Search Results (48)

Nucleocapsids protect viral genomes and play fundamental roles in viral assembly and infection. While many viruses adopt icosahedral or helical symmetries, negative-strand RNA viruses (NSVs) assemble their nucleocapsids with a distinct translation-based symmetry that is often considered helical because of their curvature. Our study analyzes the structural basis, assembly principles, and functional implications of the linear nucleocapsids. Structural coordinates of viruses were obtained from the Protein Data Bank (PDB) and examined using PyMOL version 1.3 to compare protein folds, RNA–protein interactions, inter-subunit contacts, and curvature properties across multiple nucleocapsids. We found that linear nucleocapsids share a similar 5H + 3H fold in their capsid proteins and encapsidate a fixed number of nucleotides per subunit, though the degree of nucleotide sequestration varies. Their architecture differs in inter-subunit interactions, determining whether empty capsids can assemble and influencing RNase sensitivity. Although these nucleocapsids may appear helical, they lack strict helical symmetry and instead display variable curvature that is modulated by environmental conditions. Relaxation of this curvature is likely required for viral RNA-dependent RNA polymerase to access the sequestered RNA genome during transcription/replication. In conclusion, linear nucleocapsids constitute a class of RNA–protein assemblies with variable curvature. The topologically conserved fold of the capsid protein enables genome protection while regulating exposure of RNA during viral RNA synthesis. Full article

With the advancements in instrumentation, image processing algorithms, and computational capabilities, single-particle cryo-electron microscopy (cryo-EM) has achieved atomic resolution in determining the 3D structures of viruses. The virus structures play a crucial role in studying their biological function and advancing the development of antiviral vaccines and treatments. Despite the effectiveness of artificial intelligence (AI) in general image processing, its development for identifying and extracting virus particles from cryo-EM micrographs has been hindered by the lack of manually labeled high-quality datasets. To fill the gap, we introduce CryoVirusDB, a labeled dataset containing the coordinates of expert-picked virus particles in cryo-EM micrographs. CryoVirusDB comprises 9941 micrographs from nine datasets representing seven distinct non-enveloped viruses exhibiting icosahedral or pseudo-icosahedral symmetry, along with coordinates of 339,398 labeled virus particles. It can be used to train and test AI and machine learning (e.g., deep learning) methods to accurately identify virus particles in cryo-EM micrographs for building atomic 3D structural models for viruses. Full article

The ligand-driven self-assembly of metal clusters offers a powerful strategy for constructing discrete molecular architectures with tunable magnetic and structural properties. By judiciously selecting appropriate multidentate ligands, researchers can direct the formation of polynuclear metal assemblies with diverse nuclearities, geometries, and topologies. Coordination-driven processes commonly stabilize such assemblies where multidentate ligands operate as templates and linkers. These will also determine how the metal centers are arranged in space and how they connect to each other. These clusters can take on shapes that range from basic bridging dimers to more complicated icosahedral and cubane-type motifs. They often have excellent symmetry and strong frameworks. Magnetically, these clusters are a great place to study exchange interactions, spin frustration, and the behavior of single-molecule magnets (SMMs). The magnetic characteristics depend on things like the type of metal ions, the bridging ligands, the overall shape, and the local coordination environment. Interestingly, a large number of ligand-assembled clusters exhibit high spin ground states and slow magnetization relaxation, which makes them attractive options for quantum information storage and molecular spintronic devices. This review connects coordination chemistry, supramolecular design, and molecular magnetism of pyridine–amine–carboxylate frameworks, offering insights into fundamental magnetic phenomena and guiding the development of next-generation functional materials. Continued exploration of ligand frameworks and metal combinations holds the potential to yield novel clusters with enhanced or unprecedented magnetic characteristics. Full article

This review provides a comparative analysis of the structure and physical properties of low-dimensional aperiodic crystalline solids, aiming to elucidate the origin and nature of aperiodicity in reduced-dimensional lattices. The breakdown of periodicity in low-dimensional systems arises from several mechanisms, including the suppression of specific force constants, thermodynamic instabilities, and topological constraints associated with imperfect space filling. At the nanoscale, certain cubic crystalline materials can form finite, zero-dimensional multiply twinned particles (MTPs) with decahedral or icosahedral symmetry. These clusters lack translational invariance and experience intrinsic structural strain due to solid-angle mismatch at twin junctions, which limits their characteristic size and renders them finite aperiodic solids. Particular attention is devoted to the electronic and spin properties of pentagonally symmetric MTPs: icosahedral particles exhibit symmetry-protected spin degeneracy consistent with centrosymmetric lattices, whereas non-centrosymmetric decahedral particles may display spin polarization and emergent low-dimensional magnetism. Collectively, these systems illustrate the diverse physical origins, manifestations, and consequences of aperiodicity in low-dimensional crystalline matter. Full article

