Quantum symmetries and the Weyl–Wigner product of group representations

In the usual formulation of quantum mechanics, groups of automorphisms of quantum states have ray representations by unitary and antiunitary operators on complex Hilbert space, in accordance with Wigner's theorem. In the phase-space formulation, they have real, true unitary representations in the space of square-integrable functions on phase space. Each such phase-space representation is a Weyl–Wigner product of the corresponding Hilbert space representation with its contragredient, and these can be recovered by 'factorizing' the Weyl–Wigner product. However, not every real, unitary representation on phase space corresponds to a group of automorphisms, so not every such representation is in the form of a Weyl–Wigner product and can be factorized. The conditions under which this is possible are examined. Examples are presented.

A unified and complete construction of all finite dimensional irreducible representations of gl(2|2)

Representations of the non-semisimple superalgebra gl(2/2) in the standard basis are investigated by means of the vector coherent state method and boson-fermion realization. All finite-dimensional irreducible typical and atypical representations and lowest weight (indecomposable) Kac modules of gl(2/2) are constructed explicity through the explicit construction of all gl(2) circle plus gl(2) particle states (multiplets) in terms of boson and fermion creation operators in the super-Fock space. This gives a unified and complete treatment of finite-dimensional representations of gl(2/2) in explicit form, essential for the construction of primary fields of the corresponding current superalgebra at arbitrary level.

Exact solution of the A(n-1)((1)) trigonometric vertex model with non-diagonal open boundaries

The A(n-1)((1)) trigonometric vertex model with generic non-diagonal boundaries is studied. The double-row transfer matrix of the model is diagonalized by algebraic Bethe ansatz method in terms of the intertwiner and the corresponding face-vertex relation. The eigenvalues and the corresponding Bethe ansatz equations are obtained.

Twisted parafermions

A new type of nonlocal currents (quasi-particles), which we call twisted parafermions, and its corresponding twisted Z-algebra are found. The system consists of one spin-1 bosonic field and six nonlocal fields of fractional spins. Jacobi-type identities for the twisted parafermions are derived, and a new conformal field theory is constructed from these currents. As an application, a parafermionic representation of the twisted affine current algebra A(2)((2)) is given.

Structure of Caribbean ciguatoxin isolated from Caranx latus

Caribbean ciguatoxins (C-CTXs) are responsible for the widespread occurrence of ciguatera in the Caribbean Sea. The structure and configuration of C-CTX-1 (1), the major ciguatoxin isolated from the horse-eye jack (Caranx latus), has been determined from DQF-COSY, E-COSY, TOCSY, NOESY, POESY, ge-HSQC. and HMQC experiments performed at 750 MHz and 500 MHz on a 0.13 pmol sample. C-CTX-1 ([M + H](+) m/z 1141.6 Da, molecular formula C62H92O19) has a ciguatoxin/breveroxin ladder structure comprising 14 trans-fused, ether-linked rings (7/6/6/7/8/9/7/6/8/6/7/6/7/6) assembled fi um 6 protonated fragments. The relative stereochemistry and ring configuration of 1 was determined from an analysis of coupling constant and NOE data. Like ciguatoxins in the Pacific Ocean (P-CTX), C-CTX-1 possesses a flexible nine-membered ring which may be a conserved feature among ciguatoxins. However, C-CTX-1 has a longer contiguous carbon backbone (57 vs 55 carbons for P-CTX-1), one extra ring, and a hemiketal in ring N but no spiroketal as found in P-CTX. C-CTX-1 possesses a primary hydroxyl which may allow selective derivatization. A minor analogue, C-CTX-2, was also isolated from fish and assigned the structure 56 epi-C-CTX-1 (2). since it slowly rearranged to C-CTX-1 in solution. Given the structural similarities between Caribbean and Pacific ciguatoxins, we propose that C-CTX-1 and C-CTX-2 arise from a Caribbean strain of the benthic dinoflagellate, Gambierdiscus toxicus.

