Combinatorial approach to multi-substituted 1,4-Benzodiazepines as novel non-peptide CCK-antagonists

For the drug discovery process, a library of 168 multisubstituted 1,4-benzodiazepines were prepared by a 5-step solid phase combinatorial approach. Substituents were varied in the 3,5, 7 and 8-position on the benzodiazepine scaffold. The combinatorial library was evaluated in a CCK radiolabelled binding assay and CCKA (alimentary) and CCKB (brain) selective lead structures were discovered. The template of CCKA selective 1,4-benzodiazepin-2-ones bearing the tryptophan moiety was chemically modified by selective alkylation and acylation reactions. These studies provided a series of Asperlicin naturally analogues. The fully optimised Asperlicin related compound possessed a similar CCKA activity as the natural occuring compound. 3-Alkylated 1,4-benzodiazepines with selectivity towards the CCKB receptor subtype were optimised on A) the lipophilic side chain and B) the 2-aminophenyl-ketone moiety, together with some stereochemical changes. A C3 unit in the 3-position of 1,4-benzodiazepines possessed a CCKB activity within the nanomolar range. Further SAR optimisation on the N1-position by selective alkylation resulted in an improved CCKB binding with potentially decreased activity on the GABAA/benzodiazepine receptor complex. The in vivo studies revealed two N1-alkylated compounds containing unsaturated alkyl groups with anxiolytic properties. Alternative chemical approaches have been developed, including a route that is suitable for scale up of the desired target molecule in order to provide sufficient quantities for further in vivo evaluation.

Solid-phase combinatorial chemistry and scintillation proximity assays

The Scintillation Proximity Assay (SPA) is a method that is frequently used to detect and quantify the strength of intermolecular interactions between a biological receptor and ligand molecule in aqueous media. This thesis describes the synthesis of scintillant-tagged-compounds for application in a novel cell-based SPA. A series of 4-functianlised-2,5-diphenyloxazole molecules were synthesised. These 4-functionalised-2,5-diphenyloxazoles were evaluated by Sense Proteomic Ltd. Accordingly, the molecules were evaluated for the ability to scintillate in the presence of ionising radiation. In addition, the molecules were incorporated into liposomal preparations which were subsequently evaluated for the ability to scintillate in the presence of ionising radiation. The optimal liposomal preparation was introduced into the membrane of HeLa cells that were used successfully in a cell-based SPA to detect and quantify the uptake of [14C]methionine. This thesis also describes the synthesis and subsequent polymerisation of novel poly(oxyethylene glycol)-based monomers to form a series of new polymer supports. These Poly(oxyethylene glycol)-polymer (POP) supports were evaluated for the ability to swell and mass-uptake in a variety of solvents, demonstrating that POP-supports exhibit enhanced solvent compatibilities over several commercial resins. The utility of POP-supports in solid-phase synthesis was also demonstrated successfully. The incorporation of (4’-vinyl)-4-benzyl-2,5-diphenyloxazole in varying mole percentage into the monomer composition resulted in the production of chemically functionalised scintillant-containing poly(oxyethylene glycol) polymer (POP-Sc) supports. These materials are compatible with both aqueous and organic solvents and scintillate efficiently in the presence of ionising radiation. The utility of POP-Sc supports in solid-phase synthesis and subsequent in-situ SPA to detect and quantify, in real-time, the kinetic progress of a solid-phase reaction was exemplified successfully.In addition, POP-Sc supports were used successfully both in solid-phase combinatorial synthesis of a peptide nucleic acid (PNA)-library and subsequent screening of this library for the ability to hybridise with DNA, which was labelled with a suitable radio-isotape. This data was used to identify the dependence of the number and position of complimentary codon pairs upon the extent of hybridisation. Finally, a further SPA was used to demonstrate the excellent compatibility of POP-Sc supports for use in the detection and quantification of enzyme assays conducted within the matrix of the POP-Sc support.

Novel anti-bacterials against MRSA:Synthesis of focussed combinatorial libraries of tri-substituted 2(5H)-furanones

Mucobromic and mucochloric acid were used as building blocks for the construction of a chemical combinatorial library of 3,4,5-trisubstituted 2(5H)-furanones. With these 2 butenolide building blocks, and eight alcohols a sublibrary of 16 dihalogenated 5-alkoxy-2(5H)-furanones was prepared. This sublibrary of 5-alkoxylated furanones was reacted with 16 amines generating a full size focussed combinatorial library of 256 individual compounds. This three dimensional combinatorial library of 3-halogen-4-amino-5-alkoxy-2(5H)-furanones was prepared around the benzimidazolyl furanone lead structure by applying a solution phase combinatorial chemistry concept. Typical representatives of the library were purified and fully characterized and one x-ray structures was recorded, additionally. The 3-bromo-4-benzimizazolyl-5-methoxy-2(5H)furanone, Br-A-l, showed an MIC of 8 μg/ml against the multiresistant Staphylococcus aureus ( MRSA). © 2006 Bentham Science Publishers Ltd.

