Period-doubling cascades for large perturbations of Hénon families

The Hénon family has been shown to have period-doubling cascades. We show here that the same occurs for a much larger class: Large perturbations do not destroy cascades. Furthermore, we can classify the period of a cascade in terms of the set of orbits it contains, and count the number of cascades of each period. This class of families extends a general theory explaining why cascades occur [5].     

Bioavailability and biotransformation of sulforaphane and erucin metabolites in different biological matrices determined by LC–MS–MS

The food-related isothiocyanate sulforaphane (SFN), a hydrolysis product of the secondary plant metabolite glucoraphanin, has been revealed to have cancer-preventive activity in experimental animals. However, these studies have often provided inconsistent results with regard to bioavailability, bioaccessibility, and outcome. This might be because the endogenous biotransformation of SFN metabolites to the structurally related erucin (ERN) metabolites has often not been taken into account. In this work, a fully validated liquid chromatography tandem mass spectrometry (LC–MS–MS) method was developed for the simultaneous determination of SFN and ERN metabolites in a variety of biological matrices. To reveal the importance of the biotransformation pathway, matrices including plasma, urine, liver, and kidney samples from mice and cell lysates derived from colon-cancer cell lines were included in this study. The LC–MS–MS method provides limits of detection from 1 nmol L^?1 to 25 nmol L^?1 and a mean recovery of 99 %. The intra and interday imprecision values are in the range 1–10 % and 2–13 %, respectively. Using LC–MS–MS, SFN and ERN metabolites were quantified in different matrices. The assay was successfully used to determine the biotransformation in all biological samples mentioned above. For a comprehensive analysis and evaluation of the potential health effects of SFN, it is necessary to consider all metabolites, including those formed by biotransformation of SFN to ERN and vice versa. Therefore, a sensitive and robust LC–MS–MS method was validated for the simultaneous quantification of mercapturic-acid-pathway metabolites of SFN and ERN.

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Graphical Abstract Biotransformation of sulforaphane and erucin metabolites in mice and cell culture

     

Growth-induced changes in the proteome of Helicobacter pylori

Helicobacter pylori is a major human pathogen that is responsible for a number of gastrointestinal infections. We have used 2-DE to characterise protein synthesis in bacteria grown either on solid agar-based media or in each of two broth culture media (Brucella and brain heart infusion (BHI) broth). Significant differences were observed in the proteomes of bacteria grown either on agar-based or in broth media. Major changes in protein abundance were identified using principal component analysis (PCA), which delineated the profiles derived for the three key growth conditions (i.e. agar plates, Brucella and BHI broth). Proteins detected across the gel series were identified by peptide mass mapping and Edman sequencing. A number of proteins associated with protein synthesis in general as well as specific amino acid synthesis were depressed in broth-grown bacteria compared to plate-grown bacteria. A similar reduction was also observed in the abundance of proteins involved in detoxification. Two of the most abundant spots, identified as UreB and GroEL, in plate-grown bacteria showed a >140-fold drop in abundance in bacteria grown in Brucella broth compared to bacteria grown on agar plates. Two protein spots induced in bacteria grown in broth culture were both identified as glyceraldehyde 3-phosphate dehydrogenase based on their N-terminal amino acid sequences derived by Edman degradation. The underlying causes of the changes in the proteins abundance were not clear, but it was likely that a significant proportion of the changes were due to the alkaline pH of the broth culture media.     

Thermal decomposition reactions of n‐alkylated 2‐aminobiphenyls to carbazole and phenanthridine

Thermal cyclization reactions were examined by passing vapors of N‐alkylated 2‐aminobiphenyls 1a‐c and 2 over calcium oxide at 450‐600°C under nitrogen carrier gas. The reactions yielded 9‐methylcarbazole 3 , carbazole 4 , phenanthridine 5 and phenanthrene 6. The major product for the reactions of 1a, 1b and 2 was phenanthridine 5 while that of 1c was carbazole 4.     

