Biomedical subjects

A Janner

Publications and source records attributed to A Janner.

At least 19 recordsLinked to original sources

PubMed2006

Towards a classification of icosahedral viruses in terms of indexed polyhedra.

The standard Caspar & Klug classification of icosahedral viruses by means of triangulation numbers and the more recent novel characterization of Twarock leading to a Penrose-like tessellation of the capsid of viruses not obeying the Caspar-Klug rules can be obtained as a special case in a new approach to the morphology of icosahedral viruses. Considered are polyhedra with icosahedral symmetry and rational indices. The law of rational indices, fundamental for crystals, implies vertices at points of a lattice (here icosahedral). In the present approach, in addition to the rotations of the icosahedral group 235, crystallographic scalings play an important rôle. Crystallographic means that the scalings leave the icosahedral lattice invariant or transform it to a sublattice (or to a superlattice). The combination of the rotations with these scalings (linear, planar and radial) permits edge, face and vertex decoration of the polyhedra. In the last case, satellite polyhedra are attached to the vertices of a central polyhedron, the whole being generated by the icosahedral group from a finite set of points with integer indices. Three viruses with a polyhedral enclosing form given by an icosahedron, a dodecahedron and a triacontahedron, respectively, are presented as illustration. Their cores share the same polyhedron as the capsid, both being in a crystallographic scaling relation.

Biophysical Phenomena↗

PubMed2006

Crystallographic structural organization of human rhinovirus serotype 16, 14, 3, 2 and 1A.

The architecture of the human rhinovirus is shown to be based on a crystallographic polyhedron (the ico-dodecahedron) with 60 triangular facets and 32 vertices at points of a body-centered icosahedral lattice. The ico-dodecahedron is only slightly different from the T = 3 icosadeltahedron of Caspar & Klug [Cold Spring Harbor Symp. Quant. Biol. (1962), 27, 1-24]. The capsid of the virion is encapsulated between two ico-dodecahedra in scaling relation by a factor tau, the golden number. Clusters with axial symmetry of the coat proteins VP1, VP2, VP3 and VP4 are considered (decamers, pentamers, hexamers, trimers and tetramers). Their crystallographic enclosing forms obey the same laws as a number of axial-symmetric proteins, involving planar and linear crystallographic scaling relations and having vertices at points of lattices with an integral metric tensor. These properties also occur for the icosahedral cluster of each coat protein viewed along the symmetry axes (fivefold, threefold and twofold, respectively). The structural organization of the rhinovirus in terms of all these enclosing forms is independent of the serotype (16, 14, 3, 2, 1A) and is typical for a strongly correlated system, as it depends on one single free parameter, taken to be the icosahedral lattice parameter a0, which relates the geometry with the real structure (up to small variations).

Capsid Proteins↗

PubMed2005

Remarkable features in lattice-parameter ratios of crystals. I. Orthorhombic, tetragonal and hexagonal crystals.

The investigation of the lattice-parameter ratios of tetrahedral and hexagonal-rhombohedral inorganic compounds, as reported by Constant & Shlichta [(2003), Acta Cryst. A59, 281-282], has been extended to the structural data found for organic and metal-organic compounds (CSD), for bio-macromolecular crystals (PDB) and for inorganic materials (ICSD). In this first part of the series, the frequency distribution of orthorhombic, tetragonal and hexagonal crystals is presented. The results obtained confirm the existence of sharp peaks as a function of the ratios of lattice parameters and reveal additional exponential components, decaying for large and small values of these ratios. Practically all the important peaks occur at ratios which correspond to lattices having metric tensors with rational entries, the so-called integral lattices. The exponential component is interpreted as expressing a general statistical distribution which is valid for the generic crystal lattices, i.e. those normally considered. The exponential fraction dominates the peaked component in the organic and metal-organic cases, is less important for bio-macromolecular crystals and is much less important than the sharp peaks for inorganic crystals. Remarkable is the crystallographic relevance of the isometric hexagonal lattice, characterized by the axial ratio c/a = 1 and first observed in the molecular form of a protein. In the frequency distribution of 12 117 inorganic hexagonal crystals, the highest peak of 937 crystals occurs for c = a. In the hexagonal case of the bio-macromolecules the most important peak of 422 crystals is observed near the ideal h.c.p. (hexagonal closed packing) ratio of (8/3)(1/2).

Crystallization↗

PubMed2005

Remarkable features in lattice-parameter ratios of crystals. II. Monoclinic and triclinic crystals.

