Assembly in vitro of bacteriophage HK97 proheads

A symmetry mismatch unraveled: How phage HK97 scaffold flexibly accommodates a 12-fold pore at a 5-fold viral capsid vertex

Tailed bacteriophages and herpesviruses use a transient scaffold to assemble icosahedral capsids with hexameric capsomers on the faces and pentameric capsomers at all but one vertex where a 12-fold portal is thought to nucleate the assembly. How does the scaffold orchestrate this step? We have determined the portal vertex structure of the bacteriophage HK97 procapsid, where the scaffold is a domain of the major capsid protein. The scaffold forms rigid helix-turn-strand structures on the interior surfaces of all capsomers and is further stabilized around the portal, forming trimeric coiled-coil towers, two per surrounding capsomer. These 10 towers bind identically to 10 of 12 portal subunits, adopting a pseudo-12-fold organization that explains how the symmetry mismatch is managed at this early step.

Contact-Based Analysis of Aggregation of Intrinsically Disordered Proteins

We review the contact-based description of aggregation of intrinsically disordered proteins in coarse-grained and all-atom models. We consider polyglutamines and polyalanines at various concentrations of the peptides. We also study associations of two chains of α-synuclein and up to 20 chains of a 12-residue-long segment of protein tau. We demonstrate that the total number of two-chain association events (in an aggregate that comprises at least two chains) provides a useful measure of the propensity to aggregate. This measure is consistent, for instance, with the previously reported mass spectroscopy data. The distribution of the number of association events is given essentially by a power law as a function of the duration of these events. The corresponding exponent depends on the protein and the temperature but not on the concentration of the proteins.

Triggered Reversible Disassembly of an Engineered Protein Nanocage*

Protein nanocages play crucial roles in sub-cellular compartmentalization and spatial control in all domains of life and have been used as biomolecular tools for applications in biocatalysis, drug delivery, and bionanotechnology. The ability to control their assembly state under physiological conditions would further expand their practical utility. To gain such control, we introduced a peptide capable of triggering conformational change at a key structural position in the largest known encapsulin nanocompartment. We report the structure of the resulting engineered nanocage and demonstrate its ability to disassemble and reassemble on demand under physiological conditions. We demonstrate its capacity for in vivo encapsulation of proteins of choice while also demonstrating in vitro cargo loading capabilities. Our results represent a functionally robust addition to the nanocage toolbox and a novel approach for controlling protein nanocage disassembly and reassembly under mild conditions.

Self-assembly of model proteins into virus capsids

We consider self-assembly of proteins into a virus capsid by the methods of molecular dynamics. The capsid corresponds either to SPMV or CCMV and is studied with and without the RNA molecule inside. The proteins are flexible and described by the structure-based coarse-grained model augmented by electrostatic interactions. Previous studies of the capsid self-assembly involved solid objects of a supramolecular scale, e.g. corresponding to capsomeres, with engineered couplings and stochastic movements. In our approach, a single capsid is dissociated by an application of a high temperature for a variable period and then the system is cooled down to allow for self-assembly. The restoration of the capsid proceeds to various extent, depending on the nature of the dissociated state, but is rarely complete because some proteins depart too far unless the process takes place in a confined space.

Static and dynamic hidden symmetries of icosahedral viral capsids

Viral shells self-assemble from identical proteins, which tend to form equivalent environments in the resulting assembly. However, in icosahedral capsids containing more than 60 proteins, they are enforced to occupy not only the symmetrically equivalent locations but also the quasi-equivalent ones. Due to this important fact, static and dynamic symmetries of viral shells can include additional hidden components. Here, developing the Caspar and Klug ideas concerning the quasi-equivalence of protein environments, we derive the simplest hexagonal tilings, that in principle could correspond to the local protein order in viral shells, and apply the resulting theory to nucleocytoplasmic large dsDNA viruses. In addition, analyzing the dynamic symmetry of the P22 viral shell, we demonstrate that the collective critical modes responsible for the protein reorganization during the procapsid maturation are approximately equivalent to the normal modes of the isotropic spherical membrane with O(3) symmetry. Furthermore, we establish the relationship between the dynamic symmetry of the P22 procapsid and the protein arrangement regularities that appear only in the mature capsid.

Flexible Connectors between Capsomer Subunits that Regulate Capsid Assembly

Viruses build icosahedral capsids of specific size and shape by regulating the spatial arrangement of the hexameric and pentameric protein capsomers in the growing shell during assembly. In the T=7 capsids of Escherichia coli bacteriophage HK97 and other phages, 60 capsomers are hexons, while the rest are pentons that are correctly positioned during assembly. Assembly of the HK97 capsid to the correct size and shape has been shown to depend on specific ionic contacts between capsomers. We now describe additional ionic interactions within capsomers that also regulate assembly. Each is between the long hairpin, the "E-loop," that extends from one subunit to the adjacent subunit within the same capsomer. Glutamate E153 on the E-loop and arginine R210 on the adjacent subunit's backbone alpha-helix form salt bridges in hexamers and pentamers. Mutations that disrupt these salt bridges were lethal for virus production, because the mutant proteins assembled into tubes or sheets instead of capsids. X-ray structures show that the E153-R210 links are flexible and maintained during maturation despite radical changes in capsomer shape. The E153-R210 links appear to form early in assembly to enable capsomers to make programmed changes in their shape during assembly. The links also prevent flattening of capsomers and premature maturation. Mutant phenotypes and modeling support an assembly model in which flexible E153-R210 links mediate capsomer shape changes that control where pentons are placed to create normal-sized capsids. The E-loop may be conserved in other systems in order to play similar roles in regulating assembly.

Orientational phase transitions and the assembly of viral capsids

We present a Landau theory for large-l orientational phase transitions and apply it to the assembly of icosahedral viral capsids. The theory predicts two distinct types of ordering transitions. Transitions dominated by the l=6,10,12, and 18 icosahedral spherical harmonics resemble robust first-order phase transitions that are not significantly affected by chirality. The remaining transitions depend essentially on including mixed l states denoted as l=15+16 corresponding to a mixture of l=15 and l=16 spherical harmonics. The l=15+16 transition is either continuous or weakly first-order and it is strongly influenced by chirality, which suppresses spontaneous chiral symmetry breaking. The icosahedral state is in close competition with states that have tetrahedral, D_{5}, and octahedral symmetries. We present a group-theoretic method to analyze the competition between the different symmetries. The theory is applied to a variety of viral shells.

