Modelling of icosahedral viruses

Theoretical and simulation investigations of viruses attaining icosahedral shape based on molecular models have recently become an exciting and rapidly growing research area. We discuss recent studies addressing the packing of the genome inside the capsid, thermodynamics, and the self-assembly of capsids. Special attention is given to the different packing of double-stranded and single-stranded polynucleotides in the viral capsid and its consequences.     

Sizing up large protein complexes by electrospray ionisation-based electrophoretic mobility and native mass spectrometry: morphology selective binding of Fabs to hepatitis B virus capsids

The capsid of hepatitis B virus (HBV) is a major viral antigen and important diagnostic indicator. HBV capsids have prominent protrusions (‘spikes’) on their surface and are unique in having either T?=?3 or T?=?4 icosahedral symmetry. Mouse monoclonal and also human polyclonal antibodies bind either near the spike apices (historically the ‘α-determinant’) or in the ‘floor’ regions between them (the ‘β-determinant’). Native mass spectrometry (MS) and gas-phase electrophoretic mobility molecular analysis (GEMMA) were used to monitor the titration of HBV capsids with the antigen-binding domain (Fab) of mAb 3120, which has long defined the β-determinant. Both methods readily distinguished Fab binding to the two capsid morphologies and could provide accurate masses and dimensions for these large immune complexes, which range up to ~8 MDa. As such, native MS and GEMMA provide valuable alternatives to a more time-consuming cryo-electron microscopy analysis for preliminary characterisation of virus-antibody complexes.

Models of virus capsids containing 72 pentameric capsomeres

A simple model for describing the non-quasi-equivalent icosahedral virus capsid composed of 72 pentameric capsomeres is developed. By means of six-step operations, a new 4-gons polyhedron P is obtained which contains 72 pentagons, 80 trigons and 210 quadrilaterals. More importantly, it bears icosahedral symmetry. The rationality of the existence of the 4-gons polyhedron P is further discussed. The results show that this model can be used to represent the capsids of papovaviruses.     

Burnside Rings: Application to Molecules of Icosahedral Symmetry

The Burnside ring, B(G), of a group G is the set of isomorphism classes of orbits of G together with the operations of addition and product. The addition is defined as the disjoint union, and the product as the Cartesian product. This paper describes basic facts about this algebraic structure and develops some applications in chemistry, as the labelling of atoms in molecules of high symmetry and the construction of symmetry-adapted functions. For illustrating such applications, the concept of Burnside ring is applied to the icosahedral symmetry. Sets of points which are isomorphic to the orbits of the I group are described and the multiplication table of B({I}) is obtained from the table of marks. This multiplication table allows us to obtain an elegant labelling of the atoms of the buckminsterfullerene which is consistent with the icosahedral symmetry. Also, we obtain complete sets of symmetry-adapted functions for the buckminsterfullerene which span the Boyle and Parker's icosahedral representations.     

Biotechnological Frontiers of DNA Nanomaterials Continue to Expand: Bacterial Infection using Virus-Inspired Capsids

The elegant geometry of viruses has inspired bio-engineers to synthetically explore the self-assembly of polyhedral capsids employed to protect new cargo or change an enzymatic microenvironment. Recently, Yang and co-workers used DNA nanotechnology to revisit the icosahedral capsid structure of the phiX174 bacteriophage and reloaded the original viral genome as cargo into their fully synthetic architecture. Surprisingly, when using a favorable combination of structural rigidity and dynamic multivalent cargo entrapment, the synthetic particles were able to infect non-competent bacterial cells and produce the original phiX174 bacteriophage. This work presents an exciting new direction of DNA nanotech for bio-engineering applications which involve bacterial interactions.     

Dibarium zirconium tetraoxalate trihydrate

A new mixed barium zirconium oxalate, tri­aqua­tetra‐μ‐oxalato‐dibarium(II)­zirconium(IV), Ba₂Zr(C₂O₄)₄·3H₂O or [Ba₂Zr(C₂O₄)₄(H₂O)₃]_n, has been synthesized. The complex is built from eightfold‐coordinated Zr atoms and eleven‐ and sixfold‐coordinated Ba atoms, linked by oxalate groups. The Zr atom, the two Ba atoms and one water O atom lie on crystallographic twofold axes, so that each coordination polyhedron has imposed C2 symmetry. Packing in the crystal is also assumed through hydrogen bonds.     