The frequency distributions of monoclinic crystals as a function of the lattice-parameter ratios resemble the corresponding ones of orthorhombic crystals: an exponential component, with more or less pronounced sharp peaks, with in general the most important peak at the ratio value 1. In addition, the distribution as a function of the monoclinic angle beta has a sharp peak at 90 degrees and decreases sensibly at larger angles. Similar behavior is observed for the three triclinic angular parameters alpha, beta and gamma, with characteristic differences between the organic and metal-organic, bio-macromolecular and inorganic crystals, respectively. The general behavior observed for the hexagonal, tetragonal, orthorhombic, monoclinic and triclinic crystals {in the first part of this series [de Gelder & Janner (2005). Acta Cryst. B61, 287-295] and in the present case} is summarized and commented. The data involved represent 366 800 crystals, with lattice parameters taken from the Cambridge Structural Database, CSD (294 400 entries), the Protein Data Bank, PDB (18 800 entries), and the Inorganic Crystal Structure Database, ICSD (53 600 entries). A new general structural principle is suggested.

Crystallization↗

PubMed2005

Strongly correlated structure of axial-symmetric proteins. I. Orthorhombic, tetragonal, trigonal and hexagonal symmetries.

The geometry of the molecular envelope and channel in axial-symmetric proteins is investigated in order to test the validity of rules deduced previously from several other biomacromolecules. Again, molecular forms with remarkable geometric properties are found. In particular, for order of rotation N = 2, 3, 4, 6 the molecular forms encapsulating the C(alpha) backbone of the protein have vertices at lattice points and therefore integral indices. These lattices are characterized by a height-to-width axial ratio that reduces the number of free parameters and enhances the symmetry.

Crystallography, X-Ray↗

PubMed2005

Strongly correlated structure of axial-symmetric proteins. II. Pentagonal, heptagonal, octagonal, nonagonal and ondecagonal symmetries.

The investigation of the geometry of the molecular envelope and channel in the proteins discussed in part I [Janner (2005a), Acta Cryst. D61, 247-255] is extended to axial-symmetric proteins with orders of rotation N = 5, 7, 8, 9 and 11, non-crystallographic in dimension 3. In these cases also, the vertices of the molecular form which encapsulate the C(alpha) backbone have integral coordinates (indices) in a symmetry-adapted basis which generates a polygonal lattice. As in the crystallographic case of part I, a characteristic rational axial ratio squared is observed that reduces to one the number of free lattice parameters and enhances the symmetry. Furthermore, there is a crystallographic scaling relation between the envelope and the channel which depends on the order of the axial symmetry and is expressible in terms of star polygons. Possible biological implications are suggested within a more general context.

Protein Conformation↗

PubMed2005

Strongly correlated structure of axial-symmetric proteins. III. Complexes with DNA/RNA.

Three cases are considered of protein-DNA (or protein-RNA) complexes with a strongly correlated structure based on symmetry. In the first the symmetry of the nucleic acid is the determinant element, the second contains a dominant protein and an adaptive DNA/RNA and in the third a perturbed symmetry arises from elements of both components. The first situation is exemplified by the filamentous bacteriophage Pf1 in a low- and high-temperature state. The Pyrococcus abyssi Sm core and the trp RNA-binding attenuation protein are examples of the second situation. Finally, the nucleosome core particle represents the cooperative compromise between histone and DNA. In all the cases, the strong correlation in the structure is based on polygrammal scaling relations and on a molecular polygonal form lattice which depends on a single parameter.

DNA↗

PubMed2004

Zones and sublattices of integral lattices.

Methods are presented for an analysis of zones and sublattices of integral lattices, whose relevance is revealed by sharp peaks in the frequency distribution of hexagonal and tetragonal lattices, as a function of the axial ratio c/a. Starting from a few examples, zone symmetries, lattice-sublattice relations and integral scaling transformations are derived for hexagonal lattices with axial ratios radical3/2, radical3, radical2 and 1 (the isometric case) and for the related radical3 and radical2 tetragonal lattices. Sublattices and zones connected by linear rational transformations lead to rational equivalence classes of integral lattices. For properties like the axial ratio and the point-group symmetry (lattice holohedry), rational equivalence can be extended so that also metric tensors differing by an integral factor become equivalent. These two types of equivalence classes are determined for the lattices mentioned above.

Journal Article↗

PubMed2004

Integral lattices.

