PFV) are promising candidates for gene and oncolytic therapies. Structural studies of PFV contribute to the understanding of the mechanisms of FV replication, cell entry and infection, and retroviral evolution. Here we combine cryoEM and cryoET to determine high-resolution in situ structures of the PFV icosahedral capsid (CA) and envelope glycoprotein (Env), including its type III transmembrane anchor and membrane-proximal external region (MPER), and show how they are organized in an integrated structure of assembled PFV particles. The atomic models reveal an ancient retroviral capsid architecture and an unexpected relationship between Env and other class 1 fusion proteins of the Mononegavirales. Our results represent the de novo structure determination of an assembled retrovirus particle. [Display omitted] • Integrated molecular architecture of assembled foamy virus particles • High-resolution in situ structures of Env surface glycoprotein and Gag CA capsid • Foamy virus Env is related to membrane fusogens of paramyxo- and coronaviruses • Gag CA capsid is icosahedral with features of pleomorphic orthoretroviral capsids The high-resolution in situ structural analysis of the prototype foamy virus icosahedral capsid and envelope glycoprotein provides insight into the viral infection process and evolutionary history. [ABSTRACT FROM AUTHOR]

Tick-borne encephalitis virus (TBEV) is a pathogenic, enveloped, positive-stranded RNA virus in the family Flaviviridae. Structural studies of flavivirus virions have primarily focused on mosquito-borne species, with only one cryo-electron microscopy (cryo-EM) structure of a tick-borne species published. Here, we present a 3.3 Å cryo-EM structure of the TBEV virion of the Kuutsalo-14 isolate, confirming the overall organisation of the virus. We observe conformational switching of the peripheral and transmembrane helices of M protein, which can explain the quasi-equivalent packing of the viral proteins and highlights their importance in stabilising membrane protein arrangement in the virion. The residues responsible for M protein interactions are highly conserved in TBEV but not in the structurally studied Hypr strain, nor in mosquito-borne flaviviruses. These interactions may compensate for the lower number of hydrogen bonds between E proteins in TBEV compared to the mosquito-borne flaviviruses. The structure reveals two lipids bound in the E protein which are important for virus assembly. The lipid pockets are comparable to those recently described in mosquito-borne Zika, Spondweni, Dengue, and Usutu viruses. Our results thus advance the understanding of tick-borne flavivirus architecture and virion-stabilising interactions. [ABSTRACT FROM AUTHOR]

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Alphaviruses are spherical, enveloped RNA viruses primarily transmitted by mosquitoes, and cause significant arthritogenic and neurotropic disease in humans and livestock. Previous reports have shown that—in contrast to prototypical icosahedral viruses—alphaviruses incorporate frequent defects, and these may serve important functions in the viral life cycle. We confirm the genus-wide pleomorphism in live viral particles and extend our understanding of alphavirus assembly through the discovery of an alternate architecture of Eastern equine encephalitis virus (EEEV) particles. The alternate T = 3 icosahedral architecture differs in triangulation number from the classic T = 4 icosahedral organization that typifies alphaviruses, but the alternate architecture maintains the quasi-equivalence relationship of asymmetric units. The fusion spike glycoproteins are more loosely apposed in the T = 3 form with corresponding changes in the underlying capsid protein lattice. This alternate architecture could potentially be exploited in engineering alphavirus-based particles for delivery of alphaviral or other RNA.

