2,3-Dihydro-7-benzofurancarbonsäuren

Summary The syntheses of a series of title compounds1 a–f bearing methyl groups in the heterocyclic part were described. Depending on the substitution pattern the Claisen rearrangement (path A) or the methodology of directed lithiations (path B) were used as the key steps.

Herrn o. Prof. Dr. Fritz Sauter mit den besten Wünschen zum 60. Geburtstag gewidmet     

Effects of a directed co-flow on a non-reactive turbulent jet with variable density

In the present study, the effects of a directed co-flow on the process of mixture jet with variable density have been investigated numerically. Three density ratios were considered namely R=0.55, 1.5 and 1.52, respectively, for binary mixtures methane-air, carbon dioxide-air and propane-air. The directed co-flow preserves its axial symmetry at the inlet and its direction varies between +20° and –20°. In addition, the k – model and model equation of the algebraic non-equal scales are used to investigate effects of the variable density in axisymmetric turbulent jet. Comparative studies are presented in the case of the calculations of the average variables such as the longitudinal velocity, species concentration and the turbulent kinetic energy. The results obtained indicate that the directed co-flow with positive angles enhances considerably the mixing.     

Tree,web and average web values for cycle-free directed graph games

On the class of cycle-free directed graph games with transferable utility solution concepts, called web values, are introduced axiomatically, each one with respect to a chosen coalition of players that is assumed to be an anti-chain in the directed graph and is considered as a management team. We provide their explicit formula representation and simple recursive algorithms to calculate them. Additionally the efficiency and stability of web values are studied. Web values may be considered as natural extensions of the tree and sink values as has been defined correspondingly for rooted and sink forest graph games. In case the management team consists of all sources (sinks) in the graph a kind of tree (sink) value is obtained. In general, at a web value each player receives the worth of this player together with his subordinates minus the total worths of these subordinates. It implies that every coalition of players consisting of a player with all his subordinates receives precisely its worth. We also define the average web value as the average of web values over all management teams in the graph. As application the water distribution problem of a river with multiple sources, a delta and possibly islands is considered.     

A logical approach to context-specific independence

Directed acyclic graphs (DAGs) constitute a qualitative representation for conditional independence (CI) properties of a probability distribution. It is known that every CI statement implied by the topology of a DAG is witnessed over it under a graph-theoretic criterion of d-separation. Alternatively, all such implied CI statements are derivable from the local independencies encoded by a DAG using the so-called semi-graphoid axioms. We consider Labeled Directed Acyclic Graphs (LDAGs) modeling graphically scenarios exhibiting context-specific independence (CSI). Such CSI statements are modeled by labeled edges, where labels encode contexts in which the edge vanishes. We study the problem of identifying all independence statements implied by the structure and the labels of an LDAG. We show that this problem is coNP-hard for LDAGs and formulate a sound extension of the semi-graphoid axioms for the derivation of such implied independencies. Finally we connect our study to certain qualitative versions of independence ubiquitous in database theory and teams semantics.     

Directed Evolution of Piperazic Acid Incorporation by a Nonribosomal Peptide Synthetase**

Engineering of biosynthetic enzymes is increasingly employed to synthesize structural analogues of antibiotics. Of special interest are nonribosomal peptide synthetases (NRPSs) responsible for the production of important antimicrobial peptides. Here, directed evolution of an adenylation domain of a Pro-specific NRPS module completely switched substrate specificity to the non-standard amino acid piperazic acid (Piz) bearing a labile N−N bond. This success was achieved by UPLC-MS/MS-based screening of small, rationally designed mutant libraries and can presumably be replicated with a larger number of substrates and NRPS modules. The evolved NRPS produces a Piz-derived gramicidin S analogue. Thus, we give new impetus to the too-early dismissed idea that widely accessible low-throughput methods can switch the specificity of NRPSs in a biosynthetically useful fashion.     

Alkene epoxidation catalyzed by cytochrome P450 BM-3 139-3

We recently reported conversion of cytochrome P450 BM-3, a medium-chain (C₁₂-C₁₈) fatty acid monooxygenase, into a highly efficient alkane hydroxylase by directed evolution [Nat. Biotechnol. 2002, 20, 1135]. P450 BM-3 mutant 139-3 exhibited high activity towards a variety of fatty acid and alkane substrates, including C₃-C₈ alkanes. We report here that mutant 139-3 is also active on benzene, styrene, cyclohexene, 1-hexene, and propylene. Benzene is converted to phenol, while styrene is converted to styrene oxide. Propylene oxidation generates only propylene oxide, but cyclohexene oxidation produces a mixture of cyclohexene oxide (85%) and 2-cyclohexene-1-ol (15%), and 1-hexene is converted to the allylic hydroxylation product, 1-hexene-3-ol. Initial rates of NADPH oxidation for 139-3 in the presence of the substrates greatly (17- to >100-fold) surpass the wild-type in all cases. However, NADPH consumption is only partially coupled to product formation (14-79%). This cytochrome P450 epoxidation catalyst is a suitable starting point for further evolution to improve coupling and activity.     

2p-cycle decompositions of some regular graphs and digraphs

In this paper, we consider $2k$-cycle decomposition of $K_m\times K_n$ and directed $2k$-cycle decompositions of ${(K_m°{\overline{K}}_n)}^1$ and ${(K_m\times K_n)}^1$, where $°$ and $\times$ denote the wreath product and tensor product of graphs, respectively. Using the results obtained here, we prove that for $m,n\ge 3$, the obvious necessary conditions for the existence of a $C_{2k}$-decomposition of $K_m\times K_n$ are sufficient whenever $k\in \{p,2^{?}\},$ where $p$ is a prime and $?\ge 2$. Also, we show that the necessary conditions for the existence of ${\overrightarrow{C}}_{2p}$-decompositions of ${(K_m°{\overline{K}}_n)}^1$ and ${(K_m\times K_n)}^1$ are sufficient whenever $p$ is a prime, where ${\overrightarrow{C}}_{2p}$ denotes the directed cycle of length $2p$.     

浅谈2018年诺贝尔化学奖:驾驭进化的力量

In living organisms, protein functions are constantly evolving over generations throughout the history. Through iterative rounds of genetic mutations and natural selection of fit phenotypes, protein functions have been gradually optimized. This process could be mimicked and even greatly accelerated in the laboratory, when the selection pressure is directly applied to biomolecules of interest, which forms the basis of a technique called directed evolution. The Nobel Prize in chemistry 2018 was awarded jointly to Frances Arnold, George Smith and Gregory P. Winter for their pioneering contributions to the development and applications of directed evolution. Here we briefly review the history of this technique and its impact on renewable energy and pharmaceutical industry.     

Quasi profile and directed likelihoods from estimating functions

Frequently, corresponding to a given estimating equation it would be desirable to have a scalar combinant having parametric derivative equal to the estimating function since such a combinant may serve as a quasi log likelihood. In general this cannot be achieved but it is nevertheless possible to define a quasi profile log likelihood and also a quasi directed likelihood, for an arbitrary one-dimensional parameter of interest and with the standard kind of distributional limit behaviour.     

Normative selection of Bayesian networks

This paper presents a Bayesian decision theoretic foundation to the selection of a Bayesian network from data. We introduce the class of disintegrable loss functions to diversify the loss incurred in choosing different models. Disintegrable loss functions can iteratively be built from simple 0-L loss functions over pair-wise model comparisons and decompose the search for the model with minimum risk into a sequence of local searches, thus retaining the modularity of the model selection procedures for Bayesian networks.