A brief survey of symmetry in mathematics

This paper presents a brief survey of the idea of symmetry in mathematics, as exemplified by some particular developments in algebra, differential equations, topology, and number theory.

Dendrimer-supported combinatorial chemistry.

A new methodology for the construction of combinatorial libraries is described. The approach, termed dendrimer-supported combinatorial chemistry (DCC), centers on the use of dendrimers as soluble supports. Salient features of DCC include solution phase chemistry, homogeneous purification, routine characterization of intermediates, and high support loadings. To demonstrate the feasibility of DCC, single compounds and a small combinatorial library were prepared via the Fischer indole synthesis. Excellent product yields and purities were obtained, and dendrimer-protected intermediates could be routinely analyzed by 1H and 13C NMR and by mass spectrometry. The results indicate that DCC is a general and efficient strategy for the generation of combinatorial libraries.

Combinatorial control of muscle development by basic helix-loop-helix and MADS-box transcription factors.

Members of the MyoD family of muscle-specific basic helix-loop-helix (bHLH) proteins function within a genetic pathway to control skeletal muscle development. Mutational analyses of these factors suggested that their DNA binding domains mediated interaction with a coregulator required for activation of muscle-specific transcription. Members of the myocyte enhancer binding factor 2 (MEF2) family of MADS-box proteins are expressed at high levels in muscle and neural cells and at lower levels in several other cell types. MEF2 factors are unable to activate muscle gene expression alone, but they potentiate the transcriptional activity of myogenic bHLH proteins. This potentiation appears to be mediated by direct interactions between the DNA binding domains of these different types of transcription factors. Biochemical and genetic evidence suggests that MEF2 factors are the coregulators for myogenic bHLH proteins. The presence of MEF2 and cell-specific bHLH proteins in other cell types raises the possibility that these proteins may also cooperate to regulate other programs of cell-specific gene expression. We present a model to account for such cooperative interactions.

Enzyme-mediated spatial segregation on individual polymeric support beads: application to generation and screening of encoded combinatorial libraries.

Proteolysis of short N alpha-protected peptide substrates bound to polyoxyethylene-polystyrene beads releases selectively free amino sites in the enzyme-accessible "surface" area. The substantial majority of functional sites in the "interior" of the polymeric support are not reached by the enzyme and remain uncleaved (protected). Subsequent synthesis with two classes of orthogonal protecting groups-N alpha-tert-butyloxycarbonyl (Boc) and N alpha-9-fluorenylmethyloxy-carbonyl (Fmoc)-allows generation of two structures on the same bead. The surface structure is available for receptor interactions, whereas the corresponding interior structure is used for coding. Coding structures are usually readily sequenceable peptides. This "shaving" methodology was illustrated by the preparation of a peptide-encoded model peptide combinatorial library containing 1.0 x 10(5) members at approximately 6-fold degeneracy. From this single library, good ligands were selected for three different receptors: anti-beta-endorphin anti-body, streptavidin, and thrombin, and the binding structures were deduced correctly by sequencing the coding peptides present on the same beads.

Exploring the active site of chorismate mutase by combinatorial mutagenesis and selection: the importance of electrostatic catalysis.

Chorismate mutase (EC 5.4.99.5) catalyzes the intramolecular rearrangement of chorismate to prephenate. Arg-90 in the active site of the enzyme from Bacillus subtilis is in close proximity to the substrate's ether oxygen and may contribute to efficient catalysis by stabilizing the presumed dipolar transition state that would result upon scission of the C--O bond. To test this idea, we have developed a novel complementation system for chorismate mutase activity in Escherichia coli by reengineering parts of the aromatic amino acid biosynthetic pathway. The codon for Arg-90 was randomized, alone and in combination with that for Cys-88, and active clones were selected. The results show that a positively charged residue either at position 88 (Lys) or 90 (Arg or Lys) is essential. Our data provide strong support for the hypothesis that the positive charge is required for stabilization of the transition state of the enzymatic chorismate rearrangement. The new selection system, in conjunction with combinatorial mutagenesis, renders the mechanism of the natural enzyme(s) accessible to further exploration and opens avenues for the improvement of first generation catalytic antibodies with chorismate mutase activity.