ZpdN, a Plasmid-Encoded Sigma Factor Homolog, Induces pBS32-Dependent Cell Death in Bacillus subtilis

The ancestral Bacillus subtilis strain 3610 contains an 84-kb plasmid called pBS32 that was lost during domestication of commonly used laboratory derivatives. Here we demonstrate that pBS32, normally present at 1 or 2 copies per cell, increases in copy number nearly 100-fold when cells are treated with the DNA-damaging agent mitomycin C. Mitomycin C treatment also caused cell lysis dependent on pBS32-borne prophage genes. ZpdN, a sigma factor homolog encoded by pBS32, was required for the plasmid response to DNA damage, and artificial expression of ZpdN was sufficient to induce pBS32 hyperreplication and cell death. Plasmid DNA released by cell death was protected by the capsid protein ZpbH, suggesting that the plasmid was packaged into a phagelike particle. The putative particles were further indicated by CsCl sedimentation but were not observed by electron microscopy and were incapable of killing B. subtilis cells extracellularly. We hypothesize that pBS32-mediated cell death releases a phagelike particle that is defective and unstable.

IMPORTANCE

Prophages are phage genomes stably integrated into the host bacterium's chromosome and less frequently are maintained as extrachromosomal plasmids. Here we report that the extrachromosomal plasmid pBS32 of Bacillus subtilis encodes a prophage that, when activated, kills the host. pBS32 also encodes both the sigma factor homolog ZpdN that is necessary and sufficient for prophage induction and the protein ComI, which is a potent inhibitor of DNA uptake by natural transformation. We provide evidence that the entire pBS32 sequence may be part of the prophage and thus that competence inhibition may be linked to lysogeny.

Physical Ingredients Controlling Stability and Structural Selection of Empty Viral Capsids

One of the crucial steps in the viral replication cycle is the self-assembly of its protein shell. Typically, each native virus adopts a unique architecture, but the coat proteins of many viruses have the capability to self-assemble in vitro into different structures by changing the assembly conditions. However, the mechanisms determining which of the possible capsid shapes and structures is selected by a virus are still not well-known. We present a coarse-grained model to analyze and understand the physical mechanisms controlling the size and structure selection in the assembly of empty viral capsids. Using this model and Monte Carlo simulations, we have characterized the phase diagram and stability of T = 1,3,4,7 and snub cube shells. In addition, we have studied the tolerance of different shells to changes in physical parameters related to ambient conditions, identifying possible strategies to induce misassembly or failure. Finally, we discuss the factors that select the shape of a capsid as spherical, faceted, elongated, or decapsidated. Our model sheds important light on the ingredients that control the assembly and stability of viral shells. This knowledge is essential to get capsids with well-defined size and structure that could be used for promising applications in medicine or bionanotechnology.

Correct Assembly of the Bacteriophage T5 Procapsid Requires Both the Maturation Protease and the Portal Complex

The 90-nm-diameter capsid of coliphage T5 is organized with T=13 icosahedral geometry and encloses a double-stranded DNA genome that measures 121kbp. Its assembly follows a path similar to that of phage HK97 but yielding a larger structure that includes 775 subunits of the major head protein, 12 subunits of the portal protein and 120 subunits of the decoration protein. As for phage HK97, T5 encodes the scaffold function as an N-terminal extension (∆-domain) to the major head protein that is cleaved by the maturation protease after assembly of the initial prohead I form and prior to DNA packaging and capsid expansion. Although the major head protein alone is sufficient to assemble capsid-like particles, the yield is poor and includes many deformed structures. Here we explore the role of both the portal and the protease in capsid assembly by generating constructs that include the major head protein and a combination of protease (wild type or an inactive mutant) and portal proteins and overexpressing them in Escherichia coli. Our results show that the inactive protease mutant acts to trigger assembly of the major head protein, probably through binding to the ∆-domain, while the portal protein regulates assembly into the correct T=13 geometry. A cryo-electron microscopy reconstruction of prohead I including inactivated protease reveals density projecting from the prohead interior surface toward its center that is compatible with the ∆-domain, as well as additional internal density that we assign as the inactivated protease. These results reveal complexity in T5 beyond that of the HK97 system.

Subassemblies and asymmetry in assembly of herpes simplex virus procapsid

The herpes simplex virus 1 (HSV-1) capsid is a massive particle (~200 MDa; 1,250-Å diameter) with T=16 icosahedral symmetry. It initially assembles as a procapsid with ~4,000 protein subunits of 11 different kinds. The procapsid undergoes major changes in structure and composition as it matures, a process driven by proteolysis and expulsion of the internal scaffolding protein. Assembly also relies on an external scaffolding protein, the triplex, an α₂β heterotrimer that coordinates neighboring capsomers in the procapsid and becomes a stabilizing clamp in the mature capsid. To investigate the mechanisms that regulate its assembly, we developed a novel isolation procedure for the metastable procapsid and collected a large set of cryo-electron microscopy data. In addition to procapsids, these preparations contain maturation intermediates, which were distinguished by classifying the images and calculating a three-dimensional reconstruction for each class. Appraisal of the procapsid structure led to a new model for assembly; in it, the protomer (assembly unit) consists of one triplex, surrounded by three major capsid protein (MCP) subunits. The model exploits the triplexes’ departure from 3-fold symmetry to explain the highly skewed MCP hexamers, the triplex orientations at each 3-fold site, and the T=16 architecture. These observations also yielded new insights into maturation.

This paper addresses the molecular mechanisms that govern the self-assembly of large, structurally complex, macromolecular particles, such as the capsids of double-stranded DNA viruses. Although they may consist of thousands of protein subunits of many different kinds, their assembly is precise, ranking them among the largest entities in the biosphere whose structures are uniquely defined to the atomic level. Assembly proceeds in two stages: formation of a precursor particle (procapsid) and maturation, during which major changes in structure and composition take place. Our analysis of the HSV procapsid by cryo-electron microscopy suggests a hierarchical pathway in which multisubunit “protomers” are the building blocks of the procapsid but their subunits are redistributed into different subcomplexes upon being incorporated into a nascent procapsid and are redistributed again in maturation. Assembly is a highly virus-specific process, making it a potential target for antiviral intervention.

