Cauliflower mosaic virus: a 420 subunit (T = 7), multilayer structure

Protein Nanoparticles as Vaccine Platforms for Human and Zoonotic Viruses

Vaccines are one of the most effective medical interventions, playing a pivotal role in treating infectious diseases. Although traditional vaccines comprise killed, inactivated, or live-attenuated pathogens that have resulted in protective immune responses, the negative consequences of their administration have been well appreciated. Modern vaccines have evolved to contain purified antigenic subunits, epitopes, or antigen-encoding mRNAs, rendering them relatively safe. However, reduced humoral and cellular responses pose major challenges to these subunit vaccines. Protein nanoparticle (PNP)-based vaccines have garnered substantial interest in recent years for their ability to present a repetitive array of antigens for improving immunogenicity and enhancing protective responses. Discovery and characterisation of naturally occurring PNPs from various living organisms such as bacteria, archaea, viruses, insects, and eukaryotes, as well as computationally designed structures and approaches to link antigens to the PNPs, have paved the way for unprecedented advances in the field of vaccine technology. In this review, we focus on some of the widely used naturally occurring and optimally designed PNPs for their suitability as promising vaccine platforms for displaying native-like antigens from human viral pathogens for protective immune responses. Such platforms hold great promise in combating emerging and re-emerging infectious viral diseases and enhancing vaccine efficacy and safety.

Cauliflower mosaic virus: Virus-host interactions and its uses in biotechnology and medicine

Cauliflower mosaic virus (CaMV) was the first discovered plant virus with genomic DNA that uses reverse transcriptase for replication. The CaMV 35S promoter is a constitutive promoter and thus, an attractive driver of gene expression in plant biotechnology. It is used in most transgenic crops to activate foreign genes which have been artificially inserted into the host plant. In the last century, producing food for the world's population while preserving the environment and human health is the main topic of agriculture. The damage caused by viral diseases has a significant negative economic impact on agriculture, and disease control is based on two strategies: immunization and prevention to contain virus spread, so correct identification of plant viruses is important for disease management. Here, we discuss CaMV from different aspects: taxonomy, structure and genome, host plants and symptoms, transmission and pathogenicity, prevention, control and application in biotechnology as well as in medicine. Also, we calculated the CAI index for three ORFs IV, V, and VI of the CaMV virus in host plants, the results of which can be used in the discussion of gene transfer or antibody production to identify the CaMV.

Enhancing Capsid Proteins Capacity in Plant Virus-Vector Interactions and Virus Transmission

Vector transmission of plant viruses is basically of two types that depend on the virus helper component proteins or the capsid proteins. A number of plant viruses belonging to disparate groups have developed unusual capsid proteins providing for interactions with the vector. Thus, cauliflower mosaic virus, a plant pararetrovirus, employs a virion associated p3 protein, the major capsid protein, and a helper component for the semi-persistent transmission by aphids. Benyviruses encode a capsid protein readthrough domain (CP-RTD) located at one end of the rod-like helical particle, which serves for the virus transmission by soil fungal zoospores. Likewise, the CP-RTD, being a minor component of the luteovirus icosahedral virions, provides for persistent, circulative aphid transmission. Closteroviruses encode several CPs and virion-associated proteins that form the filamentous helical particles and mediate transmission by aphid, whitefly, or mealybug vectors. The variable strategies of transmission and evolutionary ‘inventions’ of the unusual capsid proteins of plant RNA viruses are discussed.

Structural Insight into CVB3-VLP Non-Adjuvanted Vaccine

Coxsackievirus B (CVB) enteroviruses are common pathogens that can cause acute and chronic myocarditis, dilated cardiomyopathy, aseptic meningitis, and they are hypothesized to be a causal factor in type 1 diabetes. The licensed enterovirus vaccines and those currently in clinical development are traditional inactivated or live attenuated vaccines. Even though these vaccines work well in the prevention of enterovirus diseases, new vaccine technologies, like virus-like particles (VLPs), can offer important advantages in the manufacturing and epitope engineering. We have previously produced VLPs for CVB3 and CVB1 in insect cells. Here, we describe the production of CVB3-VLPs with enhanced production yield and purity using an improved purification method consisting of tangential flow filtration and ion exchange chromatography, which is compatible with industrial scale production. We also resolved the CVB3-VLP structure by Cryo-Electron Microscopy imaging and single particle reconstruction. The VLP diameter is 30.9 nm on average, and it is similar to Coxsackievirus A VLPs and the expanded enterovirus cell-entry intermediate (the 135s particle), which is ~2 nm larger than the mature virion. High neutralizing and total IgG antibody levels, the latter being a predominantly Th2 type (IgG1) phenotype, were detected in C57BL/6J mice immunized with non-adjuvanted CVB3-VLP vaccine. The structural and immunogenic data presented here indicate the potential of this improved methodology to produce highly immunogenic enterovirus VLP-vaccines in the future.

Plant virus particles with various shapes as potential adjuvants

Plant viruses are biologically safe for mammals and can be successfully used as a carrier/platform to present foreign epitopes in the course of creating novel putative vaccines. However, there is mounting evidence that plant viruses, their virus-like and structurally modified particles may also have an immunopotentiating effect on antigens not bound with their surface covalently. Here, we present data on the adjuvant properties of plant viruses with various shapes (Tobacco mosaic virus, TMV; Potato virus X, PVX; Cauliflower mosaic virus, CaMV; Bean mild mosaic virus, BMMV) and structurally modified TMV spherical particles (SPs). We have analysed the effectiveness of immune response to individual model antigens (ovalbumin, OVA/hen egg lysozyme, HEL) and to OVA/HEL in compositions with plant viruses/SPs, and have shown that CaMV, TMV and SPs can effectively induce total IgG titers to model antigen. Some intriguing data were obtained when analysing the immune response to the plant viruses/SPs themselves. Strong immunity was induced to CaMV, BMMV and PVX, whereas TMV and SPs stimulated considerably lower self-IgG titers. Our results provide new insights into the immunopotentiating properties of plant viruses and can be useful in devising adjuvants based on plant viruses.

