Everywhere surjections and related topics. Examples and counterexamples

This paper deals with everywhere surjections, i.e. functions defined on a topological space whose restrictions to any non-empty open subset are surjective. We introduce and discuss several constructions in different contexts; some constructions are easy, while others are more involved. Among other things, we prove that there is a vector space of uncountable dimension whose non-zero elements are everywhere surjections from Q to Q; we give an example of an everywhere surjection whose domain is the set of countably infinite real sequences; we construct an everywhere surjective linear map from the Cantor set into itself. Finally, we prove the existence of functions from R to R which are everywhere surjections in stronger senses

Asymmetric enone epoxidation by short solid-phase bound peptides: Further evidence for catalyst helicity and catalytic activity of individual peptide strands

In the presence of short solid-phase bound peptide catalysts, the Julia\u2013Colonna epoxidation of enones (such as chalcone) with hydrogen peroxide can be performed with high enantiomeric excess (>95% ee). It was proposed earlier (A. Berkessel, N. Gasch, K. Glaubitz, C. Koch, Organic Letters, 2001, Vol. 3, pp. 3839\u20133842) that this remarkable catalysis is governed by the N-terminus of individual and helical peptide strands. This mechanistic proposal was scrutinized further. (i) Nonaggregation of the peptide catalysts: five solid-phase bound statistic mixtures (0/100; 30/70; 50/50; 70/30; 100/0) of D-Leu and L-Leu heptamers were generated and assayed as catalysts. A linear dependence of the epoxide ee on the enantiomeric composition of the catalysts resulted. (ii) Catalyst helicity [introduction of the helix-stabilizing C-alpha\u2013methyl-L-leucine, L-(alpha-Me)Leu]: solid-phase bound Leu/(alpha-Me)Leu-pentamers of composition TentaGel\u2013NH\u2013[(alpha-Me)-L-Leu]n\u2013(L-Leu)m\u2013H (n = 0\u20134; m = 5\u2013n) were prepared and assayed as catalysts. The introduction of up to two (alpha-Me)-L-Leu residues (n = 1, 2) significantly enhanced the catalyst activity relative to the L-Leu homopentamer (n = 0). Higher (alpha-Me)-L-Leu contents (n = 3, 4) led to a decrease in both catalyst activity and enantiopurity of the product epoxide. In summary, both the individual catalytic action of the peptide strands and the helical conformation as the catalytically competent state of the peptide catalysts were further supported

Peptoid Residues and beta-Turn Formation

We synthesized and tested for intramolecularly H-bonded beta-turn formation a set of terminally protected tripeptoids containing in position i+1/i+2 either a residue of N-methylglycine or of N-isobutylglycine. By exploiting FT-IR absorption and 1H NMR techniques we compared their folding tendencies with those of a variety of reference peptides. The amount of beta-turn induction and the relative extent of the various types of intramolecularly H-bonded beta-turn conformers were determined in chloroform solution

Peptoid Residues and beta-Turn Formation

We synthesized and tested for intramolecularly H-bonded beta-turn formation a set of terminally protected tripeptoids containing in position i+1/i+2 either a residue of N-methylglycine or of N-isobutylglycine. By exploiting FT-IR absorption and 1H NMR techniques we compared their folding tendencies with those of a variety of reference peptides. The amount of beta-turn induction and the relative extent of the various types of intramolecularly H-bonded beta-turn conformers were determined in chloroform solution

Combining Radon Deficit, NAPL Concentration, and Groundwater Table Dynamics to Assess Soil and Groundwater Contamination by NAPLs and Related Attenuation Processes

Soil and groundwater contamination by NAPLs (Non-Aqueous Phase Liquids) is certainly a big issue for protecting the environment. In situ clean-up actions are routinely applied to mitigate the risk and are supplemented by monitoring surveys to assess the degree, extension, and evolution of the contamination. Radon gas is here used as a tracer of contamination because of its high solubility in non-polar solvents that produce a reduced concentration of the gas in polluted soil and groundwater with reference to radon levels in adjacent “clean” areas. This approach was employed in two sites where gasoline and diesel spillage occurred, causing soil and groundwater contamination. The two case studies were chosen because of their difference in terms of the hydrogeological features, age of the spillage, composition of residual NAPLs, and clean-up measures to test the advantages and limits of this approach in a variety of settings. Radon data, NAPL concentration in the groundwater (mainly total hydrocarbons, Methyl Tertiary-Butyl Ether and Ethyl Tertiary-Butyl Ether) and the depth of the groundwater table were periodically collected in surveys that spanned a period of two years. This dataset was statistically processed using principal component analysis to unravel which factors and attenuation processes are working in the sites and the response of the radon deficit approach to this complex series of phenomena concurrently occurring there

Adenosine-Induced Apoptosis of C2C12 Myoblastic Cells

To assess a possible role for adenosine in muscle cell apoptosis, we have studied the effects of its hydrolysis-resistant analogue 2-chloro adenosine on a myogenic cell line, C2C12, which can differentiate in vitro to giant multinucleated cells (myotubes). Exposure of cultures to the adenosine analogue resulted in time-dependent apoptotic cell death of both myoblasts and myotubes. Adenosine may therefore represent an endogenous regulator of pathophysiological apoptosis in muscle

