Supercharacters, symmetric functions in noncommuting variables (extended abstract)

International audienceWe identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras.Nous montrons que deux structures en apparence bien différentes peuvent être identifiées: les super-caractères, qui sont un outil commode pour faire de l'analyse de Fourier sur le groupe des matrices unipotentes triangulaires supérieures à coefficients dans un corps fini, et l'anneau des fonctions symétriques en variables non-commutatives. Ces deux structures sont des algèbres de Hopf isomorphes. Cette identification permet de traduire dans une structure les dévelopements conçus pour l'autre, et suggère de nombreux exemples dans le domaine nouveau des algèbres de Hopf combinatoires

The upper triangular algebra loop of degree 44

summary:A natural loop structure is defined on the set $U_4$ of unimodular upper-triangular matrices over a given field. Inner mappings of the loop are computed. It is shown that the loop is non-associative and nilpotent, of class 3. A detailed listing of the loop conjugacy classes is presented. In particular, one of the loop conjugacy classes is shown to be properly contained in a superclass of the corresponding algebra group

Supercharacters, symmetric functions in noncommuting variables (extended abstract)

We identify two seemingly disparate structures: supercharacters, a useful way of doing Fourier analysis on the group of unipotent uppertriangular matrices with coefficients in a finite field, and the ring of symmetric functions in noncommuting variables. Each is a Hopf algebra and the two are isomorphic as such. This allows developments in each to be transferred. The identification suggests a rich class of examples for the emerging field of combinatorial Hopf algebras

Genetic variants in RBFOX3 are associated with sleep latency

Time to fall asleep (sleep latency) is a major determinant of sleep quality. Chronic, long sleep latency is a major characteristic of sleep-onset insomnia and/or delayed sleep phase syndrome. In this study we aimed to discover common polymorphisms that contribute to the genetics of sleep latency. We performed a meta-analysis of genome-wide association studies (GWAS) including 2 572 737 single nucleotide polymorphisms (SNPs) established in seven European cohorts including 4242 individuals. We found a cluster of three highly correlated variants (rs9900428, rs9907432 and rs7211029) in the RNA-binding protein fox-1 homolog 3 gene (RBFOX3) associated with sleep latency (P-values=5.77 × 10-08, 6.59 × 10- 08 and 9.17 × 10- 08). These SNPs were replicated in up to 12 independent populations including 30 377 individuals (P-values=1.5 × 10- 02, 7.0 × 10- 03 and 2.5 × 10- 03; combined meta-analysis P-values=5.5 × 10-07, 5.4 × 10-07 and 1.0 × 10-07). A functional prediction of RBFOX3 based on co-expression with other genes shows that this gene is predominantly expressed in brain (P-value=1.4 × 10-316) and the central nervous system (P-value=7.5 × 10- 321). The predicted function of RBFOX3 based on co-expression analysis with other genes shows that this gene is significantly involved in the release cycle of neurotransmitte

Genomic investigations of unexplained acute hepatitis in children

Since its first identification in Scotland, over 1,000 cases of unexplained paediatric hepatitis in children have been reported worldwide, including 278 cases in the UK1. Here we report an investigation of 38 cases, 66 age-matched immunocompetent controls and 21 immunocompromised comparator participants, using a combination of genomic, transcriptomic, proteomic and immunohistochemical methods. We detected high levels of adeno-associated virus 2 (AAV2) DNA in the liver, blood, plasma or stool from 27 of 28 cases. We found low levels of adenovirus (HAdV) and human herpesvirus 6B (HHV-6B) in 23 of 31 and 16 of 23, respectively, of the cases tested. By contrast, AAV2 was infrequently detected and at low titre in the blood or the liver from control children with HAdV, even when profoundly immunosuppressed. AAV2, HAdV and HHV-6 phylogeny excluded the emergence of novel strains in cases. Histological analyses of explanted livers showed enrichment for T cells and B lineage cells. Proteomic comparison of liver tissue from cases and healthy controls identified increased expression of HLA class 2, immunoglobulin variable regions and complement proteins. HAdV and AAV2 proteins were not detected in the livers. Instead, we identified AAV2 DNA complexes reflecting both HAdV-mediated and HHV-6B-mediated replication. We hypothesize that high levels of abnormal AAV2 replication products aided by HAdV and, in severe cases, HHV-6B may have triggered immune-mediated hepatic disease in genetically and immunologically predisposed children