Protein-Protein Interfaces in Viral Capsids Are Structurally Unique

Viral capsids exhibit elaborate and symmetrical architectures of defined sizes and remarkable mechanical properties not seen with cellular macromolecular complexes. Given the uniqueness of the higher-order organization of viral capsid proteins in the virosphere, we explored the question of whether the patterns of protein-protein interactions within viral capsids are distinct from those in generic protein complexes. Our comparative analysis involving a non-redundant set of 551 inter-subunit interfaces in viral capsids from VIPERdb and 20,014 protein-protein interfaces in non-capsid protein complexes from the Protein Data Bank found 418 generic protein-protein interfaces that share similar physicochemical patterns with some protein-protein interfaces in the capsid set, using the program PCalign we developed for comparing protein-protein interfaces. This overlap in the structural space of protein-protein interfaces is significantly small, with a p-value <0.0001, based on a permutation test on the total set of protein-protein interfaces. Furthermore, the generic protein-protein interfaces that bear similarity in their spatial and chemical arrangement with capsid ones are mostly small in size with fewer than 20 interfacial residues, which results from the relatively limited choices of natural design for small interfaces rather than having significant biological implications in terms of functional relationships. We conclude based on this study that protein-protein interfaces in viral capsids are non-representative of patterns in the smaller, more compact cellular protein complexes. Our finding highlights the design principle of building large biological containers from repeated, self-assembling units and provides insights into specific targets for antiviral drug design for improved efficacy.

Nature's favorite building block: Deciphering folding and capsid assembly of proteins with the HK97-fold

For many (if not all) bacterial and archaeal tailed viruses and eukaryotic Herpesvirdae the HK97-fold serves as the major architectural element in icosahedral capsid formation while still enabling the conformational flexibility required during assembly and maturation. Auxiliary proteins or Δ-domains strictly control assembly of multiple, identical, HK97-like subunits into procapsids with specific icosahedral symmetries, rather than aberrant non-icosahedral structures. Procapsids are precursor structures that mature into capsids in a process involving release of auxiliary proteins (or cleavage of Δ-domains), dsDNA packaging, and conformational rearrangement of the HK97-like subunits. Some coat proteins built on the ubiquitous HK97-fold also have accessory domains or loops that impart specific functions, such as increased monomer, procapsid, or capsid stability. In this review, we analyze the numerous HK97-like coat protein structures that are emerging in the literature (over 40 at time of writing) by comparing their topology, additional domains, and their assembly and misassembly reactions.

The delta domain of the HK97 major capsid protein is essential for assembly

The 102 residue N-terminal extension of the HK97 major capsid protein, the delta domain, is normally present during the assembly of immature HK97 procapsids, but it is removed during maturation like well-known internal scaffolding proteins of other tailed phages and herpesviruses. The delta domain also shares other unusual properties usually found in other viral and phage scaffolding proteins, including its location on the inside of the capsid, a high predicted and measured α-helical content, and an additional prediction for the ability to form parallel coiled-coils. Viral scaffolding proteins are essential for capsid assembly and phage viability, so we tested whether the HK97 delta domain was essential for capsid assembly. We studied the effects of deleting all or parts of the delta domain on capsid assembly and on complementation of capsid-protein-defective phage, and our results demonstrate that the delta domain is required for HK97 capsid assembly.

Transient contacts on the exterior of the HK97 procapsid that are essential for capsid assembly

The G-loop is a 10-residue glycine-rich loop that protrudes from the surface of the mature bacteriophage HK97 capsid at the C-terminal end of the long backbone helix of major capsid protein subunits. The G-loop is essential for assembly, is conserved in related capsid and encapsulin proteins, and plays its role during HK97 capsid assembly by making crucial contacts between the hill-like hexamers and pentamers in precursor proheads. These contacts are not preserved in the flattened capsomers of the mature capsid. Aspartate 231 in each of the ~400 G-loops interacts with lysine 178 of the E-loop (extended loop) of a subunit on an adjacent capsomer. Mutations disrupting this interaction prevented correct assembly and, in some cases, induced abnormal assembly into tubes, or small, incomplete capsids. Assembly remained defective when D231 and K178 were replaced with larger charged residues or when their positions were exchanged. Second-site suppressors of lethal mutants containing substitution D231L replaced the ionic interaction with new interactions between neutral and hydrophobic residues of about the same size: D231L/K178V, D231L/K178I, and D231L/K178N. We conclude that it is not the charge but the size and shape of the side chains of residues 178 and 231 that are important. These two residues control the geometry of contacts between the E-loop and the G-loop, which apparently must be precisely spaced and oriented for correct assembly to occur. We present a model for how the G-loop could control HK97 assembly and identify G-loop-like protrusions in other capsid proteins that may play analogous roles.

pH-induced stability switching of the bacteriophage HK97 maturation pathway

Many viruses undergo large-scale conformational changes during their life cycles. Blocking the transition from one stage of the life cycle to the next is an attractive strategy for the development of antiviral compounds. In this work, we have constructed an icosahedrally symmetric, low-energy pathway for the maturation transition of bacteriophage HK97. By conducting constant-pH molecular dynamics simulations on this pathway, we identify which residues are contributing most significantly to shifting the stability between the states along the pathway under differing pH conditions. We further analyze these data to establish the connection between critical residues and important structural motifs which undergo reorganization during maturation. We go on to show how DNA packaging can induce spontaneous reorganization of the capsid during maturation.

An intramolecular chaperone inserted in bacteriophage P22 coat protein mediates its chaperonin-independent folding

The bacteriophage P22 coat protein has the common HK97-like fold but with a genetically inserted domain (I-domain). The role of the I-domain, positioned at the outermost surface of the capsid, is unknown. We hypothesize that the I-domain may act as an intramolecular chaperone because the coat protein folds independently, and many folding mutants are localized to the I-domain. The function of the I-domain was investigated by generating the coat protein core without its I-domain and the isolated I-domain. The core coat protein shows a pronounced folding defect. The isolated I-domain folds autonomously and has a high thermodynamic stability and fast folding kinetics in the presence of a peptidyl prolyl isomerase. Thus, the I-domain provides thermodynamic stability to the full-length coat protein so that it can fold reasonably efficiently while still allowing the HK97-like core to retain the flexibility required for conformational switching during procapsid assembly and maturation.

