Deamidation as a widespread phenomenon in two-dimensional polyacrylamide gel electrophoresis of human blood plasma proteins

The human plasma protein patterns obtained by two-dimensional polyacrylamide gel electrophoresis (2-D PAGE) is a good model system for post-translational modifications because of the existence of several "ladders" of protein spots [Anderson, N. L., Anderson, N. G., Electrophoresis 1991, 12, 883-906], so-called "trains" of spots. Our investigation of several proteins, amongst others beta2-microglobulin and the haptoglobin chains, found the differences in isoelectric points (p/) to be due to deamidation of asparagines. After enzymatic cleavage with endopeptidases in the 2-D polyacrylamide gel, the asparagine and deamidated asparagine containing peptides were separated and quantified by reversed-phase HPLC. In order to separate these peptides, a neutral pH system was established and, as a result, the differences in hydrophobicity of asparagine-containing and deamidated asparagine-containing peptides increased. But how do deamidated asparagines contribute to the observed spot pattern? One spot in the 2-D gel consists of a mixture of protein species with the same number of deamidated asparagines but on different sequence position sites. The difference between the spots in the "ladder" is a growing number of negative charges introduced in the protein by an increasing number of deamidated asparagines. As a consequence, the mass difference between two spots is exactly 1 Da, which is shown in this paper for intact protein masses and the corresponding deamidated peptides.     

Almost sure Cesàro and Euler summability of sequences of dependent random variables

For a sequence of real random variables C _α-summability is shown under conditions on the variances of weighted sums, comprehending and sharpening strong laws of large numbers (SLLN) of Rademacher-Menchoff and Cramér-Leadbetter, respectively. Further an analogue of Kolmogorov’s criterion for the SLNN is established for E _α-summability under moment and multiplicativity conditions of 4th order, which allows one to weaken Chow’s independence assumption for identically distributed square integrable random variables. The simple tool is a composition of Cesàro-type and of Euler summability methods, respectively. Received: 12 June 2006, Revised: 14 May 2007     

Symmetrisierte und zentrierte Folgen von Zufallsvariablen

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Sugar silanes: versatile reagents for stereocontrolled glycosylation via intramolecular aglycone delivery

A new method for the intramolecular glycosylation of alcohols is described. Utilizing carbohydrate-derived silanes, the catalytic dehydrogenative silylation of alcohols is followed by intramolecular glycosylation. Appropriate combinations of silane position and protecting groups allow highly selective access to β-manno, α-gluco, or β-gluco stereochemical relationships as well as 2-azido-2-deoxy-β-gluco- and 2-deoxy-β-glucosides. Intramolecular aglycone delivery from the C-2 or C-6 position provides 1,2-cis or 1,2-trans glycosides, respectively. Multifunctional acceptor substrates such as hydroxyketones and diols are tolerated and are glycosylated in a site-selective manner.     

Wachstumsverhalten zufÄlliger Potenzreihen

Summary Using the theorems collected in Chapter 2 the paper discusses growth and divergence properties of random power series (rps's) with — generally — independent coefficients a _n. In Chapter 3 assertions about rps's with a _n symmetric relative to 0 are transferred to rps's for which the medians a _n of a _n are 0. Chapter 4 treats analogies between rps's with symmetrized coefficients a _s ⁿ and rps's with centered coefficients a _n -a _n ; they concern growth of random entire functions defined by rps's with arbitrarily dependent coefficients, and local behaviour near the circle of convergence. For some kinds of singular behaviour, e.g. unboundedness of characteristic in every sector of the circle of convergence, Chapter 5 gives necessary and sufficient conditions in connection with the notion of essential divergence. The theorems hold also for -quantiles a _n ( fixed, 0<<1) instead of medians a _n .Herrn Professor Dr. F. Lösch zum 65. Geburtstag gewidmet.     

Eine Bemerkung zur Integrierbarkeit eines Produktes von zwei Funktionen in Sobolewschen Räumen

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Konvergenz und Summierbarkeit von Reihen zufälliger Variablen

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Strong universal consistency of smooth kernel regression estimates

The paper deals with kernel estimates of Nadaraya-Watson type for a regression function with square integrable response variable. For usual bandwidth sequences and smooth nonnegative kernels, e.g., Gaussian and quartic kernels, strongL ₂-consistency is shown without any further condition on the underlying distribution. The proof uses a Tauberian theorem for Cesàro summability.     

Strong Laws of Large Numbers by Elementary Tauberian Arguments

For Kolmogorovs strong law of large numbers an alternative short proof is given which weakens Etemadis condition of pairwise independence. The argument uses the known – and elementary – equivalence of (Cesàro) C₁- and C₂-summability for one-sided bounded sequences. Also other strong laws of large numbers are established, in part via Borel summability.