Symmetry properties of the lattice dynamics of nonrigid molecular crystals

The symmetry properties of the lattice dynamics of nonrigid molecular crystals are discussed on mass-weighted translational coordinates and inertia moment-weighted rotational coordinates as well as molecular internal normal coordinates in molecular principal axes frame. An equivalent reducible representation of the wavevector group and the classification of molecular crystal normal modes are provided. A detailed illustrative example is presented.     

Theoretical Study of Structural Symmetry in Ternary Clusters

The geometrical symmetry presents an intriguing theoretical problem in many kinds of clusters. The diversity of geometrical structures is associated with cluster sizes, different model functions and potential parameters, and ternary clusters are investigated to study the relationship between geometrical symmetry and homotopic symmetry. Ternary Lennard-Jones model potential is studied with different parameters, and the putative global minimum structures of A₁₃B₃₀C₁₂ clusters are optimized using an adaptive immune optimization algorithm. The results show that there mainly exist five geometrical symmetry structures, i.e., Mackay icosahedral, fivefold partial Mackay icosahedral, sixfold pancake, partial double Mackay icosahedral, and amorphous structures. Furthermore, the number of bonds is used to distinguish the geometrical symmetry. The importance of geometrical symmetry and homotopic symmetry determined by potential parameters is discussed. It was found that in the optimization it is more important to generate geometrical symmetry than to optimize homotopic symmetry.     

Kinetics of thermal denaturation of human rhinoviruses in the presence of anti-viral capsid binders analyzed by capillary electrophoresis

In vivo, the icosahedral capsid of human rhinoviruses undergoes well-defined transitions during the infection pathway. Native virus, sedimenting at 150S, is converted to subviral particles with a sedimentation coefficient of 135S, which have lost the innermost capsid protein VP4. Upon release of the genomic RNA empty 80S capsids remain. Similar structural modifications are observed in vitro upon exposure to low pH and/or elevated temperature. Virions are stabilized against these transitions by various antiviral compounds, which bind to a hydrophobic pocket in the capsid protein VP1. Using capillary electrophoresis the kinetics of viral decay in the presence of such hydrophobic drugs was investigated. Assuming first-order kinetics, the increase of the time constant reflects the extent of stabilization. Exposure of the virions to 55 degrees C after presaturation with the antivirals increased the time constants (as compared to native virus) by a factor of 8-30, from a few minutes to several ten minutes. Denaturation of the stabilized capsid gave rise to heterogeneous material rather than to defined subviral particles. This was confirmed by electron microscopy and indicates that the structural modification of the virus follows a kinetically well-defined pathway which is disturbed by the drugs resulting in disorganized disruption of the virion.     

人乳头瘤病毒HPV-16衣壳蛋白的结构特征

人乳头瘤病毒HPV-16是引发子宫颈癌的主要元凶.研究HPV-16病毒的结构特点,对于二十面体病毒几何结构的认识、描述和疫苗设计具有重要意义.综述了HPV-16病毒的衣壳结构特征、衣壳蛋白,分析了它们之间的相互作用,并试探性地指出了HPV-16衣壳几何结构的数学问题.     

仿病毒衣壳自组装体及其生物医学应用

仿病毒衣壳结构自组装体具有重要的基础研究和应用价值,是化学、材料、生物医学等多学科前沿交叉领域.本文从天然病毒衣壳的基本结构和特征出发,立足于从结构仿生到功能仿生的角度,综述了以天然病毒衣壳蛋白质和人工合成材料为组装基元构建仿病毒衣壳自组装体的策略,及其形态结构的调控和功能优化等.重点论述了近年来合成肽类分子在仿病毒衣壳自组装体结构和功能方面的进展.同时,就仿病毒衣壳自组装体在药物控释、基因传递等生物医学领域的应用也做了论述.     