Functional domains of the HK97 capsid maturation protease and the mechanisms of protein encapsidation

Tailed double-stranded DNA bacteriophages and herpesviruses build capsids by co-assembling a major capsid protein with an internal scaffolding protein that then exits from the assembled structure either intact or after digestion in situ by a protease. In bacteriophage HK97, the 102-residue N-terminal delta domain of the major capsid protein is also removed by proteolysis after assembly and appears to perform the scaffolding function. We describe the HK97 protease that carries out these maturation cleavages. Insertion mutations at seven sites in the protease gene produced mutant proteins that assemble into proheads, and those in the N-terminal two-thirds were enzymatically inactive. Plasmid-expressed protease was rapidly cleaved in vivo but was stabilized by co-expression with the delta domain. Purified protease was found to be active during the assembly of proheads in vitro. Heterologous fusions to the intact protease or to C-terminal fragments targeted fusion proteins into proheads. We confirm that the catalytic activity resides in the N-terminal two-thirds of the protease polypeptide and suggest that the C-terminal one-fifth of the protein contains a capsid targeting signal. The implications of this arrangement are compared to capsid targeting systems in other phages, herpesviruses, and encapsulins.

Involvement of the major capsid protein and two early-expressed phage genes in the activity of the lactococcal abortive infection mechanism AbiT

The dairy industry uses the mesophilic, Gram-positive, lactic acid bacterium (LAB) Lactococcus lactis to produce an array of fermented milk products. Milk fermentation processes are susceptible to contamination by virulent phages, but a plethora of phage control strategies are available. One of the most efficient is to use LAB strains carrying phage resistance systems such as abortive infection (Abi) mechanisms. Yet, the mode of action of most Abi systems remains poorly documented. Here, we shed further light on the antiviral activity of the lactococcal AbiT system. Twenty-eight AbiT-resistant phage mutants derived from the wild-type AbiT-sensitive lactococcal phages p2, bIL170, and P008 were isolated and characterized. Comparative genomic analyses identified three different genes that were mutated in these virulent AbiT-insensitive phage derivatives: e14 (bIL170 [e14(bIL170)]), orf41 (P008 [orf41(P008)]), and orf6 (p2 [orf6(p2)] and P008 [orf6(P008)]). The genes e14(bIL170) and orf41(P008) are part of the early-expressed genomic region, but bioinformatic analyses did not identify their putative function. orf6 is found in the phage morphogenesis module. Antibodies were raised against purified recombinant ORF6, and immunoelectron microscopy revealed that it is the major capsid protein (MCP). Coexpression in L. lactis of ORF6(p2) and ORF5(p2), a protease, led to the formation of procapsids. To our knowledge, AbiT is the first Abi system involving distinct phage genes.

Conformational switch-defective X174 internal scaffolding proteins kinetically trap assembly intermediates before procapsid formation

Conformational switching is an overarching paradigm in which to describe scaffolding protein-mediated virus assembly. However, rapid morphogenesis with small assembly subunits hinders the isolation of early morphogenetic intermediates in most model systems. Consequently, conformational switches are often defined by comparing the structures of virions, procapsids and aberrantly assembled particles. In contrast, X174 morphogenesis proceeds through at least three preprocapsid intermediates, which can be biochemically isolated. This affords a detailed analysis of early morphogenesis and internal scaffolding protein function. Amino acid substitutions were generated for the six C-terminal, aromatic amino acids that mediate most coat-internal scaffolding protein contacts. The biochemical characterization of mutant assembly pathways revealed two classes of molecular defects, protein binding and conformational switching, a novel phenotype. The conformational switch mutations kinetically trapped assembly intermediates before procapsid formation. Although mutations trapped different particles, they shared common second-site suppressors located in the viral coat protein. This suggests a fluid assembly pathway, one in which the scaffolding protein induces a single, coat protein conformational switch and not a series of sequential reactions. In this model, an incomplete or improper switch would kinetically trap intermediates.

Virus maturation

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.

Hydrogen/deuterium exchange analysis of HIV-1 capsid assembly and maturation

Following budding, HIV-1 virions undergo a maturation process where the Gag polyprotein in the immature virus is cleaved by the viral protease and rearranges to form the mature infectious virion. Despite the wealth of structures of isolated capsid domains and an in vitro-assembled mature lattice, models of the immature lattice do not provide an unambiguous model of capsid-molecule orientation and no structural information is available for the capsid maturation pathway. Here we have applied hydrogen/deuterium exchange mass spectrometry to immature, mature, and mutant Gag particles (CA5) blocked at the final Gag cleavage event to examine the molecular basis of capsid assembly and maturation. Capsid packing arrangements were very similar for all virions, whereas immature and CA5 virions contained an additional intermolecular interaction at the hexameric, 3-fold axis. Additionally, the N-terminal β-hairpin was observed to form as a result of capsid-SP1 cleavage rather than driving maturation as previously postulated.

The Prohead-I structure of bacteriophage HK97: implications for scaffold-mediated control of particle assembly and maturation

Virus capsid assembly requires recruiting and organizing multiple copies of protein subunits to form a closed shell for genome packaging that leads to infectivity. Many viruses encode scaffolding proteins to shift the equilibrium toward particle formation by promoting intersubunit interactions and stabilizing assembly intermediates. Bacteriophage HK97 lacks an explicit scaffolding protein, but the capsid protein (gp5) contains a scaffold-like N-terminal segment termed the delta domain. When gp5 is expressed in Escherichia coli, the delta domain guides 420 copies of the subunit into a procapsid with T=7 laevo icosahedral symmetry named Prohead-I. Prohead-I can be disassembled and reassembled under mild conditions and it cannot mature further. When the virally encoded protease (gp4) is coexpressed with gp5, it is incorporated into the capsid and digests the delta domain followed by autoproteolysis to produce the metastable Prohead-II. Prohead-I(+P) was isolated by coexpressing gp5 and an inactive mutant of gp4. Prohead-I and Prohead-I(+P) were compared by biochemical methods, revealing that the inactive protease stabilized the capsid against disassembly by chemical or physical stress. The crystal structure of Prohead-I(+P) was determined at 5.2 Å resolution, and distortions were observed in the subunit tertiary structures similar to those observed previously in Prohead-II. Prohead-I(+P) differed from Prohead-II due to the presence of the delta domain and the resulting repositioning of the N-arms, explaining why Prohead-I can be reversibly dissociated and cannot mature. Low-resolution X-ray data enhanced the density of the relatively dynamic delta domains, revealing their quaternary arrangement and suggesting how they drive proper assembly.