Quantum dynamics study of the dissociative photodetachment of HOCO-

Six-dimensional wave packet calculations are carried out to study the behavior of HOCO subsequent to the photodetachment of an electron from the negative anion, HOCO-. It is possible to form stable and/or long-lived HOCO complexes, as well as the dissociative products OH+CO and H+CO2. A variety of observables are determined: the electron kinetic energy (eKE) distributions associated with the OH+CO and H+CO2 channels, the correlated eKE and product translational energy distribution for the OH+CO channel, and product branching ratios. Most of our results are in good accord with the experimental results of Clements, Continetti, and Francisco [J. Chem. Phys. 117, 6478 (2002)], except that the calculated eKE distribution for the H+CO2 channel is noticeably colder than experiment. Reasons for this discrepancy are suggested.     

Fixed points indices and period-doubling cascades

Period-doubling cascades are among the most prominent features of many smooth one-parameter families of maps, \({F : \mathbb{R}\times\mathfrak{M} \rightarrow \mathfrak{M},}\) where \({\mathfrak{M}}\) is a locally compact manifold without boundary, typically \({\mathbb{R}^N}\). In particular, we investigate F(μ, ·) for \({\mu \in J = [\mu_{1}, \mu_{2}]}\), when F(μ ₁, ·) has only finitely many periodic orbits while F(μ ₂, ·) has exponential growth of the number of periodic orbits as a function of the period. For generic F, under additional hypotheses, we use a fixed point index argument to show that there are infinitely many “regular” periodic orbits at μ ₂. Furthermore, all but finitely many of these regular orbits at μ ₂ are tethered to their own period-doubling cascade. Specifically, each orbit ρ at μ ₂ lies in a connected component C(ρ) of regular orbits in \({J \times \mathfrak{M}}\); different regular orbits typically are contained in different components, and each component contains a period-doubling cascade. These components are one-manifolds of orbits, meaning that we can reasonably say that an orbit ρ is “tethered” or “tied” to a unique cascade. When F(μ ₂) has horseshoe dynamics, we show how to count the number of regular orbits of each period, and hence the number of cascades in \({J \times \mathfrak{M}}\).As corollaries of our main results, we give several examples, we prove that the map in each example has infinitely many cascades, and we count the cascades.     

Synthesis and characterization of photolabile o-nitrobenzyl derivatives of urea

We present here the synthesis and characterization of four photolabile derivatives of urea in which alpha-substituted 2-nitrobenzyl groups are covalently attached to the urea nitrogen. These derivatives photolyze readily in aqueous solution to release free urea. The alpha-substituents of the 2-nitrobenzyl group strongly influence the rate of the photolysis reaction measured with transient absorption spectroscopy. Rates of photolysis at pH 7.5 and room temperature (approximately 22 degrees C) for N-(2-nitrobenzyl)urea, N-(alpha-methyl-2-nitrobenzyl)urea, N-(alpha-carboxymethyl-2-nitrobenzyl)urea, and N-(alpha-carboxy-2-nitrobenzyl)urea are, respectively, 1.7 x 10(4), 8.5 x 10(4), 4.0 x 10(4), and 1.1 x 10(5) s(-)(1). The quantum yields determined by measurement of free urea following irradiation by a single laser pulse at 308 nm were 0.81 for N-(2-nitrobenzyl)urea, 0.64 for N-(alpha-methyl-2-nitrobenzyl)urea, and 0.56 for N-(alpha-carboxy-2-nitrobenzyl)urea. The caged N-(alpha-carboxy-2-nitrobenzyl)urea is not a substrate of the enzyme urease, while the photolytically released urea is. Also, neither this caged urea nor its photolytic side products inhibit hydrolysis of free urea by urease. Thus, the alpha-carboxy-2-nitrobenzyl derivative of urea is suitable for mechanistic investigations of the enzyme urease.