A family of quantum projective spaces and related q-hypergeometric orthogonal polynomials

We define a one-parameter family of two-sided coideals in U_q(gl(n)) and study the corresponding algebras of infinitesimally right invariant functions on the quantum unitary group U_q(n). The Plancherel decomposition of these algebras with respect to the natural transitive U_q(n)-action is shown to be the same as in the case of a complex projective space. By computing the radial part of a suitable Casimir operator, we identify the zonal spherical functions (i.e. infinitesimally bi-invariant matrix coefficients of finite-dimensional irreducible representations) as Askey-Wilson polynomials containing two continuous and one discrete parameter. In certain limit cases, the zonal spherical functions are expressed as big and little q-Jacobi polynomials depending on one discrete parameter.Comment: 31 pages, AMS-TeX 2.1, no figure

Quantized flag manifolds and irreducible *-representations

We study irreducible *-representations of a certain quantization of the algebra of polynomial functions on a generalized flag manifold regarded as a real manifold. All irreducible *-representations are classified for a subclass of flag manifolds containing in particular the irreducible compact Hermitian symmetric spaces. For this subclass it is shown that the irreducible *-representations are parametrized by the symplectic leaves of the underlying Poisson bracket. We also discuss the relation between the quantized flag manifolds studied in this paper and the quantum flag manifolds studied by Soibelman, Lakshimibai and Reshetikhin, Jurco and Stovicek, and Korogodsky.Comment: AMS-LaTeX v1.2, 27 pages, no figure

CQG algebras: a direct algebraic approach to compact quantum groups

The purely algebraic notion of CQG algebra (algebra of functions on a compact quantum group) is defined. In a straightforward algebraic manner, the Peter-Weyl theorem for CQG algebras and the existence of a unique positive definite Haar functional on any CQG algebra are established. It is shown that a CQG algebra can be naturally completed to a $C^\ast$-algebra. The relations between our approach and several other approaches to compact quantum groups are discussed.Comment: 14 pp., Plain TeX, accepted by Lett. Math. Phy

The gram-negative bacterium Azotobacter chroococcum NCIMB 8003 employs a new glycoside hydrolase family 70 4,6-α-glucanotransferase enzyme (GtfD) to synthesize a reuteran like polymer from maltodextrins and starch

BACKGROUND: Originally the glycoside hydrolase (GH) family 70 only comprised glucansucrases of lactic acid bacteria which synthesize α-glucan polymers from sucrose. Recently we have identified 2 novel subfamilies of GH70 enzymes represented by the Lactobacillus reuteri 121 GtfB and the Exiguobacterium sibiricum 255-15 GtfC enzymes. Both enzymes catalyze the cleavage of (α1→4) linkages in maltodextrin/starch and the synthesis of consecutive (α1→6) linkages. Here we describe a novel GH70 enzyme from the nitrogen-fixing Gram-negative bacterium Azotobacter chroococcum, designated as GtfD. METHODS: The purified recombinant GtfD enzyme was biochemically characterized using the amylose-staining assay and its products were identified using profiling chromatographic techniques (TLC and HPAEC-PAD). Glucans produced by the GtfD enzyme were analyzed by HPSEC-MALLS-RI, methylation analysis, 1D/2D Lombard et al. (2014) H/ Machius et al. (1995) C NMR spectroscopy and enzymatic degradation studies. RESULTS: The A. chroococcum GtfD is closely related to GtfC enzymes, sharing the same non-permuted domain organization also found in GH13 enzymes and displaying 4,6-α-glucanotransferase activity. However, the GtfD enzyme is unable to synthesize consecutive (α1→6) glucosidic bonds. Instead, it forms a high molecular mass α-glucan with alternating (α1→4) and (α1→6) linkages from amylose/starch, highly similar to the reuteran polymer synthesized by the L. reuteri GtfA glucansucrase from sucrose. CONCLUSIONS: In view of its origin and specificity, the GtfD enzyme represents a unique evolutionary intermediate between family GH13 (α-amylase) and GH70 (glucansucrase) enzymes. GENERAL SIGNIFICANCE: This study expands the natural repertoire of starch-converting enzymes providing the first characterization of an enzyme that converts starch into a reuteran-like α-glucan polymer, regarded as a health promoting food ingredient

