On Bateman's method for second kind integral equations

Summary Under suitable conditions, we prove the convergence of the Bateman method for integral equations defined over bounded domains inR ^d ,d1. The proof makes use of Hilbert space methods, and requires the integral operator to be non-negative definite. For one-dimensional integral equations over finite intervals, estimated rates of convergence are obtained which depend on the smoothness of the kernel, but are independent of the inhomogeneous term. In particular, for aC kernel andn reasonably spaced Bateman points, the convergence is shown to be faster than any power of 1/n. Numerical calculations support this result.     

Synthetic erythropoietic proteins: tuning biological performance by site-specific polymer attachment

Chemical synthesis in combination with precision polymer modification allows the systematic exploration of the effect of protein properties, such as charge and hydrodynamic radius, on potency using defined, homogeneous conjugates. A series of polymer-modified synthetic erythropoiesis proteins were constructed that had a polypeptide chain similar to the amino acid sequence of human erythropoietin but differed significantly in the number and type of attached polymers. The analogs differed in charge from +5 to -26 at neutral pH and varied in molecular weight from 30 to 54 kDa. All were active in an in vitro cell proliferation assay. However, in vivo potency was found to be strongly dependent on overall charge and size. The trends observed in this study may serve as starting points for the construction of more potent synthetic EPO analogs in the future.     

Fluorimetric determination of acidity constants of naphthoic and anthroic acids

A fluorimetric method of determining the acidity constants (pK_a values) of some naphthoic and anthroic acids is presented, based on the changes in fluorescence of solutions of these acids in water on changing the pH. The method is useful in the absence as well as in the presence of excited-state proton transfer. In the latter case, when the excited-state protonation occurs in the same pH region as the ground-state dissociation, resolution of the two processes can be accomplished by addition of a suitable quencher such as iodide. The method permits the accurate determination of the pK_a value of fluorescent compounds, even when they are poorly soluble in water, because of the high sensitivity of the spectrofluorimetry.     

Pd-catalyzed intermolecular amidation of aryl halides: the discovery that xantphos can be trans-chelating in a palladium complex

A general method for the intermolecular coupling of aryl halides and amides using a Xantphos/Pd catalyst is described. This system displays good functional group compatibility, and the desired C-N bond forming process proceeds in good to excellent yields with 1-4 mol % of the Pd catalyst. Additionally, the arylation of sulfonamides, oxazolidinones, and ureas is reported. The efficiency of these transformations was found to be highly dependent on reaction concentrations and catalyst loadings. A Pd complex resulting from oxidative addition of 4-bromobenzonitrile, (Xantphos)Pd(4-cyanophenyl)(Br) (II), was prepared in one step from Xantphos, Pd(2)(dba)(3), and the aryl bromide. Complex II proved to be an active catalyst for the coupling between 4-bromobenzonitrile and benzamide. X-ray crystallographic analysis of II revealed a rare trans-chelating bisphosphine-Pd(II) structure with a large bite angle of 150.7 degrees.     

Synthesis of 2- and 4-imino(1,2-a)pyridopyrimidines from allenic nitriles and 2-aminopyridines

4,4-Dialkylallenyl nitriles and 2-aminopyridines give 2-alkyl-4-iminopyrido(1,2-a)pyrimidines as monohydrates in about 90% yield and 4-monoalkylallenyl nitriles similarly give 4-alkyl-2-imino(1,2-a)pyrimidines.     

Dynamics of a triphenylene discotic molecule,HAT6, in the columnar and isotropic liquid phases

Discotic molecules have planar, disklike polyaromatic cores that can self-assemble into "molecular wires". Highly anisotropic charge transfer along the wires arises when there is sufficient intermolecular overlap of the pi-orbitals of the molecular cores. Discotic materials can be applied in molecular electronics, field-effect transistors, and-recently with record quantum efficiencies-photovoltaics (Schmidt-Mende, L.; Fechtenk?tter, A.; Müllen, K.; Moons, E.; Frien, R. H.; MacKenzie, J. D. Science 2001, 293, 1119). A combination of quasielastic neutron scattering (QENS) measurements with molecular dynamics simulations on the discotic molecule hexakis(n-hexyloxy)triphenylene (HAT6) shows that the dynamics of the cores and tails of discotic molecules are strongly correlated. Core and tail dynamics are not separated, the system being characterized by overall in-plane motion, on a time scale of 0.2 ps, and softer out-of-plane motions at 7 ps. Because charge transfer between the molecules is on similar time scales, these motions are relevant for the conducting properties of the materials. Both types of motion are dominated by van der Waals interactions. Small-amplitude in-plane motions in which the disks move over each other are almost entirely determined by tail/tail interactions, these also playing an important role in the out-of-plane motion. The QENS measurements reveal that these motions are little changed by passing from the columnar phase to the isotropic liquid phase, just above the clearing temperature. The model of four HAT6 molecules in a column reproduces the measured QENS spectrum of the liquid phase, suggesting that correlations persist within the liquid phase over about this number of disks.     

Recent advances in microwave-assisted combinatorial synthesis and library generation

Progress and developments made in microwave-assisted combinatorial synthesis and library production since 2002 are reviewed. The use of microwave technology in both solution and solid phase synthesis is discussed with special reference to agrochemical applications where appropriate.     

Characterization of amyloidogenic immunoglobulin light chains directly from serum by on-line immunoaffinity isolation

Primary systemic amyloidosis (AL) is characterized by the overproduction of immunoglobulin light chain proteins by a monoclonal, terminally differentiated B-lymphocyte or plasma cell clone. The free immunoglobulin light chains are deposited in an abnormal conformation as amyloid in a variety of organs in the body. The mechanism of amyloid formation is not well understood, but appears to be associated with some form of cleavage of the immunoglobulin light chain with subsequent aggregate formation. In an attempt to characterize the structure of amyloid-forming light chain proteins we developed an on-line immunoaffinity purification and subsequent characterization of free kappa and free lambda immunoglobulin light chains by electrospray ionization mass spectrometry. The methodology is totally automated and requires 20 micro L of serum. Mass spectral analysis of Bence Jones proteins under non-denaturing conditions was also utilized to examine the tertiary and quaternary structure of light chain proteins and clearly shows covalent dimer formation of lambda type light chain. This type of on-line assay may prove helpful in elucidating distinguishing features capable of discriminating AL from benign monoclonal gammopathies of undetermined significance as well as diagnosing AL.