Some remarks on multiplication ideals,ii

Let R bea commutative ring with identity. An R-module (ideal of R) A is called a multiplication module (ideal) if for each submodule N of A there exists an ideal I of R with N = I A. We give several characterizations of multiplication modules. Using the method of idealization we show how to reduce questions concerning multiplication modules to multiplication ideals. For example, we show that if S is a commutative R-algebra and ψ: M→an R-module homomorphism where M is a multiplication R-module and N is an S-module, then Sψ(M) is a multiplication S-module.     

Partitions of trees and {{\sf ACA}^\prime_{0}}

We show that a version of Ramsey’s theorem for trees for arbitrary exponents is equivalent to the subsystem ${{\sf ACA}^\prime_{0}}$ of reverse mathematics.     

Investigation of copper-azamacrocyclic complexes by high-performance liquid chromatography

The use of copper radioisotopes in imaging and therapy has prompted an increased interest in chelators which form stable copper complexes, such as Cu(II)-azamacrocyclic complexes. The effects of charge, stability and the size of the macrocyclic backbone of the Cu(II)-azamacrocyclic complexes on biological behavior have been evaluated. Here we report a reversed-phase high-performance liquid chromatography (HPLC) method to separate several Cu(II)-azamacrocyclic complexes, including Cu(II) complexes of 1,4,8,11-tetraazacyclotetradecane-1,4,8,11-tetraacetic acid (TETA), 4,11-bis(carboxymethyl)-1,4,8,11-tetraazabicyclo[6.6.2]hexadecane (CB-TE2A) and 4,10-bis(carboxymethyl)-1,4,7,10-tetraazabicyclo[5.5.2]tetradecane (CB-DO2A). Absorbance at 280 nm was used to monitor the complexes as they eluted from the reversed-phase column. The effects of the concentration of the buffer, the pH of the buffered mobile phase and the concentration of the organic modifier, methanol, on the separation were investigated. Separation of these copper complexes by ion-pair HPLC with the use of a mass spectrometry-compatible ion-pair reagent, triethylammonium acetate, in the mobile phase at pH 6.3 is also presented. The reversed-phase chromatographic conditions utilized also allow the pK(a)s of Cu-TETA and the log(k'w) values of Cu-CB-TE2A, Cu-TETA and Cu-CB-DO2A to be estimated.     

Incorporating postleap checks in tau-leaping

By explicitly representing the reaction times of discrete chemical systems as the firing times of independent, unit rate Poisson processes, we develop a new adaptive tau-leaping procedure. The procedure developed is novel in that accuracy is guaranteed by performing postleap checks. Because the representation we use separates the randomness of the model from the state of the system, we are able to perform the postleap checks in such a way that the statistics of the sample paths generated will not be biased by the rejections of leaps. Further, since any leap condition is ensured with a probability of one, the simulation method naturally avoids negative population values.     

Synthesis of poly(beta-amino ester)s with thiol-reactive side chains for DNA delivery

The safe and efficient delivery of DNA remains the major barrier to the clinical application of non-viral gene therapy. Here, we present novel, biodegradable polymers for gene delivery that are capable of simple graft modification and demonstrate the ability to respond to intracellular conditions. We synthesized poly(beta-amino ester)s using a new amine monomer, 2-(pyridyldithio)-ethylamine (PDA). These cationic, degradable polymers contain pyridyldithio functionalities in the side chains that react with high specificity toward thiol ligands. This reactivity is demonstrated using both mercaptoethylamine (MEA) and the thiol peptide RGDC, a ligand that binds with high affinity to certain integrin receptors. These two polymer derivatives displayed strong DNA binding as determined using electrophoresis and dye exclusion assays. In addition, the MEA-based polymer and plasmid DNA were shown to self-assemble into cationic complexes with effective diameters as low as 100 nm. Furthermore, this DNA binding ability was substantially reduced in response to intracellular glutathione concentrations, which may aid in DNA unpackaging inside the cell. These complexes also displayed low cellular toxicity and were able to mediate transfection at levels comparable to PEI in human hepatocellular carcinoma cells. These results suggest that PDA-based poly(beta-amino ester)s may serve as a modular platform for polymer-mediated gene delivery.     

Redox equilibria of iron oxides in aqueous-based magnetite dispersions: effect of pH and redox potential

The effect of pH and redox potential on the redox equilibria of iron oxides in aqueous-based magnetite dispersions was investigated. The ionic activities of each dissolved iron species in equilibrium with magnetite nanoparticles were determined and contoured within the Eh-pH framework of a composite stability diagram. Both standard redox potentials and equilibrium constants for all major iron oxide redox equilibria in magnetite dispersions were found to differ from values reported for noncolloidal systems. The "triple point" position of redox equilibrium among Fe(II) ions, magnetite, and hematite shifted to a higher standard redox potential and an equilibrium constant which was several orders of magnitude higher. The predominant area of magnetite stability was enlarged to cover a wider range of both pH and redox potentials as compared to that of a noncolloidal magnetite system.     