Sequence specificity of triplex DNA formation: Analysis by a combinatorial approach, restriction endonuclease protection selection and amplification.

We have devised a combinatorial method, restriction endonuclease protection selection and amplification (REPSA), to identify consensus ligand binding sequences in DNA. In this technique, cleavage by a type IIS restriction endonuclease (an enzyme that cleaves DNA at a site distal from its recognition sequence) is prevented by a bound ligand while unbound DNA is cleaved. Since the selection step of REPSA is performed in solution under mild conditions, this approach is amenable to the investigation of ligand-DNA complexes that are either insufficiently stable or not readily separable by other methods. Here we report the use of REPSA to identify the consensus duplex DNA sequence recognized by a G/T-rich oligodeoxyribonucleotide under conditions favoring purine-motif triple-helix formation. Analysis of 47 sequences indicated that recognition between 13 bases on the oligonucleotide 3' end and the duplex DNA was sufficient for triplex formation and indicated the possible existence of a new base triplet, G.AT. This information should help identify appropriate target sequences for purine-motif triplex formation and demonstrates the power of REPSA for investigating ligand-DNA interactions.

Hyperplane arrangements, interval orders, and trees.

A hyperplane arrangement is a finite set of hyperplanes in a real affine space. An especially important arrangement is the braid arrangement, which is the set of all hyperplanes xi - xj = 1, 1 combinatorial properties of certain deformations of the braid arrangement are surveyed. In particular, there are unexpected connections with the theory of interval orders and with the enumeration of trees. For instance, the number of labeled interval orders that can be obtained from n intervals I1,..., In of generic lengths is counted. There is also discussed an arrangement due to N. Linial whose number of regions is the number of alternating (or intransitive) trees, as defined by Gelfand, Graev, and Postnikov [Gelfand, I. M., Graev, M. I., and Postnikov, A. (1995), preprint]. Finally, a refinement is given, related to counting labeled trees by number of inversions, of a result of Shi [Shi, J.-Y. (1986), Lecture Notes in Mathematics, no. 1179, Springer-Verlag] that a certain deformation of the braid arrangement has (n + 1)n-1 regions.

Identification of a hexapeptide inhibitor of the human immunodeficiency virus integrase protein by using a combinatorial chemical library.

Integration of human immunodeficiency virus (HIV) DNA into the human genome requires the virus-encoded integrase (IN) protein, and therefore the IN protein is a suitable target for antiviral strategies. To find a potent HIV IN inhibitor, we screened a "synthetic peptide combinatorial library." We identified a hexapeptide with the sequence HCKFWW that inhibits IN-mediated 3'-processing and integration with an IC50 of 2 microM. The peptide is active on IN proteins from other retroviruses such as HIV-2, feline immunodeficiency virus, and Moloney murine leukemia virus, supporting the notion that a conserved region of IN is targeted. The hexapeptide was also tested in the disintegration reaction. This phosphoryl-transfer reaction can be carried out by the catalytic core of IN alone, and the peptide HCKFWW was found to inhibit this reaction, suggesting that the hexapeptide acts at or near the catalytic site of IN. Identification of an IN hexapeptide inhibitor provides proof of concept for the approach, and, moreover, this peptide may be useful for structure-function analysis of IN.

Sample size determination in combinatorial chemistry.

Combinatorial chemistry is gaining wide appeal as a technique for generating molecular diversity. Among the many combinatorial protocols, the split/recombine method is quite popular and particularly efficient at generating large libraries of compounds. In this process, polymer beads are equally divided into a series of pools and each pool is treated with a unique fragment; then the beads are recombined, mixed to uniformity, and redivided equally into a new series of pools for the subsequent couplings. The deviation from the ideal equimolar distribution of the final products is assessed by a special overall relative error, which is shown to be related to the Pearson statistic. Although the split/recombine sampling scheme is quite different from those used in analysis of categorical data, the Pearson statistic is shown to still follow a chi2 distribution. This result allows us to derive the required number of beads such that, with 99% confidence, the overall relative error is controlled to be less than a pregiven tolerable limit L1. In this paper, we also discuss another criterion, which determines the required number of beads so that, with 99% confidence, all individual relative errors are controlled to be less than a pregiven tolerable limit L2 (0 < L2 < 1).