Aminotriazines as locking fragments in macrocyclic synthesis

The macrocyclic compounds (6-(4',6'-diamino-1',3',5'-triazinyl)-1,4,6,8,11-pentaazacyclotetradecane)copper(II) triperchlorate dihydrate, [Cu(HL2)](ClO4)(3). 2H(2)O, (6-(6'-amino-4'-oxo-1'H-1',3',5'-triazinyl)-1,4,6,8,11-pentaazacyclotetradecane)copper(II) diperchlorate hydrate, [CuL3](ClO4)(2). H2O, and [(6-(4',6'-dioxo-1'H-1',3',5'-triazinyl) 1,4,6,8,11-pentaazacyclotetradecane)copper(II)] diperchlorate, [CuL4](ClO4)(2), have been synthesized. The macrocycles synthesized contain respectively pendant melamine, ammeline,and ammelide rings. The X-ray cyrstallographic analyses of [Cu(HL2)](ClO4)(3). 2H(2)O, triclinic, space group P (1) over bar, a = 9.489(10) Angstrom, b = 12.340(2) Angstrom, c = 24.496(4) Angstrom, alpha = 87.74(10)degrees beta = 85.51(10)degrees gamma = 70.95(10)degrees and Z = 4, and {[CuL3](ClO4)(2). H2O}2, monoclinic, space group C2/c, a = 18.624(8) Angstrom, b = 17.160(2) Angstrom, c = 15.998(6) Angstrom, beta = 117.82(2)degrees, and Z = 4, are reported. The structure of [Cu(HL2)](ClO4)(3). 2H(2)O shows the formation of linear tapes, formed by a combination of hydrogen bonds and pi-pi stacking interactions. The structure of [CuL3](ClO4)(2). H2O displays formation of dimers, formed by a coordinate bond from the oxygen in one molecule to the copper atom of another. The tautomeric forms of the ammeline and ammelide moieties have been determined. The potential of these compounds as subunits for cocrystallization has been investigated.

Coupling of a Jahn-Teller pseudorotation with a hindered internal rotation in an isolated molecule: 9-hydroxytriptycene

The irregular vibronic structure in the S-1<--S-0 resonant two-photon ionization (R2PI) spectrum of supersonically cooled triptycene is a result of a classic Exe Jahn-Teller effect [A. Furlan et al., J. Chem. Phys. 96, 7306 (1992)]. This is well characterized and can be used as an effective probe of intramolecular perturbations. Here we examine the S-1<--S-0 R2PI spectrum of 9-hydroxytriptycene and the fluorescence from various excited state vibronic levels. In this system the pseudorotation of the Jahn-Teller vibration is strongly coupled to the torsional motion of the bridgehead hydroxy group. This torsional motion results in a tunneling splitting in both the ground and excited states. The population of the upper level in the ground electronic state results in additional vibronic transitions becoming symmetry allowed in the R2PI spectrum that are forbidden in the bare triptycene molecule. The assignment of the R2PI and fluorescence spectra allows the potential energy surfaces of these vibrational modes to be accurately quantified. The full C-3v vibronic point group must be used to interpret the spectra. The time scale of the internal rotation of the-OH group and the butterfly flapping of the Jahn-Teller pseudorotation are of similar magnitude. The tunneling between the nine minima on the three dimensional potential energy surface is such that the Jahn-Teller pseudorotation occurs in concert with the-OH internal rotation. The Berry phase that is acquired during this motion is discussed. The simple physical picture emerges of the angle between two of the three benzene moieties opening in three equivalent ways in the S-1 electronic state. This geometry follows the position of the hydroxy group, which preferentially orients itself to point between these two rings. (C) 1998 American Institute of Physics. [S0021-9606(98)02348-4].

Integrability of a t - J model with impurities

A t - J model for correlated electrons with impurities is proposed. The impurities are introduced in such a way that integrability of the model in one dimension is not violated. The algebraic Bethe ansatz solution of the model is also given and it is shown that the Bethe states are highest weight states with respect to the supersymmetry algebra gl(2/1).