Hydrothermal synthesis of fluorated single crystals: BaMnF4 and BaF2·HF

Investigations to eliminate defects in the incommensurate phase BaMnF₄, led to a method of preparation at a temperature lower than the melting point of BaMnF₄. Qualitative studies of the systems BaF₂ -H₂O -HF and MnF₂ -H₂O -HF showed that very pure single crystals of BaMnF₄ could be grown at a temperature lower than 300°C. Several new phases could be isolated as single crystals, in particular: BaF_2^′HFSingle crystal X-ray analysis revealed the compound to be monoclinic (Space Group P2₁ and Z = 2) and confirmed the formula found by chemical analysis. However, because of the difficulty to distinguish between fluorine and oxygen atoms, some problems remain, which will be solved by neutron diffraction studies. Infrared analysis indicate the presence of HF^?₂ and suggest the following representation: (Ba²⁺)₂(HF^?₂)₂(F^?)₂.It is possible to extend this method of synthesis to the preparation of other fluorides and related compounds, in particular to those of europium and strontium.     

Llama-derived single-domain antibodies for the detection of botulinum A neurotoxin

Single-domain antibodies (sdAb) specific for botulinum neurotoxin serotype A (BoNT A) were selected from an immune llama phage display library derived from a llama that was immunized with BoNT A toxoid. The constructed phage library was panned using two methods: panning on plates coated with BoNT A toxoid (BoNT A Td) and BoNT A complex toxoid (BoNT Ac Td) and panning on microspheres coupled to BoNT A Td and BoNT A toxin (BoNT A Tx). Both panning methods selected for binders that had identical sequences, suggesting that panning on toxoided material may be as effective as panning on bead-immobilized toxin for isolating specific binders. All of the isolated binders tested were observed to recognize bead-immobilized BoNT A Tx in direct binding assays, and showed very little cross-reactivity towards other BoNT serotypes and unrelated protein. Sandwich assays that incorporated selected sdAb as capture and tracer elements demonstrated that all of the sdAb were able to recognize soluble (“live”) BoNT A Tx and BoNT Ac Tx with virtually no cross-reactivity with other BoNT serotypes. The isolated sdAb did not exhibit the high degree of thermal stability often associated with these reagents; after the first heating cycle most of the binding activity was lost, but the portion of the protein that did refold and recover antigen-binding activity showed only minimal loss on subsequent heating and cooling cycles. The binding kinetics of selected binders, assessed by both an equilibrium fluid array assay as well as surface plasmon resonance (SPR) using toxoided material, gave dissociation constants (K _D ) in the range 2.2 × 10⁻¹¹ to 1.6 × 10⁻¹⁰ M. These high-affinity binders may prove beneficial to the development of recombinant reagents for the rapid detection of BoNT A, particularly in field screening and monitoring applications.     

Measuring the intra-individual variability of the plasma proteome in the chicken model of spontaneous ovarian adenocarcinoma

The domestic chicken (Gallus domesticus) has emerged as a powerful experimental model for studying the onset and progression of spontaneous epithelial ovarian cancer (EOC) with a disease prevalence that can exceed 35% between 2 and 7 years of age. An experimental strategy for biomarker discovery is reported herein that combines the chicken model of EOC, longitudinal plasma sample collection with matched tissues, advanced mass spectrometry-based proteomics, and concepts derived from the index of individuality (Harris, Clin Chem 20: 1535–1542, 1974). Blood was drawn from 148 age-matched chickens starting at 2.5 years of age every 3 months for 1 year. At the conclusion of the 1 year sample collection period, the 73 birds that remained alive were euthanized, necropsied, and tissues were collected. Pathological assessment of resected tissues from these 73 birds confirmed that five birds (6.8%) developed EOC. A proteomics workflow including in-gel digestion, nanoLC coupled to high-performance mass spectrometry, and label-free (spectral counting) quantification was used to measure the biological intra-individual variability (CV_W) of the chicken plasma proteome. Longitudinal plasma sample sets from two birds within the 73-bird biorepository were selected for this study; one bird was considered “healthy” and the second bird developed late-stage EOC. A total of 116 proteins from un-depleted plasma were identified with 80 proteins shared among all sample sets. Analytical variability (CV_A) of the label-free proteomics workflow was measured using a single plasma sample analyzed five times and was found to be ≥CV_W in both birds for 16 proteins (20%) and in either bird for 25 proteins (31%). Ovomacroglobulin (ovostatin) was found to increase (p < 0.001) over a 6 month period in the late-stage EOC bird providing an initial candidate protein for further investigation.