Characterization of polyphosphoesters by fourier transform ion cyclotron resonance mass spectrometry

FT-ICR mass spectrometry, together with collision-induced dissociation and electron capture dissociation, has been used to characterize the polyphosphoester poly[1,4-bis(hydroxyethyl)terephthalate-alt-ethyloxyphosphate] and its degradation products. Three degradation pathways were elucidated: hydrolysis of the phosphate-[1,4-bis(hydroxyethyl)terephthalate] bonds; hydrolysis of the phosphate-ethoxy bonds; and hydrolysis of the ethyl-terephthalate bonds. The dominant degradation reactions were those that involved the phosphate groups. This work constitutes the first application of mass spectrometry to the characterization of polyphosphoesters and demonstrates the suitability of high mass accuracy FT-ICR mass spectrometry, with CID and ECD, for the structural analysis of polyphosphoesters and their degradation products.     

Activated ion electron capture dissociation (AI ECD) of proteins: Synchronization of infrared and electron irradiation with ion magnetron motion

Here, we show that to perform activated ion electron capture dissociation (AI-ECD) in a Fourier transform ion cyclotron resonance (FT-ICR) mass spectrometer equipped with a CO₂ laser, it is necessary to synchronize both infrared irradiation and electron capture dissociation with ion magnetron motion. This requirement is essential for instruments in which the infrared laser is angled off-axis, such as the Thermo Finnigan LTQ FT. Generally, the electron irradiation time required for proteins is much shorter (ms) than that required for peptides (tens of ms), and the modulation of ECD, AI ECD, and infrared multiphoton dissociation (IRMPD) with ion magnetron motion is more pronounced. We have optimized AI ECD for ubiquitin, cytochrome c, and myoglobin; however the results can be extended to other proteins. We demonstrate that pre-ECD and post-ECD activation are physically different and display different kinetics. We also demonstrate how, by use of appropriate AI ECD time sequences and normalization, the kinetics of protein gas-phase refolding can be deconvoluted from the diffusion of the ion cloud and measured on the time scale longer than the period of ion magnetron motion.     

Iterated Point–Line Configurations Grow Doubly-Exponentially

Begin with a set of four points in the real plane in general position. Add to this collection the intersection of all lines through pairs of these points. Iterate. Ismailescu and Radoičić (Comput. Geom. 27:257–267, 2004) showed that the limiting set is dense in the plane. We give doubly exponential upper and lower bounds on the number of points at each stage. The proof employs a variant of the Szemerédi–Trotter Theorem and an analysis of the “minimum degree” of the growing configuration.     

A new interpretation of Problem 10 of the Moscow Mathematical Papyrus

Although much discussed, the original intent of Problem 10 of the Moscow Mathematical Papyrus continues to be an unresolved question. This essay proposes a possible solution to the issue by joining together aspects of two theories on the subject advanced in the 1930s by W. W. Struve and T. E. Peet. From this point of beginning it is shown that the problem’s “basket” may originally have been intended to be understood as being of a specific actual size, thus revealing a set of correlations and insights regarding early Middle Kingdom mathematical capabilities and grain measurement concerns.     

Reconstructing bulk isotope ratios from compound‐specific isotope ratios

Carbon isotope analysis by bulk elemental analysis coupled with isotope ratio mass spectrometry has been the mainstay of δ¹³C analyses both at natural abundance and in tracer studies. More recently, compound‐specific isotope analysis (CSIA) has become established, whereby organic constituents are separated online by gas or liquid chromatography before oxidation and analysis of CO₂ for constituent δ¹³C. Theoretically, there should be concordance between bulk δ¹³C measurements and carbon‐weighted δ¹³C measurements of carbon‐containing constituents. To test the concordance between the bulk and CSIA, fish oil was chosen because the majority of carbon in fish oil is in the triacylglycerol form and ～95% of this carbon is amenable to CSIA in the form of fatty acids. Bulk isotope analysis was carried out on aliquots of oil extracted from 55 fish samples and δ¹³C values were obtained. Free fatty acids (FFAs) were produced from the oil samples by saponification and derivatised to fatty acid methyl esters (FAMEs) for CSIA by gas chromatography/combustion/isotope ratio mass spectrometry. A known amount of an internal standard (C15:0 FAME) was added to allow analyte quantitation. This internal standard was also isotopically calibrated in both its FFA (δ¹³C = ?34.30‰) and FAME (δ¹³C = ?34.94‰) form. This allowed reporting of FFA δ¹³C from measured FAME δ¹³C values. The bulk δ¹³C was reconstructed from CSIA data based on each FFA δ¹³C and the relative amount of CO₂ produced by each analyte. The measured bulk mean δ¹³C (SD) was ?23.75‰ (1.57‰) compared with the reconstructed bulk mean δ¹³C of ?23.76 (1.44‰) from CSIA and was not significantly different. Further analysis of the data by the Bland‐Altman method did not show particular bias in the data relative to the magnitude of the measurement. Good agreement between the methods was observed with the mean difference between methods (range) of 0.01‰ (?1.50 to 1.30). Copyright © 2010 John Wiley & Sons, Ltd.