Factorizations of the Complete Graph into C 5-Factors and 1-Factors

In this paper, we show that K_10n can be factored into C₅-factors and 1-factors for all non-negative integers and satisfying 2+=10n–1.Research partially supported by an NSF-AWM Mentoring Travel Grant     

Homology manifold bordism

The Bryant-Ferry-Mio-Weinberger surgery exact sequence for compact homology manifolds of dimension is used to obtain transversality, splitting and bordism results for homology manifolds, generalizing previous work of Johnston.

First, we establish homology manifold transversality for submanifolds of dimension : if is a map from an -dimensional homology manifold to a space , and is a subspace with a topological -block bundle neighborhood, and , then is homology manifold -cobordant to a map which is transverse to , with an -dimensional homology submanifold.

Second, we obtain a codimension splitting obstruction in the Wall -group for a simple homotopy equivalence from an -dimensional homology manifold to an -dimensional Poincaré space with a codimension Poincaré subspace with a topological normal bundle, such that if (and for only if) splits at up to homology manifold -cobordism.

Third, we obtain the multiplicative structure of the homology manifold bordism groups .

     

A top-down LC-FTICR MS-based strategy for characterizing oxidized calmodulin in activated macrophages

A liquid chromatography-mass spectrometry (LC-MS)-based approach for characterizing the degree of nitration and oxidation of intact calmodulin (CaM) has been used to resolve ～250 CaM oxiforms using only 500 ng of protein. The analysis was based on high-resolution data of the intact CaM isoforms obtained by Fourier-transform ion cyclotron resonance mass spectrometry (FTICR MS) coupled with an on-line reversed-phase LC separation. Tentative identifications of post-translational modifications (PTMs), such as oxidation or nitration, have been assigned by matching observed protein mass to a database containing all theoretically predicted oxidation products of CaM and verified through a combination of tryptic peptide information (generated from bottom-up analyses) and on-line collisionally induced dissociation (CID) tandem mass spectrometry (MS/MS) at the intact protein level. The reduction in abundance and diversity of oxidatively modified CaM (i.e., nitrated tyrosines and oxidized methionines) induced by macrophage activation has been explored and semiquantified for different oxidation degrees (i.e., no oxidation, moderate, and high oxidation). This work demonstrates the power of the top-down approach to identify and quantify hundreds of combinations of PTMs for single protein target such as CaM and implicate competing repair and peptidase activities to modulate cellular metabolism in response to oxidative stress.     

Trace LC/MS/MS quantitation of 17β‐estradiol as a biomarker for selective estrogen receptor modulator activity in the rat brain

A sensitive LC/MS/MS method has been developed by derivatization of 17β‐estradiol (E2) with dansyl chloride to quantitate 17β‐E2 in female rat serum. The use of E2‐d₅ minimized interferences from endogenous 17β‐E2 in order to achieve a limit of quantitation (LOQ) of 2.5 pg/ml using 150 µl of female rat serum. The recovery of the dansyl derivative was 95% or greater in quality control samples. The intra and interday assay precision was better than 8.2 and 6.2%, respectively, with accuracies ranging from 97 to 101% in the quality control samples. The assay was used for the quantitation of serum E2 as a biomarker for the estrogen receptor (ER) antagonist activity of small molecule SERMs (selective estrogen receptor modulators) in the female rat brain. The study revealed that a statistically significant upregulation of serum 17β‐E2 occurred for rats dosed with SERMs that are known to penetrate the brain and disrupt the hypothalamic‐pituitary‐ovarian (HPO) axis. Variations in 17β‐E2 in ascending dose studies also correlated with the corresponding trends in CYP17a1 levels, an mRNA biomarker for ovarian hyperstimulation. This biomarker assay has provided a useful screen for medicinal chemistry optimization to produce SERMs that do not interfere with negative feedback of estrogens on the brain and for biological hypothesis testing. Copyright © 2009 John Wiley & Sons, Ltd.     

Mass spectrometry of fluorocarbon‐labeled glycosphingolipids

A method for generation of novel fluorocarbon derivatives of glycosphingolipids (GSLs) with high affinity for fluorocarbon phases has been developed, and their potential applications to mass spectrometry (MS)‐based methodologies for glycosphingolipidomics have been investigated. Sphingolipid ceramide N‐deacylase (SCDase) is used to remove the fatty acid from the ceramide moiety, after which a fluorocarbon‐rich substituent (F‐Tag) is incorporated at the free amine of the sphingoid. In initial trials, a neutral GSL, globotriaosylceramide (Gb₃Cer), three purified bovine brain gangliosides, and four fungal glycosylinositol phosphorylceramides (GIPCs) were de‐N‐acylated, derivatized by prototype F‐Tags, and recovered by solid phase extraction on fluorocarbon‐derivatized silica (F‐SPE). The efficacy of SCDase treatment of GIPCs was here demonstrated for the first time. Compatibility with subsequent per‐N,O‐methylation was established for the F‐tagged Gb₃ Cer and purified gangliosides, and extensive mass spectra (MS¹ and MS²) consistent with all of the expected products were acquired. The potential use of F‐tagged derivatives for a comprehensive MS based profiling application was then demonstrated on a crude ganglioside mixture extracted from bovine brain. Finally, a simple trial in microarray format demonstrated fixation of F‐tagged G_M1 ganglioside to a fluorous glass surface, with the glycan intact and available for interaction with a fluorescent derivative of cholera toxin B chain. The methods described thus provide a new avenue for rapid GSL recovery or cleanup, potentially compatible with a variety of platforms for mass spectrometric profiling and structure analysis, as well as parallel analysis of functional interactions. Copyright © 2010 John Wiley & Sons, Ltd.     

Differential toxicity of amorphous silica nanoparticles toward phagocytic and epithelial cells

The objective of this study was to evaluate the influence of size and surface functionality of amorphous silica nanoparticles (SNPs) on their interaction with cultured cells. The intracellular uptake, phagocytic activity, and possible mechanisms of toxicity induced by SNPs were studied on murine alveolar macrophages and two epithelial cancer cell lines. It was found that phagocytic cells are more susceptible to amorphous SNPs than epithelial cells. SNPs with functionalized surfaces were capable to induce the formation of apoptotic cells to a higher extent than plain particles. Plain SNPs induced plasma membrane damage in phagocytic cells to a higher extent and caused cell death in a shorter period of time than surface-functionalized SNPs. The prevalence of necrotic mode of cell death was observed after treatment with plain SNPs. In the range studied surface functionality played an important role in SNPs toxicity.     

A Teacher’s Conception of Definition and Use of Examples When Doing and Teaching Mathematics

To contribute to an understanding of the nature of teachers’ mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher’s conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical knowledge, the authors give an account of the case of Lily, a prospective, then beginning, teacher who conceived of mathematical definition as an object with particular form and function and engaged in purposeful, specialized use of examples when doing and teaching mathematics. Lily’s case illustrates how a teacher’s interpretation of examples (as exemplifications or single instances) and conception of the form and function of definitions can influence her doing and teaching mathematics. An implication is that teacher preparation should foster teachers’ abilities to use examples purposefully to provide students with rich opportunities to engage in mathematical processes such as defining.