Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group

Energy evolution in time-dependent harmonic oscillator

The theory of adiabatic invariants has a long history, and very important implications and applications in many different branches of physics, classically and quantally, but is rarely founded on rigorous results. Here we treat the general time-dependent one-dimensional harmonic oscillator, whose Newton equation $\ddot{q} + \omega^2(t) q=0$ cannot be solved in general. We follow the time-evolution of an initial ensemble of phase points with sharply defined energy $E_0$ at time $t=0$ and calculate rigorously the distribution of energy $E_1$ after time $t=T$, which is fully (all moments, including the variance $\mu^2$) determined by the first moment $\bar{E_1}$. For example, $\mu^2 = E_0^2 [(\bar{E_1}/E_0)^2 - (\omega (T)/\omega (0))^2]/2$, and all higher even moments are powers of $\mu^2$, whilst the odd ones vanish identically. This distribution function does not depend on any further details of the function $\omega (t)$ and is in this sense universal. In ideal adiabaticity $\bar{E_1} = \omega(T) E_0/\omega(0)$, and the variance $\mu^2$ is zero, whilst for finite $T$ we calculate $\bar{E_1}$, and $\mu^2$ for the general case using exact WKB-theory to all orders. We prove that if $\omega (t)$ is of class ${\cal C}^{m}$ (all derivatives up to and including the order $m$ are continuous) $\mu \propto T^{-(m+1)}$, whilst for class ${\cal C}^{\infty}$ it is known to be exponential $\mu \propto \exp (-\alpha T)$.Comment: 26 pages, 5 figure

The TH1 cell lineage-determining transcription factor T-bet suppresses TH2 gene expression by redistributing GATA3 away from TH2 genes

Lineage-determining transcription factors (LD-TFs) drive the differentiation of progenitor cells into a specific lineage. In CD4+ T cells, T-bet dictates differentiation of the TH1 lineage, whereas GATA3 drives differentiation of the alternative TH2 lineage. However, LD-TFs, including T-bet and GATA3, are frequently co-expressed but how this affects LD-TF function is not known. By expressing T-bet and GATA3 separately or together in mouse T cells, we show that T-bet sequesters GATA3 at its target sites, thereby removing GATA3 from TH2 genes. This redistribution of GATA3 is independent of GATA3 DNA binding activity and is instead mediated by the T-bet DNA binding domain, which interacts with the GATA3 DNA binding domain and changes GATA3′s sequence binding preference. This mechanism allows T-bet to drive the TH1 gene expression program in the presence of GATA3. We propose that redistribution of one LD-TF by another may be a common mechanism that could explain how specific cell fate choices can be made even in the presence of other transcription factors driving alternative differentiation pathways

Time evolution, cyclic solutions and geometric phases for the generalized time-dependent harmonic oscillator

The generalized time-dependent harmonic oscillator is studied. Though several approaches to the solution of this model have been available, yet a new approach is presented here, which is very suitable for the study of cyclic solutions and geometric phases. In this approach, finding the time evolution operator for the Schr\"odinger equation is reduced to solving an ordinary differential equation for a c-number vector which moves on a hyperboloid in a three-dimensional space. Cyclic solutions do not exist for all time intervals. A necessary and sufficient condition for the existence of cyclic solutions is given. There may exist some particular time interval in which all solutions with definite parity, or even all solutions, are cyclic. Criterions for the appearance of such cases are given. The known relation that the nonadiabatic geometric phase for a cyclic solution is proportional to the classical Hannay angle is reestablished. However, this is valid only for special cyclic solutions. For more general ones, the nonadiabatic geometric phase may contain an extra term. Several cases with relatively simple Hamiltonians are solved and discussed in detail. Cyclic solutions exist in most cases. The pattern of the motion, say, finite or infinite, can not be simply determined by the nature of the Hamiltonian (elliptic or hyperbolic, etc.). For a Hamiltonian with a definite nature, the motion can changes from one pattern to another, that is, some kind of phase transition may occur, if some parameter in the Hamiltonian goes through some critical value.Comment: revtex4, 28 pages, no figur

A role for Dicer in immune regulation

Micro RNAs (miRNAs) regulate gene expression at the posttranscriptional level. Here we show that regulatory T (T reg) cells have a miRNA profile distinct from conventional CD4 T cells. A partial T reg cell–like miRNA profile is conferred by the enforced expression of Foxp3 and, surprisingly, by the activation of conventional CD4 T cells. Depleting miRNAs by eliminating Dicer, the RNAse III enzyme that generates functional miRNAs, reduces T reg cell numbers and results in immune pathology. Dicer facilitates, in a cell-autonomous fashion, the development of T reg cells in the thymus and the efficient induction of Foxp3 by transforming growth factor β. These results suggest that T reg cell development involves Dicer-generated RNAs

