Successions in Words and Compositions

We consider words over the alphabet [k] = {1, 2, . . . , k}, k ?? 2. For a fixed nonnegative integer p, a p-succession in a word w ₁ w ₂ . . . w _n consists of two consecutive letters of the form (w _i , w _i ?+ p), i = 1, 2, . . . , n ? 1. We analyze words with respect to a given number of contained p-successions. First we find the mean and variance of the number of p-successions. We then determine the distribution of the number of p-successions in words of length n as n (and possibly k) tends to infinity; a simple instance of a phase transition (Gaussian-Poisson-degenerate) is encountered. Finally, we also investigate successions in compositions of integers.     

Transformation of Phosphaalkynes into 1H- and 2H-Phosphirenes1

Abstract

The 2H-phosphirene 4 is synthesized from the spirocyclic 3H-1,2,4-diazaphosphole 1 by low temperature photolysis. The isomeric 1H-phosphirenes 7 are formed by a [2+1]-cycloaddition process of chlorocarbenes, generated from diazirines. onto the triple bond of phosphaalkynes. When the 1-chlon-1H-phosphirenes 7 are allowed to react with a series of nucleophiles substitution occurs yielding the 1H-phosphirenes 9, 11 and 12. The existance of a phosphirenium cations, for instance 13 is discussed.     

Spectral Assignment of Phenanthrene Derivatives Based on 6H-Dibenzo[C,E][1,2] Oxaphosphinine 6-Oxide by NMR and Quantum Chemical Calculations

Abstract

Organophosphorus compounds such as 6H-dibenzo[c,e][1,2]oxaphosphinine 6-oxide (DOPO, 1) and its derivatives are important and versatile compounds for a broad field of applications. However, a thorough spectral assignment is often subordinate to its chemical properties. This article presents and unambiguously attributes the ¹H and ¹³C NMR spectra of DOPO (1), selected products yielded from the Atherton–Todd reaction (2–4), DOPO-HQ (5) as well as sulfur derivatives (6–7) via a set of 1D- and 2D-NMR experiments. The complex P-C and P-H coupling patterns are discussed and compared with the derivatives possessing different chemical environments around the phosphorus atom. In addition, we compared our results with density functional theory calculations. Even though the prediction of NMR data of organophosphorus compounds via molecular modeling is limited, this study presents a method that yields good results for this class of heterocycles. This knowledge should help to quickly assign NMR spectroscopic data of other DOPO (1) derivatives and can be extrapolated to organophosphorus compounds in general.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: NMR Spectra of Compounds 1-7 (Figures S1 - S15).     

Detection and characterization of silver nanoparticles in chicken meat by asymmetric flow field flow fractionation with detection by conventional or single particle ICP-MS

A method of analysis of silver nanoparticles (AgNPs) in chicken meat was developed. The homogenized chicken meat sample, which was spiked with AgNPs, was subjected to enzymolysis by Proteinase K for 40 min at 37 °C. Transmission electron microscopy and inductively coupled plasma mass spectrometry (ICP-MS) in single particle mode were used to characterize the number-based size distribution of AgNPs in the meat digestate. Because similar size distributions were found in the meat digestate and in the aqueous suspension of AgNPs used for spiking the meat, it was shown that no detectable dissolution of the AgNPs took place during the sample preparation stage. The digestate was injected into the asymmetric flow field flow fractionation (AF⁴) -ICP-MS system, which enabled fractionation of nanoparticles from the remaining meat matrix, and resulted in one large peak in the fractograms as well as two smaller peaks eluting close to the void volume. The recovery of silver contained in the large AgNP peak was around 80 %. Size determination of AgNPs in the meat matrix, based on external size calibration of the AF⁴ channel, was hampered by non-ideal (early elution) behavior of the AgNPs. Single particle ICP-MS was applied for determination of the number-based particle size distribution of AgNPs in collected fractions. The presented work describes for the first time the coupling of AF⁴ and ICP-MS for AgNP separation in a food matrix.     

