Semigroups of Jensen set-valued functions

A set-valued function F defined on a convex cone S in a real vector space X into the set n(Y) of all non-empty subsets of a real vector space Y is said to be the Jensen function iff $${1\over 2}\lbrack F(x)+F(x)\rbrack=F\lbrack{1\over 2}(x+y)\rbrack$$ for all x, y ∈ S. This note deals with iteration semigroups of Jensen set-valued functions on S.     

Affine selections of convex set-valued functions

Summary It is shown that every convex set-valued function defined on a cone with a cone-basis in a real linear space with compact values in a real locally convex space has an affine selection. Similar results can be obtained for midconvex set-valued functions.     

Automated mass spectrometric analysis of urinary and plasma serotonin

Serotonin emerges as crucial neurotransmitter and hormone in a growing number of different physiologic processes. Besides extensive serotonin production previously noted in patients with metastatic carcinoid tumors, serotonin now is implicated in liver cell regeneration and bone formation. The aim was to develop a rapid, sensitive, and highly selective automated on-line solid-phase extraction method coupled to high-performance liquid chromatography–tandem mass spectrometry (XLC-MS/MS) to quantify low serotonin concentrations in matrices such as platelet-poor plasma and urine. Fifty microliters plasma or 2.5 μL urine equivalent were pre-purified by automated on-line solid-phase extraction, using weak cation exchange. Chromatography of serotonin and its deuterated internal standard was performed with hydrophilic interaction chromatography. Mass spectrometric detection was operated in multiple reaction monitoring mode using a quadrupole tandem mass spectrometer with positive electrospray ionization. Serotonin concentrations were determined in platelet-poor plasma of metastatic carcinoid patients (n = 23) and healthy controls (n = 22). Urinary reference intervals were set by analyzing 24-h urine collections of 120 healthy subjects. Total run-time was 6 min. Intra- and inter-assay analytical variation were <10%. Linearity in the 0–7300 μmol/L calibration range was excellent (R² > 0.99). Quantification limits were 30 and 0.9 nmol/L in urine and plasma, respectively. Platelet-poor serotonin concentrations in metastatic carcinoid patients were significantly higher than in controls. The urinary reference interval was 10–78 μmol/mol creatinine. Serotonin analysis with sensitive and specific XLC-MS/MS overcomes limitations of conventional HPLC. This enables accurate quantification of serotonin for both routine diagnostic procedures and research in serotonin-related disorders.     

Stereochemical basis for the anti-chlamydial activity of the phosphonate protease inhibitor JO146

JO146, a mixture of two diastereomers of a peptidic phosphonate inhibitor for Chlamydial HtrA (CtHtrA), has reported activity against Chlamydia species in both human and koala. In this study we isolated the individual diastereomers JO146-D1 and JO146-D2 (in ≥90% purity) and assessed their individual inhibitory activity against the serine protease human neutrophil elastase (HNE) which is structurally and functionally related to CtHtrA, as well as in Chlamydia trachomatis cell culture. JO146-D2 [S,S,R-Boc-Val-Pro-Val^P(OPh)₂], the isomer with the physiologically relevant valine at P1, had an approximate 2.5 – fold increase in in vitro HNE inhibition potency over JO146-D1 [S,S,S-Boc-Val-Pro-Val^P(OPh)₂] and greater than 100 – fold increase in cellular anti-chlamydial activity compared to JO146-D1 which possesses the unnatural valine at P1. JO146 and the individual diastereomers had excellent selectivity for the serine protease HNE over the potential off-target serine proteases trypsin and chymotrypsin. Docking studies supported the biological data with a geometrically unfavoured interaction observed between the P1 valine residue of JO146-D1 and the enzyme S1 sub-pocket.     

Additive selections of superadditive set-valued functions

Summary A set-valued functionF from a coneC with a cone-basis of a topological vector spaceX into the family of all non-empty compact convex subsets of a locally convex spaceY is called superadditive provided thatF(x) + F(y) F(x + y), for allx, y C. We show that every superadditive set-valued function admits an additive selection.Dedicated to Professor Otto Haupt on his 100th birthday