Alphaviruses engage a diverse array of attachment factors and receptors during viral entry, resulting in a broad host range and disease spectrum, and thus presenting them as a major global public health concern. The development of effective antivirals against these arboviruses relies on a comprehensive understanding of the molecular interplay between these viruses and host cell factors, as well as the wide range of immune responses that ensue following viral infection. In this review, we present the current understanding of the complex landscape of alphavirus interaction with attachment factors and entry receptors, some of which are characterized structurally, while others are characterized biochemically. Additionally, we provide an overview of the molecular bases of epitope recognition by neutralizing and non-neutralizing antibodies against alphaviruses, and how icosahedral symmetry influences these interactions, such as occupancy and neutralization potency. We further discuss the structural bases of epitope recognition of a few pan-alphavirus antibodies, their potential therapeutic implications, and offer future perspectives on the development of effective therapeutics against clinically relevant alphaviruses. Full article

Background/Objectives: Vaccination is important for controlling foot-and-mouth disease (FMD) in endemic regions and to lessen the effects of outbreaks in FMD-free countries. The adaptation of FMD virus to BHK cells is a necessary but time-consuming and costly step in vaccine production and can prove problematic for some isolates. Adaptation is, in part, driven by receptor availability and selects variants with altered receptor specificity that result from amino acid substitutions in the capsid proteins. Methods: To bypass the need for cell culture adaptation, we generated chimeric viruses with field-strain capsids and introduced amino acid substitutions associated with cell culture adaptation. We targeted two sites on the capsid: the canonical heparan sulphate binding site and the icosahedral 5-fold symmetry axes. Results: Our results show that some viruses with unmodified wild-type (wt) capsids grew well in BHK cells (suspension and adherent), whereas others showed poor growth. For viruses that showed good growth, the introduction of amino acid changes associated with cell culture adaptation improved the rate of growth but not virus titres or yields of 146S particles, whereas growth and 146S yields for viruses that grew poorly in BHK cells were greatly enhanced by some of the amino acid changes. For the latter viruses, the introduced changes did not appear to adversely affect virion stability or antigenicity. Conclusions: For FMD viruses that grow poorly in BHK cells, this approach could be a viable alternative to protracted adaptation by serial passage and could expedite the production of a new vaccine strain from a field virus. Full article

Single-stranded DNA (ssDNA) viruses are a diverse group of pathogens with broad host range, including bacteria, archaea, protists, fungi, plants, invertebrates, and vertebrates. Their small compact genomes have evolved to encode multiple proteins. This review focuses on the structure and functional diversity of the icosahedral capsids across the ssDNA viruses. To date, X-ray crystallography and cryo-electron microscopy structural studies have provided detailed capsid architectures for 8 of the 35 ssDNA virus families, illustrating variations in assembly mechanisms, symmetry, and structural adaptations of the capsid. However, common features include the conserved jelly-roll motif of the capsid protein and strategies for genome packaging, also showing evolutionary convergence. The ever-increasing availability of genomic sequences of ssDNA viruses and predictive protein modeling programs, such as using AlphaFold, allows for the extension of structural insights to the less-characterized families. Therefore, this review is a comparative analysis of the icosahedral ssDNA virus families and how the capsid proteins are arranged with different tessellations to form icosahedral spheres. It summarizes the current knowledge, emphasizing gaps in the structural characterization of the ssDNA capsidome, and it underscores the importance of continued exploration to understand the molecular underpinnings of capsid function and evolution. These insights have implications for virology, molecular biology, and therapeutic applications. Full article

