On families of quadratic surfaces having fixed intersections with two hyperplanes

We investigate families of quadrics all of which have the same intersection with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter and describe how the quadrics are transformed as the parameter changes. This research was motivated by an application in mixed integer conic optimization. In that application, we aimed to characterize the convex hull of the union of the intersections of an ellipsoid with two half-spaces arising from the imposition of a linear disjunction.     

Mapping a Noncovalent Protein–Peptide Interface by Top-Down FTICR Mass Spectrometry Using Electron Capture Dissociation

Noncovalent protein–ligand and protein–protein complexes are readily detected using electrospray ionization mass spectrometry (ESI MS). Furthermore, recent reports have demonstrated that careful use of electron capture dissociation (ECD) fragmentation allows covalent backbone bonds of protein complexes to be dissociated without disruption of noncovalent protein–ligand interactions. In this way the site of protein–ligand interfaces can be identified. To date, protein–ligand complexes, which have proven tractable to this technique, have been mediated by ionic electrostatic interactions, i.e., ion pair interactions or salt bridging. Here we extend this methodology by applying ECD to study a protein–peptide complex that contains no electrostatics interactions. We analyzed the complex between the 21 kDa p53-inhibitor protein anterior gradient-2 and its hexapeptide binding ligand (PTTIYY). ECD fragmentation of the 1:1 complex occurs with retention of protein–peptide binding and analysis of the resulting fragments allows the binding interface to be localized to a C-terminal region between residues 109 and 175. These finding are supported by a solution-phase competition assay, which implicates the region between residues 108 and 122 within AGR2 as the PTTIYY binding interface. Our study expands previous findings by demonstrating that top-down ECD mass spectrometry can be used to determine directly the sites of peptide–protein interfaces. This highlights the growing potential of using ECD and related top-down fragmentation techniques for interrogation of protein–protein interfaces.     

Generalized Markov Models of Infectious Disease Spread: A Novel Framework for Developing Dynamic Health Policies

We propose a class of mathematical models for the transmission of infectious diseases in large populations. This class of models, which generalizes the existing discrete-time Markov chain models of infectious diseases, is compatible with efficient dynamic optimization techniques to assist real-time selection and modification of public health interventions in response to evolving epidemiological situations and changing availability of information and medical resources. While retaining the strength of existing classes of mathematical models in their ability to represent the within-host natural history of disease and between-host transmission dynamics, the proposed models possess two advantages over previous models: (1) these models can be used to generate optimal dynamic health policies for controlling spreads of infectious diseases, and (2) these models are able to approximate the spread of the disease in relatively large populations with a limited state space size and computation time.     

Mechanism for degradation of Nafion in PEM fuel cells from quantum mechanics calculations

We report results of quantum mechanics (QM) mechanistic studies of Nafion membrane degradation in a polymer electrolyte membrane (PEM) fuel cell. Experiments suggest that Nafion degradation is caused by generation of trace radical species (such as OH(●), H(●)) only when in the presence of H(2), O(2), and Pt. We use density functional theory (DFT) to construct the potential energy surfaces for various plausible reactions involving intermediates that might be formed when Nafion is exposed to H(2) (or H(+)) and O(2) in the presence of the Pt catalyst. We find a barrier of 0.53 eV for OH radical formation from HOOH chemisorbed on Pt(111) and of 0.76 eV from chemisorbed OOH(ad), suggesting that OH might be present during the ORR, particularly when the fuel cell is turned on and off. Based on the QM, we propose two chemical mechanisms for OH radical attack on the Nafion polymer: (1) OH attack on the S-C bond to form H(2)SO(4) plus a carbon radical (barrier: 0.96 eV) followed by decomposition of the carbon radical to form an epoxide (barrier: 1.40 eV). (2) OH attack on H(2) crossover gas to form hydrogen radical (barrier: 0.04 eV), which subsequently attacks a C-F bond to form HF plus carbon radicals (barrier as low as 1.00 eV). This carbon radical can then decompose to form a ketone plus a carbon radical with a barrier of 0.86 eV. The products (HF, OCF(2), SCF(2)) of these proposed mechanisms have all been observed by F NMR in the fuel cell exit gases along with the decrease in pH expected from our mechanism.     

Rearrangement of 3-deoxy-D-erythro-hexos-2-ulose in aqueous solution: NMR evidence of intramolecular 1,2-hydrogen transfer

Selective (13)C- and (2)H-labeling, and (13)C NMR spectroscopy, have been used to show that the 1,2-dicarbonyl compound (osone), 3-deoxy-D-erythro-hexos-2-ulose (3-deoxy-D-glucosone) (1; 3DG), degrades to 3-deoxy-D-ribo-hexonic acid 2 and 3-deoxy-D-arabino-hexonic acid 3 exclusively via an intramolecular 1,2-hydrogen transfer mechanism in aqueous phosphate buffer at pH 7.5 at 37 °C. Acids 2 and 3 are produced in significantly different amounts (1:6 ratio) despite the prochiral C3 in 1, and two potential reaction mechanisms are considered to explain the observed stereoselectivity. One mechanism involves acyclic forms of 1 as reactants, whereas the other assumes cyclic pyranose reactants. In the former (2-keto-hydrate or 2KH mechanism), putative transition state structures based on density functional theory (DFT) calculations arise from the C1 hydrate form of acyclic 1 having the C1-H1 bond roughly orthogonal to the C2 carbonyl plane. The relative orientation of the alkoxide oxygen atom at C1 and the C2 carbonyl oxygen, and H-bonding between C(1)OH and the C2 carbonyl oxygen, contribute to the stability of the transition state. DFT calculations of the natural charges on individual atoms in the transition state show the migrating hydrogen to have an almost neutral charge, implying that it may more closely resemble a hydrogen atom than a hydride anion during transfer from C1 to C2. A second mechanism (2-keto-pyranose or 2KP mechanism) involving the cyclic 2-keto-pyranoses of 1 as reactants aligns the C1-H1 bond orthogonal to the C2 carbonyl plane in different ring conformations of both anomers, with the β-pyranose giving 3 and the α-pyranose giving 2. While both the 2KH and 2KP mechanisms are possible, the latter readily leads to a prediction of the reaction stereospecificity that is consistent with the experimental data.