BackgroundRNA-protein interactions stabilize many viruses and also the nucleoprotein cores of enveloped animal viruses (e.g. retroviruses). The nucleoprotein particles are frequently pleomorphic and generally unstable due to the lack of strong protein-protein interactions in their capsids. Principles governing their structures are unknown because crystals of such nucleoprotein particles that diffract to high resolution have not previously been produced. Cowpea chlorotic mottle virions (CCMV) are typical of particles stabilized by RNA-protein interactions and it has been found that crystals that diffract beyond 4.5 A resolution are difficult to grow. However, we report here the purification of CCMV with an exceptionally mild procedure and the growth of crystals that diffract X-rays to 3.2 A resolution.ResultsThe 3.2 A X-ray structure of native CCMV, an icosahedral (T = 3) RNA plant virus, shows novel quaternary structure interactions based on interwoven carboxyterminal polypeptides that extend from canonical capsid beta-barrel subunits. Additional particle stability is provided by intercapsomere contacts between metal ion mediated carboxyl cages and by protein interactions with regions of ordered RNA. The structure of a metal-free, swollen form of the virus was determined by cryo-electron microscopy and image reconstruction. Modeling of this structure with the X-ray coordinates of the native subunits shows that the 29 A radial expansion is due to electrostatic repulsion at the carboxyl cages and is stopped short of complete disassembly by preservation of interwoven carboxyl termini and protein-RNA contacts.ConclusionsThe CCMV capsid displays quaternary structural interactions that are unique compared with previously determined RNA virus structures. The loosely coupled hexamer and pentamer morphological units readily explain their versatile reassembly properties and the pH and metal ion dependent polymorphism observed in the virions. Association of capsomeres through inter-penetrating carboxy-terminal portions of the subunit polypeptides has been previously described only for the DNA tumor viruses, SV40 and polyoma.

The primary functions of most virus capsids are to protect the viral genome in the extra-cellular milieu and deliver it to the host. In contrast, the capsids of fungal viruses, like the cores of all other known double stranded RNA viruses, are not involved in host recognition but do shield their genomes, and they also carry out transcription and replication. Nascent (+) strands are extruded from transcribing virions. The capsids of the yeast virus L-A are composed of Gag (capsid protein; 76 kDa), with a few molecules of Gag-Pol (170 kDa). Analysis of these 420 A diameter shells and those of the fungal P4 virus by cryo-electron microscopy and image reconstruction shows that they share the same novel icosahedral structure. Both capsids consist of 60 equivalent Gag dimers, whose two subunits occupy non-equivalent bonding environments. Stoichiometry data on other double-stranded RNA viruses indicate that the 120-subunit structure is widespread, implying that this molecular architecture has features that are particularly favorable to the design of a capsid that is also a biosynthetic compartment.

BackgroundStudies of simple RNA animal viruses show that cell attachment, particle destabilization and cell entry are complex processes requiring a level of capsid sophistication that is difficult to achieve with a shell containing only a single gene product. Nodaviruses [such as Flock House virus (FHV)] are an exception. We have previously determined the structure of FHV at 3 A resolution, and now combine this information with data from cryo-electron microscopy in an attempt to clarify the process by which nodaviruses infect animal cells.ResultsA difference map was computed in which electron density at 22 A resolution, derived from the 3.0 A resolution X-ray model of the FHV capsid protein, was subtracted from the electron density derived from the cryo-electron microscopy reconstruction of FHV at 22 A resolution. Comparisons of this density with the X-ray model showed that quasi-equivalent regions of identical polypeptide sequences have markedly different interactions with the bulk RNA density. Previously reported biphasic kinetics of particle maturation and the requirement of subunit cleavage for particle infectivity are consistent with these results.ConclusionsOn the basis of this study we propose a model for nodavirus infection that is conceptually similar to that proposed for poliovirus but differs from it in detail. The constraints of a single protein type in the capsid lead to a noteworthy use of quasi-symmetry not only to control the binding of a 'pocket factor' but also to modulate maturation cleavage and to release a pentameric helical bundle (with genomic RNA attached) that may further interact with the cell membrane.

