Spherical Capsids Research Articles

Spool-Nematic Ordering of dsDNA and dsRNA under Confinement.

The ability of double-stranded DNA or RNA to locally melt and form kinks leads to strong nonlinear elasticity effects that qualitatively affect their packing in confined spaces. Using analytical theory and numerical simulation we show that kink formation entails a mixed spool-nematic ordering of double-stranded DNA or RNA in spherical capsids, consisting of an outer spool domain and an inner, twisted nematic domain. These findings explain the experimentally observed nematic domains in viral capsids and imply that nonlinear elasticity must be considered to predict the configurations and dynamics of double-stranded genomes in viruses, bacterial nucleoids or gene-delivery vehicles. The nonlinear elastic theory suggests that spool-nematic ordering is a general feature of strongly confined kinkable polymers.

Densest-known packings and phase behavior of hard spherical capsids.

By mostly using Monte Carlo numerical simulation, this work investigates the densest-known packings and phase behavior of hard spherical capsids, i.e., hard infinitesimally thin spherical caps with a subtended angle larger than the straight angle. The infinitely degenerate densest-known packings are all characterized by hard spherical capsids that interlock and can be subdivided into three families. The first family includes crystalline packings that are constructed by suitably rotating and stacking layers of hexagonally arranged and suitably tilted hard spherical capsids; depending on the successive rotations, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. The second family includes crystalline packings that are characterized by rhombic motifs; they all become the face-centered cubic crystal in the hard-sphere limit. The third family includes crystalline packings that are constructed by suitably shifting and stacking layers in which hard spherical capsids are arranged in tightly packed, straight or zigzag, columns; depending on the successive shifts, the crystalline packings of this family can become the face-centered cubic crystal, the hexagonal close-packed crystal, and their infinitely degenerate variants in the hard-sphere limit. In the plane number density vs subtended angle, the phase diagram of hard spherical capsids features a hexagonal columnar liquid-crystalline phase, toward the hard-hemispherical-cap limit, and a plastic-crystalline phase, toward the hard-sphere limit, in addition to the isotropic fluid phase and crystalline phases. On departing from the hard-sphere limit, the increasing propensity of hard spherical capsids to interlock progressively disfavors the plastic-crystalline phase while favoring auto-assemblage into mostly dimeric interlocks in the denser isotropic fluid phase so that a purely entropic isotropic-fluid-plastic-crystal-isotropic-fluid re-entrant sequence of phase transitions is observed in systems of hard spherical capsids with a subtended angle intermediate between the straight angle and the complete angle.

Molecular Engineering of E. coli Bacterioferritin: A Versatile Nanodimensional Protein Cage.

Currently, intense interest is focused on the discovery and application of new multisubunit cage proteins and spherical virus capsids to the fields of bionanotechnology, drug delivery, and diagnostic imaging as their internal cavities can serve as hosts for fluorophores or bioactive molecular cargo. Bacterioferritin is unusual in the ferritin protein superfamily of iron-storage cage proteins in that it contains twelve heme cofactors and is homomeric. The goal of the present study is to expand the capabilities of ferritins by developing new approaches to molecular cargo encapsulation employing bacterioferritin. Two strategies were explored to control the encapsulation of a diverse range of molecular guests compared to random entrapment, a predominant strategy employed in this area. The first was the inclusion of histidine-tag peptide fusion sequences within the internal cavity of bacterioferritin. This approach allowed for the successful and controlled encapsulation of a fluorescent dye, a protein (fluorescently labeled streptavidin), or a 5 nm gold nanoparticle. The second strategy, termed the heme-dependent cassette strategy, involved the substitution of the native heme with heme analogs attached to (i) fluorescent dyes or (ii) nickel-nitrilotriacetate (NTA) groups (which allowed for controllable encapsulation of a histidine-tagged green fluorescent protein). An in silico docking approach identified several small molecules able to replace the heme and capable of controlling the quaternary structure of the protein. A transglutaminase-based chemoenzymatic approach to surface modification of this cage protein was also accomplished, allowing for future nanoparticle targeting. This research presents novel strategies to control a diverse set of molecular encapsulations and adds a further level of sophistication to internal protein cavity engineering.

The effects of the shape of a capsid on the ejection rate of a single polymer chain through a nanopore.