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons

Integrable Kondo impurities in the one-dimensional supersymmetric U model of strongly correlated electrons are studied by means of the boundary graded quantum inverse scattering method. The boundary K-matrices depending on the local magnetic moments of the impurities are presented as non-trivial realizations of the reflection equation algebras in an impurity Hilbert space. Furthermore, the model Hamiltonian is diagonalized and the Bethe ansatz equations are derived. It is interesting to note that our model exhibits a free parameter in the bulk Hamiltonian but no free parameter exists on the boundaries. This is in sharp contrast to the impurity models arising from the supersymmetric t-J and extended Hubbard models where there is no free parameter in the bulk but there is a free parameter on each boundary.

Molecular recognition of macrocyclic peptidomimetic inhibitors by HIV-1 protease

High-resolution crystal structures are described for seven macrocycles complexed with HIV-1 protease (HIVPR). The macrocycles possess two amides and an aromatic group within 15-17 membered rings designed to replace N- or C-terminal tripeptides from peptidic inhibitors of HIVPR. Appended to each macrocycle is a transition state isostere and either an acyclic peptide, nonpeptide, or another macrocycle. These cyclic analogues are potent inhibitors of HIVPR, and the crystal structures show them to be structural mimics of acyclic peptides, binding in the active site of HIVPR via the same interactions. Each macrocycle is restrained to adopt a P-strand conformation which is preorganized for protease binding. An unusual feature of the binding of C-terminal macrocyclic inhibitors is the interaction between a positively charged secondary amine and a catalytic aspartate of HIVPR. A bicyclic inhibitor binds similarly through its secondary amine that lies between its component N-terminal and C-terminal macrocycles. In contrast, the corresponding tertiary amine of the N-terminal macrocycles does not interact with the catalytic aspartates. The amine-aspartate interaction induces a 1.5 Angstrom N-terminal translation of the inhibitors in the active site and is accompanied by weakened interactions with a water molecule that bridges the ligand to the enzyme, as well as static disorder in enzyme flap residues. This flexibility may facilitate peptide cleavage and product dissociation during catalysis. Proteases [Aba(67,95)]HIVPR and [Lys(7),Ile(33),Aba(67,95)]- HIVPR used in this work were shown to have very similar crystal structures.

Extended integrability regime for the supersymmetric U model

An extension of the supersymmetric U model for correlated electrons is given and integrability is established by demonstrating that the model can he constructed through the quantum inverse scattering method using an R-matrix without the difference property. Some general symmetry properties of the model are discussed and from the Bethe ansatz solution an expression for the energies is presented.

Conformations of cyclic octapeptides and the influence of heterocyclic ring constraints upon calcium binding

A comparison is made between the structures and calcium binding properties of four cyclic octapeptides that differ in the number of heterocyclic thiazole and oxazoline ring constraints. The conformations of the naturally occurring cyclic octapeptides ascidiacyclamide 1 and patellamide D 2, which each contain two oxazoline and two thiazole rings, are compared by H-1 NMR spectroscopy with the analogues cyclo(Thr-D-Val(Thz)-Ile)(2) 3 with just two thiazoles, and cyclo(Thr-D-Val-alpha Abu-Ile)(2) 4, with no 5-membered rings. The conformations observed in the solid state for ascidiacyclamide (saddle) and patellamide D (twisted figure of eight) were retained in solution, whilst peptide 3 was found to have a chair shape and peptide 4 displayed a range of conformations. The solid state structure of 4 revealed that the peptide takes a relatively planar conformation with a number of transannular hydrogen bonds, which are apparently retained in solution. Complexation studies utilising H-1 NMR and CD spectroscopy yielded 1∶1 calcium-peptide binding constants (log K) for the four peptides (2.9 (1), 2.8 (2), 4.0 (3) and 5.5 (4)) as well as a 1 : 2 metal-peptide binding constant for 3 (log K = 4.5). The affinity for Ca2+ thus decreases with increasing number of 5-membered ring constraints in the macrocycle (4 > 3 > 2 approximate to 1).