Abstract We report the revised crystal structure of a pseudo-typed human adenovirus at 3.8-Å resolution that is consistent with the atomic models of minor proteins determined by cryo-electron microscopy. The diffraction data from multiple crystals were rescaled and merged to increase the data completeness. The densities for the minor proteins were initially identified in the phase-refined omit maps that were further improved by the phases from docked poly-alanine models to build atomic structures. While the trimeric fiber molecules are disordered due to flexibility and imposition of 5-fold symmetry, the remaining major capsid proteins hexon and penton base are clearly ordered, with the exception of hypervariable region 1 of hexons, the RGD containing loop, and the N-termini of the penton base. The exterior minor protein IX together with the interior minor proteins IIIa and VIII stabilizes the adenovirus virion. A segment of N-terminal pro-peptide of VI is found in the interior cavities of peripentonal hexons, and the rest of VI is disordered. While the triskelion substructures formed by the N-termini of IX conform to excellent quasi 3-fold symmetry, the tetrameric coiled-coils formed by the C-termini and organized in parallel and anti-parallel arrangement do not exhibit any quasi-symmetry. This observation also conveys the pitfalls of using the quasi-equivalence as validation criteria for the structural analysis of extended (non-modular) capsid proteins such as IX. Together, these results remedy certain discrepancies in the previous X-ray model in agreement with the cryo-electron microscopy models. Graphical abstract Organization of minor (cement) protein scaffold in HAdV5. Shown on the left is the overall arrangement of cement proteins in HAdV5 that mostly conforms to the trail of pseudo T = 25 quasi-equivalent icosahedral lattice (yellow), depicted as hexagons and pentagons. The major capsid proteins hexons, penton base, and fiber are omitted for clarity. On the right is the zoomed-in view of the boxed region (black rectangle) on the left. Color code: IX-P (blue), IX-Q (light blue), IX-R (cyan), IX-S (purple), IIIa (green), VIII-U (orange), VIII-V (yellow), and pVIn (red). Unlabelled Image Highlights • This report describes structures and scaffolding organization of cement proteins based on the crystal structure of human adenovirus virion. • The revised structures and organization of minor proteins are consistent with the reported high-resolution cryo-EM structures. • The results highlight the limits on quasi-equivalence displayed by protein IX molecules that form a continuous hexagonal lattice. • The report also provides a word of caution in using the quasi-equivalence as a constraint in virus structure determinations. [ABSTRACT FROM AUTHOR]

The capsid of P22 bacteriophage undergoes a series of structural transitions during maturation that guide it from spherical to icosahedral morphology. The transitions include the release of scaffold proteins and capsid expansion. Although P22 maturation has been investigated for decades, a unified model that incorporates thermodynamic and biophysical analyses is not available. A general and specific model of icosahedral capsid maturation is of significant interest to theoreticians searching for fundamental principles as well as virologists and material scientists seeking to alter maturation to their advantage. To address this challenge, we have combined the results from orthogonal biophysical techniques including differential scanning fluorimetry, atomic force microscopy, circular dichroism, and hydrogen-deuterium exchange mass spectrometry. By integrating these results from single particle and population measurements, an energy landscape of P22 maturation from procapsid through expanded shell to wiffle ball emerged, highlighting the role of metastable structures and the thermodynamics guiding maturation. The propagation of weak quaternary interactions across symmetric elements of the capsid is a key component for stability in P22. A surprising finding is that the progression to wiffle ball, which lacks pentamers, shows that chemical and thermal stability can be uncoupled from mechanical rigidity, elegantly demonstrating the complexity inherent in capsid protein interactions and the emergent properties that can arise from icosahedral symmetry. On a broader scale, this work demonstrates the power of applying orthogonal biophysical techniques to elucidate assembly mechanisms for supramolecular complexes and provides a framework within which other viral systems can be compared. [ABSTRACT FROM AUTHOR]

Nudaurelia capensis w virus (NωV) is a eukaryotic RNA virus that is well suited for the study of virus maturation. The virus initially assembles at pH 7.6 into a marginally stable 480-Å procapsid formed by 240 copies of a single type of protein subunit. During maturation, which occurs during apoptosis at pH 5.0, electrostatic forces guide subunit trajectories into a robust 410-Å virion that is buttressed by subunit associated molecular switches. We discuss the competing factors in the virus capsid of requiring near-reversible interactions during initial assembly to avoid kinetic traps, while requiring robust stability to survive in the extra-cellular environment. In addition, viruses have a variety of mechanisms to deliver the genome, which must remain off while still inside the infected cell, yet turn on under the proper conditions of infection. We conclude that maturation is the process that provides a solution to these conflicting requirements through a program that is encoded in the procapsid and that leads to stability and infectivity.

