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A contractile sheath and rigid tube assembly is a widespread apparatus used by bacteriophages, tailocins, and the bacterial type VI secretion system to penetrate cell membranes. In this mechanism, contraction of an external sheath powers the motion of an inner tube through the membrane. The structure, energetics, and mechanism of the machinery imply rigidity and straightness. The contractile tail of Agrobacterium tumefaciens bacteriophage Milano is flexible and bent to varying degrees, which sets it apart from other contractile tail-like systems. Here, we report structures of the Milano tail including the sheath-tube complex, baseplate, and putative receptor-binding proteins. The flexible-to-rigid transformation of the Milano tail upon contraction can be explained by unique electrostatic properties of the tail tube and sheath. All components of the Milano tail, including sheath subunits, are crosslinked by disulfides, some of which must be reduced for contraction to occur. The putative receptor-binding complex of Milano contains a tailspike, a tail fiber, and at least two small proteins that form a garland around the distal ends of the tailspikes and tail fibers. Despite being flagellotropic, Milano lacks thread-like tail filaments that can wrap around the flagellum, and is thus likely to employ a different binding mechanism.

Large gaps exist in our understanding of how bacteriophages, the most abundant biological entities on Earth, assemble and function. The structure of the “neck” region, where the DNA-filled capsid is connected to the host-recognizing tail remains poorly understood. We describe cryo-EM structures of the neck, the neck-capsid and neck-tail junctions, and capsid of the Agrobacterium phage Milano. The Milano neck 1 protein connects the 12-fold symmetrical neck to a 5-fold vertex of the icosahedral capsid. Comparison of Milano neck 1 homologs leads to four proposed classes, likely evolved from the simplest one in siphophages to more complex ones in myo- and podophages. Milano neck is surrounded by the atypical collar, which covalently crosslinks the tail sheath to neck 1. The Milano capsid is decorated with three types of proteins, a minor capsid protein (mCP) and two linking proteins crosslinking the mCP to the major capsid protein. The extensive network of disulfide bonds within and between neck, collar, capsid and tail provides an exceptional structural stability to Milano.

Flagellar filaments function as the propellers of the bacterial flagellum and their supercoiling is key to motility. The outer domains on the surface of the filament are non-critical for motility in many bacteria and their structures and functions are not conserved. Here, we show the atomic cryo-electron microscopy structures for flagellar filaments from enterohemorrhagic Escherichia coli O157:H7, enteropathogenic E. coli O127:H6, Achromobacter, and Sinorhizobium meliloti, where the outer domains dimerize or tetramerize to form either a sheath or a screw-like surface. These dimers are formed by 180° rotations of half of the outer domains. The outer domain sheath (ODS) plays a role in bacterial motility by stabilizing an intermediate waveform and prolonging the tumbling of E. coli cells. Bacteria with these ODS and screw-like flagellar filaments are commonly found in soil and human intestinal environments of relatively high viscosity suggesting a role for the dimerization in these environments.

In eukaryotes, homologous recombination proteins such as RAD51 and RAD52 play crucial roles in DNA repair and genome stability. Human RAD52 is a member of a large single-strand annealing protein (SSAP) family [1] and stimulates Rad51-dependent recombination [2, 3]. In prokaryotes and phages, it has been difficult to establish the presence of RAD52 homologs with conserved sequences. Putative SSAPs were recently found in several phages that infect strains of Lactococcus lactis[4]. One of these SSAPs was identified as Sak and was found in the virulent L. lactis phage ul36, which belongs to the Siphoviridae family [4, 5]. In this study, we show that Sak is homologous to the N terminus of human RAD52. Purified Sak binds single-stranded DNA (ssDNA) preferentially over double-stranded DNA (dsDNA) and promotes the renaturation of long complementary ssDNAs. Sak also binds RecA and stimulates homologous recombination reactions. Mutations shown to modulate RAD52 DNA binding [6] affect Sak similarly. Remarkably, electron-microscopic reconstruction of Sak reveals an undecameric (11) subunit ring, similar to the crystal structure of the N-terminal fragment of human RAD52 [7, 8]. For the first time, we propose a viral homolog of RAD52 at the amino acid, phylogenic, functional, and structural levels.

