Casimirs and Lax operators from the structure of Lie algebras

This paper uses the structure of the Lie algebras to identify the Casimir invariant functions and Lax operators for matrix Lie groups. A novel mapping is found from the cotangent space to the dual Lie algebra which enables Lax operators to be found. The coordinate equations of motion are given in terms of the structure constants and the Hamiltonian.

Selection-mutation balance models with epistatic selection

We present an application of birth-and-death processes on configuration spaces to a generalized mutation4 selection balance model. The model describes the aging of population as a process of accumulation of mu5 tations in a genotype. A rigorous treatment demands that mutations correspond to points in abstract spaces. 6 Our model describes an infinite-population, infinite-sites model in continuum. The dynamical equation which 7 describes the system, is of Kimura-Maruyama type. The problem can be posed in terms of evolution of states 8 (differential equation) or, equivalently, represented in terms of Feynman-Kac formula. The questions of interest 9 are the existence of a solution, its asymptotic behavior, and properties of the limiting state. In the non-epistatic 10 case the problem was posed and solved in [Steinsaltz D., Evans S.N., Wachter K.W., Adv. Appl. Math., 2005, 11 35(1)]. In our model we consider a topological space X as the space of positions of mutations and the influence of epistatic potentials

Evidence for complex multigenic inheritance of radiation AML susceptibility in mice revealed using a surrogate phenotypic assay

The mapping of genes which affect individual cancer risk is an important but complex challenge. A surrogate assay of susceptibility to radiation-induced acute myeloid leukaemia (AML) in the mouse based on chromosomal radiosensitivity has been developed and validated. This assay was applied to the mapping of radiation-induced AML risk modifier loci by association with microsatellite markers. A region on chromosome (chr) 18 with strong association is identified and confirmed by backcross analysis. Additional loci on chrs 8 and 13 show significant association. A key candidate gene Rbbp8 on chr18 is identified. Rbbp8 is shown to be upregulated in response to X-irradiation in the AML sensitive CBA strain but not AML resistant C57BL/6 strain. This study demonstrates the strength of utilizing surrogate endpoints of cancer susceptibility in the mapping of mouse loci and identifies additional loci that may affect radiation cancer risk.

The structure and mechanism of serine acetyltransferase from Escherichia coli

Serine acetyltransferase (SAT) catalyzes the first step of cysteine synthesis in microorganisms and higher plants. Here we present the 2.2 Angstrom crystal structure of SAT from Escherichia coli, which is a dimer of trimers, in complex with cysteine. The SAT monomer consists of an amino-terminal alpha-helical domain and a carboxyl- terminal left-handed beta-helix. We identify His(158) and Asp(143) as essential residues that form a catalytic triad with the substrate for acetyl transfer. This structure shows the mechanism by which cysteine inhibits SAT activity and thus controls its own synthesis. Cysteine is found to bind at the serine substrate site and not the acetyl-CoA site that had been reported previously. On the basis of the geometry around the cysteine binding site, we are able to suggest a mechanism for the O-acetylation of serine by SAT. We also compare the structure of SAT with other left-handed beta-helical structures.

On the universal TRO of a JC*-triple, ideals and tensor products

In a development from material introduced in recent work, we discuss the interconnections between ternary rings of operators (TROs) and right C*-algebras generated by JC*-triples, deducing that every JC*-triple possesses a largest universally reversible ideal, that the universal TRO commutes with appropriate tensor products and establishing a reversibility criterion for type I JW*-triples.

Chemical ligation by ring opening of oxo-thiomorpholines

The invention discloses processes for preparing compounds comprising an #-amino acid motif. The compounds are useful in e.g. the chemical ligation of peptides.

The impact of liquidity on senior credit index spreads during the subprime crisis

This paper examines the effects of liquidity during the 2007–09 crisis, focussing on the Senior Tranche of the CDX.NA.IG Index and on Moody's AAA Corporate Bond Index. It aims to understand whether the sharp increase in the credit spreads of these AAA-rated credit indices can be explained by worse credit fundamentals alone or whether it also reflects a lack of depth in the relevant markets, the scarcity of risk-capital, and the liquidity preference exhibited by investors. Using cointegration analysis and error correction models, the paper shows that during the crisis lower market and funding liquidity are important drivers of the increase in the credit spread of the AAA-rated structured product, whilst they are less significant in explaining credit spread changes for a portfolio of unstructured credit instruments. Looking at the experience of the subprime crisis, the study shows that when the conditions under which securitisation can work properly (liquidity, transparency and tradability) suddenly disappear, investors are left highly exposed to systemic risk.

Realising the cup product of local Tate duality

We present an explicit description, in terms of central simple algebras, of a cup product map which occurs in the statement of local Tate duality for Galois modules of prime cardinality p. Given cocycles f and g, we construct a central simple algebra of dimension p^2 whose class in the Brauer group gives the cup product f\cup g. This algebra is as small as possible.

Activation of G-protein-coupled receptor 30 is sufficient to enhance spatial recognition memory in ovariectomized rats

In ovariectomized rats, administration of estradiol, or selective estrogen receptor agonists that activate either the alpha or beta isoforms, have been shown to enhance spatial cognition on a variety of learning and memory tasks, including those that capitalize on the preference of rats to seek out novelty. Although the effects of the putative estrogen G-protein-coupled receptor 30 (GPR30) on hippocampus-based tasks have been reported using food-motivated tasks, the effects of activation of GPR30 receptors on tasks that depend on the preference of rats to seek out spatial novelty remain to be determined. Therefore, the aim of the current study was to determine if short-term treatment of ovariectomized rats with G-1, an agonist for GPR30, would mimic the effects on spatial recognition memory observed following short-term estradiol treatment. In Experiment 1, ovariectomized rats treated with a low dose (1mug) of estradiol 48h and 24h prior to the information trial of a Y-maze task exhibited a preference for the arm associated with the novel environment on the retention trial conducted 48h later. In Experiment 2, treatment of ovariectomized rats with G-1 (25mug) 48h and 24h prior to the information trial of a Y-maze task resulted in a greater preference for the arm associated with the novel environment on the retention trial. Collectively, the results indicated that short-term treatment of ovariectomized rats with a GPR30 agonist was sufficient to enhance spatial recognition memory, an effect that also occurred following short-term treatment with a low dose of estradiol.