Repetitions in beta-integers

Classical crystals are solid materials containing arbitrarily long periodic repetitions of a single motif. In this paper, we study the maximal possible repetition of the same motif occurring in beta-integers -- one dimensional models of quasicrystals. We are interested in beta-integers realizing only a finite number of distinct distances between neighboring elements. In such a case, the problem may be reformulated in terms of combinatorics on words as a study of the index of infinite words coding beta-integers. We will solve a particular case for beta being a quadratic non-simple Parry number.Comment: 11 page

Symmetries of finite Heisenberg groups for k-partite systems

Symmetries of finite Heisenberg groups represent an important tool for the study of deeper structure of finite-dimensional quantum mechanics. This short contribution presents extension of previous investigations to composite quantum systems comprised of k subsystems which are described with position and momentum variables in Z_{n_i}, i=1,...,k. Their Hilbert spaces are given by k-fold tensor products of Hilbert spaces of dimensions n_1,...,n_k. Symmetry group of the corresponding finite Heisenberg group is given by the quotient group of a certain normalizer. We provide the description of the symmetry groups for arbitrary multipartite cases. The new class of symmetry groups represents very specific generalization of finite symplectic groups over modular rings.Comment: 6 pages, to appear in Proceedings of QTS7 "Quantum Theory and Symmetries 7", Prague, August 7-13, 201

Biocompatible glyconanomaterials based on HPMA-copolymer for specific targeting of galectin-3

Abstract Background Galectin-3 (Gal-3) is a promising target in cancer therapy with a high therapeutic potential due to its abundant localization within the tumor tissue and its involvement in tumor development and proliferation. Potential clinical application of Gal-3-targeted inhibitors is often complicated by their insufficient selectivity or low biocompatibility. Nanomaterials based on N-(2-hydroxypropyl)methacrylamide (HPMA) nanocarrier are attractive for in vivo application due to their good water solubility and lack of toxicity and immunogenicity. Their conjugation with tailored carbohydrate ligands can yield specific glyconanomaterials applicable for targeting biomedicinally relevant lectins like Gal-3. Results In the present study we describe the synthesis and the structure-affinity relationship study of novel Gal-3-targeted glyconanomaterials, based on hydrophilic HPMA nanocarriers. HPMA nanocarriers decorated with varying amounts of Gal-3 specific epitope GalNAcβ1,4GlcNAc (LacdiNAc) were analyzed in a competitive ELISA-type assay and their binding kinetics was described by surface plasmon resonance. We showed the impact of various linker types and epitope distribution on the binding affinity to Gal-3. The synthesis of specific functionalized LacdiNAc epitopes was accomplished under the catalysis by mutant β-N-acetylhexosaminidases. The glycans were conjugated to statistic HPMA copolymer precursors through diverse linkers in a defined pattern and density using Cu(I)-catalyzed azide–alkyne cycloaddition. The resulting water-soluble and structurally flexible synthetic glyconanomaterials exhibited affinity to Gal-3 in low μM range. Conclusions The results of this study reveal the relation between the linker structure, glycan distribution and the affinity of the glycopolymer nanomaterial to Gal-3. They pave the way to specific biomedicinal glyconanomaterials that target Gal-3 as a therapeutic goal in cancerogenesis and other disorders

Acceptor Specificity of β-N-Acetylhexosaminidase from Talaromyces flavus: A Rational Explanation

