Operator algebras and a theorem of Dieudonne

LetA be aC*-algebra with second dualA″. Let (φ _n)(n=1,...) be a sequence in the dual ofA such that limφ _n(a) exists for eacha εA. In general, this does not imply that limφ _n(x) exists for eachx εA″. But if limφ _n(p) exists whenever p is the range projection of a positive self-adjoint element of the unit ball ofA, then it is shown that limφ _n(x) does exist for eachx inA″. This is a non-commutative generalisation of a celebrated theorem of Dieudonné. A new proof of Dieudonné’s theorem, for positive measures, is given here. The proof of the main result makes use of Dieudonné’s original theorem.     

High Content Screening for Compounds that Induce Early Stages of Human Embryonic Stem Cell Differentiation

Embryonic stem cells, due to their self-renewal and pluripotency properties, can be used to repair damaged tissues and as an unlimited source of differentiated cells. Although stem cells represent an important opportunity for cell based therapy and small molecules screening (in the context of drug or target discovery) many drawbacks are still preventing their widespread use. One of the most significant limitations is related to the complexity, as well as the reliability, of current protocols driving stem cells into any homogeneously differentiated cellular population. In this respect there is a strong demand for molecular agents promoting differentiation and thereby enabling robust, efficient and safe production of differentiated cells. In order to identify novel molecules that enhance early stages of differentiation, we developed an image based high content screening (HCS) approach using human embryonic stem cells (hESC). In our approach, we took advantage of custom image mining software specifically adapted for the selection of stem cell differentiation agents and the rejection of false positive hits. As a proof of concept ～3500 small molecules originating from commercial libraries were screened and a number of molecules of interests were identified. These molecules show stem cell differentiation properties comparable to the phenotypic signature obtained with the reference compound retinoic acid.     

Radial oscillations of neutron stars in strong magnetic fields

The eigen frequencies of radial pulsations of neutron stars are calculated in a strong magnetic field. At low densities we use the magnetic BPS equation of state (EOS) similar to that obtained by Lai and Shapiro while at high densities the EOS obtained from the relativistic nuclear mean field theory is taken and extended to include strong magnetic field. It is found that magnetized neutron stars support higher maximum mass whereas the effect of magnetic field on radial stability for observed neutron star masses is minimal.     

Multicopy suppressors for novel antibacterial compounds reveal targets and drug efflux susceptibility

Gene dosage has frequently been exploited to select for genetic interactions between a particular mutant and clones from a random genomic library at high copy. We report here the first use of multicopy suppression as a forward genetic method to determine cellular targets and potential resistance mechanisms for novel antibacterial compounds identified through high-throughput screening. A screen of 8640 small molecules for growth inhibition of a hyperpermeable strain of Escherichia coli led to the identification of 49 leads for suppressor selection from clones harboring an E. coli genomic library. The majority of suppressors were found to encode the multidrug efflux pump AcrB, indicating that those compounds were substrates for efflux. Two leads, which produced clones containing the gene folA, encoding dihydrofolate reductase (DHFR), proved to target DHFR in vivo and were competitive inhibitors in vitro.