Most of the sharp peaks, recently reported by Constant & Shlichta [Acta Cryst. (2003), A59, 281-282], in the frequency distribution of known tetrahedral and hexagonal-rhombohedral inorganic compounds apparently correspond to integral lattices. These are characterized by an integral metric tensor of their basis vectors (up to a unit-length factor). Integral lattices also occur in molecular forms of axial-symmetric biomacromolecules, as illustrated by a RNA quadruplex. A general tendency in nature to reduce the number of structural free parameters is conjectured.

Journal Article↗

PubMed2003

The architecture of the GroEL-GroES-(ADP)(7) chaperonin complex. I. Heptagrammal molecular forms.

Molecular forms are considered with vertices that have integral coordinates (the indices) with respect to a symmetry-adapted basis and which are left invariant by a point group of crystallographic scale-rotations (represented in this basis by invertible integral matrices). The composite form enclosing the chaperonin complex GroEL-GroES-(ADP)(7) is derived and decomposed into heptagrammal forms. These are generalizations of the two-dimensional forms based on sevenfold star polygons. In the chaperonin complex, nine such heptagrammal molecular forms are found: three for each ring (trans and cis) of GroEL and three for GroES. These forms correspond to a splitting of the monomer into adjacent segments. The change in the folding of the chains in the cis ring of GroEL arising from binding to GroES leaves the chain segmentation invariant.

Adenosine Diphosphate↗

PubMed2003

The architecture of the GroEL-GroES-(ADP)(7) chaperonin complex. II. Heptagrammal characterization of the folding.

The heptagrammal forms derived in part I [Janner (2003a). Acta Cryst. D59, 783-794] enclose chain segments of symmetry-related monomers in the GroEL-GroES-(ADP)(7) chaperonin complex. A chain reaching the boundary of a given form either ends, proceeds to a neighbouring form or has to fold. C(alpha) atoms corresponding to these folding points are identified in each of the nine forms of the chaperonin and are approximated by ideal positions having integral coordinates (the indices) with respect to a symmetry-adapted basis. Mutual structural relations between the indexed positions are derived in terms of integral scale-rotations (similar to those that leave the form invariant). The magnesium ions at the binding sites of the nucleotides ADP and ATP are shown to be symmetry-related to these folding points. The change in folding (polymorphism) observed in the cis ring of GroEL arising from binding to GroES is discussed. In particular, the form segmentation is conserved in the polymorphic transition. The geometric and algebraic restrictions imposed on the indexed positions and on their structural relations by the integrality condition are presented in an appendix.

Adenosine Diphosphate↗

PubMed2003

Hidden order in the GroEL-GroES-(ADP)7 chaperonin: forms, folding, and ADP-binding sites.

A molecular crystallography approach reveals the existence of a hidden order in GroEL-GroES-(ADP)(7). The new crystallographic symmetry concepts required are first illustrated for a hypothetical planar molecule. Their application to the chaperonin complex leads to molecular forms with vertices having integral coordinates (the indices) with respect to a symmetry-adapted basis and to folding points approximated by ideal C(alpha) positions with rational indices connected by integral scale-rotations, just as for the vertices of the molecular forms. The Mg(+2)-ions at nucleotide binding sites are symmetry-related in a similar way to C(alpha)'s folding points.

Adenosine Diphosphate↗

PubMed2002

Morphological possibilities in general crystallography. Snow crystals.

Morphological features of snow crystals are analyzed on the basis of concepts of a general crystallography, where point groups of infinite order are possible. The observations are first formulated in a set of rules, leading to a macroscopic growth lattice and to continuous growth boundaries. Both are brought in connection with two-dimensional integral invertible transformations. Families of boundaries are considered, labeled by a set of indices restricted by selection rules and generalizing the law of rational indices. These properties are indicated graphically on a sample of 12 natural snow crystals. Their geometric and arithmetic properties are summarized in a table.

Journal Article↗

PubMed2001

Introduction to a general crystallography.

The definition of an extended crystallographic group is given, based on an n-dimensional Euclidean space, carrier of a faithful integral representation of a permutation group of atomic positions. The Euclidean crystallography of normal crystals and the higher-dimensional one applied to incommensurately modulated crystals, intergrowth crystals and quasicrystals are special cases of a general crystallography. The same is true for the multimetrical crystallographic characterization of ice and of snow crystals. This approach can also be applied to single molecules, leading to what may be denoted as molecular crystallography. It possibly allows non-trivial structural relations between atomic positions belonging to the asymmetric unit of the molecular point group to be obtained. Two simple molecules, polycyclic aromatic hydrocarbons, are treated as illustrative examples.

Journal Article↗

PubMed1996