A computational study of hydration, solution structure, and dynamics in dilute carbohydrate solutions

We report results from a molecular simulation study of the structure and dynamics of water near single carbohydrate molecules (glucose, trehalose, and sucrose) at 0 and 30 degrees C. The presence of a carbohydrate molecule has a number of significant effects on the microscopic water structure and dynamics. All three carbohydrates disrupt the tetrahedral arrangement of proximal water molecules and restrict their translational and rotational mobility. These destructuring effects and slow dynamics are the result of steric constraints imposed by the carbohydrate molecule and of the ability of a carbohydrate to form stable H bonds with water, respectively. The carbohydrates induce a pronounced decoupling between translational and rotational motions of proximal water molecules.     

catena‐Poly­[1,4‐diazo­niabicyclo­[2.2.2]­octane [silver(I)‐tri‐μ‐thio­cyanato‐κ6S:S]]

The title compound, {(C₆H₁₄N₂)[Ag(NCS)₃]}_n, is a polymeric silver(I) complex. The Ag^I atom is hexacoordinated by the S atoms of six thio­cyanate anions, with each thio­cyanate S atom acting in a bridging mode to link the Ag atoms together. The unique Ag^I atom lies at a cell origin and has crystallo­graphically imposed symmetry. The diazonia[2.2.2]octane molecule lies about a site with imposed symmetry with the unique N atom on a threefold axis. The S and N atoms of the thio­cyanate ligands sit on a mirror plane and a threefold axis, respectively. The crystal structure consists of one‐dimensional chains, which are stabilized by N—H⋯N hydrogen bonds to form a three‐dimensional network.     

Carbon-13 spin–lattice relaxation of tropane alkaloids. Anisotropic rotational motion of tropine and pseudotropine

The ¹³C spin–lattice relaxation times of tropine and pseudotropine have been measured in CDCl₃ as a function of concentration. The same relative increase in concentration serves to increase the relaxation rates much less in the region 0.9–5.0 wt.% than in the region 5.0–14.3 wt.%. The rotational diffusion coefficients have been calculated from the relaxation data using Woessner's anisotropic rotational diffusion model. Reorientation of both molecules is shown to be moderately anisotropic. The principal axes of the rotational diffusion tensor in the symmetry plane of both molecules are rotationally shifted from the principal axes of the moment of inertia tensor of the free molecules, and the main rotational axis is parallel with a line passing through the centre of mass of the molecule and the nitrogen atom.     

High relaxivity gadolinium hydroxypyridonate-viral capsid conjugates: nanosized MRI contrast agents

High relaxivity macromolecular contrast agents based on the conjugation of gadolinium chelates to the interior and exterior surfaces of MS2 viral capsids are assessed. The proton nuclear magnetic relaxation dispersion (NMRD) profiles of the conjugates show up to a 5-fold increase in relaxivity, leading to a peak relaxivity (per Gd3+ ion) of 41.6 mM(-1) s(-1) at 30 MHz for the internally modified capsids. Modification of the exterior was achieved through conjugation to flexible lysines, while internal modification was accomplished by conjugation to relatively rigid tyrosines. Higher relaxivities were obtained for the internally modified capsids, showing that (i) there is facile diffusion of water to the interior of capsids and (ii) the rigidity of the linker attaching the complex to the macromolecule is important for obtaining high relaxivity enhancements. The viral capsid conjugated gadolinium hydroxypyridonate complexes appear to possess two inner-sphere water molecules (q = 2), and the NMRD fittings highlight the differences in the local motion for the internal (tauRl = 440 ps) and external (tauRl = 310 ps) conjugates. These results indicate that there are significant advantages of using the internal surface of the capsids for contrast agent attachment, leaving the exterior surface available for the installation of tissue targeting groups.     

Comparison of the structural and chemical composition of giant T-even phage heads.

A study has been made of the structure of the capsids of T4D giant phage produced from mutants in gene 23 and temperature-sensitive mutants in gene 24, and T4D and T2L giant phage formed by the addition of L-canavanine followed by an Larginine chase in the growth medium. All the giant phage capsids have been shown to be built according to the same geometrical architecture. This consists of a near-hexagonal surface net, lattice constant 129.5 A, folded into a left-handed T = 13 prolate icosahedron elongated along one of its fivefold symmetry axes. Their only apparent difference from wild-type T-even phage capsids is their abnormally elongated tubular part. A comparison of the capsomere morphologies and protein compositions of the giant phage capsids showed that all T4D giants are identical but differ from T2L: The T4D capsomere has a complex (6 + 6 + 1)-type morphology, whereas the T2L has a simple 6-type. T2L phage, however, lack two capsid proteins, "soc" and "hoc", present in T4D. The difference in capsomere morphology can therefore be related to the difference in the protein compositions of these two phage. Possible differences between the initiation and means of length regulation of giant phage heads and the aberrant polyheads are discussed.     