Structural basis for scaffolding-mediated assembly and maturation of a dsDNA virus

Formation of many dsDNA viruses begins with the assembly of a procapsid, containing scaffolding proteins and a multisubunit portal but lacking DNA, which matures into an infectious virion. This process, conserved among dsDNA viruses such as herpes viruses and bacteriophages, is key to forming infectious virions. Bacteriophage P22 has served as a model system for this study in the past several decades. However, how capsid assembly is initiated, where and how scaffolding proteins bind to coat proteins in the procapsid, and the conformational changes upon capsid maturation still remain elusive. Here, we report Cα backbone models for the P22 procapsid and infectious virion derived from electron cryomicroscopy density maps determined at 3.8- and 4.0-Å resolution, respectively, and the first procapsid structure at subnanometer resolution without imposing symmetry. The procapsid structures show the scaffolding protein interacting electrostatically with the N terminus (N arm) of the coat protein through its C-terminal helix-loop-helix motif, as well as unexpected interactions between 10 scaffolding proteins and the 12-fold portal located at a unique vertex. These suggest a critical role for the scaffolding proteins both in initiating the capsid assembly at the portal vertex and propagating its growth on a T = 7 icosahedral lattice. Comparison of the procapsid and the virion backbone models reveals coordinated and complex conformational changes. These structural observations allow us to propose a more detailed molecular mechanism for the scaffolding-mediated capsid assembly initiation including portal incorporation, release of scaffolding proteins upon DNA packaging, and maturation into infectious virions.

A conformational switch involved in maturation of Staphylococcus aureus bacteriophage 80α capsids

Bacteriophages are involved in many aspects of the spread and establishment of virulence factors in Staphylococcus aureus, including the mobilization of genetic elements known as S. aureus pathogenicity islands (SaPIs), which carry genes for superantigen toxins and other virulence factors. SaPIs are packaged into phage-like transducing particles using proteins supplied by the helper phage. We have used cryo-electron microscopy and icosahedral reconstruction to determine the structures of the procapsid and the mature capsid of 80α, a bacteriophage that can mobilize several different SaPIs. The 80α capsid has T=7 icosahedral symmetry with the capsid protein organized into pentameric and hexameric clusters that interact via prominent trimeric densities. The 80α capsid protein was modeled based on the capsid protein fold of bacteriophage HK97 and fitted into the 80α reconstructions. The models show that the trivalent interactions are mediated primarily by a 22-residue β hairpin structure called the P loop that is not found in HK97. Capsid expansion is associated with a conformational switch in the spine helix that is propagated throughout the subunit, unlike the domain rotation mechanism in phage HK97 or P22.

In vitro assembly of the T=13 procapsid of bacteriophage T5 with its scaffolding domain

The Siphoviridae coliphage T5 differs from other members of this family by the size of its genome (121 kbp) and by its large icosahedral capsid (90 nm), which is organized with T=13 geometry. T5 does not encode a separate scaffolding protein, but its head protein, pb8, contains a 159-residue aminoterminal scaffolding domain (Delta domain) that is the mature capsid. We have deciphered the early events of T5 shell assembly starting from purified pb8 with its Delta domain (pb8p). The self assembly of pb8p is regulated by salt conditions and leads to structures with distinct morphologies. Expanded tubes are formed in the presence of NaCl, whereas Ca(2+) promotes the association of pb8p into contracted tubes and procapsids. Procapsids display an angular organization and 20-nm-long internal radial structures identified as the Delta domain. The T5 head maturation protease pb11 specifically cleaves the Delta domain of contracted and expanded tubes. Ca(2+) is not required for proteolytic activity but for the organization of the Delta domain. Taken together, these data indicate that pb8p carries all of the information in its primary sequence to assemble in vitro without the requirement of the portal and accessory proteins. Furthermore, Ca(2+) plays a key role in introducing the conformational diversity that permits the formation of a stable procapsid. Phage T5 is the first example of a viral capsid consisting of quasi-equivalent hexamers and pentamers whose assembly can be carried out in vitro, starting from the major head protein with its scaffolding domain, and whose endpoint is an icosahedral T=13 particle.

Critical salt bridges guide capsid assembly, stability, and maturation behavior in bacteriophage HK97

HK97 is a double-stranded DNA bacteriophage that undergoes dramatic conformational changes during viral capsid maturation and for which x-ray structures, at near atomic resolution, of multiple intermediate and mature capsid states are available. Both amide H/(2)H exchange and crystallographic comparisons between the pre-expanded Prohead II particles and the expanded Head II of bacteriophage HK97 revealed quaternary interactions that remain fixed throughout maturation and appear to maintain intercapsomer integrity at all quasi- and icosahedral 3-fold axes. These 3-fold staples are formed from Arg and Glu residues and a metal binding site. Mutations of either Arg-347 or Arg-194 or a double mutation of E344Q and E363A resulted in purification of the phage in capsomer form (hexamers and pentamers). Mutants that did assemble had both decreased thermal stability and decreased in vitro expansion rates. Amide H/(2)H exchange mass spectrometry showed that in the wild type capsid some subunits had a bent "spine" helix (highly exchanging), whereas others were straight (less exchanging). Similar analysis of the never assembled mutant capsomers showed uniform amide exchange in all of these that was higher than that of the straight spine helices (characterized in more mature intermediates), suggesting that the spine helix is somewhat bent prior to capsid assembly. The result further supports a previously proposed mechanism for capsid expansion in which the delta domains of each subunit induce a high energy intermediate conformation, which now appears to include a bent helix during capsomer assembly.