Comparative Study of Non-Enveloped Icosahedral Viruses Size

Now, as before, transmission electron microscopy (TEM) is a widely used technique for the determination of virions size. In some studies, dynamic light scattering (DLS) has also been applied for this purpose. Data obtained by different authors and using different methods could vary significantly. The process of TEM sample preparation involves drying on the substrate, which can cause virions to undergo morphology changes. Therefore, other techniques should be used for measurements of virions size in liquid, (i.e. under conditions closer to native). DLS and nanoparticle tracking analysis (NTA) provide supplementary data about the virions hydrodynamic diameter and aggregation state in liquid. In contrast to DLS, NTA data have a higher resolution and also are less sensitive to minor admixtures. In the present work, the size of non-enveloped icosahedral viruses of different nature was analyzed by TEM, DLS and NTA: the viruses used were the encephalomyocarditis virus (animal virus), and cauliflower mosaic virus, brome mosaic virus and bean mild mosaic virus (plant viruses). The same, freshly purified, samples of each virus were used for analysis using the different techniques. The results were compared with earlier published data and description databases. DLS data about the hydrodynamic diameter of bean mild mosaic virus, and NTA data for all examined viruses, were obtained for the first time. For all virus samples, the values of size obtained by TEM were less than virions sizes determined by DLS and NTA. The contribution of the electrical double layer (EDL) in virions hydrodynamic diameter was evaluated. DLS and NTA data adjusted for EDL thickness were in better agreement with TEM results.

Plant pararetroviruses: replication and expression

True retroviruses are not known in plants; however, plant pararetroviruses (caulimoviridae) share many retroviral properties, replicating by transcription in the nucleus followed by reverse transcription in the cytoplasm. Pararetroviruses have circular DNA genomes that do not integrate into the host genome, and display several unique expression strategies. Typical of plant pararetroviral pregenomic RNA is a highly structured leader of about 600nt long that is bypassed by scanning ribosomes. Caulimoviruses and Soymoviruses have a further interesting translation mechanism: at least six of the seven open reading frames are translated via polycistronic translation mediated by a specific transactivator (TAV), which modifies the translation complex. TAV also forms large intracellular inclusion bodies, which are the site of translation and virus assembly.

Host cell processes to accomplish mechanical and non-circulative virus transmission

Mechanical vector-less transmission of viruses, as well as vector-mediated non-circulative virus transmission, where the virus attaches only to the exterior of the vector during the passage to a new host, are apparently simple processes: the viruses are carried along with the wind, the food or by the vector to a new host. We discuss here, using the examples of the non-circulatively transmitted Cauliflower mosaic virus that binds to its aphid vector's exterior mouthparts, and that of the mechanically (during feeding activity) transmitted Autographa californica multicapsid nucleopolyhedrovirus, that transmission of these viruses is not so simple as previously thought. Rather, these viruses prepare their transmission carefully and long before the actual acquisition event. Host-virus interactions play a pivotal and specialised role in the future encounter with the vector or the new host. This ensures optimal propagation and enlarges the tremendous bottleneck transmission presents for viruses and other pathogens.

Three-dimensional reconstruction of Heterocapsa circularisquama RNA virus by electron cryo-microscopy

Heterocapsa circularisquama RNA virus is a non-enveloped icosahedral ssRNA virus infectious to the harmful bloom-forming dinoflagellate, H. circularisquama, and which is assumed to be the major natural agent controlling the host population. The viral capsid is constructed from a single gene product. Electron cryo-microscopy revealed that the virus has a diameter of 34 nm and T = 3 symmetry. The 180 quasi-equivalent monomers have an unusual arrangement in that each monomer contributes to a 'bump' on the surface of the protein. Though the capsid protein probably has the classic 'jelly roll' β-sandwich fold, this is a new packing arrangement and is distantly related to the other positive-sense ssRNA virus capsid proteins. The handedness of the structure has been determined by a novel method involving high resolution scanning electron microscopy of the negatively stained viruses and secondary electron detection.

Zernike phase plate cryoelectron microscopy facilitates single particle analysis of unstained asymmetric protein complexes

Single particle reconstruction from cryoelectron microscopy images, though emerging as a powerful means in structural biology, is faced with challenges as applied to asymmetric proteins smaller than megadaltons due to low contrast. Zernike phase plate can improve the contrast by restoring the microscope contrast transfer function. Here, by exploiting simulated Zernike and conventional defocused cryoelectron microscope images with noise characteristics comparable to those of experimental data, we quantified the efficiencies of the steps in single particle analysis of ice-embedded RNA polymerase II (500 kDa), transferrin receptor complex (290 kDa), and T7 RNA polymerase lysozyme (100 kDa). Our results show Zernike phase plate imaging is more effective as to particle identification and also sorting of orientations, conformations, and compositions. Moreover, our analysis on image alignment indicates that Zernike phase plate can, in principle, reduce the number of particles required to attain near atomic resolution by 10-100 fold for proteins between 100 kDa and 500 kDa.

Structural insights into the molecular mechanisms of cauliflower mosaic virus transmission by its insect vector

Cauliflower mosaic virus (CaMV) is transmitted from plant to plant through a seemingly simple interaction with insect vectors. This process involves an aphid receptor and two viral proteins, P2 and P3. P2 binds to both the aphid receptor and P3, itself tightly associated with the virus particle, with the ensemble forming a transmissible viral complex. Here, we describe the conformations of both unliganded CaMV P3 protein and its virion-associated form. X-ray crystallography revealed that the N-terminal domain of unliganded P3 is a tetrameric parallel coiled coil with a unique organization showing two successive four-stranded subdomains with opposite supercoiling handedness stabilized by a ring of interchain disulfide bridges. A structural model of virus-liganded P3 proteins, folding as an antiparallel coiled-coil network coating the virus surface, was derived from molecular modeling. Our results highlight the structural and biological versatility of this coiled-coil structure and provide new insights into the molecular mechanisms involved in CaMV acquisition and transmission by the insect vector.