The shape of a viral capsid affects the equilibrium conformation of DNA inside the capsid: the equilibrium DNA conformation inside a spherical capsid is a concentric spool while the equilibrium conformation inside an elongated capsid is a twisted toroid. The conformation of DNA, jammed inside the capsid due to high internal pressure, influences the ejection kinetics of the DNA from the capsid. Therefore, one would expect that the DNA ejection kinetics would be subject to the shape of the viral capsid. The effects of the capsid shape on the ejection, however, remain elusive partly due to a plethora of viral capsid shapes. In this work, we perform Langevin dynamics simulations for the ejection of a polymer chain from three different types of viral capsids: (1) spherical, (2) cubic, and (3) cuboid capsids. We find that the ejection rate of the polymer chain from the spherical capsid is much faster than that from either cubic or cuboid capsids. The polymer chain in the spherical capsid may undergo collective rotational relaxation more readily such that the polymer chain becomes more mobile inside the spherical capsid, which enhances the ejection kinetics. On the other hand, a threading motion is dominant inside cubic and cuboid capsids. We also find that the effects of the collective rotational motion become more significant for a more rigid chain inside a capsid.

Coronavirus peplomer charge heterogeneity

Recent advancements in viral hydrodynamics afford the calculation of the transport properties of particle suspensions from first principles, namely, from the detailed particle shapes. For coronavirus suspensions, for example, the shape can be approximated by beading (i) the spherical capsid and (ii) the radially protruding peplomers. The general rigid bead-rod theory allows us to assign Stokesian hydrodynamics to each bead. Thus, viral hydrodynamics yields the suspension rotational diffusivity, but not without first arriving at a configuration for the cationic peplomers. Prior work considered identical peplomers charged identically. However, a recent pioneering experiment uncovers remarkable peplomer size and charge heterogeneities. In this work, we use energy minimization to arrange the spikes, charged heterogeneously to obtain the coronavirus spike configuration required for its viral hydrodynamics. For this, we use the measured charge heterogeneity. We consider 20 000 randomly generated possibilities for cationic peplomers with formal charges ranging from 30 to 55. We find the configurations from energy minimization of all of these possibilities to be nearly spherically symmetric, all slightly oblate, and we report the corresponding breadth of the dimensionless rotational diffusivity, the transport property around which coronavirus cell attachment revolves.

Close packings of identical proteins in small spherical capsids and similar proteinaceous shells.

Understanding the principles governing protein arrangement in viral capsids and structurally similar protein shells can enable the development of new antiviral strategies and the design of artificial protein cages for various applications. We study these principles within the context of the close packing problem, by analyzing dozens of small spherical shells assembled from a single type of protein. First, we use icosahedral spherical close packings containing 60T identical disks, where T ≤ 4, to rationalize the protein arrangement in twenty real icosahedral shells both satisfying and violating the paradigmatic Caspar-Klug model. We uncover a striking correspondence between the protein mass centers in the considered shells and the centers of disks in the close packings. To generalize the packing model, we consider proteins with a weak shape anisotropy and propose an interaction energy, minimization of which allows us to obtain spherical dense packings of slightly anisotropic structural units. In the case of strong anisotropy, we model the proteins as sequences of overlapping discs of different sizes, with minimum energy configuration not only resulting in packings, accurately reproducing locations and orientations of individual proteins, but also revealing that icosahedral packings that display the handedness of real capsids are energetically more favorable. Finally, by introducing effective disc charges, we rationalize the formation of inter-protein bonds in protein shells.

Protein cargo encapsulation by virus-like particles: Strategies and applications.

Viruses and the recombinant protein cages assembled from their structural proteins, known as virus-like particles (VLPs), have gained wide interest as tools in biotechnology and nanotechnology. Detailed structural information and their amenability to genetic and chemical modification make them attractive systems for further engineering. This review describes the range of non-enveloped viruses that have been co-opted for heterologous protein cargo encapsulation and the strategies that have been developed to drive encapsulation. Spherical capsids of a range of sizes have been used as platforms for protein cargo encapsulation. Various approaches, based on native and non-native interactions between the cargo proteins and inner surface of VLP capsids, have been devised to drive encapsulation. Here, we outline the evolution of these approaches, discussing their benefits and limitations. Like the viruses from which they are derived, VLPs are of interest in both biomedical and materials applications. The encapsulation of protein cargo inside VLPs leads to numerous uses in both fundamental and applied biocatalysis and biomedicine, some of which are discussed herein. The applied science of protein-encapsulating VLPs is emerging as a research field with great potential. Developments in loading control, higher order assembly, and capsid optimization are poised to realize this potential in the near future. This article is categorized under: Nanotechnology Approaches to Biology > Nanoscale Systems in Biology Biology-Inspired Nanomaterials > Protein and Virus-Based Structures.