Determining the topology of virus assembly intermediates using ion mobility spectrometry–mass spectrometry

We have combined ion mobility spectrometry–mass spectrometry with tandem mass spectrometry to characterise large, non‐covalently bound macromolecular complexes in terms of mass, shape (cross‐sectional area) and stability (dissociation) in a single experiment. The results indicate that the quaternary architecture of a complex influences its residual shape following removal of a single subunit by collision‐induced dissociation tandem mass spectrometry. Complexes whose subunits are bound to several neighbouring subunits to create a ring‐like three‐dimensional (3D) architecture undergo significant collapse upon dissociation. In contrast, subunits which have only a single neighbouring subunit within a complex retain much of their original shape upon complex dissociation. Specifically, we have determined the architecture of two transient, on‐pathway intermediates observed during in vitro viral capsid assembly. Knowledge of the mass, stoichiometry and cross‐sectional area of each viral assembly intermediate allowed us to model a range of potential structures based on the known X‐ray structure of the coat protein building blocks. Comparing the cross‐sectional areas of these potential architectures before and after dissociation provided tangible evidence for the assignment of the topologies of the complexes, which have been found to encompass both the 3‐fold and the 5‐fold symmetry axes of the final icosahedral viral shell. Such insights provide unique information about virus assembly pathways that could allow the design of anti‐viral therapeutics directed at the assembly step. This methodology can be readily applied to the structural characterisation of many other non‐covalently bound macromolecular complexes and their assembly pathways. Copyright © 2010 John Wiley & Sons, Ltd.     

Efficient nonbonded interactions for molecular dynamics on a graphics processing unit

We describe an algorithm for computing nonbonded interactions with cutoffs on a graphics processing unit. We have incorporated it into OpenMM, a library for performing molecular simulations on high‐performance computer architectures. We benchmark it on a variety of systems including boxes of water molecules, proteins in explicit solvent, a lipid bilayer, and proteins with implicit solvent. The results demonstrate that its performance scales linearly with the number of atoms over a wide range of system sizes, while being significantly faster than other published algorithms. © 2009 Wiley Periodicals, Inc. J Comput Chem, 2010     

Pseudo‐merohedrally twinned praseodymium hexa­cyano­ferrate(III) tetrahydrate

Crystals of the title compound, di­aqua­hexa‐μ‐cyano‐ferrate(III)­praseo­dym­ium(III) dihydrate, Pr[Fe(CN)₆]·4H₂O or [PrFe(CN)₆(H₂O)₂]·2H₂O, are twinned with three components. The Pr atom is coordinated by eight atoms, viz. six N and two symmetry‐related water O atoms. The Pr polyhedron (Pr has site symmetry m2m, Wyckoff position 4c) is linked to an FeC₆ octahedron (Fe located on a site with imposed 2/m symmetry, Wyckoff position 4b) through N atoms, forming an infinite array. The second (symmetry independent) water mol­ecule lies on a mirror plane, is not included in coordination and is weakly hydrogen bonded to N atoms.     

Shell and subshell periodic structures of icosahedral nickel nanoclusters

Using the modified analytic embedded atom method and molecular dynamics, the binding energies and their second order finite differences (stability functions) of icosahedral Ni clusters with shell and subshell periodicity are studied in detail via atomic evolution. The results exhibit shell and subshell structures of the clusters with atoms from 147 to 250,000, and the atomic numbers corresponding to shell or subshell structures are in good agreement with the experimental magic numbers obtained in time-of-flight mass spectra of threshold photoionization, and Martin's theoretical proposition of progressive formation of atomic umbrellas. Clusters with size from 147 to 561 atoms are energetically investigated via one-by-one atomic evolution and their magic numbers are theoretically proved. For medium-size Ni clusters with 561 to 2057 atoms, the prediction of magic numbers with atomic numbers is performed on the basis of umbrella-like subshell growth in near face-edge-vertex order. The similarity of the energy curves makes it possible to extend the prediction to even larger Ni nanoclusters in hierarchical Mackay icosahedral configurations.