Pain Predicts Dropout From Substance Use Treatment.

Objective: This project aimed to characterize the relationship between physical pain experienced at time of entry to residential treatment for substance use disorders (SUDs) and the frequency of treatment dropout. We hypothesized that both endorsement of recent pain and higher magnitude of endorsed pain intensity would be associated with higher dropout rates. We further hypothesized that these effects would be exacerbated among patients with opioid use disorder (OUD).

Co-occurring pain and addiction: prognostic implications for healthcare professionals in residential treatment for substance use disorder.

: Chronic pain is both an important antecedent and consequence of substance use. Although evidence suggests healthcare professionals may be uniquely vulnerable to chronic pain, this vulnerability remains largely unexamined in the context of recovery from substance use disorders (SUDs). We characterized pain in a sample of treatment-seeking individuals, examined potential differences in pain trajectories between healthcare professionals and non-healthcare patients, and interrogated potential pain-related vulnerabilities in treatment outcomes between these groups.

Symmetry-adapted digital modeling III. Coarse-grained icosahedral viruses.

Considered is the coarse-grained modeling of icosahedral viruses in terms of a three-dimensional lattice (the digital modeling lattice) selected among the projected points in space of a six-dimensional icosahedral lattice. Backbone atomic positions (Cα's for the residues of the capsid and phosphorus atoms P for the genome nucleotides) are then indexed by their nearest lattice point. This leads to a fine-grained lattice point characterization of the full viral chains in the backbone approximation (denoted as digital modeling).

Symmetry-adapted digital modeling II. The double-helix B-DNA.

The positions of phosphorus in B-DNA have the remarkable property of occurring (in axial projection) at well defined points in the three-dimensional space of a projected five-dimensional decagonal lattice, subdividing according to the golden mean ratio τ:1:τ [with τ = (1+\sqrt {5})/2] the edges of an enclosing decagon. The corresponding planar integral indices n1, n2, n3, n4 (which are lattice point coordinates) are extended to include the axial index n5 as well, defined for each P position of the double helix with respect to the single decagonal lattice ΛP(aP, cP) with aP = 2.222 Å and cP = 0.

Symmetry-adapted digital modeling I. Axial symmetric proteins.

Considered are axial symmetric proteins exemplified by the octameric mitochondrial creatine kinase, the Pyr RNA-binding attenuation protein, the D-aminopeptidase and the cyclophilin A-cyclosporin complex, with tetragonal (422), trigonal (32), pentagonal (52) and pentagonal (52) point-group symmetry, respectively. One starts from the protein enclosing form, which is characterized by vertices at points of a lattice (the form lattice) whose dimension depends on the point group. This allows the indexing of Cα's at extreme radial positions.

Origin of weak magnetism in compounds with cubic laves structure.

The origin of the weak itinerant magnetism in materials such as TiBe2 and ZrZn2 is investigated. The huge peak in the density of states at the Fermi energy is attributed to a special symmetry of the C15 structure: no crystal field splitting of the d levels occurs in the case of coordination by spherical ligands. Crystal field splitting is also investigated for the f orbitals in C15 structures such as PuZn2 and ThMg2.

Aperiodic crystals and superspace concepts.

For several decades the lattice periodicity of crystals, as shown by Laue, was considered to be their essential property. In the early sixties of the last century compounds were found which for many reasons should be called crystals, but were not lattice periodic. This opened the field of aperiodic crystals.

Alternative approaches to onion-like icosahedral fullerenes.

The fullerenes of the C60 series (C60, C240, C540, C960, C1500, C2160 etc.) form onion-like shells with icosahedral Ih symmetry. Up to C2160, their geometry has been optimized by Dunlap & Zope from computations according to the analytic density-functional theory and shown by Wardman to obey structural constraints derived from an affine-extended Ih group.

From an affine extended icosahedral group towards a toolkit for viral architecture.

The affine extensions (there are 55 different ones) of the icosahedral group developed by T. Keef and R. Twarock of the York Centre for Complex Systems Analysis of the University of York [see in particular Keef et al.

