Summations and transformations for multiple basic and elliptic hypergeometric series by determinant evaluations

Using multiple q-integrals and a determinant evaluation, we establish a multivariable extension of Bailey's nonterminating 1009 transformation. From this result, we deduce new multivariable terminating ₁₀φ₉ transformations, ₈φ₇ summations and other identities. We also use similar methods to derive new multivariable l ₁ψ₁ summations. Some of our results are extended to the case of elliptic hypergeometric series.     

Magnetization and compensation temperature of transition-metal–rare-earth multilayers in a model with long-range interactions

A model is proposed to describe the behavior of magnetization and compensation temperature in transition-metal–rare-earth multilayers. Long-range exponentially decreasing ferromagnetic (antiferromagnetic) interactions are considered between the same (different) kind of atoms. The magnetization and compensation temperature are shown to decrease with increasing single layer thickness. Good agreement is obtained with experimental data on Tb/Co system.     

Electrochemical oxidation and cleavage of peptides analyzed with on-line mass spectrometric detection

An on-line electrochemistry/electrospray mass spectrometry system (EC/MS) is described that allows fast analysis of the oxidation products of peptides. A range of peptides was oxidized in an electrochemical cell by application of a potential ramp from 0 to 1.5 V during passage of the sample. Electrochemical oxidation of peptides was found to occur readily when tyrosine was present. Tyrosine was found to be oxidized between 0.5 and 1.0 V to various oxidation products, including peptide fragments formed by hydrolysis at the C-terminal side of tyrosine. The results confirm earlier knowledge on the mechanisms and reaction products of chemical and electrochemical peptide oxidation. Methionine residues are also readily oxidized, but do not induce peptide cleavage. At potentials higher than about 1.1 V, additional oxidation products were observed in some peptides, including loss of 28 Da from the C-terminus and dimerization. The tyrosine-specific cleavage reaction suggests a possible use of the EC/MS system as an on-line protein digestion and peptide mapping system. In addition, the system can be used to distinguish phosphorylated from unphosphorylated tyrosine residues. Four forms of the ZAP-70 peptide ALGADDSYYTAR with both, either or neither tyrosine phosphorylated were subjected to a 0-1.5 V potential ramp. Oxidation of, and cleavage adjacent to, tyrosine was observed exclusively at unphosphorylated tyrosine residues.     

A concept for miniaturized 3-D cell culture using an extracellular matrix gel

This paper presents a novel method to embed, anchor, and cultivate cells in a controlled 3-D flow-through microenvironment. This is realized using an etched silicon pillar flow chamber filled with extracellular matrix (ECM) gel mixed with cells. At 4 degrees C, while in liquid form, ECM gel is mixed with cells and injected into the chamber. Raising the temperature to 37 degrees C results in a gel, with cells embedded. The silicon pillars both stabilize and increase the surface to volume ratio of the gel. During polymerization the gel shrinks, thus creating channels, which enables perfusion through the chip. The pillars increase the mechanical stability of the gel permitting high surface flow rates without surface modifications. Within the structure cells were still viable and proliferating after 6 days of cultivation. Our method thus makes it possible to perform medium- to long-term cultivation of cells in a controlled 3-D environment. This concept opens possibilities to perform studies of cells in a more physiological environment compared to traditional 2-D cultures on flat substrates.     

Microcin J25 has a threaded sidechain-to-backbone ring structure and not a head-to-tail cyclized backbone

Microcin J25 is a 21 amino acid bacterial peptide that has potent antibacterial activity against Gram-negative bacteria, resulting from its interaction with RNA polymerase. The peptide was previously proposed to have a head-to-tail cyclized peptide backbone and a tight globular structure (Blond, A., Péduzzi, J., Goulard, C., Chiuchiolo, M. J., Barthélémy, M., Prigent, Y., Salomón, R. A., Farías, R. N., Moreno, F. & Rebuffat, S. Eur. J. Biochem. 1999, 259, 747-755). It exhibits remarkable thermal stability for a peptide of its size lacking disulfide bonds and in part this was previously proposed to derive from its macrocyclic structure. We show here that in fact the peptide does not have a head-to-tail cyclic structure but rather a side chain to backbone cyclization between Glu8 and the N-terminus. This creates an embedded ring that is threaded by the C-terminal tail of the molecule, forming a noose-like feature. The three-dimensional structure deduced from NMR data suggests that slippage of the noose is prevented by two aromatic residues flanking the embedded ring. Unthreading does not occur even when the molecule is enzymatically digested with thermolysin. The new structural interpretation fully accounts for previously reported NMR and biophysical data and is consistent with the remarkable stability of this potent antimicrobial peptide.     

Harmonic Analysis on the SU(2) Dynamical Quantum Group

Dynamical quantum groups were recently introduced by Etingof and Varchenko as an algebraic framework for studying the dynamical Yang–Baxter equation, which is precisely the Yang–Baxter equation satisfied by 6j-symbols. We investigate one of the simplest examples, generalizing the standard SU(2) quantum group. The matrix elements for its corepresentations are identified with Askey–Wilson polynomials, and the Haar measure with the Askey–Wilson measure. The discrete orthogonality of the matrix elements yield the orthogonality of q-Racah polynomials (or quantum 6j-symbols). The Clebsch–Gordan coefficients for representations and corepresentations are also identified with q-Racah polynomials. This results in new algebraic proofs of the Biedenharn–Elliott identity satisfied by quantum 6j-symbols.     

Inclusions of Waterman–Shiba spaces into generalized Wiener classes

The characterization of the inclusion of Waterman–Shiba spaces ΛBV^(p)$\Lambda {\mathit{BV}}^{(p)}$ into generalized Wiener classes of functions BV(q;δ)$\mathit{BV}(q;\delta )$ is given. It uses a new and shorter proof and extends an earlier result of U. Goginava.