On Exceptional Vertex Operator (Super) Algebras

We consider exceptional vertex operator algebras and vertex operator superalgebras with the property that particular Casimir vectors constructed from the primary vectors of lowest conformal weight are Virasoro descendents of the vacuum. We show that the genus one partition function and characters for simple ordinary modules must satisfy modular linear differential equations. We show the rationality of the central charge and module lowest weights, modularity of solutions, the dimension of each graded space is a rational function of the central charge and that the lowest weight primaries generate the algebra. We also discuss conditions on the reducibility of the lowest weight primary vectors as a module for the automorphism group. Finally we analyse solutions for exceptional vertex operator algebras with primary vectors of lowest weight up to 9 and for vertex operator superalgebras with primary vectors of lowest weight up to 17/2. Most solutions can be identified with simple ordinary modules for known algebras but there are also four conjectured algebras generated by weight two primaries and three conjectured extremal vertex operator algebras generated by primaries of weight 3, 4 and 6 respectively.Comment: 37 page

Butyrate Transcriptionally Enhances Peptide Transporter PepT1 Expression and Activity

Background: PepT1, an intestinal epithelial apical di/tripeptide transporter, is normally expressed in the small intestine and induced in colon during chronic inflammation. This study aimed at investigating PepT1 regulation by butyrate, a short-chain fatty acid produced by commensal bacteria and accumulated inside inflamed colonocyte. Results: We found that butyrate treatment of human intestinal epithelial Caco2-BBE cells increased human PepT1 (hPepT1) promoter activity in a dose- and time-dependent manner, with maximal activity observed in cells treated with 5 mM butyrate for 24 h. Under this condition, hPepT1 promoter activity, mRNA and protein expression levels were increased as assessed by luciferase assay, real-time RT-PCR and Western blot, respectively. hPepT1 transport activity was accordingly increased by,2.5-fold. Butyrate did not alter hPepT1 mRNA half-life indicating that butyrate acts at the transcriptional level. Molecular analyses revealed that Cdx2 is the most important transcription factor for butyrate-induced increase of hPepT1 expression and activity in Caco2-BBE cells. Butyrate-activated Cdx2 binding to hPepT1 promoter was confirmed by gel shift and chromatin immunoprecipitation. Moreover, Caco2-BBE cells overexpressing Cdx2 exhibited greater hPepT1 expression level than wild-type cells. Finally, treatment of mice with 5 mM butyrate added to drinking water for 24 h increased colonic PepT1 mRNA and protein expression levels, as well as enhanced PepT1 transport activity in colonic apical membranes vesicles