Albumin-linked prostate-specific antigen-activated thapsigargin- and niclosamide-based molecular grenades targeting the microenvironment in metastatic castration-resistant prostate cancer

Localized prostate cancer is curable via annihilation of the entire cancer neighborhood by surgery or local radiation. Unfortunately, once metastatic, no available therapy is curative. The vast majority will die despite aggressive systemic combinational androgen-ablation therapies. Thus, there is an urgent need for effective systemic therapeutics that sterilize the entire microenvironment in metastatic castration-resistant prostate cancer (mCRPC). To accomplish this goal, advantage can be taken of the unique biology of mCRPC cells. Like their normal cell of origin, mCRPCs retain expression of the prostate-specific differentiation protein, prostate-specific antigen (PSA), which they abundantly secrete into their extracellular fluid (ECF). This unique, and essentially universal, secretion of enzymatically active PSA into the ECF by mCRPCs creates an exploitable therapeutic index for activation of systemically delivered highly lipophilic toxins as “molecular grenades” covalently linked to cysteine-34 of human serum albumin (HSA) via a stable maleimide containing PSA cleavable peptide such that PSA-dependent hydrolysis (i.e., “detonation”) releases the grenades restrictively within the ECF of mCRPC. This approach decreases dose-limiting host toxicity while enhancing plasma half-life from minutes to days (i.e., pharmacokinetic effect) and increasing the tissue concentration of the maleimide coupled albumin delivery (MAD) in the ECF at sites of cancer due to the enhanced permeability of albumin at these sites (i.e., enhanced permeability and retention effect). This allows the MAD-PSA detonated grenades to circulate throughout the body in a non-toxic form. Only within sites of mCRPC is there a sufficiently high level of enzymatically active PSA to efficiently “pull the pin” on the grenades releasing their lipophilic cell-penetrant toxins from HSA. Thus, if a sufficient level of “detonation” occurs, this will kill mCRPC cells, and sterilize the entire PSA-rich metastatic sites via a bystander effect. In this review, two examples of such MAD-PSA detonated molecular grenades are presented—one based upon thapsigagin and the other on niclosamide. Keywords: Albumin-linked prodrug, Maleimide coupled albumin delivery, Thapsigargin, Niclosamid

Mipsagargin: The Beginning—Not the End—of Thapsigargin Prodrug-Based Cancer Therapeutics

Søren Brøgger Christensen isolated and characterized the cell-penetrant sesquiterpene lactone Thapsigargin (TG) from the fruit Thapsia garganica. In the late 1980s/early 1990s, TG was supplied to multiple independent and collaborative groups. Using this TG, studies documented with a large variety of mammalian cell types that TG rapidly (i.e., within seconds to a minute) penetrates cells, resulting in an essentially irreversible binding and inhibiting (IC50~10 nM) of SERCA 2b calcium uptake pumps. If exposure to 50–100 nM TG is sustained for >24–48 h, prostate cancer cells undergo apoptotic death. TG-induced death requires changes in the cytoplasmic Ca2+, initiating a calmodulin/calcineurin/calpain-dependent signaling cascade that involves BAD-dependent opening of the mitochondrial permeability transition pore (MPTP); this releases cytochrome C into the cytoplasm, activating caspases and nucleases. Chemically unmodified TG has no therapeutic index and is poorly water soluble. A TG analog, in which the 8-acyl groups is replaced with the 12-aminododecanoyl group, afforded 12-ADT, retaining an EC50 for killing of <100 nM. Conjugation of 12-ADT to a series of 5–8 amino acid peptides was engineered so that they are efficiently hydrolyzed by only one of a series of proteases [e.g., KLK3 (also known as Prostate Specific Antigen); KLK2 (also known as hK2); Fibroblast Activation Protein Protease (FAP); or Folh1 (also known as Prostate Specific Membrane Antigen)]. The obtained conjugates have increased water solubility for systemic delivery in the blood and prevent cell penetrance and, thus, killing until the TG-prodrug is hydrolyzed by the targeting protease in the vicinity of the cancer cells. We summarize the preclinical validation of each of these TG-prodrugs with special attention to the PSMA TG-prodrug, Mipsagargin, which is in phase II clinical testing