TorsinA is an ER-resident AAA + ATPase, whose deletion of glutamate E303 results in the genetic neuromuscular disease primary dystonia. TorsinA is an unusual AAA + ATPase that needs an external activator. Also, it likely does not thread a peptide substrate through a narrow central channel, in contrast to its closest structural homologs. Here, we examined the oligomerization of TorsinA to get closer to a molecular understanding of its still enigmatic function. We observe TorsinA to form helical filaments, which we analyzed by cryo-electron microscopy using helical reconstruction. The 4.4 Å structure reveals long hollow tubes with a helical periodicity of 8.5 subunits per turn, and an inner channel of ~ 4 nm diameter. We further show that the protein is able to induce tubulation of membranes in vitro, an observation that may reflect an entirely new characteristic of AAA + ATPases. We discuss the implications of these observations for TorsinA function., National Institutes of Health (Grant AR065484), U.S. Army Medical Research Acquisition Activity Peer Reviewed Medical Research Program (Award W81XWH1810515)

Uropathogenic E. coli (UPEC), which cause urinary tract infections (UTI), utilize type 1 pili, a chaperone usher pathway (CUP) pilus, to cause UTI and colonize the gut. The pilus rod, comprised of repeating FimA subunits, provides a structural scaffold for displaying the tip adhesin, FimH. We solved the 4.2 Å resolution structure of the type 1 pilus rod using cryo-electron microscopy. Residues forming the interactive surfaces that determine the mechanical properties of the rod were maintained by selection based on a global alignment of fimA sequences. We identified mutations that did not alter pilus production in vitro but reduced the force required to unwind the rod. UPEC expressing these mutant pili were significantly attenuated in bladder infection and intestinal colonization in mice. This study elucidates an unappreciated functional role for the molecular spring-like property of type 1 pilus rods in host-pathogen interactions and carries important implications for other pilus-mediated diseases.

Urinary tract infections (UTIs) are caused by a wide range of pathogens, but the most common causative agent of UTIs is uropathogenic Escherichia coli (UPEC). Virtually all uropathogenic strains of E. coli encode filamentous surface adhesive organelles called type 1 pili, which are a subset of Chaperone-usher pathway (CUP) pili. CUP pili are also ubiquitously expressed on the surface of many other Gram-negative bacterial pathogens. They are important virulence factors facilitating host-pathogen interactions that are crucial for the establishment and persistence of an infection, and involved in regulating other key processes such as biofilm formation. We have solved the 4.2 Å resolution cryo-EM structure of the type 1 pilus, which was present as a background contaminant in a prep of type 4 pili. We have taken advantage of the strength of cryo-EM to separate different molecules and conformations present in solution to show that filament images which might otherwise have been discarded as a contaminant can actually be used to build an atomic model. The model reveals the residues that allow a long chain of FimA subunits, linked by the insertion of a β-strand of one subunit into the β-sheet of an adjacent subunit, to coil into a rigid rod. We show that site-specific mutation of these residues reduces the force needed to unwind the rod. Strikingly, one mutation (A22R) which showed the greatest reduction in unwinding force, eliminated bladder infections in a mouse model. This is presumably due to the fact that the altered mechanics of the A22R pilus rod cannot withstand the shear forces due to urinary flow in the bladder and bacteria harboring this mutation are cleared from the bladder. This provides new insights into the important role of pili mechanics in bacterial pathogenesis.

Uropathogenic E. coli (UPEC), which cause urinary tract infections (UTI), utilize type 1 pili, a chaperone usher pathway (CUP) pilus, to cause UTI and colonize the gut. The pilus rod, comprised of repeating FimA subunits, provides a structural scaffold for displaying the tip adhesin, FimH. We solved the 4.2 Å resolution structure of the type 1 pilus rod using cryo-electron microscopy. Residues forming the interactive surfaces that determine the mechanical properties of the rod were maintained by selection based on a global alignment of fimA sequences. We identified mutations that did not alter pilus production in vitro but reduced the force required to unwind the rod. UPEC expressing these mutant pili were significantly attenuated in bladder infection and intestinal colonization in mice. This study elucidates an unappreciated functional role for the molecular spring-like property of type 1 pilus rods in host-pathogen interactions and carries important implications for other pilus-mediated diseases.

