A treatment of the Cauchy--Schwarz inequality in C∗C^*-modules

We study the Cauchy--Schwarz and some related inequalities in a semi-inner product module over a $C^*$-algebra \A. The key idea is to consider a semi-inner product \A-module as a semi-inner product \A-module with respect to another semi-inner product. In this way, we improve some inequalities such as the Ostrowski inequality and an inequality related to the Gram matrix. The induced semi-inner products are also related to the the notion of covariance and variance. Furthermore, we obtain a sequence of nested inequalities that emerges from the Cauchy--Schwarz inequality. As a consequence, we derive some interesting operator-theoretical corollaries. In particular, we show that the sequence arising from our construction, when applied to a positive element of a $C^*$-algebra, converges to its pseudo-inverse.Comment: 18 pages, to appear in J. Math. Anal. Appl. (JMAA

Rh-POP Pincer Xantphos Complexes for C-S and C-H Activation. Implications for Carbothiolation Catalysis

The neutral Rh­(I)–Xantphos complex [Rh­(κ³-_P,O,P-Xantphos)­Cl]_<i>n</i>, <b>4</b>, and cationic Rh­(III) [Rh­(κ³-_P,O,P-Xantphos)­(H)₂]­[BAr^F₄], <b>2a</b>, and [Rh­(κ³-_P,O,P-Xantphos-3,5-C₆H₃(CF₃)₂)­(H)₂]­[BAr^F₄], <b>2b</b>, are described [Ar^F = 3,5-(CF₃)₂C₆H₃; Xantphos = 4,5-bis­(diphenylphosphino)-9,9-dimethylxanthene; Xantphos-3,5-C₆H₃(CF₃)₂ = 9,9-dimethylxanthene-4,5-bis­(bis­(3,5-bis­(trifluoromethyl)­phenyl)­phosphine]. A solid-state structure of <b>2b</b> isolated from C₆H₅Cl solution shows a κ¹-chlorobenzene adduct, [Rh­(κ³-_P,O,P-Xantphos-3,5-C₆H₃(CF₃)₂)­(H)₂(κ¹-ClC₆H₅)]­[BAr^F₄], <b>3</b>. Addition of H₂ to <b>4</b> affords, crystallographically characterized, [Rh­(κ³-_P,O,P-Xantphos)­(H)₂Cl], <b>5</b>. Addition of diphenyl acetylene to <b>2a</b> results in the formation of the C–H activated metallacyclopentadiene [Rh­(κ³-_P,O,P-Xantphos)­(ClCH₂Cl)­(σ,σ-(C₆H₄)­C­(H)CPh)]­[BAr^F₄], <b>7</b>, a rare example of a crystallographically characterized Rh–dichloromethane complex, alongside the Rh­(I) complex <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(η²-PhCCPh)]­[BAr^F₄], <b>6</b>. Halide abstraction from [Rh­(κ³-_P,O,P-Xantphos)­Cl]_<i>n</i> in the presence of diphenylacetylene affords <b>6</b> as the only product, which in the solid state shows that the alkyne binds perpendicular to the κ³-POP Xantphos ligand plane. This complex acts as a latent source of the [Rh­(κ³-_P,O,P-Xantphos)]⁺ fragment and facilitates <i>ortho</i>-directed C–S activation in a number of 2-arylsulfides to give <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(σ,κ¹-Ar)­(SMe)]­[BAr^F₄] (Ar = C₆H₄COMe, <b>8</b>; C₆H₄(CO)­OMe, <b>9</b>; C₆H₄NO₂, <b>10</b>; C₆H₄CNCH₂CH₂O, <b>11</b>; C₆H₄C₅H₄N, <b>12</b>). Similar C–S bond cleavage is observed with allyl sulfide, to give <i>fac</i>-[Rh­(κ³-_P,O,P-Xantphos)­(η³-C₃H₅)­(SPh)]­[BAr^F₄], <b>13</b>. These products of C–S activation have been crystallographically characterized. For <b>8</b> in situ monitoring of the reaction by NMR spectroscopy reveals the initial formation of <i>fac</i>-κ³-<b>8</b>, which then proceeds to isomerize to the <i>mer</i>-isomer. With the <i>para</i>-ketone aryl sulfide, 4-SMeC ₆H₄COMe, C–H activation <i>ortho</i> to the ketone occurs to give <i>mer</i>-[Rh­(κ³-_P,O,P-Xantphos)­(σ,κ¹-4-(COMe)­C₆H₃SMe)­(H)]­[BAr^F₄], <b>14</b>. The temporal evolution of carbothiolation catalysis using <i>mer</i>-κ³-<b>8</b>, and phenyl acetylene and 2-(methylthio)­acetophenone substrates shows initial fast catalysis and then a considerably slower evolution of the product. We suggest that the initially formed <i>fac</i>-isomer of the C–S activation product is considerably more active than the <i>mer</i>-isomer (i.e., <i>mer</i>-<b>8</b>), the latter of which is formed rapidly by isomerization, and this accounts for the observed difference in rates. A likely mechanism is proposed based upon these data

A rhodium-catalysed Sonogashira-type coupling exploiting C–S functionalisation: orthogonality with palladium-catalysed variants

This report concerns the development of an efficient Sonogashira-type coupling of arylmethylsulfides and terminal alkynes to generate aryl alkyne motifs. Orthogonal reactivity between traditional Pd catalysts, and the Rh catalysts employed, results in the ability to selectively activate either the C–S bond or C–X bond through catalyst choice. The Rh–bisphosphine catalyst has further been shown to be able to effect a hydroacylation-Sonogashira tandem sequence, and in combination with further onward reactions has been used in the synthesis of heterocycles and polycyclic systems

A rhodium-catalysed Sonogashira-type coupling exploiting C–S functionalisation: orthogonality with palladium-catalysed variants

This report concerns the development of an efficient Sonogashira-type coupling of arylmethylsulfides and terminal alkynes to generate aryl alkyne motifs. Orthogonal reactivity between traditional Pd catalysts, and the Rh catalysts employed, results in the ability to selectively activate either the C–S bond or C–X bond through catalyst choice. The Rh–bisphosphine catalyst has further been shown to be able to effect a hydroacylation-Sonogashira tandem sequence, and in combination with further onward reactions has been used in the synthesis of heterocycles and polycyclic systems

AKAP-Lbc mediates protection against doxorubicin-induced cardiomyocyte toxicity.