Crystallization and preliminary X-ray diffraction analysis of recombinant hepatitis E virus-like particle

Hepatitis E virus (HEV) accounts for the majority of enterically transmitted hepatitis infections worldwide. Currently, there is no specific treatment for or vaccine against HEV. The major structural protein is derived from open reading frame (ORF) 2 of the viral genome. A potential oral vaccine is provided by the virus-like particles formed by a protein construct of partial ORF3 protein (residue 70-123) fused to the N-terminus of the ORF2 protein (residues 112-608). Single crystals obtained by the hanging-drop vapour-diffusion method at 293 K diffract X-rays to 8.3 A resolution. The crystals belong to space group P2(1)2(1)2(1), with unit-cell parameters a = 337, b = 343, c = 346 A, alpha = beta = gamma = 90 degrees , and contain one particle per asymmetric unit.

Ab initio random model method facilitates 3D reconstruction of icosahedral particles

Model-based, three-dimensional (3D) image reconstruction procedures require a starting model to initiate data analysis. We have designed an ab initio method, which we call the random model (RM) method, that automatically generates models to initiate structural analysis of icosahedral viruses imaged by cryo-electron microscopy. The robustness of the RM procedure was demonstrated on experimental sets of images for five representative viruses. The RM method also provides a straightforward way to generate unbiased starting models to derive independent 3D reconstructions and obtain a more reliable assessment of resolution. The fundamental scheme embodied in the RM method should be relatively easy to integrate into other icosahedral software packages.

Nuclear import and export of plant virus proteins and genomes

SUMMARY Nuclear import and export are crucial processes for any eukaryotic cell, as they govern substrate exchange between the nucleus and the cytoplasm. Proteins involved in the nuclear transport network are generally conserved among eukaryotes, from yeast and fungi to animals and plants. Various pathogens, including some plant viruses, need to enter the host nucleus to gain access to its replication machinery or to integrate their DNA into the host genome; the newly replicated viral genomes then need to exit the nucleus to spread between host cells. To gain the ability to enter and exit the nucleus, these pathogens encode proteins that recognize cellular nuclear transport receptors and utilize the host's nuclear import and export pathways. Here, we review and discuss our current knowledge about the molecular mechanisms by which plant viruses find their way into and out of the host cell nucleus.

A coiled-coil interaction mediates cauliflower mosaic virus cell-to-cell movement

The function of the virion-associated protein (VAP) of cauliflower mosaic virus (CaMV) has long been only poorly understood. VAP is associated with the virion but is dispensable for virus morphogenesis and replication. It mediates virus transmission by aphids through simultaneous interaction with both the aphid transmission factor and the virion. However, although insect transmission is not fundamental to CaMV survival, VAP is indispensable for spreading the virus infection within the host plant. We used a GST pull-down technique to demonstrate that VAP interacts with the viral movement protein through coiled-coil domains and surface plasmon resonance to measure the interaction kinetics. We mapped the movement protein coiled-coil to the C terminus of the protein and proved that it self-assembles as a trimer. Immunogold labeling/electron microscopy revealed that the VAP and viral movement protein colocalize on CaMV particles within plasmodesmata. These results highlight the multifunctional potential of the VAP protein conferred by its efficient coiled-coil interaction system and show a plant virus possessing a surface-exposed protein (VAP) mediating viral entry into host cells.

Structure of the Mature P3-virus Particle Complex of Cauliflower Mosaic Virus Revealed by Cryo-electron Microscopy

The cauliflower mosaic virus (CaMV) has an icosahedral capsid composed of the viral protein P4. The viral product P3 is a multifunctional protein closely associated with the virus particle within host cells. The best-characterized function of P3 is its implication in CaMV plant-to-plant transmission by aphid vectors, involving a P3-virion complex. In this transmission process, the viral protein P2 attaches to virion-bound P3, and creates a molecular bridge between the virus and a putative receptor in the aphid's stylets. Recently, the virion-bound P3 has been suggested to participate in cell-to-cell or long-distance movement of CaMV within the host plant. Thus, as new data accumulate, the importance of the P3-virion complex during the virus life-cycle is becoming more and more evident. To provide a first insight into the knowledge of the transmission process of the virus, we determined the 3D structures of native and P3-decorated virions by cryo-electron microscopy and computer image processing. By difference mapping and biochemical analysis, we show that P3 forms a network around the capsomers and we propose a structural model for the binding of P3 to CaMV capsid in which its C terminus is anchored deeply in the inner shell of the virion, while the N-terminal extremity is facing out of the CaMV capsid, forming dimers by coiled-coil interactions. Our results combined with existing data reinforce the hypothesis that this coiled-coil N-terminal region of P3 could coordinate several functions during the virus life-cycle, such as cell-to-cell movement and aphid-transmission.

Three-dimensional structure of penicillium chrysogenum virus: a double-stranded RNA virus with a genuine T=1 capsid

Although double-stranded (ds) RNA viruses are a rather diverse group, they share general architectural principles and numerous functional features. All dsRNA viruses, from the mammalian reoviruses to the bacteriophage phi6, including fungal viruses, share a specialized capsid involved in transcription and replication of the dsRNA genome, and release of the viral plus strand RNA. This ubiquitous capsid consists of 120 protein subunits in a so-called T=2 organization. The stringent requirements of dsRNA metabolism may explain the similarities observed in capsid architecture among a broad spectrum of dsRNA viruses. We have used cryo-electron microscopy combined with three-dimensional reconstruction techniques and complementary biophysical techniques, to determine the structure at 26A resolution of the Penicillium chrysogenum virus (PcV) capsid. In contrast to all previous studies of dsRNA viruses, PcV capsid is an authentic T=1 capsid with 60 equivalent protein subunits. This T=1 capsid is built with the largest structural protein (110 kDa). Structural comparison between viral particles and capsids devoid of RNA show changes along the inner surface of the capsid, mostly located around the icosahedral 5 and 3-fold axis. Considering that there may be numerous interactions between the inner surface of the protein shell and the underlying RNA, the genome could have an important role in the conformation of the structural subunits. The empty capsid structure suggests a mechanism for transcript release from actively transcribing particles. Furthermore, sequence analysis of the PcV coat protein revealed that both halves of the protein share numerous regions of similar amino acid residues. These results open new perspectives when considering the structural organization of dsRNA virus capsids.