Uropathogenic E. coli (UPEC), which cause urinary tract infections (UTI), utilize type 1 pili, a chaperone usher pathway (CUP) pilus, to cause UTI and colonize the gut. The pilus rod, comprised of repeating FimA subunits, provides a structural scaffold for displaying the tip adhesin, FimH. We solved the 4.2 Å resolution structure of the type 1 pilus rod using cryo-electron microscopy. Residues forming the interactive surfaces that determine the mechanical properties of the rod were maintained by selection based on a global alignment of fimA sequences. We identified mutations that did not alter pilus production in vitro but reduced the force required to unwind the rod. UPEC expressing these mutant pili were significantly attenuated in bladder infection and intestinal colonization in mice. This study elucidates an unappreciated functional role for the molecular spring-like property of type 1 pilus rods in host-pathogen interactions and carries important implications for other pilus-mediated diseases.

Uropathogenic E. coli (UPEC), which cause urinary tract infections (UTI), utilize type 1 pili, a chaperone usher pathway (CUP) pilus, to cause UTI and colonize the gut. The pilus rod, comprised of repeating FimA subunits, provides a structural scaffold for displaying the tip adhesin, FimH. We solved the 4.2 Å resolution structure of the type 1 pilus rod using cryo-electron microscopy. Residues forming the interactive surfaces that determine the mechanical properties of the rod were maintained by selection based on a global alignment of fimA sequences. We identified mutations that did not alter pilus production in vitro but reduced the force required to unwind the rod. UPEC expressing these mutant pili were significantly attenuated in bladder infection and intestinal colonization in mice. This study elucidates an unappreciated functional role for the molecular spring-like property of type 1 pilus rods in host-pathogen interactions and carries important implications for other pilus-mediated diseases.

Uropathogenic E. coli (UPEC), which cause urinary tract infections (UTI), utilize type 1 pili, a chaperone usher pathway (CUP) pilus, to cause UTI and colonize the gut. The pilus rod, comprised of repeating FimA subunits, provides a structural scaffold for displaying the tip adhesin, FimH. We solved the 4.2 Å resolution structure of the type 1 pilus rod using cryo-electron microscopy. Residues forming the interactive surfaces that determine the mechanical properties of the rod were maintained by selection based on a global alignment of fimA sequences. We identified mutations that did not alter pilus production in vitro but reduced the force required to unwind the rod. UPEC expressing these mutant pili were significantly attenuated in bladder infection and intestinal colonization in mice. This study elucidates an unappreciated functional role for the molecular spring-like property of type 1 pilus rods in host-pathogen interactions and carries important implications for other pilus-mediated diseases.

The prokaryotic origins of the actin cytoskeleton have been firmly established, but it has become clear that the bacterial actins form a wide variety of different filaments, different both from each other and from eukaryotic F-actin. We have used electron cryomicroscopy (cryo-EM) to examine the filaments formed by the protein crenactin (a crenarchaeal actin) from Pyrobaculum calidifontis, an organism that grows optimally at 90 degrees C. Although this protein only has similar to 20% sequence identity with eukaryotic actin, phylogenetic analyses have placed it much closer to eukaryotic actin than any of the bacterial homologs. It has been assumed that the crenactin filament is double-stranded, like F-actin, in part because it would be hard to imagine how a single-stranded filament would be stable at such high temperatures. We show that not only is the crenactin filament single-stranded, but that it is remarkably similar to each of the two strands in F-actin. A large insertion in the crenactin sequence would prevent the formation of an F-actin-like double-stranded filament. Further, analysis of two existing crystal structures reveals six different subunit-subunit interfaces that are filament-like, but each is different from the others in terms of significant rotations. This variability in the subunit-subunit interface, seen at atomic resolution in crystals, can explain the large variability in the crenactin filaments observed by cryo-EM and helps to explain the variability in twist that has been observed for eukaryotic actin filaments.

Repair of DNA double strand breaks by homologous recombination (HR) is initiated by Rad51 filament nucleation on single-stranded DNA (ssDNA), which catalyzes strand exchange with homologous duplex DNA. BRCA2 and the Rad51 paralogs are tumor suppressors and critical mediators of Rad51. To gain insight into Rad51 paralog function, we investigated a heterodimeric Rad51 paralog complex, RFS-1/RIP-1, and uncovered the molecular basis by which Rad51 paralogs promote HR. Unlike BRCA2, which nucleates RAD-51-ssDNA filaments, RFS-1/RIP-1 binds and remodels pre-synaptic filaments to a stabilized, "open," and flexible conformation, in which the ssDNA is more accessible to nuclease digestion and RAD-51 dissociation rate is reduced. Walker box mutations in RFS-1, which abolish filament remodeling, fail to stimulate RAD-51 strand exchange activity, demonstrating that remodeling is essential for RFS-1/RIP-1 function. We propose that Rad51 paralogs stimulate HR by remodeling the Rad51 filament, priming it for strand exchange with the template duplex.