Coronavirus pleomorphism

The coronavirus is always idealized as a spherical capsid with radially protruding spikes. However, histologically, in the tissues of infected patients, capsids in cross section are elliptical, and only sometimes spherical [Neuman et al., “Supramolecular architecture of severe acute respiratory syndrome coronavirus revealed by electron cryomicroscopy,” J Virol, 80, 7918 (2006)]. This capsid ellipticity implies that coronaviruses are oblate or prolate or both. We call this diversity of shapes, pleomorphism. Recently, the rotational diffusivity of the spherical coronavirus in suspension was calculated, from first principles, using general rigid bead-rod theory [Kanso et al., “Coronavirus rotational diffusivity,” Phys Fluids 32, 113101 (2020)]. We did so by beading the spherical capsid and then also by replacing each of its bulbous spikes with a single bead. In this paper, we use energy minimization for the spreading of the spikes, charged identically, over the oblate or prolate capsids. We use general rigid bead-rod theory to explore the role of such coronavirus cross-sectional ellipticity on its rotational diffusivity, the transport property around which its cell attachment revolves. We learn that coronavirus ellipticity drastically decreases its rotational diffusivity, be it oblate or prolate.

Structural and Functional Characterizations of Cancer Targeting Nanoparticles Based on Hepatitis B Virus Capsid.

Cancer targeting nanoparticles have been extensively studied, but stable and applicable agents have yet to be developed. Here, we report stable nanoparticles based on hepatitis B core antigen (HBcAg) for cancer therapy. HBcAg monomers assemble into spherical capsids of 180 or 240 subunits. HBcAg was engineered to present an affibody for binding to human epidermal growth factor receptor 1 (EGFR) and to present histidine and tyrosine tags for binding to gold ions. The HBcAg engineered to present affibody and tags (HAF) bound specifically to EGFR and exterminated the EGFR-overexpressing adenocarcinomas under alternating magnetic field (AMF) after binding with gold ions. Using cryogenic electron microscopy (cryo-EM), we obtained the molecular structures of recombinant HAF and found that the overall structure of HAF was the same as that of HBcAg, except with the affibody on the spike. Therefore, HAF is viable for cancer therapy with the advantage of maintaining a stable capsid form. If the affibody in HAF is replaced with a specific sequence to bind to another targetable disease protein, the nanoparticles can be used for drug development over a wide spectrum.

Crystal morphology of spherical viruses

The article discusses modern views on the structure of spherical virus capsids, which have the shape of icosahedrons (icosahedral viruses). Each face of icosahedron is composed of a single-layer closest packing of protein globules, which can have different orientation relative to the edges of icosahedron. If the lines of globules are parallel to the edges of icosahedron, then the capsid has a point symmetry group Ih (with symmetry planes), if they are not parallel – the symmetry group I (without planes). From a mathematical point of view, in both symmetry groups there are series that unite equally (up to similarity) arranged capsids. They are connected pairwise by transitions to dual forms (homologous series). A hypothesis is formulated that the largest spherical viruses can have even more diverse and complex capsid structures. Along with icosahedron, their basic forms can be any simple shapes, allowed in Ih and I symmetry groups (8 in total). A suggestion is made that transitions within similarity series and between homologous series have a phylogenetic significance. There are known spherical viruses of both symmetry groups. For example, the SARS-CoV-2 coronavirus has a symmetry group Ih and belongs to a well-known series. The crystallographic approach allows to construct a strict morphological classification of spherical viruses. This is important for their early recognition and separate examination. The article demonstrates practical application of crystal morphology in the study of viral systems – an urgent problem of geoecology and life protection.

Peplomer bulb shape and coronavirus rotational diffusivity.

Recently, the rotational diffusivity of the coronavirus particle in suspension was calculated, from first principles, using general rigid bead-rod theory [M. A. Kanso, Phys. Fluids 32, 113101 (2020)]. We did so by beading the capsid and then also by replacing each of its bulbous spikes with a single bead. However, each coronavirus spike is a glycoprotein trimer, and each spike bulb is triangular. In this work, we replace each bulbous coronavirus spike with a bead triplet, where each bead of the triplet is charged identically. This paper, thus, explores the role of bulb triangularity on the rotational diffusivity, an effect not previously considered. We thus use energy minimization for the spreading of triangular bulbs over the spherical capsid. The latter both translates and twists the coronavirus spikes relative to one another, and we then next arrive at the rotational diffusivity of the coronavirus particle in suspension, from first principles. We learn that the triangularity of the coronavirus spike bulb decreases its rotational diffusivity. For a typical peplomer population of 74, bulb triangularity decreases the rotational diffusivity by .

The expression in plants of an engineered VP2 protein of Infectious Bursal Disease Virus induces formation of structurally heterogeneous particles that protect from a very virulent viral strain.

