Chaotic Expansion of Elements of the Universal Enveloping Algebra of a Lie Algebra Associated with a Quantum Stochastic Calculus

The functional Ito formula, in the form df() = f( + d ) –f(),is formulated and proved in the context of a Lie algebra L associatedwith a quantum (non-commutative) stochastic calculus. Here fis an element of the universal enveloping algebra U of L, andf() + d() – f() is given a meaning using the coproductstructure of U even though the individual terms of this expressionhave no meaning. The Ito formula is equivalent to a chaoticexpansion formula for f() which is found explicitly. 1991 MathematicsSubject Classification: primary 81S25; secondary 60H05; tertiary18B25.     

A novel approach to high-throughput quality control of parallel synthesis libraries

Combinatorial chemistry is a powerful tool to enhance drug discovery efforts in the pharmaceutical industry. One type of combinatorial chemistry, parallel synthesis, is now widely used to prepare numerous compounds of structural diversity. A novel high-throughput method for quality control of parallel synthesis libraries has been developed. The method uses flow injection MS, for proof of structure and estimation of purity, and a novel direct injection CLND technique for quantitation of amount. Following the synthesis of a small molecule library, compounds analyzed using this technique were characterized by mass spectrometry, and an accurate concentration of the compound was assessed by CLND. Characterization of one compound is completed in 60 s, allowing for up to 1000 compounds to be analyzed in a single day. The data is summarized using pass/fail criteria using internally developed software.     

Software for automating analysis of encoded combinatorial libraries

This paper describes the applications which are used to automate the analysis of encoded combinatorial libraries. Commercial packages from MDL, Oracle and Agilent are linked with application software written in C/C++, in Microsoft Access and in ChemStation macro language. Encoding correspondence lists for each of up to three synthetic steps are conveniently associated with building block lists using the first application, CodeGen. The second application Decode allows the user to identify the individual beads picked onto a 96-well plate and the pool number for each bead. The decoding chromatography data for each well is then loaded into the program. The chromatography data is used to identify the tags used in the synthesis. Along with the building block information from ISIS/Host, the building block used in each step of the synthesis can be identified. A third routine, Code-to-Structure, takes the coded library building blocks and creates the connection table in ISIS for each structure found by the decode program. For quality control of encoded library synthesis, the decoded structures on a set of beads is compared to the LC/UV/MS data for the ligand cleaved from the same bead. CAPTURE, a GlaxoSmithKline proprietary application, is used to display and analyze the decoded structures and associated mass spectral data. This application uses simple isotopic composition and electrospray ionization rule sets to predict mass spectra and judge the concordance of a structure- mass spectrum data set. An ancillary program, EIC, is used to extract predicted single ion chromatograms from the full scan LC/MS data.