Vector Combinatorial Problems in a Space of Combinations with Linear Fractional Functions of Criteria

The paper considers vector discrete optimization problem with linear fractional functions of criteria on a feasible set that has combinatorial properties of combinations. Structural properties of a feasible solution domain and of Pareto–optimal (efficient), weakly efficient, strictly efficient solution sets are examined. A relation between vector optimization problems on a combinatorial set of combinations and on a continuous feasible set is determined. One possible approach is proposed in order to solve a multicriteria combinatorial problem with linear- fractional functions of criteria on a set of combinations.

Constructing a Canonical form of a Matrix in Several Problems about Combinatorial Designs

Partially supported by the Bulgarian Science Fund contract with TU Varna, No 487.

M-Solid Subvarieties of some Varieties of Commutative Semigroups

∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.

Randomized Parallelization – a New Method for Solving Hard Combinatorial Problems

A new method for solving some hard combinatorial optimization problems is suggested, admitting a certain reformulation. Considering such a problem, several different similar problems are prepared which have the same set of solutions. They are solved on computer in parallel until one of them will be solved, and that solution is accepted. Notwithstanding the evident overhead, the whole run-time could be significantly reduced due to dispersion of velocities of combinatorial search in regarded cases. The efficiency of this approach is investigated on the concrete problem of finding short solutions of non-deterministic system of linear logical equations.

Lagrangean Approximation for Combinatorial Inverse Problems

Various combinatorial problems are effectively modelled in terms of (0,1) matrices. Origins are coming from n-cube geometry, hypergraph theory, inverse tomography problems, or directly from different models of application problems. Basically these problems are NP-complete. The paper considers a set of such problems and introduces approximation algorithms for their solutions applying Lagragean relaxation and related set of techniques.

Representing Equivalence Problems for Combinatorial Objects

Methods for representing equivalence problems of various combinatorial objects as graphs or binary matrices are considered. Such representations can be used for isomorphism testing in classification or generation algorithms. Often it is easier to consider a graph or a binary matrix isomorphism problem than to implement heavy algorithms depending especially on particular combinatorial objects. Moreover, there already exist well tested algorithms for the graph isomorphism problem (nauty) and the binary matrix isomorphism problem as well (Q-Extension). ACM Computing Classification System (1998): F.2.1, G.4.

On Nilpotent Subsemigroups in some Matrix Semigroups

2000 Mathematics Subject Classification: 20M20, 20M10.

Orbits of semigroups of truncated convolution operators

We prove that a semigroup generated by finitely many truncated convolution operators on $L_p[0, 1]$ with 1 ≤ p < ∞ is non-supercyclic. On the other hand, there is a truncated convolution operator, which possesses irregular vectors.

GRASP and statistical bounds for heuristic solutions to combinatorial problems

The quality of a heuristic solution to a NP-hard combinatorial problem is hard to assess. A few studies have advocated and tested statistical bounds as a method for assessment. These studies indicate that statistical bounds are superior to the more widely known and used deterministic bounds. However, the previous studies have been limited to a few metaheuristics and combinatorial problems and, hence, the general performance of statistical bounds in combinatorial optimization remains an open question. This work complements the existing literature on statistical bounds by testing them on the metaheuristic Greedy Randomized Adaptive Search Procedures (GRASP) and four combinatorial problems. Our findings confirm previous results that statistical bounds are reliable for the p-median problem, while we note that they also seem reliable for the set covering problem. For the quadratic assignment problem, the statistical bounds has previously been found reliable when obtained from the Genetic algorithm whereas in this work they found less reliable. Finally, we provide statistical bounds to four 2-path network design problem instances for which the optimum is currently unknown.

On the extension complexity of combinatorial polytopes

In this paper we extend recent results of Fiorini et al. on the extension complexity of the cut polytope and related polyhedra. We first describe a lifting argument to show exponential extension complexity for a number of NP-complete problems including subset-sum and three dimensional matching. We then obtain a relationship between the extension complexity of the cut polytope of a graph and that of its graph minors. Using this we are able to show exponential extension complexity for the cut polytope of a large number of graphs, including those used in quantum information and suspensions of cubic planar graphs.

Climbing Combinatorial Fitness Landscapes

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