Acid-induced movements in the glycoprotein shell of an alphavirus turn the spikes into membrane fusion mode

In the icosahedral (T = 4) Semliki Forest virus, the envelope protomers, i.e. E1-E2 heterodimers, make one-to-one interactions with capsid proteins below the viral lipid bilayer, transverse the membrane and form an external glycoprotein shell with projections. The shell is organized by protomer domains interacting as hexamers and pentamers around shell openings at icosahedral 2- and 5-fold axes, respectively, and the projections by other domains associating as trimers at 3- and quasi 3-fold axes. We show here, using cryo- electron microscopy, that low pH, as occurs in the endosomes during virus uptake, results in the relaxation of protomer interactions around the 2- and the 5-fold axes in the shell, and movement of protomers towards 3- and quasi 3-fold axes in a way that reciprocally relocates their putative E1 and E2 domains. This seemed to be facilitated by a trimerization of transmembrane segments at the same axes. The alterations observed help to explain several key features of the spike-mediated membrane fusion reaction, including shell dissolution, heterodimer dissociation, fusion peptide exposure and E1 homotrimerization.

Regulated nuclear targeting of cauliflower mosaic virus

The mature cauliflower mosaic virus (CaMV) capsid protein (CP), if expressed in the absence of other viral proteins, is transported into the plant cell nucleus by the action of a nuclear localization signal (NLS) close to the N terminus. In contrast, virus particles do not enter the nucleus, but dock at the nuclear membrane, a process inhibited by anti-NLS antibodies or by GTP gamma S, and apparently mediated by interaction of CP with host importin alpha. The very acidic N-terminal extension of the viral CP precursor inhibits nuclear targeting of the protein and hence the precursor is localized in the cytoplasm. We hypothesize that this provides a control mechanism which ensures that the CP precursor is used for virus assembly in the cytoplasm and that only mature virus particles reach the nuclear pore.

Degradation signals within both terminal domains of the cauliflower mosaic virus capsid protein precursor

Targeted protein degradation plays an important regulatory role in the cell, but only a few protein degradation signals have been characterized in plants. Here we describe three instability determinants in the termini of the cauliflower mosaic virus (CaMV) capsid protein precursor, of which one is still present in the mature capsid protein p44. A modified ubiquitin protein reference technique was used to show that these motifs are still active when fused to a heterologous reporter gene. The N-terminus of p44 contains a degradation motif characterized by proline, glutamate, aspartate, serine and threonine residues (PEST), which can be inactivated by mutation of three glutamic acid residues to alanines. The signals from the precursor do not correspond to known degradation motifs, although they confer high instability on proteins expressed in plant protoplasts. All three instability determinants were also active in mammalian cells. The PEST signal had a significantly higher degradation activity in HeLa cells, whereas the precursor signals were less active. Inhibition studies suggest that only the signal within the N-terminus of the precursor is targeting the proteasome in plants. This implies that the other two signals may target a novel degradation pathway.

The product of ORF III in cauliflower mosaic virus interacts with the viral coat protein through its C-terminal proline rich domain

Using the yeast two-hybrid system, we show that the ORF III product of cauliflower mosaic virus (pIII) interacts through its C-terminus with the viral coat protein. The last five amino acids of pIII were essential for the interaction and virus infectivity. Deletion of the last three amino acids or the mutation F129A decreased the strength of the interaction by 90%. We further show that pIII is closely associated with virus particles found in the inclusion bodies of infected plants but not in viral particles released from the inclusion bodies by urea treatment.

Interaction between the open reading frame III product and the coat protein is required for transmission of cauliflower mosaic virus by aphids

Transmission of cauliflower mosaic virus (CaMV) by aphids requires two viral nonstructural proteins, the open reading frame (ORF) II and ORF III products (P2 and P3). An interaction between a C-terminal domain of P2 and an N-terminal domain of P3 is essential for transmission. Purified particles of CaMV are efficiently transmitted only if aphids, previously fed a P2-containing solution, are allowed to acquire a preincubated mixture of P3 and virions in a second feed, thus suggesting a direct interaction between P3 and coat protein. Herein we demonstrate that P3 directly interacts with purified viral particles and unassembled coat protein without the need for any other factor and that P3 mediates the association of P2 with purified virus particles. The interaction domain of P3 is located in its C-terminal half, downstream of the P3-P2 interaction domain but overlapping a region which binds nucleic acids. Mutagenesis of P3 which interferes with the interaction between P3 and virions is correlated with the loss of transmission by aphids. Taken together, our results demonstrate that P3 plays a crucial role in the formation of the CaMV transmissible complex by serving as a bridge between P2 and virus particles.

Reconstruction principles of icosahedral virus structure determination using electron cryomicroscopy

Electron cryomicroscopy is a useful tool for studying the three-dimensional structure of icosahedral viruses. This review is intended to provide beginners with an understanding of icosahedral virus structure determination focusing on the data processing aspects. We begin with an overview of the entire structure determination process and a brief summary of the sample preparation and imaging aspects. Next, we provide detailed descriptions of each data processing step leading to three-dimensional reconstruction, including application of image corrections, resolution assessment, and structure visualization. To aid in understanding this reconstruction process we provide a variety of illustrative examples. Last, we summarize future prospects for icosahedral virus structural studies.

Membrane proteins organize a symmetrical virus

Alphaviruses are enveloped icosahedral viruses that mature by budding at the plasma membrane. According to a prevailing model maturation is driven by binding of membrane protein spikes to a preformed nucleocapsid (NC). The T = 4 geometry of the membrane is thought to be imposed by the NC through one-to-one interactions between spike protomers and capsid proteins (CPs). This model is challenged here by a Semliki Forest virus capsid gene mutant. Its CPs cannot assemble into NCs, or its intermediate structures, due to defective CP-CP interactions. Nevertheless, it can use its horizontal spike-spike interactions on membrane surface and vertical spike-CP interactions to make a particle with correct geometry and protein stoichiometry. Thus, our results highlight the direct role of membrane proteins in organizing the icosahedral conformation of alphaviruses.