The prokaryotic origins of the actin cytoskeleton have been firmly established, but it has become clear that the bacterial actins form a wide variety of different filaments, different both from each other and from eukaryotic F-actin. We have used electron cryomicroscopy (cryo-EM) to examine the filaments formed by the protein crenactin (a crenarchaeal actin) from Pyrobaculum calidifontis, an organism that grows optimally at 90 degrees C. Although this protein only has similar to 20% sequence identity with eukaryotic actin, phylogenetic analyses have placed it much closer to eukaryotic actin than any of the bacterial homologs. It has been assumed that the crenactin filament is double-stranded, like F-actin, in part because it would be hard to imagine how a single-stranded filament would be stable at such high temperatures. We show that not only is the crenactin filament single-stranded, but that it is remarkably similar to each of the two strands in F-actin. A large insertion in the crenactin sequence would prevent the formation of an F-actin-like double-stranded filament. Further, analysis of two existing crystal structures reveals six different subunit-subunit interfaces that are filament-like, but each is different from the others in terms of significant rotations. This variability in the subunit-subunit interface, seen at atomic resolution in crystals, can explain the large variability in the crenactin filaments observed by cryo-EM and helps to explain the variability in twist that has been observed for eukaryotic actin filaments.

Repair of DNA double strand breaks by homologous recombination (HR) is initiated by Rad51 filament nucleation on single-stranded DNA (ssDNA), which catalyzes strand exchange with homologous duplex DNA. BRCA2 and the Rad51 paralogs are tumor suppressors and critical mediators of Rad51. To gain insight into Rad51 paralog function, we investigated a heterodimeric Rad51 paralog complex, RFS-1/RIP-1, and uncovered the molecular basis by which Rad51 paralogs promote HR. Unlike BRCA2, which nucleates RAD-51-ssDNA filaments, RFS-1/RIP-1 binds and remodels pre-synaptic filaments to a stabilized, "open," and flexible conformation, in which the ssDNA is more accessible to nuclease digestion and RAD-51 dissociation rate is reduced. Walker box mutations in RFS-1, which abolish filament remodeling, fail to stimulate RAD-51 strand exchange activity, demonstrating that remodeling is essential for RFS-1/RIP-1 function. We propose that Rad51 paralogs stimulate HR by remodeling the Rad51 filament, priming it for strand exchange with the template duplex.

This Meeting Review describes the proceedings and conclusions from the inaugural meeting of the Electron Microscopy Validation Task Force organized by the Unified Data Resource for 3DEM (http://www.emdatabank.org) and held at Rutgers University in New Brunswick, NJ on September 28 and 29, 2010. At the workshop, a group of scientists involved in collecting electron microscopy data, using the data to determine three-dimensional electron microscopy (3DEM) density maps, and building molecular models into the maps explored how to assess maps, models, and other data that are deposited into the Electron Microscopy Data Bank and Protein Data Bank public data archives. The specific recommendations resulting from the workshop aim to increase the impact of 3DEM in biology and medicine.

Previous studies showed that the K342E substitution in the Saccharomyces cerevisiae Rad51 protein increases the interaction with Rad54 protein in the two-hybrid system, leads to increased sensitivity to the alkylating agent MMS and hyper-recombination in an oligonucleotide-mediated gene targeting assay. K342 localizes in loop 2, a region of Rad51 whose function is not well understood. Here, we show that Rad51-K342E displays DNA-independent and DNA-dependent ATPase activities, owing to its ability to form filaments in the absence of a DNA lattice. These filaments exhibit a compressed pitch of 81 A, whereas filaments of wild-type Rad51 and Rad51-K342E on DNA form extended filaments with a 97 A pitch. Rad51-K342E shows near normal binding to ssDNA, but displays a defect in dsDNA binding, resulting in less stable protein-dsDNA complexes. The mutant protein is capable of catalyzing the DNA strand exchange reaction and is insensitive to inhibition by the early addition of dsDNA. Wild-type Rad51 protein is inhibited under such conditions, because of its ability to bind dsDNA. No significant changes in the interaction between Rad51-K342E and Rad54 could be identified. These findings suggest that loop 2 contributes to the primary DNA-binding site in Rad51, controlling filament formation and ATPase activity.

