Two-step peer methods with continuous output

The essential feature of peer methods for initial value problems is that all stages have the same order. Hence, dense output is easily available by interpolation. However, continuity of the output requires that the methods possess the FSAL-property (first same as last) well known from one-step methods. An additional advantage of such methods is an increase of the number of stages and the order without increasing the computational effort of the scheme or the number of computing cores for parallel methods. We derive several FSAL peer methods with 3 to 9 stages and compare their numerical efficiency with existing methods in the case of explicit parallel and implicit sequential peer methods.     

Impurity distribution and electrical characteristics of boron-doped Si1−x Ge x /Si p +/N heterojunction diodes produced using pulsed UV-laser-induced epitaxy and Gas-immersion laser doping

A two-step pulsed UV-laser process which independently controls the metallurgical and electrical junction depth of a Si_1–x Ge _x /Si heterojunction diode has been implemented. Pulsed Laser-Induced Epitaxy (PLIE) combined with Gas-immersion Laser Doping (GILD) are used to fabricate boron-doped heteroepitaxial p ⁺/N Si_1–x Ge _x /Si layers and diodes. Borontrifluoride is used as the gaseous dopant source in the GILD process step. Boron incorporation and activation are investigated as a function of laser energy fluence and the number of laser pulses using SIMS and Halleffect measurements. The dose of incorporated dopant is on the order of 10¹³ cm^–2 per pulse. The B profiles obtained are flat except for a peak at the interface resulting from segregation effects. The B and Ge distributions are compared with shifts in the turn-on voltage of p ⁺/N Si_1–x /Si heterojunction diodes produced by the process. The GILD/PLIE process is spatially selective with the resulting diodes fabricated being quasiplanar. Hole mobilities in the heavily doped Si_1–x Ge _x films are found to be slightly lower than in comparable Si films.Presently at the Oregon Graduate Institute, Beaverton, OR 97006, USA     

Small point sets of PG(n, p 3h ) intersecting each line in 1 mod p h points

The main result of this paper is that point sets of PG(n, q), q = p ^3h , p ≥ 7 prime, of size < 3(q ^n-1 + 1)/2 intersecting each line in 1 modulo ${\sqrt[3] q}$ points (these are always small minimal blocking sets with respect to lines) are linear blocking sets. As a consequence, we get that minimal blocking sets of PG(n, p ³), p ≥ 7 prime, of size < 3(p ^3(n-1) + 1)/2 with respect to lines are always linear.     

Implicit peer methods for large stiff ODE systems

Implicit two-step peer methods are introduced for the solution of large stiff systems. Although these methods compute s-stage approximations in each time step one-by-one like diagonally-implicit Runge-Kutta methods the order of all stages is the same due to the two-step structure. The nonlinear stage equations are solved by an inexact Newton method using the Krylov solver FOM (Arnoldi??s method). The methods are zero-stable for arbitrary step size sequences. We construct different methods having order p=s in the multi-implicit case and order p=s?1 in the singly-implicit case with arbitrary step sizes and s??5. Numerical tests in Matlab for several semi-discretized partial differential equations show the efficiency of the methods compared to other Krylov codes.     

Photoisomerization of dichlorocarbene adducts of 2,4-cyclohexadienones

Irradiation of the nπ* band of the dichlorocyclopropyl enones $\text{1}$ and $\text{7}$ resulted in ring expansion and 1,2-chlorine migration to give $\text{2}$ and $\text{8}$ respectively, whereas the dihydrogen analog $\text{11}$ gave the vinylcyclopropane-cyclopentene rearrangement product $\text{12}$.     

Generation of free radicals by emodic acid and its [D-Lys6]GnRH-conjugate

In an attempt to develop an efficient chemotherapeutic agent targeted at malignant cells that express receptors to gonadotropin releasing hormone (GnRH) we coupled [D-Lys6]GnRH covalently to an emodin derivative, i.e. emodic acid (Emo) to yield [D-Lys6(Emo)]GnRH. Emodin is a naturally occurring anthraquinone which is widely used as a laxative and has other versatile biological activities. Physico-chemical studies employing electron paramagnetic resonance and electrochemistry of the conjugate as well as the (Emo) moiety showed that these compounds could be easily reduced either chemically, photochemically or enzymatically to their corresponding semiquinones. In the presence of oxygen the semiquinones generated reactive oxygen species (ROS), mainly superoxide and hydroxyl radicals, which were detected by the spin trapping method. Moreover, upon irradiation with visible light these compounds produced ROS and a highly reactive excited triplet state of Emo, which by itself may cause the oxidation of certain electron acceptors such as amino acids and bases of nucleic acids. Thus, [D-Lys6]GnRH-photosensitizer conjugates may be potentially used for targeted photodynamic chemotherapy aimed at treating cancer cells that carry GnRH receptors. These conjugates may also induce cytotoxicity in the dark similar to common conventional chemotherapeutic agents. The peptidic moiety, [D-Lys6]GnRH, was found to be stable toward highly reactive ROS generated either from enzymatic reduction or upon photoirradiation. The physico-chemical properties of Emo were only marginally influenced by the peptidic [D-Lys6]GnRH carrier.     