We report the results of our computations of the spectral polynomials and spectra of a number of graphs possessing automorphism symmetries beyond cubic and icosahedral symmetries. The spectral (characteristic) polynomials are computed in fully expanded forms. The coefficients of these polynomials contain a wealth of combinatorial information that finds a number of applications in many areas including nanomaterials, genetic networks, dynamic stereochemistry, chirality, and so forth. This study focuses on a number of symmetric and semi-symmetric graphs with automorphism groups of high order. In particular, Heawood, Coxeter, Pappus, Möbius–Kantor, Tutte–Coxeter, Desargues, Meringer, Dyck, n-octahedra, n-cubes, icosahedral fullerenes such as C₈₀(I_h), golden supergiant C₂₄₀(I_h), Archimedean (I_h), and generalized Petersen graphs up to 720 vertices, among others, have been studied. The spectral polynomials are computed in fully expanded forms as opposed to factored forms. Several applications of these polynomials are briefly discussed. Full article

The whimsical Las Vegas/Monte Carlo cubic dice are generalized to construct the combinatorial problem of enumerating all n-dimensional hypercube dice and dice of other shapes that exhibit cubic, icosahedral, and higher symmetries. By utilizing powerful generating function techniques for various irreducible representations, we derive the combinatorial enumerations of all possible dice in n-dimensional space with hyperoctahedral symmetries. Likewise, a number of shapes that exhibit icosahedral symmetries such as a truncated dodecahedron and a truncated icosahedron are considered for the combinatorial problem of dice enumerations with the corresponding shapes. We consider several dice with cubic symmetries such as the truncated octahedron, dodecahedron, and Rubik’s cube shapes. It is shown that all enumerated dice are chiral, and we provide the counts of chiral pairs of dice in the n-dimensional space. During the combinatorial enumeration, it was discovered that two different shapes of dice exist with the same chiral pair count culminating to the novel concept of isochiral polyhedra. The combinatorial problem of dice enumeration is generalized to multi-coloring partitions. Applications to chirality in n-dimension, molecular clusters, zeolites, mesoporous materials, cryptography, and biology are also pointed out. Applications to the nonlinear n-dimensional hypercube and other dicey encryptions are exemplified with romantic, clandestine messages: “I love U” and “V Elope at 2”. Full article

In the present study, first-principles molecular dynamics simulations were employed to study the effects of small amounts of B and C substituted for P on the structure and magnetic properties of Fe₈₀P₁₃C₇, Fe₈₀P₁₀C₇B₃, and Fe₈₀P₈C₉B₃ amorphous alloys. A small amount of B and C replacing P atoms increases the icosahedral structure of the amorphous alloys, especially the increase in the regular icosahedral structure. The saturation magnetization of the three kinds of amorphous alloys gradually increases with the addition of B and C atoms, and the results of experimental and simulated calculations show consistent trends. The substitution of P atoms by B and C atoms leads to the aggregation of Fe atoms, which increases the magnetic moment of the iron atoms. In addition, the improvement of local structural symmetry may be one of the reasons for the increase in saturation magnetization of amorphous alloys. The substitution of a small number of B and C atoms plays an important role in improving the saturation magnetization of the amorphous alloy, which has a certain guiding significance for the development of amorphous alloys with excellent soft magnetic properties. Full article

This paper is part of a series that describes the Fibonacci icosagrid quasicrystal (FIG) and its relation to the $E_8$ root lattice. The FIG was originally constructed to represent the intersection points of an icosahedrally symmetric collection of planar grids in three dimensions, with the grid spacing of each following a Fibonacci chain. It was found to be closely related to a five-fold compound of 3D sections taken from the 4D Elser–Sloane quasicrystal (ESQC), which is derived via a cut-and-project process from $E_8$. More recently, a direct cut-and-project from $E_8$ has been found which yields the FIG (presented in another paper of this series). The present paper focuses not on the full quasicrystal, but on the relationship between the root polytope of $E_8$ (Gosset’s $4_{21}$ polytope) and the core polyhedron generated in the FIG, a compound of 20 tetrahedra referred to simply as a 20-Group. In particular, the $H_3$ symmetry of the FIG can be seen as a five-fold or “golden” composition of tetrahedral symmetry (referring to the characteristic appearance of the golden ratio). This is shown to mirror a connection between tetrahedral and five-fold symmetries present in the $4_{21}$. Indeed, the rotations that connect tetrahedra contained within the $4_{21}$ are shown to induce, in a certain natural way, the tetrahedron orientations in the 20-Group. Full article