'Let the phage do the work': using the phage P22 coat protein structures as a framework to understand its folding and assembly mutants

The amino acid sequence of viral capsid proteins contains information about their folding, structure and self-assembly processes. While some viruses assemble from small preformed oligomers of coat proteins, other viruses such as phage P22 and herpesvirus assemble from monomeric proteins (Fuller and King, 1980; Newcomb et al., 1999). The subunit assembly process is strictly controlled through protein:protein interactions such that icosahedral structures are formed with specific symmetries, rather than aberrant structures. dsDNA viruses commonly assemble by first forming a precursor capsid that serves as a DNA packaging machine (Earnshaw, Hendrix, and King, 1980; Heymann et al., 2003). DNA packaging is accompanied by a conformational transition of the small precursor procapsid into a larger capsid for isometric viruses. Here we highlight the pseudo-atomic structures of phage P22 coat protein and rationalize several decades of data about P22 coat protein folding, assembly and maturation generated from a combination of genetics and biochemistry.

Optimal architectures of elongated viruses

Many viruses protect their genetic material by a closed elongated protein shell. Unlike spherical viruses, the structure of these prolates is not yet well understood, and only a few of them have been fully characterized. We present the results of a simple phenomenological model, which describes the remarkable structures of prolate or bacilliform viral shells. Surprisingly, we find that the special well-defined geometry of these elongated viruses arises just as a consequence of free-energy minimization of a generic interaction between the structural units of the capsid. Hemispherical T-number caps centered along the 5-, 3-, and 2-fold axes with hexagonally ordered cylindrical bodies are found to be local energy minima, thus justifying their occurrence as optimal viral structures. Moreover, closed elongated viruses show a sequence of magic numbers for the end-caps, leading to strict selection rules for the length and structure of the body as well as for the number of capsomers and proteins of the capsid. The model reproduces the architecture of spherical and bacilliform viruses, both in vivo and in vitro, and constitutes an important step towards understanding viral assembly and its potential control for biological and nanotechnological applications.

HK97 maturation studied by crystallography and H/2H exchange reveals the structural basis for exothermic particle transitions

HK97 is an exceptionally amenable system for characterizing major conformational changes associated with capsid maturation in double-stranded DNA bacteriophage. HK97 undergoes a capsid expansion of approximately 20%, accompanied by major subunit rearrangements during genome packaging. A previous 3.44-A-resolution crystal structure of the mature capsid Head II and cryo-electron microscopy studies of other intermediate expansion forms of HK97 suggested that, primarily, rigid-body movements facilitated the maturation process. We recently reported a 3.65-A-resolution structure of the preexpanded particle form Prohead II (P-II) and found that the capsid subunits undergo significant refolding and twisting of the tertiary structure to accommodate expansion. The P-II study focused on major twisting motions in the P-domain and on refolding of the spine helix during the transition. Here we extend the crystallographic comparison between P-II and Head II, characterizing the refolding events occurring in each of the four major domains of the capsid subunit and their effect on quaternary structure stabilization. In addition, hydrogen/deuterium exchange, coupled to mass spectrometry, was used to characterize the structural dynamics of three distinct capsid intermediates: P-II, Expansion Intermediate, and the nearly mature Head I. Differences in the solvent accessibilities of the seven quasi-equivalent capsid subunits, attributed to differences in secondary and quaternary structures, were observed in P-II. Nearly all differences in solvent accessibility among subunits disappear after the first transition to Expansion Intermediate. We show that most of the refolding is coupled to this transformation, an event associated with the transition from asymmetric to symmetric hexamers.

An unexpected twist in viral capsid maturation

Lambda-like double-stranded (ds) DNA bacteriophage undergo massive conformational changes in their capsid shell during the packaging of their viral genomes. Capsid shells are complex organizations of hundreds of protein subunits that assemble into intricate quaternary complexes that ultimately are able to withstand over 50 atm of pressure during genome packaging. The extensive integration between subunits in capsids requires the formation of an intermediate complex, termed a procapsid, from which individual subunits can undergo the necessary refolding and structural rearrangements needed to transition to the more stable capsid. Although various mature capsids have been characterized at atomic resolution, no such procapsid structure is available for a dsDNA virus or bacteriophage. Here we present a procapsid X-ray structure at 3.65 A resolution, termed prohead II, of the lambda-like bacteriophage HK97, the mature capsid structure of which was previously solved to 3.44 A (ref. 2). A comparison of the two largely different capsid forms has unveiled an unprecedented expansion mechanism that describes the transition. Crystallographic and hydrogen/deuterium exchange data presented here demonstrate that the subunit tertiary structures are significantly different between the two states, with twisting and bending motions occurring in both helical and beta-sheet regions. We also identified subunit interactions at each three-fold axis of the capsid that are maintained throughout maturation. The interactions sustain capsid integrity during subunit refolding and provide a fixed hinge from which subunits undergo rotational and translational motions during maturation. Previously published calorimetric data of a closely related bacteriophage, P22, showed that capsid maturation was an exothermic process that resulted in a release of 90 kJ mol(-1) of energy. We propose that the major tertiary changes presented in this study reveal a structural basis for an exothermic maturation process probably present in many dsDNA bacteriophage and possibly viruses such as herpesvirus, which share the HK97 subunit fold.

Generalized structural polymorphism in self-assembled viral particles

The protein shells, called capsids, of nearly all spherical viruses adopt icosahedral symmetry; however, self-assembly of such empty structures often occurs with multiple misassembly steps resulting in the formation of aberrant structures. Using simple models that represent the coat proteins preassembled in the two different predetermined species that are common motifs of viral capsids (i.e., pentameric and hexameric capsomers), we perform molecular dynamics simulations of the spontaneous self-assembly of viral capsids of different sizes containing T = 1,3,4,7,9,12,13,16, and 19 proteins in their icosahedral repeating unit. We observe, in addition to icosahedral capsids, a variety of nonicosahedral yet highly ordered and enclosed capsules. Such structural polymorphism is demonstrated to be an inherent property of the coat proteins, independent of the capsid complexity and the elementary kinetic mechanisms. Moreover, there exist two distinctive classes of polymorphic structures: aberrant capsules that are larger than their respective icosahedral capsids, in T = 1-7 systems; and capsules that are smaller than their respective icosahedral capsids when T = 7-19. Different kinetic mechanisms responsible for self-assembly of those classes of aberrant structures are deciphered, providing insights into the control of the self-assembly of icosahedral capsids.