Phytoreovirus T = 1 core plays critical roles in organizing the outer capsid of T = 13 quasi-equivalence

The structures of the double-shelled rice dwarf virus and of its single-shell core have been determined by cryoelectron microscopy and image reconstruction. The core carries a prominent density located at each of the icosahedral faces of its T = 1 lattice. These protrusions are formed by outer shell trimers, tightly inserted at the threefold positions of the core. Such configuration of the core may guide the assembly of the outer shell, aided by lateral interactions between its subunits, into a T = 13 lattice. The organization of the phytoreovirus capsid elucidates for the first time a general model for assembling two unique T numbers of quasi-equivalence.

"Local rules" theory applied to polyomavirus polymorphic capsid assemblies

The papovaviruses are nonenveloped dsDNA viruses whose capsids are characterized by a non-quasi-equivalent bonding pattern in which 72 pentameric capsomeres occupy positions having either five or six neighboring capsomeres. The local rules theory of Berger et al. (1994, Proc. Natl. Acad. Sci. USA, 91, 7732-7736), previously developed to explain aspects of icosahedral capsid assembly, has been applied to the papovavirus geometry. Local rules describe capsid symmetry patterns in terms of the local interactions of assembly units, such as coat proteins or capsomeres. Polymorphic assemblies, including T = 1 icosahedral, dodecahedral, spiral, and tubular structures of the polyomavirus VP1 protein, can be induced by specific mutations or changes in the solvent conditions during in vitro assembly of the recombinant coat protein. Local rules models were developed to model the wild-type capsid and several polymorphic assemblies. Some assemblies corresponded to structures modeled by small deviations from wild-type local rules. We conclude that aspects of polyomavirus assembly are consistent with local rules models, although they do not explain all polymorphisms. These results may provide insights into the nature of papovavirus assembly, constraints on assembly pathways, and strategies for disrupting assembly.

Distinct cellular receptor interactions in poliovirus and rhinoviruses

Receptor binding to human poliovirus type 1 (PV1/M) and the major group of human rhinoviruses (HRV) was studied comparatively to uncover the evolution of receptor recognition in picornaviruses. Surface plas- mon resonance showed receptor binding to PV1/M with faster association and dissociation rates than to HRV3 and HRV16, two serotypes that have similar binding kinetics. The faster rate for receptor association to PV1/M suggested a relatively more accessible binding site. Thermodynamics for receptor binding to the viruses and assays for receptor-mediated virus uncoating showed a more disruptive receptor interaction with PV1/M than with HRV3 or HRV16. Cryo-electron microscopy and image reconstruction of receptor-PV1/M complexes revealed receptor binding to the 'wall' of surface protrusions surrounding the 'canyon', a depressive surface in the capsid where the rhinovirus receptor binds. These data reveal more exposed receptor-binding sites in poliovirus than rhinoviruses, which are less protected from immune surveillance but more suited for receptor-mediated virus uncoating and entry at the cell surface.

The rice tungro bacilliform virus gene II product interacts with the coat protein domain of the viral gene III polyprotein

Rice tungro bacilliform virus (RTBV) is a plant pararetrovirus whose DNA genome contains four genes encoding three proteins and a large polyprotein. The function of most of the viral proteins is still unknown. To investigate the role of the gene II product (P2), we searched for interactions between this protein and other RTBV proteins. P2 was shown to interact with the coat protein (CP) domain of the viral gene III polyprotein (P3) both in the yeast two-hybrid system and in vitro. Domains involved in the P2-CP association have been identified and mapped on both proteins. To determine the importance of this interaction for viral multiplication, the infectivity of RTBV gene II mutants was investigated by agroinoculation of rice plants. The results showed that virus viability correlates with the ability of P2 to interact with the CP domain of P3. This study suggests that P2 could participate in RTBV capsid assembly.

Recombinant hepatitis E capsid protein self-assembles into a dual-domain T = 1 particle presenting native virus epitopes

The three-dimensional structure of a self-assembled, recombinant hepatitis E virus particle has been solved to 22-A resolution by cryo-electron microscopy and three-dimensional image reconstruction. The single subunit of 50 kDa is derived from a truncated version of the open reading frame-2 gene of the virus expressed in a baculovirus system. This is the first structure of a T = 1 particle with protruding dimers at the icosahedral two-fold axes solved by cryo-electron microscopy. The protein shell of these hollow particles extends from a radius of 50 A outward to a radius of 135 A. In the reconstruction, the capsid is dominated by dimers that define the 30 morphological units. The outer domain of the homodimer forms a protrusion, which corresponds to the spike-like density seen in the cryo-electron micrograph. This particle retains native virus epitopes, suggesting its potential value as a vaccine.

Adding the third dimension to virus life cycles: three-dimensional reconstruction of icosahedral viruses from cryo-electron micrographs

Viruses are cellular parasites. The linkage between viral and host functions makes the study of a viral life cycle an important key to cellular functions. A deeper understanding of many aspects of viral life cycles has emerged from coordinated molecular and structural studies carried out with a wide range of viral pathogens. Structural studies of viruses by means of cryo-electron microscopy and three-dimensional image reconstruction methods have grown explosively in the last decade. Here we review the use of cryo-electron microscopy for the determination of the structures of a number of icosahedral viruses. These studies span more than 20 virus families. Representative examples illustrate the use of moderate- to low-resolution (7- to 35-A) structural analyses to illuminate functional aspects of viral life cycles including host recognition, viral attachment, entry, genome release, viral transcription, translation, proassembly, maturation, release, and transmission, as well as mechanisms of host defense. The success of cryo-electron microscopy in combination with three-dimensional image reconstruction for icosahedral viruses provides a firm foundation for future explorations of more-complex viral pathogens, including the vast number that are nonspherical or nonsymmetrical.