Form, symmetry and packing of biomacromolecules. V. Shells with boundaries at anti-nodes of resonant vibrations in icosahedral RNA viruses.

The RNA viruses cowpea chlorotic mottle, satellite tobacco mosaic, pariacoto and MS2, already considered in part IV of this series of papers [Janner, A. (2011a), Acta Cryst. A67, 517-520], are investigated further, with the aim to arrive at a possible physical basis for their structural properties.

Form, symmetry and packing of biomacromolecules. IV. Filled capsids of cowpea, tobacco, MS2 and pariacoto RNA viruses.

Four icosahedral RNA viruses are considered: the cowpea chlorotic mottle virus, the satellite tobacco mosaic virus, the pariacoto virus and the MS2 bacteriophage. The validity of the phenomenological rules derived in previous publications (crystallographic scaling, indexed forms enclosing axial-symmetric clusters, packing lattices of viral crystals) is confirmed and shown to apply equally well to the coat proteins as to the (ordered) RNA chains.

Form, symmetry and packing of biomacromolecules. III. Antigenic, receptor and contact binding sites in picornaviruses.

The relation between serotype differentiation and crystallographic symmetry, revealed by the contact fingerprint diagrams investigated in Part II [Janner (2010). Acta Cryst. A66, 312-326] for the human rhinovirus, is extended to the Picornaviridae family.

Form, symmetry and packing of biomacromolecules. II. Serotypes of human rhinovirus.

The differentiation of the human rhinovirus into serotypes, all having very similar structures and the same architecture, is shown to be related to the packing of the viruses in the crystal and to its space-group symmetry. The molecular crystallographic properties (here described in terms of a molecular lattice Lambda(M) instead of the form lattice Lambda(F) considered in previous publications) appear to be compatible with the crystal structure and with the packing lattice Lambda(P), introduced in Part I [Janner (2010). Acta Cryst.

Form, symmetry and packing of biomacromolecules. I. Concepts and tutorial examples.

The aim of this paper is to relate morphological properties of single biomacromolecules based on molecular enclosing forms indexed by an appropriate form lattice to the symmetry of the crystal where the molecules are periodically packed. Similar to the way in which the 'molécule intégrante' of Haüy permitted a molecular interpretation of the law of rational indices of crystal growth forms, alternative molecular enclosing forms, indexed by a so-called packing lattice, allow one to bridge the gap between form and crystal lattices. In this first part, selected tutorial examples illustrate the validity of the approach and the crystallographic compatibility between molecular and crystal structures.

Comparative architecture of octahedral protein cages. II. Interplay between structural elements.

In paper I [Janner (2008). Acta Cryst. A64, 494-502], the enclosing forms of the monomers of four octahedral holoenzymes (bacterio and mitochondrial ferritins, small heat-shock protein and sulfur oxygenase reductase) were derived, with vertices at points of a cubic lattice and indexed accordingly.

Comparative architecture of octahedral protein cages. I. Indexed enclosing forms.

The architectural elements of four protein cages (bacterio ferritin, human mitochondrial ferritin, sulfur oxygenase reductase and small heat-shock protein) are compared top-to-bottom. The starting points are polyhedra with octahedral symmetry 432 enclosing the cage and delimiting the central cavity, respectively, which have vertices at points of a species-dependent cubic form lattice. The approach is extended from the whole cage to axial-symmetric clusters down to polyhedral forms of single monomers viewed along the fourfold, the threefold and the twofold axes, respectively.

Higher-dimensional point groups in superspace crystallography.

Crystallographic puzzles not covered by the present crystallography, like integral indexing and crystallographic scaling of axial-symmetric biomacromolecules and icosahedral viral capsids and/or integral lattices, can possibly be explained by extending (n,d)-dimensional superspace crystallography to include finite subgroups of the higher-dimensional orthogonal group O(n) and not only those of O(d), as restricted by the physical dimension d.

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).

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.

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.

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.

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.

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.

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.

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.