Reaction kinetics and galactooligosaccharide product profiles of the β-galactosidases from Bacillus circulans, Kluyveromyces lactis and Aspergillus oryzae

β-Galactosidase enzymes are used in the dairy industry to convert lactose into galactooligosaccharides (GOS) that are added to infant formula to mimic the molecular sizes and prebiotic functions of human milk oligosaccharides. Here we report a detailed analysis of the clearly different GOS profiles of the commercial β-galactosidases from Bacillus circulans, Kluyveromyces lactis and Aspergillus oryzae. Also the GOS yields of these enzymes differed, varying from 48.3% (B. circulans) to 34.9% (K. lactis), and 19.5% (A. oryzae). Their incubation with lactose plus the monosaccharides Gal or Glc resulted in altered GOS profiles. Experiments with (13)C6 labelled Gal and Glc showed that both monosaccharides act as acceptor substrates in the transgalactosylation reactions. The data shows that the lactose isomers β-d-Galp-(1→2)-d-Glcp, β-d-Galp-(1→3)-d-Glcp and β-d-Galp-(1→6)-d-Glcp are formed from acceptor reactions with free Glc and not by rearrangement of Glc in the active site.</p

Highly hydrolytic reuteransucrase from probiotic Lactobacillus reuteri strain ATCC 55730

Lactobacillus reuteri strain ATCC 55730 (LB BIO) was isolated as a pure culture from a Reuteri tablet purchased from the BioGaia company. This probiotic strain produces a soluble glucan (reuteran), in which the majority of the linkages are of the α-(1→4) glucosidic type (∼70%). This reuteran also contains α-(1→6)- linked glucosyl units and 4,6-disubstituted α-glucosyl units at the branching points. The LB BIO glucansucrase gene (gtfO) was cloned and expressed in Escherichia coli, and the GTFO enzyme was purified. The recombinant GTFO enzyme and the LB BIO culture supernatants synthesized identical glucan polymers with respect to linkage type and size distribution. GTFO thus is a reuteransucrase, responsible for synthesis of this reuteran polymer in LB BIO. The preference of GTFO for synthesizing α-(1→4) linkages is also evident from the oligosaccharides produced from sucrose with different acceptor substrates, e.g., isopanose from isomaltose. GTFO has a relatively high hydrolysis/transferase activity ratio. Complete conversion of 100 mM sucrose by GTFO nevertheless yielded large amounts of reuteran, although more than 50% of sucrose was converted into glucose. This is only the second example of the isolation and characterization of a reuteransucrase and its reuteran product, both found in different L. reuteri strains. GTFO synthesizes a reuteran with the highest amount of α-(1→4) linkages reported to date

Efficient screening methods for glucosyltransferase genes in Lactobacillus strains

Limited information is available about homopolysaccharide synthesis in the genus Lactobacillus. Using efficient screening techniques, extracellular glucosyltransferase (GTF) enzyme activity, resulting in α-glucan synthesis from sucrose, was detected in various lactobacilli. PCR with degenerate primers based on homologous boxes of known glucosyltransferase (gtf) genes of lactic acid bacteria strains allowed cloning of fragments of 10 putative gtf genes from eight different glucan producing Lactobacillus strains (five Lactobacillus reuteri strains, one Lactobacillus fermentum strain, one Lactobacillus sake strain and one Lactobacillus parabuchneri strain). Sequence analysis revealed that these lactobacilli possess a large variation of (putative) gtf genes, similar to what has been observed for Leuconostoc and Streptococcus strains. Homologs of GTFA of Lb. reuteri 121 (synthesizing reuteran, a unique glucan with α-(1→4) and α-(1→6) glycosidic bonds) were found in three of the four other Lb. reuteri strains tested. The other Lactobacillus GTF fragments showed the highest similarity with GTF enzymes of Leuconostoc spp.