Nuclear targeting of the cauliflower mosaic virus coat protein

The entry of the viral genomic DNA of cauliflower mosaic virus into the nucleus is a critical step of viral infection. We have shown by transient expression in plant protoplasts that the viral coat protein (CP), which is processed from the product of open reading frame IV, contains an N-terminal nuclear localization signal (NLS). The NLS is exposed on the surface of the virion and is thus available for interaction with a putative NLS receptor. Phosphorylation of the matured CP did not influence the nuclear localization of the protein but improved protein stability. Mutation of the NLS completely abolished viral infectivity, thus indicating its importance in the virus life cycle. The NLS seems to be regulated by the N terminus of the precapsid, which inhibits its nuclear targeting. This regulation could be important in allowing virus assembly in the cytoplasm.

The cauliflower mosaic virus capsid protein: assembly and nucleic acid binding in vitro

The capsid protein of the cauliflower mosaic virus (CaMV) was expressed in a bacterial system to study CaMV assembly. Bacterial lysates contained soluble particulate material and insoluble inclusion bodies that were both used for analysis. In vitro renaturation of pIV derivatives lead to the appearance of folded sheets or large tubular structures in electron microscopy. The region between amino acid positions 77 and 332 is sufficient for self-aggregation of pIV in vitro. C-terminal deletion to amino acid position 265 still allowed dimerization but prevented further aggregation. Nucleic acid binding assays of immobilized pIV derivatives demonstrated that a region located upstream of the retroviral "zinc finger-like" motif is involved in unspecific binding dsDNA, ssDNA and RNA.

The open reading frame III product of cauliflower mosaic virus forms a tetramer through a N-terminal coiled-coil

The open reading frame III product of cauliflower mosaic virus is a protein of 15 kDa (p15) that is essential for the virus life cycle. It was shown that the 34 N-terminal amino acids are sufficient to support protein-protein interaction with the full-length p15 in the yeast two-hybrid system. A corresponding peptide was synthesized and a recombinant p15 was expressed in Escherichia coli and purified. Circular dichroism spectroscopy showed that the peptide and the full-length protein can assume an alpha-helical conformation. Analytical centrifugation allowed to determine that p15 assembles as a rod-shaped tetramer. Oxidative cross-linking of N-terminal cysteines of the peptide generated specific covalent oligomers, indicating that the N terminus of p15 is a coiled-coil that assembles as a parallel tetramer. Mutation of Lys22 into Asp destabilized the tetramer and put forward the presence of a salt bridge between Lys22 and Asp24 in a model building of the stalk. These results suggest a model in which the stalk segment of p15 is located at its N terminus, followed by a hinge that provides the space for presenting the C terminus for interactions with nucleic acids and/or proteins.

Antibody-mediated neutralization of human rhinovirus 14 explored by means of cryoelectron microscopy and X-ray crystallography of virus-Fab complexes

The structures of three different human rhinovirus 14 (HRV14)-Fab complexes have been explored with X-ray crystallography and cryoelectron microscopy procedures. All three antibodies bind to the NIm-IA site of HRV14, which is the beta-B-beta-C loop of the viral capsid protein VP1. Two antibodies, Fab17-IA (Fab17) and Fab12-IA (Fab12), bind bivalently to the virion surface and strongly neutralize viral infectivity whereas Fab1-IA (Fab1) strongly aggregates and weakly neutralizes virions. The structures of the two classes of virion-Fab complexes clearly differ and correlate with observed binding neutralization differences. Fab17 and Fab12 bind in essentially identical, tangential orientations to the viral surface, which favors bidentate binding over icosahedral twofold axes. Fab1 binds in a more radial orientation that makes bidentate binding unlikely. Although the binding orientations of these two antibody groups differ, nearly identical charge interactions occur at all paratope-epitope interfaces. Nucleotide sequence comparisons suggest that Fab17 and Fab12 are from the same progenitor cell and that some of the differing residues contact the south wall of the receptor binding canyon that encircles each of the icosahedral fivefold vertices. All of the antibodies contact a significant proportion of the canyon region and directly overlap much of the receptor (intercellular adhesion molecule 1 [ICAM-1]) binding site. Fab1, however, does not contact the same residues on the upper south wall (the side facing away from fivefold axes) at the receptor binding region as do Fab12 and Fab17. All three antibodies cause some stabilization of HRV14 against pH-induced inactivation; thus, stabilization may be mediated by invariant contacts with the canyon.

Mapping regions of the cauliflower mosaic virus ORF III product required for infectivity

The open reading frame (ORF) III product (PIII) of the pararetrovirus cauliflower mosaic virus (CaMV) has nucleic acid-binding properties in vitro, but its biological role is not yet determined. ORF III is closely linked to ORF II and overlaps ORF IV out of frame in the CaMV genome. A new CaMV-derived vector (Ca delta) devoid of ORF III and containing unique restriction sites between ORFs II and IV was designed. Introduction of the wild-type CaMV ORF III into Ca delta results in a clone (Ca3) infectious in turnip plants. Truncated or point-mutated versions of ORF III were then inserted into Ca delta and tested in vivo. Inoculation of the different mutants into turnip revealed that the four C-terminal amino acid residues of PIII are dispensable for infectivity as well as an internal domain (amino acids 61 to 80). Taken together the results show that PIII possesses a functional two-domain organization. Moreover, the CaMV PIII function(s) cannot be replaced either by the PIII protein of another caulimovirus, the figwort mosaic virus, or by the P2 protein of the cacao swollen shoot badnavirus, a member of the second plant pararetrovirus group.

Refinement of herpesvirus B-capsid structure on parallel supercomputers

Electron cryomicroscopy and icosahedral reconstruction are used to obtain the three-dimensional structure of the 1250-A-diameter herpesvirus B-capsid. The centers and orientations of particles in focal pairs of 400-kV, spot-scan micrographs are determined and iteratively refined by common-lines-based local and global refinement procedures. We describe the rationale behind choosing shared-memory multiprocessor computers for executing the global refinement, which is the most computationally intensive step in the reconstruction procedure. This refinement has been implemented on three different shared-memory supercomputers. The speedup and efficiency are evaluated by using test data sets with different numbers of particles and processors. Using this parallel refinement program, we refine the herpesvirus B-capsid from 355-particle images to 13-A resolution. The map shows new structural features and interactions of the protein subunits in the three distinct morphological units: penton, hexon, and triplex of this T = 16 icosahedral particle.

