Mesoionic pyridopyrimidinylium and pyridooxazinylium olates and non-mesoionic pyridopyrimidinones. Structures in the solid state, solution, and matrices

X-Ray crystal structures, C-13 NMR spectra and theoretical calculations (B3LYP/6-31G*) are reported for the mesoionic (zwitterionic) pyridopyrimidinylium- and pyridooxazinyliumolates 2a, 3a and 5a,b as well as the enol ether 11b and the enamine 11c. The 1-NH compounds like 1a, 2a and 3a exist in the mesoionic form in the crystal and in solution, but the OH tautomers such as 1b and 2b dominate in the gas phase as revealed by the Ar matrix IR spectra in conjunction with DFT calculations. All data indicate that the mesoionic compounds can be regarded as intramolecular pyridine-ketene zwitterions (cf. 16 --> 17) with a high degree of positive charge on the pyridinium nitrogen, a long pyridinium N-CO bond (ca. 1.44-1.49 Angstrom), and normal C=O double bonds (ca. 1.22 Angstrom). All mesoionic compounds exhibit a pronounced tilting of the olate C=O groups (the C=O groups formally derived from a ketene) towards the pyridinium nitrogen, giving NCO angles of 110-118 degrees. Calculations reveal a hydrogen bond with 6-CH, analogous to what is found in ketene-pyridine zwitterions and the C3O2-pyridine complex. The 2-OH tautomers of type 1b, 2b, and 11 also show a high degree of zwitterionic character as indicated by the canonical structures 11 12.

A structural basis for the selection of dominant alpha beta T cell receptors in antiviral immunity

We have examined the basis for immunodominant or public TCR usage in an antiviral CTL response. Residues encoded by each of the highly selected genetic elements of an immunodominant clonotype recognizing Epstein-Barr virus were critical to the antigen specificity of the receptor. Upon recognizing antigen the immunodominant TCR undergoes extensive conformational changes in the complementarity determining regions (CDRs), including the disruption of the canonical structures of the germline-encoded CDR1alpha and CDR2alpha loops to produce an enhanced fit with the HLA-peptide complex. TCR ligation induces conformational changes in the TCRalpha constant domain thought to form part of the docking site for CD3epsilon. These findings indicate that TCR immunodominance is associated with structural properties conferring receptor specificity and suggest a novel structural link between TCR ligation and intracellular signaling.

Solution structure of CnErg1 (Ergtoxin), a HERG specific scorpion toxin

The three-dimensional structure of chemically synthesized CnErg1 (Ergtoxin), which specifically blocks HERG (human ether-a-go-go-related gene) K+ channels, was determined by nuclear magnetic resonance spectroscopy. CnErg1 consists of a triple-stranded beta-sheet and an a-helix, as is typical of K+ channel scorpion toxins. The peptide structure differs from the canonical structures in that the first beta-strand is shorter and is nearer to the second beta-strand rather than to the third beta-strand on the C-terminus. There is also a large hydrophobic patch on the surface of the toxin, surrounding a central lysine residue, Lys13. We postulate that this hydrophobic patch is likely to form part of the binding surface of the toxin. (C) 2003 Published by Elsevier Science B.V. on behalf of the Federation of European Biochemical Societies.

A minimal i-motif stabilized by minor groove G:T:G:T tetrads

The repetitive DNA sequences found at telomeres and centromeres play a crucial role in the structure and function of eukaryotic chromosomes. This role may be related to the tendency observed in many repetitive DNAs to adopt non-canonical structures. Although there is an increasing recognition of the importance of DNA quadruplexes in chromosome biology, the co-existence of different quadruplex-forming elements in the same DNA structure is still a matter of debate. Here we report the structural study of the oligonucleotide d(TCGTTTCGT) and its cyclic analog d. Both sequences form dimeric quadruplex structures consisting of a minimal i-motif capped, at both ends, by a slipped minor groove-aligned G:T:G:T tetrad. These mini i-motifs, which do not exhibit the characteristic CD spectra of other i-motif structures, can be observed at neutral pH, although they are more stable under acidic conditions. This finding is particularly relevant since these oligonucleotide sequences do not contain contiguous cytosines. Importantly, these structures resemble the loop moiety adopted by an 11-nucleotide fragment of the conserved centromeric protein B (CENP-B) box motif, which is the binding site for the CENP-B.