We consider Bose-Einstein condensation (BEC) on graphs with transient adjacency matrix. We prove the equivalence of BEC and non-factoriality of the quasi-free state. Moreover, quasi-free states exhibiting BEC decompose into generalized coherent states. We review necessary and sufficient conditions that a quasi-free state is faithful, factor, and pure and quasi-free states are quasi-equivalent, including the papers of Araki and Shiraishi [1], Araki [2], and Araki and Yamagami [3]. Using their formats and results, we prove necessary and sufficient conditions that a generalized coherent state is faithful, factor, and pure and generalized coherent states are quasi-equivalent as well. [ABSTRACT FROM AUTHOR]

It is known that the disordered phase of the classical Ising model on the Caley tree is extreme in some region of the temperature. If one considers the Ising model with competing interactions on the same tree, then about the extremity of the disordered phase there is no any information. In the present paper, we first aiming to analyze the correspondence between Gibbs measures and QMC's on trees. Namely, we establish that states associated with translation invariant Gibbs measures of the model can be seen as diagonal quantum Markov chains on some quasi local algebra. Then as an application of the established correspondence, we study some algebraic property of the disordered phase of the Ising model with competing interactions on the Cayley tree of order two. More exactly, we prove that a state corresponding to the disordered phase is not quasi-equivalent to other states associated with translation invariant Gibbs measures. This result shows how the translation invariant states relate to each other, which is even a new phenomena in the classical setting. To establish the main result we basically employ methods of quantum Markov chains. [ABSTRACT FROM AUTHOR]

The main aim of the present paper is to prove the existence of a phase transition in quantum Markov chain (QMC) scheme for the Ising type models on a Cayley tree. Note that this kind of models do not have one-dimensional analogous, i.e. the considered model persists only on trees. In this paper, we provide a more general construction of forward QMC. In that construction, a QMC is defined as a weak limit of finite volume states with boundary conditions, i.e. QMC depends on the boundary conditions. Our main result states the existence of a phase transition for the Ising model with competing interactions on a Cayley tree of order two. By the phase transition we mean the existence of two distinct QMC which are not quasi-equivalent and their supports do not overlap. We also study some algebraic property of the disordered phase of the model, which is a new phenomena even in a classical setting. [ABSTRACT FROM AUTHOR]

Nudaurelia capensis ω virus (NωV) is a eukaryotic RNA virus that is well suited for the study of virus maturation. The virus initially assembles at pH 7.6 into a marginally stable 480-Å procapsid formed by 240 copies of a single type of protein subunit. During maturation, which occurs during apoptosis at pH 5.0, electrostatic forces guide subunit trajectories into a robust 410-Å virion that is buttressed by subunit associated molecular switches. We discuss the competing factors in the virus capsid of requiring near-reversible interactions during initial assembly to avoid kinetic traps, while requiring robust stability to survive in the extra-cellular environment. In addition, viruses have a variety of mechanisms to deliver the genome, which must remain off while still inside the infected cell, yet turn on under the proper conditions of infection. We conclude that maturation is the process that provides a solution to these conflicting requirements through a program that is encoded in the procapsid and that leads to stability and infectivity. [ABSTRACT FROM AUTHOR]

The capsid of hepatitis B virus (HBV) is a major viral antigen and important diagnostic indicator. HBV capsids have prominent protrusions ('spikes') on their surface and are unique in having either T = 3 or T = 4 icosahedral symmetry. Mouse monoclonal and also human polyclonal antibodies bind either near the spike apices (historically the 'α-determinant') or in the 'floor' regions between them (the 'β-determinant'). Native mass spectrometry (MS) and gas-phase electrophoretic mobility molecular analysis (GEMMA) were used to monitor the titration of HBV capsids with the antigen-binding domain (Fab) of mAb 3120, which has long defined the β-determinant. Both methods readily distinguished Fab binding to the two capsid morphologies and could provide accurate masses and dimensions for these large immune complexes, which range up to ~8 MDa. As such, native MS and GEMMA provide valuable alternatives to a more time-consuming cryo-electron microscopy analysis for preliminary characterisation of virus-antibody complexes. [Figure not available: see fulltext.] [ABSTRACT FROM AUTHOR]