Infectious Bursal Disease Virus (IBDV), the etiological agent of Gumboro disease, causes mortality and immunosuppression in chickens and major losses to poultry industry worldwide. The IBDV major capsid protein VP2 is considered the best candidate for the production of novel subunit vaccines. This structural protein contains the major conformational epitopes responsible for the induction of IBDV neutralizing antibodies in chickens and has been demonstrated able to form supramolecular structures in yeast and insect cells. The aim of this study was to express an engineered version of the VP2 protein (His-pVP2) to verify its ability to self-assemble into virus-like particles in plants. The recombinant VP2 was transiently expressed by agroinfiltration in Nicotiana benthamiana and transmission electron microscopy of sucrose density gradient fractions revealed the presence of a mixed population of differently shaped particles ranging from spherical capsids, with a diameter between ~25 and ~70 nm, to tubular structures, with variable length (from 100 to 400 nm). The recombinant VP2-based particles when used for the intramuscular immunization of specific-pathogen-free chicks resulted able to induce the production of anti-IBDV specific antibodies at titers comparable to those induced by a commercial vaccine. Moreover, all the immunized birds survived to the challenge with a Moroccan very virulent IBDV strain with no major histomorphological alterations of the Bursa of Fabricius, similarly to what obtained with the commercial inactivated vaccine.

Coronavirus rotational diffusivity.

Just 11 weeks after the confirmation of first infection, one team had already discovered and published [D. Wrapp et al., “Cryo-EM structure of the 2019-nCoV spike in the prefusion conformation,” Science 367(6483), 1260–1263 (2020)] in exquisite detail about the new coronavirus, along with how it differs from previous viruses. We call the virus particle causing the COVID-19 disease SARS-CoV-2, a spherical capsid covered with spikes termed peplomers. Since the virus is not motile, it relies on its own random thermal motion, specifically the rotational component of this thermal motion, to align its peplomers with targets. The governing transport property for the virus to attack successfully is thus the rotational diffusivity. Too little rotational diffusivity and too few alignments are produced to properly infect. Too much, and the alignment intervals will be too short to properly infect, and the peplomer is wasted. In this paper, we calculate the rotational diffusivity along with the complex viscosity of four classes of virus particles of ascending geometric complexity: tobacco mosaic, gemini, adeno, and corona. The gemini and adeno viruses share icosahedral bead arrangements, and for the corona virus, we use polyhedral solutions to the Thomson problem to arrange its peplomers. We employ general rigid bead–rod theory to calculate complex viscosities and rotational diffusivities, from first principles, of the virus suspensions. We find that our ab initio calculations agree with the observed complex viscosity of the tobacco mosaic virus suspension. From our analysis of the gemini virus suspension, we learn that the fine detail of the virus structure governs its rotational diffusivity. We find the characteristic time for the adenovirus from general rigid bead–rod theory. Finally, from our analysis of the coronavirus suspension, we learn that its rotational diffusivity descends monotonically with its number of peplomers.

Functional Peptide Nanocapsules Self-Assembled from β-Annulus Peptides.

Spherical viruses are unique nanocapsules formed by self-assembly of coat proteins (capsids). By mimicking natural spherical capsids, various artificial viral capsids are developed by using self-assembled proteins and peptides as building blocks. We developed an artificial viral capsid consisting of a β-annulus peptide designed from natural viruses. The "β-annulus capsid" can be functionalized by encapsulating guest molecules to the inside and decoration of exogenous molecules on the outside. Here, we describe the encapsulation and decoration on the β-annulus capsids by connecting additional sequences to the β-annulus peptide, conjugation with objective molecules, and subsequent self-assembly in aqueous solutions.

New Insights from Chemical Biology: Molecular Basis of Transmission, Diagnosis, and Therapy of SARS-CoV-2

Coronavirus disease 2019 (COVID-19) is caused by a novel strain of coronavirus, designated as severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2). It has caused a global pandemic rapidly s...

Packing of semiflexible polymers into viral capsid in crowded environments.

We use coarse-grained Langevin dynamics simulations to study packing of semiflexible polymers into a spherical capsid, with and without a tail, inside a crowded cell. We use neutral and charged, but highly screened, polymers and compare packing rates of the two. Such packing conditions are relevant, for example, to λ DNA packing inside Escherichia coli bacterial cells, where the crowd particles are proteins, bacterial DNA, and salts. For a neutral polymer packing into a capsid with a tail, attractive interactions with the crowd particles make packing slightly harder at higher crowd densities, but repulsive interactions make it easier. Our results indicate that packing into a tailless capsid is less efficient at low crowd densities than into one with a long tail. However, this trend becomes opposite at higher densities. In addition, packing into a capsid with a long tail shows a highly variable waiting time before packing initiates, a feature absent for a tailless capsid. Electrical interactions at physiological conditions do not have much effect. Some bacterial cells, such as Pseudomonas chlororaphis, form a nucleuslike structure encapsulating the phage 201ϕ2-1 DNA. We also study here the packing dynamics with the nucleus present. We find packing is faster compared to the case of no-nucleus packing. We also observe knot formations but these knots untangle quickly while the polymer translocates. This knot formation is independent of polymer charge and presence of crowd particles.