Protein–protein interaction and quaternary structure

Protein–protein recognition plays an essential role in structure and function. Specific non-covalent interactions stabilize the structure of macromolecular assemblies, exemplified in this review by oligomeric proteins and the capsids of icosahedral viruses. They also allow proteins to form complexes that have a very wide range of stability and lifetimes and are involved in all cellular processes. We present some of the structure-based computational methods that have been developed to characterize the quaternary structure of oligomeric proteins and other molecular assemblies and analyze the properties of the interfaces between the subunits. We compare the size, the chemical and amino acid compositions and the atomic packing of the subunit interfaces of protein–protein complexes, oligomeric proteins, viral capsids and protein–nucleic acid complexes. These biologically significant interfaces are generally close-packed, whereas the non-specific interfaces between molecules in protein crystals are loosely packed, an observation that gives a structural basis to specific recognition. A distinction is made within each interface between a core that contains buried atoms and a solvent accessible rim. The core and the rim differ in their amino acid composition and their conservation in evolution, and the distinction helps correlating the structural data with the results of site-directed mutagenesis and in vitro studies of self-assembly.

Exploring the parameter space of complex self-assembly through virus capsid models

We use discrete event stochastic simulations to characterize the parameter space of a model of icosahedral viral capsid assembly as functions of monomer-monomer binding rates. The simulations reveal a parameter space characterized by three major assembly mechanisms, a standard nucleation-limited monomer-accretion pathway and two distinct hierarchical assembly pathways, as well as unproductive regions characterized by kinetically trapped species. Much of the productive parameter space also consists of border regions between these domains where hybrid pathways are likely to operate. A simpler octamer system studied for comparison reveals three analogous pathways, but is characterized by much lesser sensitivity to parameter variations in contrast to the sharp changes visible in the icosahedral model. The model suggests that modest changes in assembly conditions, consistent with expected differences between in vitro and in vivo assembly environments, could produce substantial shifts in assembly pathways. These results suggest that we must be cautious in drawing conclusions about in vivo capsid self-assembly dynamics from theoretical or in vitro models, as the nature of the basic assembly mechanisms accessible to a system can substantially differ between simple and complex model systems, between theoretical models and simulation results, and between in vitro and in vivo assembly conditions.

The Crystal Structure of a Virus-like Particle from the Hyperthermophilic Archaeon Pyrococcus furiosus Provides Insight into the Evolution of Viruses

Pyrococcus furiosus is a hyperthermophilic archaeal microorganism found near deep-sea thermal vents and its optimal growth temperature of 100 degrees C. Recently, a 38.8-kDa protein from P. furiosus DSM 3638 was isolated and characterized. Electron microscopy revealed that this protein aggregated as spheres of approximately 30 nm in diameter, which we designated P. furiosus virus-like particles (PfVs). X-ray crystallographic analysis at 3.6-A resolution revealed that each PfV consisted of 180 copies of the 38.8-kDa protein and retained T=3 icosahedral symmetry, as is often the case in spherical viruses. The total molecular mass of each particle was approximately 7 MDa. An examination of capsid structures suggested strong evolutionary links among PfV, tailed double-stranded DNA bacteriophages, and herpes viruses. The similar three-dimensional structures of the various coat proteins indicate that these viral capsids might have originated and evolved from a common ancestor. The structure of PfV provides a previously undescribed example of viral relationships across the three domains of life (Eukarya, Bacteria, and Archaea).

In vitro assembly of a prohead-like structure of the Rhodobacter capsulatus gene transfer agent

The gene transfer agent (GTA) is a phage-like particle capable of exchanging double-stranded DNA fragments between cells of the photosynthetic bacterium Rhodobacter capsulatus. Here we show that the major capsid protein of GTA, expressed in E. coli, can be assembled into prohead-like structures in the presence of calcium ions in vitro. Transmission electron microscopy (TEM) of uranyl acetate staining material and thin sections of glutaraldehyde-fixed material demonstrates that these associates have spherical structures with diameters in the range of 27-35 nm. The analysis of scanning TEM images revealed particles of mass approximately 4.3 MDa, representing 101+/-11 copies of the monomeric subunit. The establishment of this simple and rapid method to form prohead-like particles permits the GTA system to be used for genome manipulation within the photosynthetic bacterium, for specific targeted drug delivery, and for the construction of biologically based distributed autonomous sensors for environmental monitoring.

A Dissection of the Protein–Protein Interfaces in Icosahedral Virus Capsids

We selected 49 icosahedral virus capsids whose crystal structures are reported in the Protein Data Bank. They belong to the T=1, T=3, pseudo T=3 and other lattice types. We identified in them 779 unique interfaces between pairs of subunits, all repeated by icosahedral symmetry. We analyzed the geometric and physical chemical properties of these interfaces and compared with interfaces in protein-protein complexes and homodimeric proteins, and with crystal packing contacts. The capsids contain one to 16 subunits implicated in three to 66 unique interfaces. Each subunit loses 40-60% of its accessible surface in contacts with an average of 8.5 neighbors. Many of the interfaces are very large with a buried surface area (BSA) that can exceed 10,000 A(2), yet 39% are small with a BSA<800 A(2) comparable to crystal packing contacts. Pairwise capsid interfaces overlap, so that one-third of the residues are part of more than one interface. Those with a BSA>800 A(2) resemble homodimer interfaces in their chemical composition. Relative to the protein surface, they are non-polar, enriched in aliphatic residues and depleted of charged residues, but not of neutral polar residues. They contain one H-bond per about 200 A(2) BSA. Small capsid interfaces (BSA<800 A(2)) are only slightly more polar. They have a similar amino acid composition, but they bury fewer atoms and contain fewer H-bonds for their size. Geometric parameters that estimate the quality of the atomic packing suggest that the small capsid interfaces are loosely packed like crystal packing contacts, whereas the larger interfaces are close-packed as in protein-protein complexes and homodimers. We discuss implications of these findings on the mechanism of capsid assembly, assuming that the larger interfaces form first to yield stable oligomeric species (capsomeres), and that medium-size interfaces allow the stepwise addition of capsomeres to build larger intermediates.

