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.     

Intramolecular dimers: a new design strategy for fluorescence-quenched probes

Fluorogenic probes dual-labeled with reporter and quencher dyes use a change in fluorescence to monitor biochemical events (e.g., substrate binding or enzyme digestion). Such events change the reporter-quencher distance, which affects fluorescence. Recently, it is has been shown that static quenching through intramolecular dimers is an important mechanism that can sometimes be more efficient than F?rster resonance energy transfer (FRET).     

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.