RNA Homopolymers Form Higher-Curvature Virus-like Particles Than Do Normal-Composition RNAs

Unlike double-stranded DNA, single-stranded RNA can be spontaneously packaged into spherical capsids by viral capsid protein (CP) because it is a more compact and flexible polymer. Many systematic investigations of this self-assembly process have been carried out using CP from cowpea chlorotic mottle virus, with a wide range of sequences and lengths of single-stranded RNA. Among these studies are measurements of the relative packaging efficiencies of these RNAs into spherical capsids. In this work, we address a fundamental issue that has received very little attention, namely the question of the preferred curvature of the capsid formed around different RNA molecules. We show in particular that homopolymers of RNA—polyribouridylic acid and polyriboadenylic acid—form exclusively T = 2-sized (∼22-nm diameter) virus-like particles (VLPs) when mixed with cowpea chlorotic mottle virus CP, independent of their length, ranging from 500 to more than 4000 nucleotides. This is in contrast to “normal-composition” RNAs (i.e., molecules with comparable numbers of each of the four nucleotides and hence capable of developing a large amount of secondary structure because of intramolecular complementarity/basepairing); a curvature corresponding to T = 3-size (∼28 nm in diameter) is preferred for the VLPs formed with such RNAs. Our work is consistent with the preferred curvature of VLPs being a consequence of interaction of CP with RNA—in particular, the presence or absence of short RNA duplexes—and suggests that the equilibrium size of the capsid results from a trade-off between this optimum size and the cost of confinement.

Chemical mimicry of viral capsid self-assembly via corannulene-based pentatopic tectons

Self-assembly of twelve pentatopic tectons, which have complementary edges or can be linked using either digonal or trigonal connectors, represents the optimal synthetic strategy to achieve spherical objects, such as chemical capsids. This process requires conditions that secure uninterrupted equilibria of binding and self-correction en route to the global energy minimum. Here we report the synthesis of a highly soluble, deca-heterosubstituted corannulene that bears five terpyridine ligands. Spontaneous self-assembly of twelve such tectons with 30 cadmium(II) cations produces a giant icosahedral capsid as a thermodynamically stable single product in high yield. Nuclear magnetic resonance (NMR) methods, mass spectrometry analyses, small-angle X-ray scattering, transmission electron microscopy, and atomic force microscopy indicate that this spherical capsid has an external diameter of nearly 6 nm and shell thickness of 1 nm, in agreement with molecular modeling. NMR and liquid chromatography evidences imply that chiral self-sorting complexation generates a racemic mixture of homochiral capsids.

Confining annealed branched polymers inside spherical capsids.

The Lifshitz equation for the confinement of a linear polymer in a spherical cavity of radius R has the form of the Schrödinger equation for a quantum particle trapped in a potential well with flat bottom and infinite walls at radius R. We show that the Lifshitz equation of a confined annealed branched polymer has the form of the Schrödinger equation for a quantum harmonic oscillator. The resulting confinement energy has a 1/R4 dependence on the confinement radius R, in contrast to the case of confined linear polymers, which have a 1/R2 dependence. We discuss the application of this result to the problem of the confinement of single-stranded RNA molecules inside spherical capsids.

Synthetic approaches to construct viral capsid-like spherical nanomaterials.

This feature article describes recent progress in synthetic strategies to construct viral capsid-like spherical nanomaterials using the self-assembly of peptides and/or proteins. By mimicking the self-assembly of spherical viral capsids and clathrin, trigonal peptide conjugates bearing β-sheet-forming peptides, glutathiones, or coiled-coil-forming peptides were developed to construct viral capsid-like particles. β-Annulus peptides from tomato bushy stunt virus self-assembled into viral capsid-like nanocapsules with a size of 30-50 nm, which could encapsulate various guest molecules and be decorated with different molecules on their surface. Rationally designed fusion proteins bearing symmetric assembling units afforded precise viral capsid-like polyhedral assemblies. These synthetic approaches to construct artificial viruses could become useful guidelines to develop novel drug carriers, vaccine platforms, nanotemplates and nanoreactors.