Doxorubicin (DOX) is a chemotherapic agent that is widely used to treat hematological and solid tumors. Despite its efficacy, DOX displays significant cardiac toxicity associated with cardiomyocytes death and heart failure. Cardiac toxicity is mainly associated with the ability of DOX to alter mitochondrial function. The current lack of treatments to efficiently prevent DOX cardiotoxicity underscores the need of new therapeutic approaches. Our current findings show that stimulation of cardiomyocytes with the α1-adrenergic receptor (AR) agonist phenylephrine (PE) significantly inhibits the apoptotic effect of DOX. Importantly, our results indicate that AKAP-Lbc is critical for transducing protective signals downstream of α1-ARs. In particular, we could show that suppression of AKAP-Lbc expression by infecting primary cultures of ventricular myocytes with lentiviruses encoding AKAP-Lbc specific short hairpin (sh) RNAs strongly impairs the ability of PE to reduce DOX-induced apoptosis. AKAP-Lbc-mediated cardiomyocyte protection requires the activation of anchored protein kinase D1 (PKD1)-dependent prosurvival pathways that promote the expression of the anti-apoptotic protein Bcl2 and inhibit the translocation of the pro-apoptotic protein Bax to mitochondria. In conclusion, AKAP-Lbc emerges as a coordinator of signals that protect cardiomyocytes against the toxic effects of DOX

A-Kinase Anchoring Protein 2 Promotes Protection against Myocardial Infarction.

Myocardial infarction (MI) is a leading cause of maladaptive cardiac remodeling and heart failure. In the damaged heart, loss of function is mainly due to cardiomyocyte death and remodeling of the cardiac tissue. The current study shows that A-kinase anchoring protein 2 (AKAP2) orchestrates cellular processes favoring cardioprotection in infarcted hearts. Induction of AKAP2 knockout (KO) in cardiomyocytes of adult mice increases infarct size and exacerbates cardiac dysfunction after MI, as visualized by increased left ventricular dilation and reduced fractional shortening and ejection fraction. In cardiomyocytes, AKAP2 forms a signaling complex with PKA and the steroid receptor co-activator 3 (Src3). Upon activation of cAMP signaling, the AKAP2/PKA/Src3 complex favors PKA-mediated phosphorylation and activation of estrogen receptor α (ERα). This results in the upregulation of ER-dependent genes involved in protection against apoptosis and angiogenesis, including Bcl2 and the vascular endothelial growth factor a (VEGFa). In line with these findings, cardiomyocyte-specific AKAP2 KO reduces Bcl2 and VEGFa expression, increases myocardial apoptosis and impairs the formation of new blood vessels in infarcted hearts. Collectively, our findings suggest that AKAP2 organizes a transcriptional complex that mediates pro-angiogenic and anti-apoptotic responses that protect infarcted hearts

Metoclopramide treatment blocks CD93-signaling-mediated self-renewal of chronic myeloid leukemia stem cells.

Self-renewal is a key characteristic of leukemia stem cells (LSCs) responsible for the development and maintenance of leukemia. In this study, we identify CD93 as an important regulator of self-renewal and proliferation of murine and human LSCs, but not hematopoietic stem cells (HSCs). The intracellular domain of CD93 promotes gene transcription via the transcriptional regulator SCY1-like pseudokinase 1 independently of ligation of the extracellular domain. In a drug library screen, we identify the anti-emetic agent metoclopramide as an efficient blocker of CD93 signaling. Metoclopramide treatment reduces murine and human LSCs in vitro and prolongs survival of chronic myeloid leukemia (CML) mice through downregulation of pathways related to stemness and proliferation in LSCs. Overall, these results identify CD93 signaling as an LSC-specific regulator of self-renewal and proliferation and a targetable pathway to eliminate LSCs in CML

Identification and analysis of functional associations among natural eukaryotic genome editing components

During development in the ciliate Paramecium, excess DNA interspersed throughout the germline genome is deleted to generate a new somatic genome. In this process, most of the intervening DNA is excised by a Piggybac-derived transposase, assisted by small RNAs (scnRNAs and iesRNAs) and chromatin remodelling. As the list of genes involved in DNA elimination has been growing, a need for a general approach to discover functional relationships among these genes now exists. We show that deep sequencing-based comparisons of experimentally-induced DNA retention provide a sensitive, quantitative approach to identify and analyze functional associations among genes involved in native genome editing. This reveals two functional molecular groups: (i) iesRNAs/scnRNAs, the putative Piwi- and RNA-binding Nowa1/2 proteins, and the transcription elongation factor TFIIS4; and (ii) PtCAF1 and Ezl1, two proteins involved in chromatin remodelling. Comparative analyses of silencing effects upon the largely unstudied regions comprising most developmentally eliminated DNA in Paramecium suggests a continuum between precise and imprecise DNA elimination. These findings show there is now a way forward to systematically elucidate the main components of natural eukaryotic genome editing systems