Crystal-state 3D-structural characterization of novel 310-helical peptides

The crystal-state conformations of two octapeptides, pBrBz-(D-Iva)(8)-OtBu (SI) and Ac-[L-(alphaMe)Val](8)-OH (8II), the heptapeptide Z-[L-(alphaMe)Val](7)-OH (7), the hexapeptide Z-[L-(alphaMe)Leu](6)-OtBu (6) and the tetrapeptide alkylamide Z-(Aib)(2)-L-Glu(OMe)-L-Ala-L-Lol (5) were assessed by x-ray diffraction analyses. Two independent molecules are observed in the asymmetric unit of each L-(alphaMe)Val homo-peptide. All four homo-peptides are folded in a regular 3(10)-helical structure (only the C-terminal H-bonded conformation of the D-Iva octapeptide is distorted to a type-I beta-turn)

First Direct Observation of C=O\ub7\ub7\ub7H-N Intramolecular Hydrogen Bonds in 3-10-Helical Peptides.

Differentiating helices: The direct observation of hydrogen bonds by 3hJN,C\u2032 scalar couplings (see picture) is not only possible for alpha-helix and \u3b2-sheet peptides and proteins, but for 310-helical peptides as well. The method also provides information on terminal fraying of helices and allows the discrimination between alpha and 310 helices

Concomitant occurrence of peptide 3(10)- and alpha-helices probed by NMR

Oligopeptides based on protein (C\u3b1-trisubstituted) \u3b1-amino acids are known to undergo \u3b1-helix to unordered conformation transitions under appropriate experimental conditions. On the other hand, oligopeptides rich in C\u3b1-tetrasubstituted \u3b1-amino acids present a rather peculiar stereochemistry due to significant constraints imposed on their conformational freedom by these residues. Specifically, most of the C\u3b1-tetrasubstituted \u3b1-amino acids have been extensively documented to possess a very high intrinsic helix-forming capacity. The narrow conformational space accessible includes both the classical \u3b1-helix and the 310-helix. It was shown that among the C\u3b1-tetrasubstituted chiral \u3b1-amino acids the \u3b2-branched C\u3b1-methyl-L-valine [L-(\u3b1Me)Val] is the residue with the most pronounced bias toward the right-handed 310-helix. Strong initial experimental evidence has indicated that the terminally blocked 12[L-(\u3b1Me)Val]8 12 sequence adopts a fully developed, right-handed 310-helical conformation both in the crystal state and in structure-supporting solvents. More recently, the interesting property of this peptide to fold in solution both in the 310- and in the \u3b1-helix has emerged. The type of helical conformation adopted was found to depend on experimental conditions, as clearly shown by vibrational and electronic CD techniques. Under appropriate conditions, the conformational transition from 310- to \u3b1-helix is very slow (the time scale is on the order of several days)

A Combined Spectroscopic and Theoretical Study of a Series of Conformationally Restricted Hexapeptides Carrying a Rigid Binaphthyl-Nitroxide Donor-Acceptor Pair

The structural features of a series of linear hexapeptides of general formula Boc-B-Ac-r-A(m)-OtBu, where A is L-Ala or Aib (alpha-aminoisobutyric acid), B is (R)-Bin, a binaphthyl-based C-alpha,C-alpha-disubstituted Gly residue, T is Toac, a nitroxide spin-labeled C-alpha,C-alpha-disubstituted Gly, and r+m = 4, were investigated in methanol solution by fluorescence, transient absorption, IR and CD spectroscopic studies, and by molecular mechanics calculations. These peptides are denoted as B-T/r-m, to emphasize the different position of Toac with respect to that of the Bin fluorophore in the amino acid sequence. The rigidity of the B-T donor - acceptor pair and of the Aib-rich backbone allowed us to investigate the influence of the interchromophoric distance and orientation on the photophysics of the peptides examined. The excited state relaxation processes of binaphthyl were investigated by time-resolved fluorescence and transient absorption experiments. Dynamic quenching of the excited singlet state of binaphthyl by Toac was successfully interpreted by the Forster energy transfer model, provided that the mutual orientation of the chromophores is taken into account. This implies that interconversion among conformational substates, which involves puckering of the Toac piperidine ring, is slow on the time scale of the transfer process, that is slower than 5 ns. By comparison of the experimental and theoretical data, the type of secondary structure (right-handed 3(10) helix) from the B-T/r-m peptides in solution was determined; this would not have been achievable by using the CD and NMR data only, as the data are not diagnostic in this case. Static quenching was observed in all peptides examined but B-T/1-3, where the effect can be ascribed to a non-fluorescent complex. Among the computed low-energy conformers of these peptides, there is one structure exhibiting a NO.-naphthalene center-to-center distance <6 Angstrom, which might be assigned to this complex. The overall results emphasize the versatility of fluorescence experiments in 3D-structural studies in solution