Conformational flexibility and polymerization of vesicular stomatitis virus matrix protein

The matrix protein of vesicular stomatitis virus (VSV) plays a pivotal role in viral assembly. We previously demonstrated the ability of M protein to self-associate at low salt concentrations. Now, we show the ability of M protein to polymerize in the presence of ZnCl2 in a nucleation-dependent manner. Analysis of kinetics revealed that the nuclei are probably made of three or four molecules of M. These results are consistent with the idea that in vitro self association of M protein is not due to amorphous aggregation but rather reflects an intrinsic ability of M to polymerize. Using attenuated total reflectance Fourier transform infrared spectroscopy, we showed that M polymerization is associated with an increase in the beta-sheet content of the protein. We propose a model explaining both the apparent M protein solubility in infected cells and how M polymerization could promote viral assembly. Data available for other negative strand viruses suggest that M polymerization may be the general basis of viral assembly.

Localization of the C terminus of the assembly domain of hepatitis B virus capsid protein: implications for morphogenesis and organization of encapsidated RNA

The capsid protein of hepatitis B virus, consisting of an "assembly" domain (residues 1-149) and an RNA-binding "protamine" domain (residues 150-183), assembles from dimers into icosahedral capsids of two different sizes. The C terminus of the assembly domain (residues 140-149) functions as a morphogenetic switch, longer C termini favoring a higher proportion of the larger capsids, it also connects the protamine domain to the capsid shell. We now have defined the location of this peptide in capsids assembled in vitro by engineering a mutant assembly domain with a single cysteine at its C terminus (residue 150), labeling it with a gold cluster and visualizing the cluster by cryo-electron microscopy. The labeled protein is unimpaired in its ability to form capsids. Our density map reveals a single undecagold cluster under each fivefold and quasi-sixfold vertex, connected to sites at either end of the undersides of the dimers. Considering the geometry of the vertices, the C termini must be more crowded at the fivefolds. Thus, a bulky C terminus would be expected to favor formation of the larger (T = 4) capsids, which have a greater proportion of quasi-sixfolds. Capsids assembled by expressing the full-length protein in Escherichia coli package bacterial RNAs in amounts equivalent to the viral pregenome. Our density map of these capsids reveals a distinct inner shell of density-the RNA. The RNA is connected to the protein shell via the C-terminal linkers and also makes contact around the dimer axes.

High-resolution icosahedral reconstruction: fulfilling the promise of cryo-electron microscopy

Two recent papers have defined the secondary structure of the hepatitis virus capsid using a combination of cryo-electron microscopy and icosahedral image reconstruction. These two papers do more than reveal a new fold for a virus protein; they herald a new era in which image reconstruction of single particles will provide reliable high-resolution structural information. In revealing the promise of these techniques to the structural biology community, their two papers should play a seminal role for single particle work, similar to that of the work of Unwin and Henderson on bacteriorhodopsin in revealing the potential of electron microscopy of membrane protein crystals. Indeed, the success of these single particle methods owes much to the development of high-resolution techniques for two-dimensional crystals. This review will summarize some of the history of icosahedral reconstruction from cryo-electron micrographs, compare the two different approaches used to obtain the recent results and outline some of the challenges and promises for the future.

The structure of cucumber mosaic virus: cryoelectron microscopy, X-ray crystallography, and sequence analysis

The three-dimensional structure of cucumber mosaic virus (CMV) was analyzed at 23 A resolution by cryoelectron microscopy and image reconstruction, demonstrating structural similarity to cowpea chlorotic mottle virus (CCMV), another member of the Bromoviridae family. The CMV structure was determined at 8 A resolution by X-ray crystallography with phases determined by single isomorphous replacement and refined by fivefold noncrystallographic symmetry averaging. The X-ray structure agreed with the electron microscopy reconstruction; the electron density is consistent with beta-barrel subunits arranged with T = 3 quasi-symmetry in an orientation similar to that observed in CCMV. Strong density surrounding the icosahedral threefold axes (quasi sixfold axes in the T = 3 particle) between 80 and 100 A from the particle center formed a cylinder of radius 11 A, similar to the density observed in the same region of CCMV. This density corresponds to the beta-annulus of CCMV, which differentiates hexamers from pentamers and determines the formation of the T = 3 particles. The CMV and CCMV amino acid sequences were aligned, providing information (based on the CCMV atomic model) about the probable distribution of residues in the three-dimensional structure of CMV.

Putative receptor binding sites on alphaviruses as visualized by cryoelectron microscopy

The structures of Sindbis virus and Ross River virus complexed with Fab fragments from monoclonal antibodies have been determined from cryoelectron micrographs. Both antibodies chosen for this study bind to regions of the virions that have been implicated in cell-receptor recognition and recognize epitopes on the E2 glycoprotein. The two structures show that the Fab fragments bind to the outermost tip of the trimeric envelope spike protein. Hence, the same region of both the Sindbis virus and Ross River virus envelope spike is composed of E2 and is involved in recognition of the cellular receptor.

Evolutionary conservation in the hepatitis B virus core structure: comparison of human and duck cores

BACKGROUND

Hepatitis B virus is a major human pathogen which has been extensively studied, yet its structure is unknown. Cryo-electron microscopy of the viral cores expressed in Escherichia coli or isolated from infected liver provides a means for determining the structure of the hepatitis B nucleocapsid.

RESULTS

Using cryo-electron microscopy and three-dimensional image reconstruction, we have determined the structures of duck and human hepatitis B virus cores and find that they have similar dimer-clustered T = 3 and T = 4 icosahedral organizations. The duck virus core protein sequence differs from the human in both length and amino acid content; however, the only significant structural differences observed are the lobes of density on the lateral edges of the projecting (distal) domain of the core protein dimer. The different cores contain varying amounts of nucleic acid, but exhibit similar contacts between the core protein and the nucleic acid. Immunoelectron microscopy of intact cores has localized two epitopes on the core surface corresponding to residues 76-84 and 129-132.