Previous studies showed that the K342E substitution in the Saccharomyces cerevisiae Rad51 protein increases the interaction with Rad54 protein in the two-hybrid system, leads to increased sensitivity to the alkylating agent MMS and hyper-recombination in an oligonucleotide-mediated gene targeting assay. K342 localizes in loop 2, a region of Rad51 whose function is not well understood. Here, we show that Rad51-K342E displays DNA-independent and DNA-dependent ATPase activities, owing to its ability to form filaments in the absence of a DNA lattice. These filaments exhibit a compressed pitch of 81 A, whereas filaments of wild-type Rad51 and Rad51-K342E on DNA form extended filaments with a 97 A pitch. Rad51-K342E shows near normal binding to ssDNA, but displays a defect in dsDNA binding, resulting in less stable protein-dsDNA complexes. The mutant protein is capable of catalyzing the DNA strand exchange reaction and is insensitive to inhibition by the early addition of dsDNA. Wild-type Rad51 protein is inhibited under such conditions, because of its ability to bind dsDNA. No significant changes in the interaction between Rad51-K342E and Rad54 could be identified. These findings suggest that loop 2 contributes to the primary DNA-binding site in Rad51, controlling filament formation and ATPase activity.

In eukaryotes, homologous recombination proteins such as RAD51 and RAD52 play crucial roles in DNA repair and genome stability. Human RAD52 is a member of a large single-strand annealing protein (SSAP) family [1] and stimulates Rad51-dependent recombination [2, 3]. In prokaryotes and phages, it has been difficult to establish the presence of RAD52 homologs with conserved sequences. Putative SSAPs were recently found in several phages that infect strains of Lactococcus lactis[4]. One of these SSAPs was identified as Sak and was found in the virulent L. lactis phage ul36, which belongs to the Siphoviridae family [4, 5]. In this study, we show that Sak is homologous to the N terminus of human RAD52. Purified Sak binds single-stranded DNA (ssDNA) preferentially over double-stranded DNA (dsDNA) and promotes the renaturation of long complementary ssDNAs. Sak also binds RecA and stimulates homologous recombination reactions. Mutations shown to modulate RAD52 DNA binding [6] affect Sak similarly. Remarkably, electron-microscopic reconstruction of Sak reveals an undecameric (11) subunit ring, similar to the crystal structure of the N-terminal fragment of human RAD52 [7, 8]. For the first time, we propose a viral homolog of RAD52 at the amino acid, phylogenic, functional, and structural levels.

Rad51 and Rad54 are key proteins that collaborate during homologous recombination. Rad51 forms a presynaptic filament with ATP and ssDNA active in homology search and DNA strand exchange, but the precise role of its ATPase activity is poorly understood. Rad54 is an ATP-dependent dsDNA motor protein that can dissociate Rad51 from dsDNA, the product complex of DNA strand exchange. Kinetic analysis of the budding yeast proteins revealed that the catalytic efficiency of the Rad54 ATPase was stimulated by partial filaments of wild-type and Rad51-K191R mutant protein on dsDNA, unambiguously demonstrating that the Rad54 ATPase activity is stimulated under these conditions. Experiments with Rad51-K191R as well as with wild-type Rad51-dsDNA filaments formed in the presence of ATP, ADP or ATP-gamma-S showed that efficient Rad51 turnover from dsDNA requires both the Rad51 ATPase and the Rad54 ATPase activities. The results with Rad51-K191R mutant protein also revealed an unexpected defect in binding to DNA. Once formed, Rad51-K191R-DNA filaments appeared normal upon electron microscopic inspection, but displayed significantly increased stability. These biochemical defects in the Rad51-K191R protein could lead to deficiencies in presynapsis (filament formation) and postsynapsis (filament disassembly) in vivo.