Capsid conformational sampling in HK97 maturation visualized by X-ray crystallography and cryo-EM

Maturation of the bacteriophage HK97 capsid from a precursor (Prohead II) to the mature state (Head II) involves a 60 A radial expansion. The mature particle is formed by 420 copies of the major capsid protein organized on a T = 7 laevo lattice with each subunit covalently crosslinked to two neighbors. Well-characterized pH 4 expansion intermediates make HK97 valuable for investigating quaternary structural dynamics. Here, we use X-ray crystallography and cryo-EM to demonstrate that in the final transition in maturation (requiring neutral pH), pentons in Expansion Intermediate IV (EI-IV) reversibly sample 14 A translations and 6 degrees rotations relative to a fixed hexon lattice. The limit of this trajectory corresponds to the Head II conformation that is secured at this extent only by the formation of the final class of covalent crosslinks. Mutants that cannot crosslink or EI-IV particles that have been rendered incapable of forming the final crosslink remain in the EI-IV state.

Irreversible growth model for virus capsid assembly

We model the spontaneous assembly of a capsid (a virus' closed outer shell) from many copies of identical units, using entirely irreversible steps and only information local to the growing edge. Our model is formulated in terms of (i) an elastic Hamiltonian with stretching and bending stiffness and a spontaneous curvature, and (ii) a set of rate constants for the addition of new units or bonds. An ensemble of highly irregular capsids is generated, unlike the well-known icosahedrally symmetric viruses, but (we argue) plausible as a way to model the irregular capsids of retroviruses such as HIV. We found that (i) the probability of successful capsid completion decays exponentially with capsid size; (ii) capsid size depends strongly on spontaneous curvature and weakly on the ratio of the bending and stretching elastic stiffnesses of the shell; (iii) the degree of localization of Gaussian curvature (a measure of facetedness) depends heavily on the ratio of elastic stiffnesses.

A free energy cascade with locks drives assembly and maturation of bacteriophage HK97 capsid

We investigated the thermodynamic basis of HK97 assembly by scanning calorimetry and cryo-electron microscopy. This pathway involves self-assembly of hexamers and pentamers of the precursor capsid protein gp5 into procapsids; proteolysis of their N-terminal Delta-domains; expansion, a major conformational change; and covalent crosslinking. The thermal denaturation parameters convey the changes in stability at successive steps in assembly, and afford estimates of the corresponding changes in free energy. The procapsid represents a kinetically accessible local minimum of free energy. In maturation, it progresses to lower minima in a cascade punctuated by irreversible processes ("locks"), i.e. proteolysis and crosslinking, that lower kinetic barriers and prevent regression. We infer that Delta-domains not only guide assembly but also restrain the procapsid from premature expansion; their removal by proteolysis is conducive to initiating expansion and to its proceeding to completion. We also analyzed the mutant E219K, whose capsomers reassemble in vitro into procapsids with vacant vertices called "whiffleballs". E219K assemblies all have markedly reduced stability compared to wild-type gp5 (DeltaT(p) approximately -7 degrees C to -10 degrees C; where T(p) is the denaturation temperature). As the mutated residue is buried in the core of gp5, we attribute the observed reduction in stability to steric and electrostatic perturbations of the packing of side-chains in the subunit interior. To explain the whiffleball phenotype, we suggest that these effects propagate to the capsomer periphery in such a way as to differentially affect the stability or solubility of dissociated pentamers, leaving only hexamers to reassemble.

Symmetry, equivalence, and molecular self-assembly

Molecular self-assembly at equilibrium is fundamental to the fields of biological self-organization, the development of novel environmentally responsive polymeric materials, and nanofabrication. Our approach to understanding the principles governing this process is inspired by existing models and measurements for the self-assembly of actin, tubulin, and the ubiquitous icosahedral shell structures of viral capsids. We introduce a family of simple potentials that give rise to the self-assembly of linear polymeric, random surface ("membrane"), tubular ("nanotube"), and hollow icosahedral structures that are similar in many respects to their biological counterparts. The potentials involve equivalent particles and an interplay between directional (dipolar, multipolar) and short-range (van der Waals) interactions. Specifically, we find that the dipolar potential, having a continuous rotational symmetry about the dipolar axis, gives rise to chain formation, while particles with multipolar potentials, having discrete rotational symmetries (square quadrupole or triangular ring of dipoles or "hexapole"), lead to the self-assembly of open sheet, nanotube, and hollow icosahedral geometries. These changes in the geometry of self-assembly are accompanied by significant changes in the kinetics of the organization.

Control of virus assembly: HK97 "Whiffleball" mutant capsids without pentons

The capsid of Escherichia coli bacteriophage HK97 assembles as a 420 subunit icosahedral shell called Prohead I which undergoes a series of maturation steps, including proteolytic cleavage, conformational rearrangements, and covalent cross-linking among all the subunits to yield the highly stable mature Head II shell. Prohead I have been shown to assemble from pre-formed hexamers and pentamers of the capsid protein subunit. We report here the properties of a mutant of the capsid protein, E219K, which illuminate the assembly of Prohead I. The mutant capsid protein is capable of going through all of the biochemically and morphologically defined steps of capsid maturation, and when it is expressed by itself from a plasmid it assembles efficiently into a Prohead I that is morphologically indistinguishable from the wild-type Prohead I, with a full complement of both hexamers and pentamers. Unlike the wild-type Prohead I, when the mutant structure is dissociated into capsomers in vitro, only hexamers are found. When such preparations are put under assembly conditions, these mutant hexamers assemble into "Whiffleballs", particles that are identical with Prohead I except that they are missing the 12 pentamers. These Whiffleballs can even be converted to Prohead I by specifically binding wild-type pentamers. We argue that the ability of the mutant hexamers to assemble in the absence of pentamers implies that they retain a memory of their earlier assembled state, most likely as a conformational difference relative to assembly-naive hexamers. The data therefore favor a model in which Prohead I assembly is regulated by conformational switching of the hexamer.

Origin of icosahedral symmetry in viruses

With few exceptions, the shells (capsids) of sphere-like viruses have the symmetry of an icosahedron and are composed of coat proteins (subunits) assembled in special motifs, the T-number structures. Although the synthesis of artificial protein cages is a rapidly developing area of materials science, the design criteria for self-assembled shells that can reproduce the remarkable properties of viral capsids are only beginning to be understood. We present here a minimal model for equilibrium capsid structure, introducing an explicit interaction between protein multimers (capsomers). Using Monte Carlo simulation we show that the model reproduces the main structures of viruses in vivo (T-number icosahedra) and important nonicosahedral structures (with octahedral and cubic symmetry) observed in vitro. Our model can also predict capsid strength and shed light on genome release mechanisms.