Development of an online SPE�CLC�CMS-based assay using endogenous substrate for investigation of soluble epoxide hydrolase (sEH) inhibitors

Soluble epoxide hydrolase (sEH) is a promising therapeutic target for the treatment of hypertension, pain, and inflammation-related diseases. In order to enable the development of sEH inhibitors (sEHIs), assays are needed for determination of their potency. Therefore, we developed a new method utilizing an epoxide of arachidonic acid (14(15)-EpETrE) as substrate. Incubation samples were directly injected without purification into an online solid phase extraction (SPE) liquid chromatography electrospray ionization tandem mass spectrometry (LC-ESI-MS-MS) setup allowing a total run time of only 108 s for a full gradient separation. Analytes were extracted from the matrix within 30 s by turbulent flow chromatography. Subsequently, a full gradient separation was carried out on a 50X2.1 mm RP-18 column filled with 1.7 μm core-shell particles. The analytes were detected with high sensitivity by ESI-MS-MS in SRM mode. The substrate 14(15)-EpETrE eluted at a stable retention time of 96 ± 1 s and its sEH hydrolysis product 14,15-DiHETrE at 63 ± 1 s with narrow peak width (full width at half maximum height: 1.5 ± 0.1 s). The analytical performance of the method was excellent, with a limit of detection of 2 fmol on column, a linear range of over three orders of magnitude, and a negligible carry-over of 0.1% for 14,15-DiHETrE. The enzyme assay was carried out in a 96-well plate format, and near perfect sigmoidal dose-response curves were obtained for 12 concentrations of each inhibitor in only 22 min, enabling precise determination of IC(50) values. In contrast with other approaches, this method enables quantitative evaluation of potent sEHIs with picomolar potencies because only 33 pmol L(-1) sEH were used in the reaction vessel. This was demonstrated by ranking ten compounds by their activity; in the fluorescence method all yielded IC(50) ≤ 1 nmol L(-1). Comparison of 13 inhibitors with IC(50) values >1 nmol L(-1) showed a good correlation with the fluorescence method (linear correlation coefficient 0.9, slope 0.95, Spearman's rho 0.9). For individual compounds, however, up to eightfold differences in potencies between this and the fluorescence method were obtained. Therefore, enzyme assays using natural substrate, as described here, are indispensable for reliable determination of structure-activity relationships for sEH inhibition.     

The Khavinson-Shapiro conjecture and polynomial decompositions

The main result of the paper states the following: Let ψ be a polynomial in n variables. Suppose that there exists a constant C>0 such that any polynomial f has a polynomial decomposition f=ψqf+hf with Δkhf=0 and . Then . Here Δk is the kth iterate of the Laplace operator Δ. As an application, new classes of domains in Rn are identified for which the Khavinson-Shapiro conjecture holds.     

A Theory of <Emphasis Type="Italic">L</Emphasis><Superscript>1</Superscript>-Dissipative Solvers for Scalar Conservation Laws with Discontinuous Flux

We propose a general framework for the study of L ¹ contractive semigroups of solutions to conservation laws with discontinuous flux:

Unconditionally Stable Methods for Hamilton–Jacobi Equations

We present new numerical methods for constructing approximate solutions to the Cauchy problem for Hamilton–Jacobi equations of the form u_t+H(D_xu)=0. The methods are based on dimensional splitting and front tracking for solving the associated (non-strictly hyperbolic) system of conservation laws p_t+D_xH(p)=0, where p=D_xu. In particular, our methods depend heavily on a front tracking method for one-dimensional scalar conservation laws with discontinuous coefficients. The proposed methods are unconditionally stable in the sense that the time step is not limited by the space discretization and they can be viewed as “large-time-step” Godunov-type (or front tracking) methods. We present several numerical examples illustrating the main features of the proposed methods. We also compare our methods with several methods from the literature.     

Multiple single-peaked solutions of a class of semilinear Neumann problems via the category of the domain boundary

For a smooth domain with compact boundary we investigate the problem with Neumann boundary conditions, where f has superlinear but subcritical growth. Provided that is sufficiently small we show the existence of at least positive solutions with single maximum points that lie on . We replace the standard variational setting used in the case of homogeneous f by considering the restriction of the free functional to a suitable submanifold of the Sobolev Space . Received May 25, 1997 / Accepted October 3, 1997     

Constant-cutoff approach to radiative decays of hyperons: E2/M1 transition ratios

We suggest a quantum stabilization method for theSU(2) σ-model, based on the constant-cutoff limit of the cutoff quantization method developed by Balakrishnaet al., which avoids the difficulties with the usual soliton boundary conditions pointed out by Iwasaki and Ohyama. We investigate the baryon numberB=1 sector of the model and show that after the collective coordinate quantization it admits a stable soliton solution which depends on a single dimensional arbitrary constant. We then study the radiative decays ofJ ^π=3/2⁺ baryons using the constant-cutoff approach to theSU(3) collective treatment of the Skyrme model for hyperons. Thus we evaluate the widths and E2/M1 ratios, showing that there is a general qualitative agreement with the results obtained using the complete Skyrme model, as well as the nonrelativistic quark model and quenched lattice model, for the total widths.