A minimal i-motif stabilized by minor groove G:T:G:T tetrads

The repetitive DNA sequences found at telomeres and centromeres play a crucial role in the structure and function of eukaryotic chromosomes. This role may be related to the tendency observed in many repetitive DNAs to adopt non-canonical structures. Although there is an increasing recognition of the importance of DNA quadruplexes in chromosome biology, the co-existence of different quadruplex-forming elements in the same DNA structure is still a matter of debate. Here we report the structural study of the oligonucleotide d(TCGTTTCGT) and its cyclic analog d. Both sequences form dimeric quadruplex structures consisting of a minimal i-motif capped, at both ends, by a slipped minor groove-aligned G:T:G:T tetrad. These mini i-motifs, which do not exhibit the characteristic CD spectra of other i-motif structures, can be observed at neutral pH, although they are more stable under acidic conditions. This finding is particularly relevant since these oligonucleotide sequences do not contain contiguous cytosines. Importantly, these structures resemble the loop moiety adopted by an 11-nucleotide fragment of the conserved centromeric protein B (CENP-B) box motif, which is the binding site for the CENP-B.

Darboux-Egoroff metrics, rational Landau-Ginzburg potentials and the Painleve VI equation

We present a class of three-dimensional integrable structures associated with the Darboux-Egoroff metric and classical Euler equations of free rotations of a rigid body. They are obtained as canonical structures of rational Landau-Ginzburg potentials and provide solutions to the Painleve VI equation.

The hierarchical structures of the NEO-PI-R and the 16PF5

The present study compares the higher-level dimensions and the hierarchical structures of the fifth edition of the 16 PF with those of the NEO PI-R. Both inventories measure personality according to five higher-level dimensions. These inventories were however constructed according to different methods (bottom-up vs. top-down). 386 participants filled out both questionnaires. Correlations, regressions and canonical correlations made it possible to compare the inventories. As expected they roughly measure the same aspects of personality. There is a coherent association among four of the five dimensions measured in the tests. However Agreeableness, the remaining dimension in the NEO PI-R, is not represented in the 16 PF 5. Our analyses confirmed the hierarchical structures of both instruments, but this confirmation was more complete in the case of the NEO PI-R. Indeed, a parallel analysis indicated that a four-factor solution should be considered in the case of the 16 PF 5. On the other hand, the NEO PI-R's five-factor solution was confirmed. The top-down construction of this instrument seems to make for a more legible structure. Of the two five-dimension constructs, the NEO PI-R thus seems the more reliable. This confirms the relevance of the Five Factor Model of personality.

Lagrangian and Hamiltonian BRST structures of the antysimmetric tensor gauge theory

We study the Becchi-Rouet-Stora-Tyutin (BRST) structure of a self-interacting antisymmetric tensor gauge field, which has an on-shell null-vector gauge transformation. The Batalin-Vilkovisky covariant general formalism is briefly reviewed, and the issue of on-shell nilpotency of the BRST transformation is elucidated. We establish the connection between the covariant and the canonical BRST formalisms for our particular theory. Finally, we point out the similarities and differences with Wittens string field theory.

