Convergence of bounded solutions of nonlinear parabolic problems on a bounded interval: the singular case

In this article we prove that for every ${1 < p \le 2}$ and for every continuous function ${f: [0,1]\times\mathbb{R}\to\mathbb{R}}$ , which is Lipschitz continuous in the second variable, uniformly with respect to the first one, each bounded solution of the one-dimensional heat equation $$\begin{array}{ll}u_{t}-\{|u_{x}|^{p-2}u_{x} \}_{x}+f(x,u)=0\qquad{\rm in} \quad (0,1)\times (0,+\infty) \end{array}$$ with homogeneous Dirichlet boundary conditions converges as ${t\to+\infty}$ to a stationary solution. The proof follows an idea of Matano which is based on a comparison principle. Thus, a key step is to prove a comparison principle on non-cylindrical open sets.     

A filter paper-based assay for laboratory evolution of hydrolases and dehydrogenases

Industrially important enzyme classes such as hydrolases and dehydrogenases are often not amenable to laboratory evolution methods due to a lack of sensitive and reliable high-throughput screening (HTS) systems. We developed a conceptually novel and technically simple high-throughput screening system based on detection of volatile aldehydes with the sensitive reagent Purpald (4-amino-3-hydrazino-5-mercapto-1,2,4-triazole). The aldehyde detection takes place on a filter-paper that is pre-soaked with Purpald and covers the microtiter plate. The filter paper-based Purpald assay separates aldehyde detection from biocatalytical conversion and thereby avoids interferences from biological materials with assay components. This screening principle allows, to our knowledge, for the first time to determine the synthetic activity of hydrolases such as lipases and esterases in organic solvents in a 96-well whole-cell format. Its simplicity and cost-effectiveness make the reported HTS system suitable as fast pre-screen in laboratory evolution experiments and for semi-quantitative assays of improved mutants.     

Ueber Quellung und Elastizität des normalen und gequollenen Hornes

Ohne Zusammenfassung     

Non-local symmetries of first-order equations

It is shown how one can transform scalar first-order ordinarydifferential equations which admit non-local symmetries of theexponential type to integrable equations admitting canonicalexponential non-local symmetries. As examples we invoke theAbel equation of the second kind, the Riccati equation and naturalgeneralizations of these. Moreover, our method describes howa double reduction of order for a second-order ordinary differentialequation which admits a two-dimensional Lie algebra of generatorsof point symmetries can be affected if the second-order equationis first reduced in order once by a symmetry which does notspan an ideal of the two-dimensional Lie algebra.     

New Generation of Biocatalysts for Organic Synthesis

The use of enzymes as catalysts for the preparation of novel compounds has received steadily increasing attention over the past few years. High demands are placed on the identification of new biocatalysts for organic synthesis. The catalysis of more ambitious reactions reflects the high expectations of this field of research. Enzymes play an increasingly important role as biocatalysts in the synthesis of key intermediates for the pharmaceutical and chemical industry, and new enzymatic technologies and processes have been established. Enzymes are an important part of the spectrum of catalysts available for synthetic chemistry. The advantages and applications of the most recent and attractive biocatalysts—reductases, transaminases, ammonia lyases, epoxide hydrolases, and dehalogenases—will be discussed herein and exemplified by the syntheses of interesting compounds.     

Entropy is Key to the Formation of Pentacyclic Terpenoids by Enzyme‐Catalyzed Polycyclization

Polycyclizations constitute a cornerstone of chemistry and biology. Multicyclic scaffolds are generated by terpene cyclase enzymes in nature through a carbocationic polycyclization cascade of a prefolded polyisoprene backbone, for which electrostatic stabilization of transient carbocationic species is believed to drive catalysis. Computational studies and site‐directed mutagenesis were used to assess the contribution of entropy to the polycyclization cascade catalyzed by the triterpene cyclase from A. acidocaldarius. Our results show that entropy contributes significantly to the rate enhancement through the release of water molecules through specific channels. A single rational point mutation that results in the disruption of one of these water channels decreased the entropic contribution to catalysis by 60 kcal mol^?1. This work demonstrates that entropy is the key to enzyme‐catalyzed polycyclizations, which are highly relevant in biology since 90 % of all natural products contain a cyclic subunit.     

Biocompatible functionalisation of starch

The enzyme catalysed esterification of starch and fatty acids with terminal triple bonds is described. This material can be used as an acceptor for azide containing molecules, through azide/alkyne cycloaddition. The potential is illustrated by the production of fluorescently-labelled starch, and a biotinylated derivative which can bind streptavidin.     

Recent applications of THERMUS

Some of the most recent applications of the statistical-thermal model package, THERMUS, are reviewed. These applications focus on fluctuation and correlation observables in an ideal particle and anti-particle gas in limited momentum space segments, as well as in a hadron resonance gas. In the case of the latter, a Monte Carlo event generator, utilising THERMUS functionality and assuming thermal production of hadrons, is discussed. The system under consideration is sampled grand canonically in the Boltzmann approximation. A re-weighting scheme is then introduced to account for conservation of charges (baryon number, strangeness, electric charge) and energy and momentum, effectively allowing for extrapolation of grand canonical results to the micro canonical limit. The approach utilised in this and other applications suggests improvements to existing THERMUS calculations.