Bregman distances and Chebyshev sets

A closed set of a Euclidean space is said to be Chebyshev if every point in the space has one and only one closest point in the set. Although the situation is not settled in infinite-dimensional Hilbert spaces, in 1932 Bunt showed that in Euclidean spaces a closed set is Chebyshev if and only if the set is convex. In this paper, from the more general perspective of Bregman distances, we show that if every point in the space has a unique nearest point in a closed set, then the set is convex. We provide two approaches: one is by nonsmooth analysis; the other by maximal monotone operator theory. Subdifferentiability properties of Bregman nearest distance functions are also given

Cytochrome P450-catalyzed insertion of carbenoids into N–H bonds

Expanding nature’s catalytic repertoire to include reactions important in synthetic chemistry will open new opportunities for ‘green’ chemistry and biosynthesis. We demonstrate the first enzyme-catalyzed insertion of carbenoids into N–H bonds. This type of bond disconnection, which has no counterpart in nature, can be mediated by variants of the cytochrome P450 from Bacillus megaterium. The N–H insertion reaction takes place in water, provides the desired products in 26–83% yield, forms the single addition product exclusively, and does not require slow addition of the diazo component

P450-catalyzed asymmetric cyclopropanation of electron-deficient olefins under aerobic conditions

A variant of P450 from Bacillus megaterium five mutations away from wild type is a highly active catalyst for cyclopropanation of a variety of acrylamide and acrylate olefins with ethyl diazoacetate (EDA). The very high rate of reaction enabled by histidine ligation allowed the reaction to be conducted under aerobic conditions. The promiscuity of this catalyst for a variety of substrates containing amides has enabled synthesis of a small library of precursors to levomilnacipran derivatives

Antibodies against prM protein distinguish between previous infection with dengue and Japanese encephalitis viruses.

BACKGROUND: In Southeast Asia, dengue viruses often co-circulate with other flaviviruses such as Japanese encephalitis virus, and due to the presence of shared antigenic epitopes it is often difficult to use serological methods to distinguish between previous infections by these flaviviruses. RESULTS: Convalescent sera from 69 individuals who were known to have had dengue or Japanese encephalitis virus infection were tested by western blotting against dengue, Japanese encephalitis and West Nile virus antigens. We determined that individuals who had been infected with dengue viruses had IgG responses against the premembrane protein of dengue viruses but not Japanese encephalitis, whereas individuals who had been infected with Japanese encephalitis had IgG specific for the premembrane protein of Japanese encephalitis virus but not the dengue viruses. None reacted with the premembrane protein of West Nile virus. Using the Pearson Chi Square test, it was determined that the difference between the two groups was highly significant with a p value of <0.001. CONCLUSION: The use of flavivirus premembrane protein in seroepidemiological studies will be useful in determining what flaviviruses have circulated in a community

Tackling unemployment in China: state capacity and governance issues

This paper considers China's state capacity and changing governance as revealed through its policies to tackle unemployment. Despite high levels of growth, economic restructuring has resulted in rising unemployment over the last decade. The Chinese state has been able to manage job losses from state enterprises, demonstrating some state capacity in relation to this sector and some persistent command economy governance mechanisms. However both design and implementation of policies to compensate and assist particular groups among the unemployed have been shaped by weak state capacity in several other areas. First, capacity to gather accurate employment data is limited, meaning local and central governments do not have a good understanding of the extent and nature of unemployment. Second, the sustainability of supposedly mandatory unemployment insurance schemes is threatened by poor capacity to enforce participation. Third, poor central state capacity to ensure local governments implement policies effectively leads to poor unemployment insurance fund capacity, resulting in provision for only a narrow segment of the unemployed and low quality employment services. Although the adoption of unemployment insurance (and its extension to employers and employees in the private sector), the introduction of a Labour Contract Law in 2007, and the delivery of employment services by private businesses indicate a shift towards the use of new governance mechanisms based on entitlement, contract and private sector delivery of public-sector goods, that shift is undermined by poor state capacity in relation to some of these new mechanisms

Deep sequencing of HPV E6/E7 genes reveals loss of genotypic diversity and gain of clonal dominance in high-grade intraepithelial lesions of the cervix

Table S2. HPV E6/E7 sequencing: dideoxy (Sanger) vs. deep (Illumina). (PDF 236 kb

Improved Cyclopropanation Activity of Histidine-Ligated Cytochrome P450 Enables the Enantioselective Formal Synthesis of Levomilnacipran

Engineering enzymes capable of modes of activation unprecedented in nature will increase the range of industrially important molecules that can be synthesized through biocatalysis. However, low activity for a new function is often a limitation in adopting enzymes for preparative-scale synthesis, reaction with demanding substrates, or when a natural substrate is also present. By mutating the proximal ligand and other key active-site residues of the cytochrome P450 enzyme from Bacillus megaterium (P450-BM3), a highly active His-ligated variant of P450-BM3 that can be employed for the enantioselective synthesis of the levomilnacipran core was engineered. This enzyme, BM3-Hstar, catalyzes the cyclopropanation of N,N-diethyl-2-phenylacrylamide with an estimated initial rate of over 1000 turnovers per minute and can be used under aerobic conditions. Cyclopropanation activity is highly dependent on the electronic properties of the P450 proximal ligand, which can be used to tune this non-natural enzyme activity