Linear independence of Gamma values in positive characteristic

We investigate the arithmetic nature of special values of Thakur's function field Gamma function at rational points. Our main result is that all linear independence relations over the field of algebraic functions are consequences of the known relations of Anderson and Thakur arising from the functional equations of the Gamma function.Comment: 51 page

Zero Order Estimates for Analytic Functions

The primary goal of this paper is to provide a general multiplicity estimate. Our main theorem allows to reduce a proof of multiplicity lemma to the study of ideals stable under some appropriate transformation of a polynomial ring. In particular, this result leads to a new link between the theory of polarized algebraic dynamical systems and transcendental number theory. On the other hand, it allows to establish an improvement of Nesterenko's conditional result on solutions of systems of differential equations. We also deduce, under some condition on stable varieties, the optimal multiplicity estimate in the case of generalized Mahler's functional equations, previously studied by Mahler, Nishioka, Topfer and others. Further, analyzing stable ideals we prove the unconditional optimal result in the case of linear functional systems of generalized Mahler's type. The latter result generalizes a famous theorem of Nishioka (1986) previously conjectured by Mahler (1969), and simultaneously it gives a counterpart in the case of functional systems for an important unconditional result of Nesterenko (1977) concerning linear differential systems. In summary, we provide a new universal tool for transcendental number theory, applicable with fields of any characteristic. It opens the way to new results on algebraic independence, as shown in Zorin (2010).Comment: 42 page

Permutable entire functions satisfying algebraic differential equations

It is shown that if two transcendental entire functions permute, and if one of them satisfies an algebraic differential equation, then so does the other one.Comment: 5 page

Zero estimates on group varieties II

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/46615/1/222_2005_Article_BF01388605.pd

Linear spaces on the intersection of cubic hypersurfaces

Upper bounds for the number of variables necessary to imply the existence of an m -dimensional linear variety on the intersection of r cubic hypersurfaces over local and global fields are given.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41633/1/605_2006_Article_BF02349626.pd

Reactive Oxygen Species Suppress Cardiac NaV1.5 Expression through Foxo1

NaV1.5 is a cardiac voltage-gated Na+ channel αsubunit and is encoded by the SCN5a gene. The activity of this channel determines cardiac depolarization and electrical conduction. Channel defects, including mutations and decrease of channel protein levels, have been linked to the development of cardiac arrhythmias. The molecular mechanisms underlying the regulation of NaV1.5 expression are largely unknown. Forkhead box O (Foxo) proteins are transcriptional factors that bind the consensus DNA sequences in their target gene promoters and regulate the expression of these genes. Comparative analysis revealed conserved DNA sequences, 5′-CAAAACA-3′ (insulin responsive element, IRE), in rat, mouse and human SCN5a promoters with the latter two containing two overlapping Foxo protein binding IREs, 5′-CAAAACAAAACA-3′. This finding led us to hypothesize that Foxo1 regulates NaV1.5 expression by directly binding the SCN5a promoter and affecting its transcriptional activity. In the present study, we determined whether Foxo1 regulates NaV1.5 expression at the transcriptional level and also defined the role of Foxo1 in hydrogen peroxide (H2O2)-mediated NaV1.5 suppression in HL-1 cardiomyocytes using chromatin immunoprecipitation (ChIP), constitutively nuclear Foxo1 expression, and RNAi Foxo1 knockdown as well as whole cell voltage-clamp recordings. ChIP with anti-Foxo1 antibody and follow-up semi-quantitative PCR with primers flanking Foxo1 binding sites in the proximal SCN5a promoter region clearly demonstrated enrichment of DNA, confirming Foxo1 recruitment to this consensus sequence. Foxo1 mutant (T24A/S319A-GFP, Foxo1-AA-GFP) was retained in nuclei, leading to a decrease of NaV1.5 expression and Na+ current, while silencing of Foxo1 expression by RNAi resulted in the augmentation of NaV1.5 expression. H2O2 significantly reduced NaV1.5 expression by promoting Foxo1 nuclear localization and this reduction was prevented by RNAi silencing Foxo1 expression. These studies indicate that Foxo1 negatively regulates NaV1.5 expression in cardiomyocytes and reactive oxygen species suppress NaV1.5 expression through Foxo1

L-Ilf3 and L-NF90 Traffic to the Nucleolus Granular Component: Alternatively-Spliced Exon 3 Encodes a Nucleolar Localization Motif

Ilf3 and NF90, two proteins containing double-stranded RNA-binding domains, are generated by alternative splicing and involved in several functions. Their heterogeneity results from posttranscriptional and posttranslational modifications. Alternative splicing of exon 3, coding for a 13 aa N-terminal motif, generates for each protein a long and short isoforms. Subcellular fractionation and localization of recombinant proteins showed that this motif acts as a nucleolar localization signal. Deletion and substitution mutants identified four arginines, essential for nucleolar targeting, and three histidines to stabilize the proteins within the nucleolus. The short isoforms are never found in the nucleoli, whereas the long isoforms are present in the nucleoplasm and the nucleoli. For Ilf3, only the posttranslationally-unmodified long isoform is nucleolar, suggesting that this nucleolar targeting is abrogated by posttranslational modifications. Confocal microscopy and FRAP experiments have shown that the long Ilf3 isoform localizes to the granular component of the nucleolus, and that L-Ilf3 and L-NF90 exchange rapidly between nucleoli. The presence of this 13 aminoacid motif, combined with posttranslational modifications, is responsible for the differences in Ilf3 and NF90 isoforms subcellular localizations. The protein polymorphism of Ilf3/NF90 and the various subcellular localizations of their isoforms may partially explain the various functions previously reported for these proteins

Co-Depletion of Cathepsin B and uPAR Induces G0/G1 Arrest in Glioma via FOXO3a Mediated p27Kip1 Upregulation

Cathepsin B and urokinase plasminogen activator receptor (uPAR) are both known to be overexpressed in gliomas. Our previous work and that of others strongly suggest a relationship between the infiltrative phenotype of glioma and the expression of cathepsin B and uPAR. Though their role in migration and adhesion are well studied the effect of these molecules on cell cycle progression has not been thoroughly examined.Cathepsin B and uPAR single and bicistronic siRNA plasmids were used to downregulate these molecules in SNB19 and U251 glioma cells. FACS analysis and BrdU incorporation assay demonstrated G0/G1 arrest and decreased proliferation with the treatments, respectively. Immunoblot and immunocyto analysis demonstrated increased expression of p27(Kip1) and its nuclear localization with the knockdown of cathepsin B and uPAR. These effects could be mediated by alphaVbeta3/PI3K/AKT/FOXO pathway as observed by the decreased alphaVbeta3 expression, PI3K and AKT phosphorylation accompanied by elevated FOXO3a levels. These results were further confirmed with the increased expression of p27(Kip1) and FOXO3a when treated with Ly294002 (10 microM) and increased luciferase expression with the siRNA and Ly294002 treatments when the FOXO binding promoter region of p27(Kip1) was used. Our treatment also reduced the expression of cyclin D1, cyclin D2, p-Rb and cyclin E while the expression of Cdk2 was unaffected. Of note, the Cdk2-cyclin E complex formation was reduced significantly.Our study indicates that cathepsin B and uPAR knockdown induces G0/G1 arrest by modulating the PI3K/AKT signaling pathway and further increases expression of p27(Kip1) accompanied by the binding of FOXO3a to its promoter. Taken together, our findings provide molecular mechanism for the G0/G1 arrest induced by the downregulation of cathepsin B and uPAR in SNB19 and U251 glioma cells