Liquid-phase combinatorial synthesis.

A concept termed liquid-phase combinatorial synthesis (LPCS) is described. The central feature of this methodology is that it combines the advantages that classic organic synthesis in solution offers with those that solid-phase synthesis can provide, through the application of a linear homogeneous polymer. To validate this concept two libraries were prepared, one of peptide and the second of nonpeptide origin. The peptide-based library was synthesized by a recursive deconvolution strategy [Erb, E., Janda, K. D. & Brenner, S. (1994) Proc. Natl. Acad. Sci. USA 91, 11422-11426] and several ligands were found within this library to bind a monoclonal antibody elicited against beta-endorphin. The non-peptide molecules synthesized were arylsulfonamides, a class of compounds of known clinical bactericidal efficacy. The results indicate that the reaction scope of LPCS should be general, and its value to multiple, high-throughput screening assays could be of particular merit, since multimilligram quantities of each library member can readily be attained.

A paradigm for drug discovery employing encoded combinatorial libraries.

Very large combinatorial libraries of small molecules on solid supports can now be synthesized and each library element can be identified after synthesis by using chemical tags. These tag-encoded libraries are potentially useful in drug discovery, and, to test this utility directly, we have targeted carbonic anhydrase (carbonate dehydratase; carbonate hydro-lyase, EC 4.2.1.1) as a model. Two libraries consisting of a total of 7870 members were synthesized, and structure-activity relationships based on the structures predicted by the tags were derived. Subsequently, an active representative of each library was resynthesized (2-[N-(4-sulfamoylbenzoyl)-4'-aminocyclohexanespiro]-4-oxo-7 -hydroxy- 2,3-dihydrobenzopyran and [N-(4-sulfamoylbenzoyl)-L-leucyl]piperidine-3-carboxylic acid) and these compounds were shown to have nanomolar dissociation constants (15 and 4 nM, respectively). In addition, a focused sublibrary of 217 sulfamoylbenzamides was synthesized and revealed a clear, testable structure-activity relationship describing isozyme-selective carbonic anhydrase inhibitors.

Library of libraries: approach to synthetic combinatorial library design and screening of "pharmacophore" motifs.

Construction of synthetic combinatorial libraries is described that allows for the generation of a library of motifs rather than a library of compounds. Peptide libraries based on this strategy were synthesized and screened with model targets streptavidin and anti-beta-endorphin antibody. The screens resulted in observation of expected motifs providing evidence of the effectiveness of the suggested approach.

Combinatorial association and abundance of components of interferon-stimulated gene factor 3 dictate the selectivity of interferon responses.

Genes containing the interferon-stimulated response element (ISRE) enhancer have been characterized as transcriptionally responsive primarily to type I interferons (IFN alpha/beta). Induction is due to activation of a multimeric transcription factor, interferon-stimulated gene factor 3 (ISGF3), which is activated by IFN alpha/beta but not by IFN gamma. We found that ISRE-containing genes were induced by IFN gamma as well as by IFN alpha in Vero cells. The IFN gamma response was dependent on the ISRE and was accentuated by preexposure of cells to IFN alpha, a treatment that increases the abundance of ISGF3 components. Overexpression of ISGF3 polypeptides showed that the IFN gamma response depended on the DNA-binding protein ISGF3 gamma (p48) as well as on the 91-kDa protein STAT91 (Stat1 alpha). The transcriptional response to IFN alpha required the 113-kDa protein STAT113 (Stat2) in addition to STAT91 and p48. Mutant fibrosarcoma cells deficient in each component of ISGF3 were used to confirm that IFN gamma induction of an ISRE reporter required p48 and STAT91, but not STAT113. A complex containing p48 and phosphorylated STAT91 but lacking STAT113 bound the ISRE in vitro. IFN gamma-induced activation of this complex, preferentially formed at high concentrations of p48 and STAT91, may explain some of the overlapping responses to IFN alpha and IFN gamma.