Dengue virus is an enveloped virus with an icosahedral assembly of envelope proteins (E). The E proteins are arranged as a head-to-tail homodimer, and domain III (EDIII) is placed at the edge of the dimer, converging to a pentamer interface. For a structure-based approach, cholera toxin B (CTB) was harnessed as a structural scaffold for the five-fold symmetry of EDIII. Pivoted by an RNA-mediated chaperone for the protein folding and assembly, CTB-EDIII of dengue serotype 1 (DV1) was successfully produced as soluble pentamers in an E. coli host with a high yield of about 28 mg/L. Immunization of mice with CTB-DV1EDIII elicited increased levels of neutralizing antibodies against infectious viruses compared to the control group immunized with DV1EDIII without CTB fusion. IgG isotype switching into a balanced Th1/Th2 response was also observed, probably triggered by the intrinsic adjuvant activity of CTB. Confirming the immune-enhancing potential of CTB in stabilizing the pentamer assembly of EDIII, this study introduces a low-cost bacterial production platform designed to augment the soluble production of subunit vaccine candidates, particularly those targeting flaviviruses. Full article

The symmetries of a Riemann surface $\mathsf{\Sigma }\setminus \left\{a_i\right\}$ with n punctures $a_i$ are encoded in its fundamental group ${\pi }_1\left(\mathsf{\Sigma }\right)$. Further structure may be described through representations (homomorphisms) of ${\pi }_1$ over a Lie group G as globalized by the character variety $\mathcal{C}=\mathrm{Hom}({\pi }_1,G)/G$. Guided by our previous work in the context of topological quantum computing (TQC) and genetics, we specialize on the four-punctured Riemann sphere $\mathsf{\Sigma }=S_2^{\left(4\right)}$ and the ‘space-time-spin’ group $G=S{L}_2\left(\mathbb{C}\right)$. In such a situation, $\mathcal{C}$ possesses remarkable properties: (i) a representation is described by a three-dimensional cubic surface $V_{a,b,c,d}(x,y,z)$ with three variables and four parameters; (ii) the automorphisms of the surface satisfy the dynamical (non-linear and transcendental) Painlevé VI equation (or $P_{VI}$); and (iii) there exists a finite set of 1 (Cayley–Picard)+3 (continuous platonic)+45 (icosahedral) solutions of $P_{VI}$. In this paper, we feature the parametric representation of some solutions of $P_{VI}$: (a) solutions corresponding to algebraic surfaces such as the Klein quartic and (b) icosahedral solutions. Applications to the character variety of finitely generated groups $f_p$ encountered in TQC or DNA/RNA sequences are proposed. Full article

The topological partition theory states that icosahedral group affine extensions (fullerenes symmetry) are the most effective way to energetically optimize the surface covering. In recent decades, potential applications of fullerene symmetry have emerged in the major fields of biology, like enzyme inhibition and antiviral therapy. This research suggests a novel perspective to interpret the underlying spatial organization of cell populations in tissues from the polyhedral graph theory. We adopted this theoretical framework to study HUVEC cell in vitro angiogenesis assays on Matrigel. This work underscores the importance of extracellular ${\mathrm{C}\mathrm{a}}^{2+}$ gradients, both from conditioned BJ and pretreated HUVEC cells, in angiogenesis fullerene-rule spatial minimization. Full article

Japanese encephalitis virus (JEV) is an enveloped icosahedral capsid virus with a prime neutralizing epitope present in E protein domain III (EDIII). E dimers are rearranged into a five-fold symmetry of icosahedrons. Cholera toxin B (CTB) and heat-labile enterotoxin B (LTB) of AB₅-type toxin was used as the structural scaffold for emulating the pentameric axis of EDIII. We produced homo-pentameric EDIII through the genetic fusion of LTB or CTB in E. coli without recourse to additional refolding steps. Harnessing an RNA-mediated chaperone further enhanced the soluble expression and pentameric assembly of the chimeric antigen. The pentameric assembly was validated by size exclusion chromatography (SEC), non-reduced gel analysis, and a GM1 binding assay. CTB/LTB−EDIII chimeric antigen triggered high neutralizing antibodies against the JEV Nakayama strain after immunization in mice. Altogether, our proof-of-principle study creating a JEV-protective antigen via fusion with an AB₅-type toxin as both a pentameric scaffold and a built-in adjuvant posits the bacterially produced recombinant chimeric antigen as a cost-effective alternative to conventional inactivated vaccines against JEV. Full article