Rad51 and Rad54 are key proteins that collaborate during homologous recombination. Rad51 forms a presynaptic filament with ATP and ssDNA active in homology search and DNA strand exchange, but the precise role of its ATPase activity is poorly understood. Rad54 is an ATP-dependent dsDNA motor protein that can dissociate Rad51 from dsDNA, the product complex of DNA strand exchange. Kinetic analysis of the budding yeast proteins revealed that the catalytic efficiency of the Rad54 ATPase was stimulated by partial filaments of wild-type and Rad51-K191R mutant protein on dsDNA, unambiguously demonstrating that the Rad54 ATPase activity is stimulated under these conditions. Experiments with Rad51-K191R as well as with wild-type Rad51-dsDNA filaments formed in the presence of ATP, ADP or ATP-gamma-S showed that efficient Rad51 turnover from dsDNA requires both the Rad51 ATPase and the Rad54 ATPase activities. The results with Rad51-K191R mutant protein also revealed an unexpected defect in binding to DNA. Once formed, Rad51-K191R-DNA filaments appeared normal upon electron microscopic inspection, but displayed significantly increased stability. These biochemical defects in the Rad51-K191R protein could lead to deficiencies in presynapsis (filament formation) and postsynapsis (filament disassembly) in vivo.

Contraction of muscle involves the cyclic interaction of myosin heads on the thick filaments with actin subunits in the thin filaments. Muscles relax when this interaction is blocked by molecular switches on either or both filaments. Insight into the relaxed (switched OFF) structure of myosin has come from electron microscopic studies of smooth muscle myosin molecules, which are regulated by phosphorylation. These studies suggest that the OFF state is achieved by an asymmetric, intramolecular interaction between the actin-binding region of one head and the converter region of the other, switching both heads off. Although this is a plausible model for relaxation based on isolated myosin molecules, it does not reveal whether this structure is present in native myosin filaments. Here we analyse the structure of a phosphorylation-regulated striated muscle thick filament using cryo-electron microscopy. Three-dimensional reconstruction and atomic fitting studies suggest that the 'interacting-head' structure is also present in the filament, and that it may underlie the relaxed state of thick filaments in both smooth and myosin-regulated striated muscles over a wide range of species.

Mini-chromosome maintenance (MCM) proteins form a conserved family found in all eukaryotes and are essential for DNA replication. They exist as heteromultimeric complexes containing as many as six different proteins. These complexes are believed to be the replicative helicases, functioning as hexameric rings at replication forks. In most archaea a single MCM protein exists. The protein from Methanobacterium thermoautotrophicum (mtMCM) has been reported to assemble into a large complex consistent with a dodecamer. We show that mtMCM can assemble into a heptameric ring. This ring contains a C-terminal helicase domain that can be fit with crystal structures of ring helicases and an N-terminal domain of unknown function. While the structure of the ring is very similar to that of hexameric replicative helicases such as bacteriophage T7 gp4, our results show that such ring structures may not be constrained to have only six subunits.

Mini-chromosome maintenance (MCM) proteins form a conserved family found in all eukaryotes and are essential for DNA replication. They exist as heteromultimeric complexes containing as many as six different proteins. These complexes are believed to be the replicative helicases, functioning as hexameric rings at replication forks. In most archaea a single MCM protein exists. The protein from Methanobacterium thermoautotrophicum (mtMCM) has been reported to assemble into a large complex consistent with a dodecamer. We show that mtMCM can assemble into a heptameric ring. This ring contains a C-terminal helicase domain that can be fit with crystal structures of ring helicases and an N-terminal domain of unknown function. While the structure of the ring is very similar to that of hexameric replicative helicases such as bacteriophage T7 gp4, our results show that such ring structures may not be constrained to have only six subunits.

Mini-chromosome maintenance (MCM) proteins form a conserved family found in all eukaryotes and are essential for DNA replication. They exist as heteromultimeric complexes containing as many as six different proteins. These complexes are believed to be the replicative helicases, functioning as hexameric rings at replication forks. In most archaea a single MCM protein exists. The protein from Methanobacterium thermoautotrophicum (mtMCM) has been reported to assemble into a large complex consistent with a dodecamer. We show that mtMCM can assemble into a heptameric ring. This ring contains a C-terminal helicase domain that can be fit with crystal structures of ring helicases and an N-terminal domain of unknown function. While the structure of the ring is very similar to that of hexameric replicative helicases such as bacteriophage T7 gp4, our results show that such ring structures may not be constrained to have only six subunits.