Characterization of the sequential non-covalent and covalent interactions of the antitumour antibiotic hedamycin with double stranded DNA by NMR spectroscopy

Hedamycin, a member of the pluramycin class of antitumour antibiotics, consists of a planar anthrapyrantrione chromophore to which is attached two aminosugar rings at one end and a bisepoxide-containing sidechain at the other end, Binding to double-stranded DNA is known to involve both reversible and non-reversible modes of interaction. As a part of studies directed towards elucidating the structural basis for the observed 5'-pyGT-3' sequence selectivity of hedamycin, we conducted one-dimensional NMR titration experiments at low temperature using the hexadeoxyribonucleotide duplexes d(CACGTG)(2) and d(CGTACG)(2). Spectral changes which occurred during these titrations are consistent with hedamycin initially forming a reversible complex in slow exchange on the NMR timescale and binding through intercalation of the chromophore. Monitoring of this reversible complex over a period of hours revealed a second type of spectral change which corresponds with formation of a non-reversible complex. Copyright (C) 1999 John Wiley & Sons, Ltd.

Change in the rate of shell deposition and shell microstructure in response to shell borers in the abalone Haliotis rubra

Gastropod shells consist of two crystal types of calcium carbonate, an outer, prismatic calcite layer and an inner nacreous layer made of aragonite. In cross-section, the nacre of the nacreous layer appears to have a regular brick-like microstructure composed of thin laminae of aragonite crystals, separated by very thin sheets of protein (Lutz and Rhoads, 1980; Nakahara, 1983). In abalone (Genus, Haliotis) and other gastropods, thin layers of non-lamellar pigmented material occur within the nacre and have been termed alternatively, fine lines, growth rings or growth lines (Shepherd et al., 1995). It has been suggested that these pigmented layers are small, prismatic, calcite layers (Shepherd and Avalos-Borja, 1997; Zaremba et al., 1996) but investigations using a Raman laser in Haliotis rubra show that they contain aragonite rather than calcite (Hawkes et al, 1996). Day and Fleming (1992) suggest that the occurrence of pigmented layers is correlated with regular exogenous cues such as reproduction or temperature changes and indeed in some species, pigmented layers in the shell can be used to age abalone (review: Shepherd and Triantafillos, 1997). However, McShane and Smith (1992) suggest that pigmented layers can occur irregularly and therefore may be unreliable indicators of age.

Homomeric ring assemblies of eukaryotic Sm proteins have affinity for both RNA and DNA - Crystal structure of an oligomeric complex of yeast SmF

Sm and Sm-like proteins are key components of small ribonucleoproteins involved in many RNA and DNA processing pathways. In eukaryotes, these complexes contain seven unique Sm or Sm-like (Lsm) proteins assembled as hetero-heptameric rings, whereas in Archaea and bacteria six or seven-membered rings are made from only a single polypeptide chain. Here we show that single Sm and Lsm proteins from yeast also have the capacity to assemble into homo-oligomeric rings. Formation of homo-oligomers by the spliceosomal small nuclear ribonucleoprotein components SmE and SmF preclude hetero-interactions vital to formation of functional small nuclear RNP complexes in vivo. To better understand these unusual complexes, we have determined the crystal structure of the homomeric assembly of the spliceosomal protein SmF. Like its archaeal/bacterial homologs, the SmF complex forms a homomeric ring but in an entirely novel arrangement whereby two heptameric rings form a co-axially stacked dimer via interactions mediated by the variable loops of the individual SmF protein chains. Furthermore, we demonstrate that the homomeric assemblies of yeast Sm and Lsm proteins are capable of binding not only to oligo(U) RNA but, in the case of SmF, also to oligo(dT) single-stranded DNA.