For every pair of inverse systems X, Y in a category A, where Y is cofinite, there exists a complete ultrametric structure on the set pro"-A(X,Y ). The corresponding hom-bifunctor is the internal and invariant Hom of a subcategory, containing tow"-A, in the category of complete metric spaces. Several applications to the shapes (ordinary, coarse and weak) are considered. AMS subject classifications: Primary 55P55; Secondary 54E50. [ABSTRACT FROM AUTHOR]

This is a personal history of my structural studies of icosahedral viruses that evolved from crystallographic studies, to hybrid methods with electron cryo-microscopy and image reconstruction (cryoEM) and then developed further by incorporating a variety of physical methods to augment the high resolution crystallographic studies. It is not meant to be comprehensive, even for my own work, but hopefully provides some perspective on the growth of our understanding of these remarkable biologic assemblies. The goal is to provide a historical perspective for those new to the field and to emphasize the limitations of any one method, even those that provide atomic resolution information about viruses. [ABSTRACT FROM AUTHOR]

Abstract: We investigate the fundamental concept of a closed quantum subgroup of a locally compact quantum group. Two definitions — one due to S. Vaes and one due to S.L. Woronowicz — are analyzed and relations between them discussed. Among many reformulations we prove that the former definition can be phrased in terms of quasi-equivalence of representations of quantum groups while the latter can be related to an old definition of Podleś from the theory of compact quantum groups. The cases of classical groups, duals of classical groups, compact and discrete quantum groups are singled out and equivalence of the two definitions is proved in the relevant context. A deep relationship with the quantum group generalization of the Herz restriction theorem from classical harmonic analysis is also established, in particular, in the course of our analysis we give a new proof of the Herz restriction theorem. [Copyright &y& Elsevier]

We examine virus maturation of selected nonenveloped and enveloped single-stranded RNA viruses, retroviruses, bacteriophages, and herpesviruses. Processes associated with maturation in the RNA viruses range from subtle (nodaviruses and picornaviruses) to dramatic (tetraviruses and togaviruses). The elaborate assembly and maturation pathway of HIV is discussed in contrast to the less sophisticated but highly efficient processes associated with togaviruses. Bacteriophage assembly and maturation are discussed in general terms, with specific examples chosen for emphasis. Finally the herpesviruses are compared with bacteriophages. The data support divergent evolution of nodaviruses, picornaviruses, and tetraviruses from a common ancestor and divergent evolution of alphaviruses and flaviviruses from a common ancestor. Likewise, bacteriophages and herpesviruses almost certainly share a common ancestor in their evolution. Comparing all the viruses, we conclude that maturation is a convergent process that is required to solve conflicting requirements in biological dynamics and function. [ABSTRACT FROM AUTHOR]

Effective antiviral agents are difficult to develop because of the close relationship between the cell biology of the virus and host. However, viral capsid maturation, the in vivo process where the particle transitions from a noninfectious provirion to an infectious virion, is an ideal process to interrupt because the provirion is usually fragile and the conversion to the virion often involves large conformational changes and autocatalytic chemistry that can be hampered by small molecules. The Nudaurelia capensis ω virus (NωV) is one of the few eukaryotic viruses where this process can be investigated in vitro with a variety of biophysical methods, allowing fundamental chemical and structural principles of the maturation to be established. It has a T = 4 quasi-equivalent capsid with a dramatic maturation pathway that includes a particle size reduction of 100 A and an autocatalytic cleavage. Here we use cryo-EM and difference maps, computed at three time points following maturation initiation, to show that regions of NoN sub-unit folding are maturation dependent and occur at rates deter- mined by their quasi-equivalent position in the capsid, explaining the unusual kinetics of the maturation cleavage. This study shows that folding is rapid and peptide chain self-cleavage occurs early for subunits adjacent to 3-fold and 5-fold icosahedral symmetry elements and that folding is slower in regions where molecular switches are required for the formation of the proper interfacial contacts. The results connect viral maturation to the well-studied assembly-dependent folding that occurs in the formation of cellular complexes. [ABSTRACT FROM AUTHOR]