Multidimensional nano-HPLC coupled with tandem mass spectrometry for analyzing biotinylated proteins

Multidimensional high-performance liquid chromatography (HPLC) is a key method in shotgun proteomics approaches for analyzing highly complex protein mixtures by complementary chromatographic separation principles. Here, we describe an integrated 3D-nano-HPLC/nano-electrospray ionization quadrupole time-of-flight mass spectrometry system that allows an enzymatic digestion of proteins followed by an enrichment and subsequent separation of the created peptide mixtures. The online 3D-nano-HPLC system is composed of a monolithic trypsin reactor in the first dimension, a monolithic affinity column with immobilized monomeric avidin in the second dimension, and a reversed phase C18 HPLC-Chip in the third dimension that is coupled to a nano-ESI-Q-TOF mass spectrometer. The 3D-LC/MS setup is exemplified for the identification of biotinylated proteins from a simple protein mixture. Additionally, we describe an online 2D-nano-HPLC/nano-ESI-LTQ-Orbitrap-MS/MS setup for the enrichment, separation, and identification of cross-linked, biotinylated species from chemical cross-linking of cytochrome c and a calmodulin/peptide complex using a novel trifunctional cross-linker with two amine-reactive groups and a biotin label.

DFT in a nutshell

The purpose of this short essay is to introduce students and other newcomers to the basic ideas and uses of modern electronic density functional theory, including what kinds of approximations are in current use, and how well they work (or not). The complete newcomer should find it orients them well, while even longtime users and aficionados might find something new outside their area. Important questions varying in difficulty and effort are posed in the text, and are answered in the Supporting Information. © 2012 Wiley Periodicals, Inc.     

Synthesis and Crystal Structures of Novel Copper(I) Clusters with Bridging Silyl Amide Ligands

Treatment of copper(I) chloride with R₂Si(NLiPh)₂ (R = Me, Ph) in thf led to the formation of the octanuclear cluster compounds [Cu₈{(R₂Si(NPh)₂}₄] [R = Me ( 1 ), Ph ( 2 ).] Compound 1 crystallizes in the tetragonal space group P4/n, with a = 1505.41(5) and c = 1911.32(7) pm. The X‐ray crystal structure determination revealed a cube shaped Cu₈ cluster core with μ₄ bridging Me₂Si(NPh)₂^2– ligands. The copper atoms display an almost linear coordination with Cu–N distances in the range of 191.1(3)–191.4(3) pm. The Cu–Cu distances are 265.7(1)–267.3(1) pm. Compound 2 forms monoclinic crystals, space group P2₁/n, with a = 1461.87(4), b = 2483.77(6), c = 2725.49(8) pm, β = 100.77(1)°. The cluster core of compound 2 consists formally of two mutually perpendicular arranged trigonal prisms, which share a common square face. Like in the case of compound 1 the square faces of the cluster core are capped by μ₄ bridging Ph₂Si(NPh)₂^2– ligands. The copper atoms adopt a nearly linear N–Cu–N coordination with Cu–N distances of 190.0(4)–195.1(4) pm. The Cu–Cu distances are 252.3(1)–305.6(1) pm.     

Analysis of monoclonal antibody by a novel CE‐UV/MALDI‐MS interface

mAbs are highly complex proteins that present a wide range of microheterogeneity that requires multiple analytical methods for full structure assessment and quality control. As a consequence, the characterization of mAbs on different levels is particularly product‐ and time‐consuming. CE‐MS couplings, especially to MALDI, appear really attractive methods for the characterization of biological samples. In this work, we report the last instrumental development and performance of the first totally automated off‐line CE‐UV/MALDI‐MS/MS. This interface is based on the removal of the original UV cell of the CE apparatus, modification of the spotting device geometry, and creation of an integrated delivery matrix system. The performance of the method was evaluated with separation of five intact proteins and a tryptic digest mixture of nine proteins. Intact protein application shows the acquisition of electropherograms with high resolution and high repeatability. In the peptide mapping approach, a total number of 154 unique identified peptides were characterized using MS/MS spectra corresponding to average sequence coverage of 64.1%. Comparison with NanoLC/MALDI‐MS/MS showed complementarity at the peptide level with an increase of 42% when using CE/MALDI‐MS coupling. Finally, this work represents the first analysis of intact mAb charge variants by CZE using an MS detection. Moreover, using a peptide mapping approach CE‐UV/MALDI‐MS/MS fragmentation allowed 100% sequence coverage of the light chain and 92% of the heavy chain, and the separation of four major glycosylated peptides and their structural characterization.