Sur une classe de structures kählériennes généralisées toriques

Cette thèse concerne le problème de trouver une notion naturelle de «courbure scalaire» en géométrie kählérienne généralisée. L'approche utilisée consiste à calculer l'application moment pour l'action du groupe des difféomorphismes hamiltoniens sur l'espace des structures kählériennes généralisées de type symplectique. En effet, il est bien connu que l'application moment pour la restriction de cette action aux structures kählériennes s'identifie à la courbure scalaire riemannienne. On se limite à une certaine classe de structure kählériennes généralisées sur les variétés toriques notée $DGK_{\omega}^{\mathbb{T}}(M)$ que l'on reconnaît comme étant classifiées par la donnée d'une matrice antisymétrique $C$ et d'une fonction réelle strictement convexe $\tau$ (ayant un comportement adéquat au voisinage de la frontière du polytope moment). Ce point de vue rend évident le fait que toute structure kählérienne torique peut être déformée en un élément non kählérien de $DGK_{\omega}^{\mathbb{T}}(M)$, et on note que cette déformation à lieu le long d'une des classes que R. Goto a démontré comme étant libre d'obstruction. On identifie des conditions suffisantes sur une paire $(\tau,C)$ pour qu'elle donne lieu à un élément de $DGK_{\omega}^{\mathbb{T}}(M)$ et on montre qu'en dimension 4, ces conditions sont également nécessaires. Suivant l'adage «l'application moment est la courbure» mentionné ci-haut, des formules pour des notions de «courbure scalaire hermitienne généralisée» et de «courbure scalaire riemannienne généralisée» (en dimension 4) sont obtenues en termes de la fonction $\tau$. Enfin, une expression de la courbure scalaire riemannienne généralisée en termes de la structure bihermitienne sous-jacente est dégagée en dimension 4. Lorsque comparée avec le résultat des physiciens Coimbra et al., notre formule suggère un choix canonique pour le dilaton de leur théorie.

Testing isotherm models and recovering empirical relationships for adsorption in microporous carbons using virtual carbon models and grand canonical Monte Carlo simulations

Using the plausible model of activated carbon proposed by Harris and co-workers and grand canonical Monte Carlo simulations, we study the applicability of standard methods for describing adsorption data on microporous carbons widely used in adsorption science. Two carbon structures are studied, one with a small distribution of micropores in the range up to 1 nm, and the other with micropores covering a wide range of porosity. For both structures, adsorption isotherms of noble gases (from Ne to Xe), carbon tetrachloride and benzene are simulated. The data obtained are considered in terms of Dubinin-Radushkevich plots. Moreover, for benzene and carbon tetrachloride the temperature invariance of the characteristic curve is also studied. We show that using simulated data some empirical relationships obtained from experiment can be successfully recovered. Next we test the applicability of Dubinin's related models including the Dubinin-Izotova, Dubinin-Radushkevich-Stoeckli, and Jaroniec-Choma equations. The results obtained demonstrate the limits and applications of the models studied in the field of carbon porosity characterization.

An application of lattice basis reduction to polynomial identities for algebraic structures

The authors` recent classification of trilinear operations includes, among other cases, a fourth family of operations with parameter q epsilon Q boolean OR {infinity}, and weakly commutative and weakly anticommutative operations. These operations satisfy polynomial identities in degree 3 and further identities in degree 5. For each operation, using the row canonical form of the expansion matrix E to find the identities in degree 5 gives extremely complicated results. We use lattice basis reduction to simplify these identities: we compute the Hermite normal form H of E(t), obtain a basis of the nullspace lattice from the last rows of a matrix U for which UE(t) = H, and then use the LLL algorithm to reduce the basis. (C) 2008 Elsevier Inc. All rights reserved.