Cryptic Polyketide Synthase Genes in Non-Pathogenic Clostridium SPP

Modular type I polyketide synthases (PKS) produce a vast array of bacterial metabolites with highly diverse biological functions. Notably, all known polyketides were isolated from aerobic bacteria, and yet no example has been reported for strict anaerobes. In this study we explored the diversity and distribution of PKS genes in the genus Clostridium. In addition to comparative genomic analyses combined with predictions of modular type I polyketide synthase (PKS) gene clusters in sequenced genomes of Clostridium spp., a representative selection of other species inhabiting a variety of ecological niches was investigated by PCR screening for PKS genes. Our data reveal that all studied pathogenic Clostridium spp. are devoid of putative PKS genes. In stark contrast, cryptic PKS genes are widespread in genomes of non-pathogenic Clostridium species. According to phylogenetic analyses, the Clostridium PKS genes have unusual and diverse origins. However, reverse transcription quantitative PCR demonstrates that these genes are silent under standard cultivation conditions, explaining why the related metabolites have been overlooked until now. This study presents clostridia as a putative source for novel bioactive polyketides

Preparation of anti-vicinal amino alcohols: asymmetric synthesis of D-erythro-Sphinganine, (+)-spisulosine and D-ribo-phytosphingosine

Two variations of the Overman rearrangement have been developed for the highly selective synthesis of anti-vicinal amino alcohol natural products. A MOM-ether directed palladium(II)-catalyzed rearrangement of an allylic trichloroacetimidate was used as the key step for the preparation of the protein kinase C inhibitor D-erythro-sphinganine and the antitumor agent (+)-spisulosine, while the Overman rearrangement of chiral allylic trichloroacetimidates generated by asymmetric reduction of an alpha,beta-unsaturated methyl ketone allowed rapid access to both D-ribo-phytosphingosine and L-arabino-phytosphingosine

Cyclin-dependent kinase 9 as a potential target for anti-TNF resistant inflammatory bowel disease

BACKGROUND AND AIMS: Resistance to single cytokine blockade, namely anti-TNF therapy, is a growing concern for patients with inflammatory bowel disease (IBD). The transcription factor T-bet is a critical regulator of intestinal homeostasis, is genetically linked to mucosal inflammation and controls the expression of multiples genes such as the pro-inflammatory cytokines IFN-γ and TNF. Inhibiting T-bet may therefore offer a more attractive prospect for treating IBD but remains challenging to target therapeutically. In this study, we evaluate the effect of targeting the transactivation function of T-bet using inhibitors of P-TEFb (CDK9-cyclin T), a transcriptional elongation factor downstream of T-bet. METHODS: Using an adaptive immune-mediated colitis model, human colonic lymphocytes from IBD patients and multiple large clinical datasets, we investigate the effect of CDK9 inhibitors on cytokine production and gene expression in colonic CD4+ T cells and link these genetic modules to clinical response in patients with IBD. RESULTS: Systemic CDK9 inhibition led to histological improvement of immune-mediated colitis and was associated with targeted suppression of colonic CD4+ T cell-derived IFN-γ and IL-17A. In colonic lymphocytes from IBD patients, CDK9 inhibition potently repressed genes responsible for pro-inflammatory signalling, and in particular genes regulated by T-bet. Remarkably, CDK9 inhibition targeted genes that were highly expressed in anti-TNF resistant IBD and that predicted non-response to anti-TNF therapy. CONCLUSION: Collectively, our findings reveal CDK9 as a potential target for anti-TNF resistant IBD, which has the potential for rapid translation to the clinic

Discovery of 3-Formyl-Tyrosine Metabolites from Pseudoalteromonas tunicata through Heterologous Expression

Genome mining and identification of natural product gene clusters typically relies on the presence of canonical nonribosomal polypeptide synthetase (NRPS) or polyketide synthase (PKS) domains. Recently, other condensation enzymes, such as the ATP-grasp ligases, have been recognized as important players in natural product biosynthesis. In this study, sequence based searching for homologues of DdaF, the ATP-grasp amide ligase from dapdiamide biosynthesis, led to the identification of a previously unannotated biosynthetic gene cluster in Pseudoalteromonas tunicata. Heterologous expression of the cluster in Escherichia coli allowed for the production and structure determination of two new 3-formyl tyrosine metabolites.Molecular and Cellular Biolog