M-matrix asymptotics for Sturm–Liouville problems on graphs

We consider a system formulation for Sturm–Liouville operators with formally self-adjoint boundary conditions on a graph. An M-matrix associated with the boundary value problem is defined and related to the matrix Prüfer angle associated with the system boundary value problem, and consequently with the boundary value problem on the graph. Asymptotics for the M-matrix are obtained as the eigenparameter tends to negative infinity. We show that the boundary conditions may be recovered, up to a unitary equivalence, from the M-matrix and that the M-matrix is a Herglotz function. This is the first in a series of papers devoted to the reconstruction of the Sturm–Liouville problem on a graph from its M-matrix.     

Can density functional theory (DFT) be used as an aid to a deeper understanding of tandem mass spectrometric fragmentation pathways?

Prediction of tandem mass spectrometric (MS/MS) fragmentation for non‐peptidic molecules based on structure is of immense interest to the mass spectrometrist. If a reliable approach to MS/MS prediction could be achieved its impact within the pharmaceutical industry could be immense. Many publications have stressed that the fragmentation of a molecular ion or protonated molecule is a complex process that depends on many parameters, making prediction difficult. Commercial prediction software relies on a collection of general heuristic rules of fragmentation, which involve cleaving every bond in the structure to produce a list of ‘expected’ masses which can be compared with the experimental data. These approaches do not take into account the thermodynamic or molecular orbital effects that impact on the molecule at the point of protonation which could influence the potential sites of bond cleavage based on the structural motif. A series of compounds have been studied by examining the experimentally derived high‐resolution MS/MS data and comparing it with the in silico modelling of the neutral and protonated structures. The effect that protonation at specific sites can have on the bond lengths has also been determined. We have calculated the thermodynamically most stable protonated species and have observed how that information can help predict the cleavage site for that ion. The data have shown that this use of in silico techniques could be a possible way to predict MS/MS spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

Phosphorylated serine and threonine residues promote site‐specific fragmentation of singly charged,arginine‐containing peptide ions

In order to investigate gas‐phase fragmentation reactions of phosphorylated peptide ions, matrix‐assisted laser desorption/ionization (MALDI) and electrospray ionization (ESI) tandem mass (MS/MS) spectra were recorded from synthetic phosphopeptides and from phosphopeptides isolated from natural sources. MALDI‐TOF/TOF (TOF: time‐of‐flight) spectra of synthetic arginine‐containing phosphopeptides revealed a significant increase of y ions resulting from bond cleavages on the C‐terminal side of phosphothreonine or phosphoserine. The same effect was found in ESI‐MS/MS spectra recorded from the singly charged but not from the doubly charged ions of these phosphopeptides. ESI‐MS/MS spectra of doubly charged phosphopeptides containing two arginine residues support the following general fragmentation rule: Increased amide bond cleavage on the C‐terminal side of phosphorylated serines or threonines mainly occurs in peptide ions which do not contain mobile protons. In MALDI‐TOF/TOF spectra of phosphopeptides displaying N‐terminal fragment ions, abundant b–H₃PO₄ ions resulting from the enhanced dissociation of the pSer/pThr–X bond were detected (X denotes amino acids). Cleavages at phosphoamino acids were found to be particularly predominant in spectra of phosphopeptides containing pSer/pThr–Pro bonds. A quantitative evaluation of a larger set of MALDI‐TOF/TOF spectra recorded from phosphopeptides indicated that phosphoserine residues in arginine‐containing peptides increase the signal intensities of the respective y ions by almost a factor of 3. A less pronounced cleavage‐enhancing effect was observed in some lysine‐containing phosphopeptides without arginine. The proposed peptide fragmentation pathways involve a nucleophilic attack by phosphate oxygen on the carbon center of the peptide backbone amide, which eventually leads to cleavage of the amide bond. Copyright © 2009 John Wiley & Sons, Ltd.     

2-Aminobenzimidazoles as potent ITK antagonists: de novo design of a pyrrole system targeting additional hydrogen bonding interaction

Based on information from molecular modeling, a series of 2-aminobenzimidazoles with pyrrole moieties were designed and synthesized as ITK antagonists. Results showed that a significant improvement of intrinsic and cell-based potency was achieved. X-ray crystallographic analysis of an inhibitor complex with ITK confirmed the prediction from the de novo design that the pyrrole moiety of the inhibitor would form an additional hydrogen bonding interaction with Glu436 in the catalytic domain, and hence improve overall binding affinity of the inhibitor.