Attribution of the discrepancy between ELISA and LC-MS/MS assay results of a PEGylated scaffold protein in post-dose monkey plasma samples due to the presence of anti-drug antibodies

High-performance liquid chromatography-tandem mass spectrometry (LC-MS/MS) and enzyme-linked immunosorbent assay (ELISA) methods were developed for the quantification of a PEGylated scaffold protein drug in monkey plasma samples. The LC-MS/MS method was based on the extraction of the therapeutic protein with a water-miscible organic solvent and the subsequent trypsin digestion of the extract followed by the detection of a surrogate peptide. The assay was linear over a range of 10-3,000 ng/mL. The ELISA method utilized a therapeutic target-binding format in which the recombinant target antigen was used to capture the drug in the sample, followed by detection with an anti-PEG monoclonal antibody. The assay range was 30-2,000 ng/mL. A correlation study between the two methods was performed by measuring the drug concentrations in plasma samples from a single-dose pharmacokinetic (PK) study in cynomolgus monkeys following a 5-mg/kg subcutaneous administration (n = 4). In the early time points of the PK profile, the drug concentrations obtained by the LC-MS/MS method agreed very well with those obtained by the ELISA method. However, at later time points, the drug concentrations measured by the LC-MS/MS method were consistently higher than those measured by the ELISA method. The PK parameters calculated based on the concentration data showed that the two methods gave equivalent peak exposure (C(max)) at 24-48 h. However, the LC-MS/MS results exhibited about 1.53-fold higher total exposure (AUC(tot)) than the ELISA results. The discrepancy between the LC-MS/MS and ELISA results was investigated by conducting immunogenicity testing, anti-drug antibody (ADA) epitope mapping, and Western blot analysis of the drug concentrations coupled with Protein G separation. The results demonstrated the presence of ADA specific to the engineered antigen-binding region of the scaffold protein drug that interfered with the ability of the drug to bind to the target antigen used in the ELISA method. In the presence of the ADAs, the ELISA method measured only the active circulating drug (target-binding), while the LC-MS/MS method measured the total circulating drug. The work presented here indicates that the bioanalysis of protein drugs may be complicated owing to the presence of drug-binding endogenous components or ADAs in the post-dose (incurred) samples. The clear understanding of the behavior of different bioanalytical techniques vis-à-vis the potentially interfering components found in incurred samples is critical in selecting bioanalytical strategies for measuring protein drugs.     

Potential of mean force between hydrophobic solutes in the Jagla model of water and implications for cold denaturation of proteins

Using the Jagla model potential we calculate the potential of mean force (PMF) between hard sphere solutes immersed in a liquid displaying water-like properties. Consistent estimates of the PMF are obtained by (a) umbrella sampling, (b) calculating the work done by the mean force acting on the hard spheres as a function of their separation, and (c) determining the position dependent chemical potential after calculating the void space in the liquid. We calculate the PMF for an isobar along which cold denaturation of a model protein has previously been reported. We find that the PMF at contact varies non-monotonically, which is consistent with the observed cold denaturation. The Henry constant also varies non-monotonically with temperature. We find, on the other hand, that a second (solvent separated) minimum of the PMF becomes deeper as temperature decreases. We calculate the solvent-solvent pair correlation functions for solvents near the solute and in the bulk, and show that, as temperature decreases, the two pair correlation functions become indistinguishable, suggesting that the perturbation of solvent structure by the solute diminishes as temperature decreases. The solvent-solute pair correlation function at contact grows as the temperature decreases. We calculate the cavity correlation function and show the development of a solvent-separated peak upon decrease of temperature. These observations together suggest that cold denaturation occurs when the solvent penetrates between hydrophobic solutes in configurations with favorable free energy. Our results thus suggest that cold denatured proteins are structured and that cold denaturation arises from strong solvent-solute interactions, rather than from entropic considerations as in heat denaturation.