On the convergence of multipoint Padé-type approximants and quadrature formulas associated with the unit circle

We study the convergence of rational interpolants with prescribed poles on the unit circle to the Herglotz-Riesz transform of a complex measure supported on [–, ]. As a consequence, quadrature formulas arise which integrate exactly certain rational functions. Estimates of the rate of convergence of these quadrature formulas are also included.This research was performed as part of the European project ROLLS under contract CHRX-CT93-0416.     

Reaction mechanism of soluble epoxide hydrolase: insights from molecular dynamics simulations

Molecular dynamics simulations have been performed to gain insights into the catalytic mechanism of the hydrolysis of epoxides to vicinal diols by soluble epoxide hydrolase (sEH). The binding of a substrate, 1S,2S-trans-methylstyrene oxide, was studied in two conformations in the active site of the enzyme. It was found that only one is likely to be found in the active enzyme. In the preferred conformation the phenyl group of the substrate is pi-sandwiched between two aromatic residues, Tyr381 and His523, whereas the other conformation is pi-stacked with only one aromatic residue, Trp334. Two simulations were carried out to 1 ns for each conformation to evaluate the protonation state of active site residue His523. It was found that a protonated histidine is essential for keeping the active site from being disrupted. Long time scale, 4 ns, molecular dynamics simulation was done for the structure with the most likely combination of binding conformation and protonation state of His523. Near Attack Conformers (NACs) are present 5.3% of the time and nucleophilic attack on either epoxide carbon atom, approximately 75% on C(1) and approximately 25% on C(2), is found. A maximum of one hydrogen bond between the epoxide oxygen and either of the active site tyrosines, Tyr465 and Tyr381, is present, in agreement with experimental mutagenesis results that reveal a slight loss in activity if one tyrosine is mutated and essential loss of all activity upon double mutation of the two tyrosines in question. It was found that a hydrogen bond from Tyr465 to the substrate oxygen is essential for controlling the regioselectivity of the reaction. Furthermore, a relationship between the presence of this hydrogen bond and the separation of reactants was found. Two groups of amino acid segments were identified each as moving collectively. Furthermore, an overall anti-correlation was found between the movements of these two individually collectively moving groups, made up by parts of the cap-region, including the two tyrosines, and the site of the catalytic triad, respectively. This overall anti-correlated collective domain motion is, perhaps, involved in the conversion of E.NAC to E.TS.     

Theory for migration of ions in capillary electrochromatography

The fundamental migration theories for chromatography and electrophoresis are both based on a solution of the mass balance equation. The corresponding analysis for an electrochromatographic system has previously been published and is analysed in more detail in this paper. It is shown that the resulting equation, Eq. (8) in this paper, is in agreement with both electrophoretic and chromatographic theories and that when these migration modes are mixed a complicated migration behaviour emerge. These complications arise, if the comparison is done with electrophoretic theory, because the presence of the stationary phase creates a number of new restrictions on the system (electroneutrality on the stationary phase and simultaneous equilibrium for all components between the eluent and stationary phase). From a mathematical point of view, these restrictions make it difficult for the system to satisfy the coherence condition and this in turn may lead to an anomalous behaviour. To minimise the possibility for a complicated behaviour it is advisable to avoid too much mixing of the two migration mechanisms and/or to match the mobilities of the ionic components in the eluent phase with the mobility of the analyte ion.