• 1.80-Å structure of the potato leafroll virus coat protein (PLRV68-208). • PLRV68-208 crystallizes in flat sheets stabilized by hexameric interactions. • PLRV68-208 sheets exhibit 2-, 3-, and 6-fold non-crystallographic symmetry. • Structural comparison with virus-like particles gives insights into capsid assembly. Luteoviruses, poleroviruses, and enamoviruses are insect-transmitted, agricultural pathogens that infect a wide array of plants, including staple food crops. Previous cryo-electron microscopy studies of virus-like particles show that luteovirid viral capsids are built from a structural coat protein that organizes with T = 3 icosahedral symmetry. Here, we present the crystal structure of a truncated version of the coat protein monomer from potato leafroll virus at 1.80-Å resolution. In the crystal lattice, monomers pack into flat sheets that preserve the two-fold and three-fold axes of icosahedral symmetry and show minimal structural deviations when compared to the full-length subunits of the assembled virus-like particle. These observations have important implications in viral assembly and maturation and suggest that the CP N-terminus and its interactions with RNA play an important role in generating capsid curvature. [ABSTRACT FROM AUTHOR]

In 1962, Donald Caspar and Aaron Klug published their classic theory of virus structure. They developed their theory with an explicit analogy between spherical viruses and Buckminster Fuller's geodesic domes. In this paper, I use the spherical virus-geodesic dome case to develop an account of analogy and deductive analogical inference based on the notion of an isomorphism. I also consider under what conditions there is a good reason to claim an experimentally untested analogy is plausible. [ABSTRACT FROM AUTHOR]

To investigate the range of antigenic variation of HBV capsids, we have characterized the epitopes for two anti-capsid antibodies by cryo-electron microscopy and image reconstruction of Fab-labeled capsids to ∼10Å resolution followed by molecular modeling. Both antibodies engage residues on the protruding spikes but their epitopes and binding orientations differ. Steric interference effects limit maximum binding to ∼50% average occupancy in each case. However, the occupancies of the two copies of a given epitope that are present on a single spike differ, reflecting subtle distinctions in structure and hence, binding affinity, arising from quasi-equivalence. The epitope for mAb88 is conformational but continuous, consisting of a loop–helix motif (residues 77–87) on one of the two polypeptide chains in the spike. In contrast, the epitope for mAb842, like most conformational epitopes, is discontinuous, consisting of a loop on one polypeptide chain (residues 74–78) combined with a loop–helix element (residues 78–83) on the other. The epitope of mAb842 is essentially identical with that previously mapped for mAb F11A4, although the binding orientations of the two monoclonal antibodies (mAbs) differ, as do their affinities measured by surface plasmon resonance. From the number of monoclonals (six) whose binding had to be characterized to give the first duplicate epitope, we estimate the total number of core antigen (cAg) epitopes to be of the order of 20. Given that different antibodies may share the same epitope, the potential number of distinct anti-cAg clones should be considerably higher. The observation that the large majority of cAg epitopes are conformational reflects the relative dimensions of a Fab (large) and the small size and close packing of the motifs that are exposed and accessible on the capsid surface. [Copyright &y& Elsevier]