Integrability vs supersymmetry: Poisson structures of the pohlmeyer reduction

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Homogeneous structures and rigidity of isoparametric submanifolds in Hilbert space

We study isoparametric submanifolds of rank at least two in a separable Hilbert space, which are known to be homogeneous by the main result in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181], and with such a submanifold M and a point x in M we associate a canonical homogeneous structure I" (x) (a certain bilinear map defined on a subspace of T (x) M x T (x) M). We prove that I" (x) , together with the second fundamental form alpha (x) , encodes all the information about M, and we deduce from this the rigidity result that M is completely determined by alpha (x) and (Delta alpha) (x) , thereby making such submanifolds accessible to classification. As an essential step, we show that the one-parameter groups of isometries constructed in [E. Heintze and X. Liu, Ann. of Math. (2), 149 (1999), 149-181] to prove their homogeneity induce smooth and hence everywhere defined Killing fields, implying the continuity of I" (this result also seems to close a gap in [U. Christ, J. Differential Geom., 62 (2002), 1-15]). Here an important tool is the introduction of affine root systems of isoparametric submanifolds.

Annealed Ising model on hierarchical structures: a transfer matrix approach.

Spin systems in the presence of disorder are described by two sets of degrees of freedom, associated with orientational (spin) and disorder variables, which may be characterized by two distinct relaxation times. Disordered spin models have been mostly investigated in the quenched regime, which is the usual situation in solid state physics, and in which the relaxation time of the disorder variables is much larger than the typical measurement times. In this quenched regime, disorder variables are fixed, and only the orientational variables are duly thermalized. Recent studies in the context of lattice statistical models for the phase diagrams of nematic liquid-crystalline systems have stimulated the interest of going beyond the quenched regime. The phase diagrams predicted by these calculations for a simple Maier-Saupe model turn out to be qualitative different from the quenched case if the two sets of degrees of freedom are allowed to reach thermal equilibrium during the experimental time, which is known as the fully annealed regime. In this work, we develop a transfer matrix formalism to investigate annealed disordered Ising models on two hierarchical structures, the diamond hierarchical lattice (DHL) and the Apollonian network (AN). The calculations follow the same steps used for the analysis of simple uniform systems, which amounts to deriving proper recurrence maps for the thermodynamic and magnetic variables in terms of the generations of the construction of the hierarchical structures. In this context, we may consider different kinds of disorder, and different types of ferromagnetic and anti-ferromagnetic interactions. In the present work, we analyze the effects of dilution, which are produced by the removal of some magnetic ions. The system is treated in a “grand canonical" ensemble. The introduction of two extra fields, related to the concentration of two different types of particles, leads to higher-rank transfer matrices as compared with the formalism for the usual uniform models. Preliminary calculations on a DHL indicate that there is a phase transition for a wide range of dilution concentrations. Ising spin systems on the AN are known to be ferromagnetically ordered at all temperatures; in the presence of dilution, however, there are indications of a disordered (paramagnetic) phase at low concentrations of magnetic ions.

Canonical group quantization and boundary conditions

In the present thesis, we study quantization of classical systems with non-trivial phase spaces using the group-theoretical quantization technique proposed by Isham. Our main goal is a better understanding of global and topological aspects of quantum theory. In practice, the group-theoretical approach enables direct quantization of systems subject to constraints and boundary conditions in a natural and physically transparent manner -- cases for which the canonical quantization method of Dirac fails. First, we provide a clarification of the quantization formalism. In contrast to prior treatments, we introduce a sharp distinction between the two group structures that are involved and explain their physical meaning. The benefit is a consistent and conceptually much clearer construction of the Canonical Group. In particular, we shed light upon the 'pathological' case for which the Canonical Group must be defined via a central Lie algebra extension and emphasise the role of the central extension in general. In addition, we study direct quantization of a particle restricted to a half-line with 'hard wall' boundary condition. Despite the apparent simplicity of this example, we show that a naive quantization attempt based on the cotangent bundle over the half-line as classical phase space leads to an incomplete quantum theory; the reflection which is a characteristic aspect of the 'hard wall' is not reproduced. Instead, we propose a different phase space that realises the necessary boundary condition as a topological feature and demonstrate that quantization yields a suitable quantum theory for the half-line model. The insights gained in the present special case improve our understanding of the relation between classical and quantum theory and illustrate how contact interactions may be incorporated.