Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Synthesis and anti-tetrabenazine activity of c-3 analogues of dimethyl-2-phenylmorpholines

A series of analogues of 2-phenylmorpholines with alkyl substituents at the C-3 position were synthesized for anti-tetrabenazine (anti-TBZ) testing in mice. The target compounds were prepared by reaction of (2-bromoalkyl) phenyl ketones 21a-h with the appropriate aminoalcohol 20a-b to form morpholinols 22a-h . Hydride reduction of the morpholinols gave aminodiols 23a-h which were cyclized to morpholines 6, 8, 10–12, 14–16, 18 and 19 by acid catalaysis. Compounds 7, 9, 13 and 17 were prepared by reductive formylation. The smaller straight chain substituents of 6, 8, 12 and 15 , and the beta branching of the iso-butyl group of 16 were well tolerated; anti-tetrabenazine ED_50′s were comparable to compounds 2–5 . The α-branched, N-methylated, and side chain aryl derivatives were less active.     

Determination of pentachlorophenol residues in wine and corks by solvent extraction methodology and specific gas chromatography detection

Summary A gas chromatographic methodology with selective detection is presented for the analysis in wines and corks of pentachlorophenol residues, which are suspected to be the most likely precursors of some off-flavours described in several wine samples. After derivatisation, pentachlorophenol acetate residues were monitored by electrolytic conductivity detection and/or mass spectrometric detection in the selective ion mode at m/z 264 and 266. Recoveries varied from 80 to 96% for wine samples fortified with 5 to 100 g l^–1 and from 83 to 91% for corks (fortified at 25 to 100 g kg^–1). The proposed methodology allowed for a determination limit of g l^–1 for wine and 10 g kg^–1 for corks.     

Minimalist protein design: a beta-hairpin peptide that binds ssDNA

A 28-residue beta-hairpin dimer (WKWK)2 with two Trp and two Lys residues on one face of each beta-sheet was shown to form a complex with single-stranded oligonucleotides at low micromolar concentrations. Each beta-hairpin of the dimer contains a cross-strand Trp-Trp pair in a diagonal orientation which has previously been shown to create a cleft for the intercalation of aromatic guests such as adenine (J. Am. Chem. Soc. 2003, 125, 9580). The beta-hairpin dimer binds 5-residue ssDNA sequences 5'-AAAAA-3', 5'-TTTTT-3', and 5'-CCCCC-3' in water with dissociation constants in the range of 12-30 muM. A weak energetic preference for binding to sequence 5'-AAAAA-3' was observed, which is believed to result from stronger stacking interactions between Trp and the adenine base. The interaction of 5'-AAAAA-3' with the Lys and Trp residues of the peptide was evident by NMR, and a 1:1 association was demonstrated. The recognition of an 11-residue ssDNA sequence occurred with a dissociation constant of 3 muM under near-physiological ionic strength and pH, demonstrating that the beta-hairpin dimer binds ssDNA as strongly as many naturally occurring proteins. The salt dependence of the interaction of the 11-residue oligonucleotide with the peptide dimer indicates that Trp-nucleobase stacking interactions contribute about -4 kcal/mol to recognition, which is much greater than the contribution of nonionic interactions in unstructured peptides containing Trp. Moreover, recognition of the ssDNA demonstrated reduced salt dependence relative to the corresponding duplex, resulting in selectivity for ssDNA under high salt conditions. Peptide (WKWK)2 is a relevant mimic of OB-fold (oligonucleotide/oligosaccharide-binding) proteins which bind ssDNA on the surface of a beta-sheet.     

Facility location in the presence of forbidden regions,I: Formulation and the case of Euclidean distance with one forbidden circle

A constrained form of the Weber problem is formulated in which no path is permitted to enter a prespecified forbidden region $\text{R}$ of the plane. Using the calculus of variations the shortest path between two points $\text{x}\text{,}\text{y}\text{?}\text{R}$ which does not intersect $\text{R}$ is determined. If $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is unconstrained distance, we denote the shortes distance along a feasible path by $\text{d}\text{(}\text{x}\text{y}\text{)}$. The constrained Weber problem is, then: given points $\text{x}{}_{\mathrm{j}}\text{?}\text{R}$ and positive weights w_j, j = 1,2,…,n, find a point $\text{x}\text{?}\text{R}$ such that

$\text{f(}\text{x}\text{)=}\text{Σ}\text{n}\text{j=1}\text{d(}\text{x}\text{,}\text{x}{}_{\mathrm{j}}\text{)}$

is a minimum.An algorithm is formulated for the solution of this problem when $\text{d(}\text{x}\text{,}\text{y}\text{)}$ is Euclidean distance and $\text{R}$ is a single circular region. Numerical results are presented.