Large-scale reorganization of protein interactions characterizes many biological processes, yet few systems are accessible to biophysical studies that display this property. The capsid protein of Nudaurelia capensis ω Virus (NωV) has previously been characterized in two dramatically different T = 4 quasi-equivalent assembly states when expressed as virus-like particles (VLPs) in a baculovirus system. The procapsid (pH 7), is round, porous, and approximately 450 A˚ in diameter. It converts, in vitro, to the capsid form at pH 5 and the capsid is sealed shut, shaped like an icosahedron, has a maximum diameter of 410 A˚ and undergoes an autocatalytic cleavage at residue 570. Residues 571–644, the γ peptide, remain associated with the particle and are partially ordered. The interconversion of these states has been previously studied by solution X-ray scattering, electron cryo microscopy (CryoEM), and site-directed mutagenesis. The particle structures appear equivalent in authentic virions and the low pH form of the expressed and assembled protein. Previously, and before the discovery of the multiple morphological forms of the VLPs, we reported the X-ray structure of authentic NωV at 2.8 A˚ resolution. These coordinates defined the fold of the protein but were not refined at the time because of technical issues associated with the approximately 2.5 million reflection data set. We now report the refined, authentic virus structure that has added 29 residues to the original model and allows the description of the chemistry of molecular switching for T = 4 capsid formation and the multiple morphological forms. The amino and carboxy termini are internal, predominantly helical, and disordered to different degrees in the four structurally independent subunits; however, the refined structure shows significantly more ordered residues in this region, particularly at the amino end of the B subunit that is now seen to invade space occupied by the A subunits. These additional residues revealed a previously unnoticed strong interaction between the pentameric, γ peptide helices of the A and B subunits that are largely proximal to the quasi-6-fold axes. One C-terminal helix is ordered in the C and D subunits and stabilizes a flat interaction in two interfaces between the protein monomers while the other, quasi-equivalent, interactions are bent. As this helix is arginine rich, the comparable, disordered region in the A and B subunits probably interacts with RNA. One of the subunit–subunit interfaces has an unusual arrangement of carboxylate side chains. Based on this observation, we propose a mechanism for the control of the pH-dependent transitions of the virus particle. [Copyright &y& Elsevier]

The HK97 bacteriophage capsid is a unique example of macromolecular catenanes: interlocked rings of covalently attached protein subunits. The chain mail organization of the subunits stabilizes a particle in which the maximum thickness of the protein shell is 18 A˚ and the maximum diameter is 550 A˚. The electron density has the appearance of a balloon illustrating the extraordinary strength conferred by the unique subunit organization. The refined structure shows novel qualities of the HK97 shell protein, gp5 that, together with the protease gp4, guides the assembly and maturation of the virion. Although gp5 forms hexamers and pentamers and the subunits exist in different structural environments, the tertiary structures of the seven protein molecules in the viral asymmetric unit are closely similar. The interactions of the subunits in the shell are exceptionally complex with each subunit interacting with nine other subunits. The interactions of the N-terminus released after gp5 cleavage appear important for organization of the loops that become crosslinked to the core of a neighboring subunit at the maturation. A comparison with a model of the Prohead II structure revealed that the surfaces of non-covalent contact between the monomers that build up hexamers/pentamers are completely redefined during maturation. [Copyright &y& Elsevier]

The structural protein VP6 of rotavirus, an important pathogen responsible for severe gastroenteritis in children, forms the middle layer in the triple-layered viral capsid. Here we present the crystal structure of VP6 determined to 2 Å resolution and describe its interactions with other capsid proteins by fitting the atomic model into electron cryomicroscopic reconstructions of viral particles. VP6, which forms a tight trimer, has two distinct domains: a distal β-barrel domain and a proximal α-helical domain, which interact with the outer and inner layer of the virion, respectively. The overall fold is similar to that of protein VP7 from bluetongue virus, with the subunits wrapping about a central 3-fold axis. A distinguishing feature of the VP6 trimer is a central Zn2+ ion located on the 3-fold molecular axis. The crude atomic model of the middle layer derived from the fit shows that quasi-equivalence is only partially obeyed by VP6 in the T = 13 middle layer and suggests a model for the assembly of the 260 VP6 trimers onto the T = 1 viral inner layer. [ABSTRACT FROM AUTHOR]