On Turing dynamical systems and the Atiyah problem

Main theorems of the article concern the problem of M. Atiyah on possible values of l^2-Betti numbers. It is shown that all non-negative real numbers are l^2-Betti numbers, and that "many" (for example all non-negative algebraic) real numbers are l^2-Betti numbers of simply connected manifolds with respect to a free cocompact action. Also an explicit example is constructed which leads to a simply connected manifold with a transcendental l^2-Betti number with respect to an action of the threefold direct product of the lamplighter group Z/2 wr Z. The main new idea is embedding Turing machines into integral group rings. The main tool developed generalizes known techniques of spectral computations for certain random walk operators to arbitrary operators in groupoid rings of discrete measured groupoids.Comment: 35 pages; essentially identical to the published versio

Probing the urea dependence of residual structure in denatured human α-lactalbumin

Backbone 15N relaxation parameters and 15N–1HN residual dipolar couplings (RDCs) have been measured for a variant of human α-lactalbumin (α-LA) in 4, 6, 8 and 10 M urea. In the α-LA variant, the eight cysteine residues in the protein have been replaced by alanines (all-Ala α-LA). This protein is a partially folded molten globule at pH 2 and has been shown previously to unfold in a stepwise non-cooperative manner on the addition of urea. 15N R2 values in some regions of all-Ala α-LA show significant exchange broadening which is reduced as the urea concentration is increased. Experimental RDC data are compared with RDCs predicted from a statistical coil model and with bulkiness, average area buried upon folding and hydrophobicity profiles in order to identify regions of non-random structure. Residues in the regions corresponding to the B, D and C-terminal 310 helices in native α-LA show R2 values and RDC data consistent with some non-random structural propensities even at high urea concentrations. Indeed, for residues 101–106 the residual structure persists in 10 M urea and the RDC data suggest that this might include the formation of a turn-like structure. The data presented here allow a detailed characterization of the non-cooperative unfolding of all-Ala α-LA at higher concentrations of denaturant and complement previous studies which focused on structural features of the molten globule which is populated at lower concentrations of denaturant

Kinetically E-selective macrocyclic ring-closing metathesis

Macrocyclic compounds are central to the development of new drugs, but preparing them can be challenging because of the energy barrier that must be surmounted in order to bring together and fuse the two ends of an acyclic precursor such as an alkene (also known as an olefin). To this end, the catalytic process known as ring-closing metathesis (RCM) has allowed access to countless biologically active macrocyclic organic molecules, even for large-scale production. Stereoselectivity is often critical in such cases: The potency of a macrocyclic compound can depend on the stereochemistry of its alkene; alternatively, one isomer of the compound can be subjected to stereoselective modification (such as dihydroxylation). Kinetically controlled Z-selective RCM reactions have been reported, but the only available metathesis approach for accessing macrocyclic E-olefins entails selective removal of the Z-component of a stereoisomeric mixture by ethenolysis, sacrificing substantial quantities of material if E/Z ratios are near unity. Use of ethylene can also cause adventitious olefin isomerization- A particularly serious problem when the E-alkene is energetically less favoured. Here, we show that dienes containing an E-alkenyl-B(pinacolato) group, widely used in catalytic cross-coupling, possess the requisite electronic and steric attributes to allow them to be converted stereoselectively to E-macrocyclic alkenes. The reaction is promoted by a molybdenum monoaryloxide pyrrolide complex and affords products at a yield of up to 73 per cent and an E/Z ratio greater than 98/2. We highlight the utility of the approach by preparing recifeiolide (a 12-membered-ring antibiotic) and pacritinib (an 18-membered-ring enzyme inhibitor), the Z-isomer of which is less potent than the E-isomer. Notably, the 18-membered-ring moiety of pacritinib- A potent anti-cancer agent that is in advanced clinical trials for treating lymphoma and myelofibrosis-was prepared by RCM carried out at a substrate concentration 20 times greater than when a ruthenium carbene was used.National Institutes of Health (U.S.) (Grant GM-59426)National Science Foundation (U.S.) (Grant CHE-1362763

Dimethyl Sulfoxide Damages Mitochondrial Integrity and Membrane Potential in Cultured Astrocytes

Dimethyl sulfoxide (DMSO) is a polar organic solvent that is used to dissolve neuroprotective or neurotoxic agents in neuroscience research. However, DMSO itself also has pharmacological and pathological effects on the nervous system. Astrocytes play a central role in maintaining brain homeostasis, but the effect and mechanism of DMSO on astrocytes has not been studied. The present study showed that exposure of astrocyte cultures to 1 % DMSO for 24 h did not significantly affect cell survival, but decreased cell viability and glial glutamate transporter expression, and caused mitochondrial swelling, membrane potential impairment and reactive oxygen species production, and subsequent cytochrome c release and caspase-3 activation. DMSO at concentrations of 5 % significantly inhibited cell variability and promoted apoptosis of astrocytes, accompanied with more severe mitochondrial damage. These results suggest that mitochondrial impairment is a primary event in DMSO-induced astrocyte toxicity. The potential cytotoxic effects on astrocytes need to be carefully considered during investigating neuroprotective or neurotoxic effects of hydrophobic agents dissolved by DMSO