Fungal β-N-acetylhexosaminidases, though hydrolytic enzymes in vivo, are useful tools in the preparation of oligosaccharides of biological interest. The β-N-acetylhexosaminidase from Talaromyces flavus is remarkable in terms of its synthetic potential, broad substrate specificity, and tolerance to substrate modifications. It can be heterologously produced in Pichia pastoris in a high yield. The mutation of the Tyr470 residue to histidine greatly enhances its transglycosylation capability. The aim of this work was to identify the structural requirements of this model β-N-acetylhexosaminidase for its transglycosylation acceptors and formulate a structure–activity relationship study. Enzymatic reactions were performed using an activated glycosyl donor, 4-nitrophenyl N-acetyl-β-d-glucosaminide or 4-nitrophenyl N-acetyl-β-d-galactosaminide, and a panel of glycosyl acceptors of varying structural features (N-acetylglucosamine, glucose, N-acetylgalactosamine, galactose, N-acetylmuramic acid, and glucuronic acid). The transglycosylation products were isolated and structurally characterized. The C-2 N-acetamido group in the acceptor molecule was found to be essential for recognition by the enzyme. The presence of the C-2 hydroxyl moiety strongly hindered the normal course of transglycosylation, yielding unique non-reducing disaccharides in a low yield. Moreover, whereas the gluco-configuration at C-4 steered the glycosylation into the β(1-4) position, the galacto-acceptor afforded a β(1-6) glycosidic linkage. The Y470H mutant enzyme was tested with acceptors based on β-glycosides of uronic acid and N-acetylmuramic acid. With the latter acceptor, we were able to isolate and characterize one glycosylation product in a low yield. To our knowledge, this is the first example of enzymatic glycosylation of an N-acetylmuramic acid derivative. In order to explain these findings and predict enzyme behavior, a modeling study was accomplished that correlated with the acquired experimental data

Voting by Committees with Exit

We study the problem of a society choosing a subset of new members from a finite set of candidates (as in Barberà Sonnenschein, and Zhou, 1991). However, we explicitly consider the possibility that initial members of the society (founders) may want to leave it if they do not like the resulting new society. We show that, if founders have separable (or additive) preferences, the unique strategy-proof and stable social choice function satisfying voters' sovereignty (on the set of candidates) is the one where candidates are chosen unanimously and no founder leaves the society

Multi-omics signatures in new-onset diabetes predict metabolic response to dietary inulin: findings from an observational study followed by an interventional trial

Abstract Aim The metabolic performance of the gut microbiota contributes to the onset of type 2 diabetes. However, targeted dietary interventions are limited by the highly variable inter-individual response. We hypothesized (1) that the composition of the complex gut microbiome and metabolome (MIME) differ across metabolic spectra (lean-obese-diabetes); (2) that specific MIME patterns could explain the differential responses to dietary inulin; and (3) that the response can be predicted based on baseline MIME signature and clinical characteristics. Method Forty-nine patients with newly diagnosed pre/diabetes (DM), 66 metabolically healthy overweight/obese (OB), and 32 healthy lean (LH) volunteers were compared in a cross-sectional case-control study integrating clinical variables, dietary intake, gut microbiome, and fecal/serum metabolomes (16 S rRNA sequencing, metabolomics profiling). Subsequently, 27 DM were recruited for a predictive study: 3 months of dietary inulin (10 g/day) intervention. Results MIME composition was different between groups. While the DM and LH groups represented opposite poles of the abundance spectrum, OB was closer to DM. Inulin supplementation was associated with an overall improvement in glycemic indices, though the response was very variable, with a shift in microbiome composition toward a more favorable profile and increased serum butyric and propionic acid concentrations. The improved glycemic outcomes of inulin treatment were dependent on better baseline glycemic status and variables related to the gut microbiota, including the abundance of certain bacterial taxa (i.e., Blautia, Eubacterium halii group, Lachnoclostridium, Ruminiclostridium, Dialister, or Phascolarctobacterium), serum concentrations of branched-chain amino acid derivatives and asparagine, and fecal concentrations of indole and several other volatile organic compounds. Conclusion We demonstrated that obesity is a stronger determinant of different MIME patterns than impaired glucose metabolism. The large inter-individual variability in the metabolic effects of dietary inulin was explained by differences in baseline glycemic status and MIME signatures. These could be further validated to personalize nutritional interventions in patients with newly diagnosed diabetes