CONCLUSIONS

The bacterial expression system faithfully reproduces the native hepatitis B virus core structure even in the absence of the complete viral genome. This confirms that proper assembly of the core is independent of genome packaging. Difference imaging and antibody binding map three sequence positions in the structure: the C terminus and the regions near amino acids 80 and 130. Finally, we suggest that the genome-core interactions and the base (proximal) domain of the core dimer are evolutionarily conserved whereas the projecting domain, which interacts with the envelope proteins, is more variable.

In vitro folding of phage P22 coat protein with amino acid substitutions that confer in vivo temperature sensitivity

The coat protein that forms the icosahedral shell of phage P22 can be efficiently refolded in vitro [Teschke, C. M., & King, J. (1993) Biochemistry 32, 10839-10847]. Temperature-sensitive mutants of coat protein interfere with folding or assembly in vivo [Gordon, C. L., & King, J. (1993) J. Biol. Chem. 268, 9358-9368]. The folding of a set of phage P22 coat proteins carrying the temperature-sensitive for folding (tsf) substitutions W48Q, A108V, G232D, T294I, and F353L has been investigated in vitro. Denatured tsf polypeptides were able to fold into soluble species with high efficiency. The efficiency of folding of the wild-type (WT) and mutant polypeptides at different temperatures showed sharp transitions where aggregation predominated over folding. The refolding of the tsf mutant proteins did not show an obvious thermal defect in yield. The tsf polypeptides folded through the long-lived kinetic intermediate previously described for WT coat protein with similar relaxation times. The folding kinetics of the tsf polypeptides in bisANS, a hydrophobic fluorescent dye, were also similar to those of the WT protein. However, the folded tsf proteins showed decreased secondary structure compared to WT coat protein. Analysis of the folded state by native gel electrophoresis revealed that the tsf coat proteins folded into dimers and trimers, not monomers. The dimer and trimer species were incompetent for assembly. Once formed, dimers and trimers showed no propensity toward aggregation. The folding pathway of the mutant polypeptides must be quite similar to the WT pathway, but at some step inappropriate intersubunit interactions occur due to the amino acid substitutions, trapping the subunits from assembly.

Nucleocapsid and glycoprotein organization in an enveloped virus

Alphaviruses are a group of icosahedral, positive-strand RNA, enveloped viruses. The membrane bilayer, which surrounds the approximately 400 A diameter nucleocapsid, is penetrated by 80 spikes arranged in a T = 4 lattice. Each spike is a trimer of heterodimers consisting of glycoproteins E1 and E2. Cryoelectron microscopy and image reconstruction of Ross River virus showed that the T = 4 quaternary structure of the nucleocapsid consists of pentamer and hexamer clusters of the capsid protein, but not dimers, as have been observed in several crystallographic studies. The E1-E2 heterodimers form one-to-one associations with the nucleocapsid monomers across the lipid bilayer. Knowledge of the atomic structure of the capsid protein and our reconstruction allows us to identify capsid-protein residues that interact with the RNA, the glycoproteins, and adjacent capsid-proteins.

Structures of the native and swollen forms of cowpea chlorotic mottle virus determined by X-ray crystallography and cryo-electron microscopy

BACKGROUND

RNA-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.

RESULTS

The 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.

CONCLUSIONS

The 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.

Functional implications of quasi-equivalence in a T = 3 icosahedral animal virus established by cryo-electron microscopy and X-ray crystallography

BACKGROUND

Studies 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.

RESULTS

A 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.

CONCLUSIONS

On 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.

Crystallographic and cryo EM analysis of virion-receptor interactions

Cryoelectron microscopy has been used to determine the first structure of a virus when complexed with its glycoprotein cellular receptor. Human rhinovirus 16 (HRV16) complexed with the two amino-terminal, immunoglobulin-like domains of the intercellular adhesion molecule-1 (ICAM-1) shows that ICAM-1 binds into the 12 A deep "canyon" on the surface of the virus. This is consistent with the prediction that the viral receptor attachment site lies in a cavity inaccessible to the host's antibodies. The atomic structures of HRV14 and CD4, homologous to HRV16 and ICAM-1, showed excellent correspondence with observed density, thus establishing the virus-receptor interactions.

Pattern formation in icosahedral virus capsids: the papova viruses and Nudaurelia capensis beta virus

The capsids of the spherical viruses all show underlying icosahedral symmetry, yet they differ markedly in capsomere shape and in capsomere position and orientation. The capsid patterns presented by the capsomere shapes, positions, and orientations of three viruses (papilloma, SV40, and N beta V) have been generated dynamically through a bottom-up procedure which provides a basis for understanding the patterns. A capsomere shape is represented in two-dimensional cross-section by a mass or charge density on the surface of a sphere, given by an expansion in spherical harmonics, and referred to herein as a morphological unit (MU). A capsid pattern is represented by an icosahedrally symmetrical superposition of such densities, determined by the positions and orientations of its MUs on the spherical surface. The fitness of an arrangement of MUs is measured by an interaction integral through which all capsid elements interact with each other via an arbitrary function of distance. A capsid pattern is generated by allowing the correct number of approximately shaped MUs to move dynamically on the sphere, positioning themselves until an extremum of the fitness function is attained. The resulting patterns are largely independent of the details of both the capsomere representation and the interaction function; thus the patterns produced are generic. The simplest useful fitness function is sigma 2, the average square of the mass (or charge) density, a minimum of which corresponds to a "uniformly spaced" MU distribution; to good approximation, the electrostatic free energy of charged capsomeres, calculated from the linearized Poisson-Boltzmann equation, is proportional to sigma 2. With disks as MUs, the model generates the coordinated lattices familiar from the quasi-equivalence theory, indexed by triangulation numbers. Using fivefold MUs, the model generates the patterns observed at different radii within the T = 7 capsid of papilloma and at the surface of SV40; threefold MUs give the T = 4 pattern of Nudaurelia capensis beta virus. In all cases examined so far, the MU orientations are correctly found.