Combinatorial representation

The term virtual library is used quite frequently in the literature these days. Unfortunately there is no common definition on what a virtual library really is. In the simplest case it is a database of fully enumerated structures of products that are under consideration to be made. The generation of such a virtual library involves software that maps the reaction sequence and the corresponding sets of building blocks onto a combinatorial representation (7) (see Note 4). This combinatorial representation can be partially or fully enumerated to generate product structures, which are then stored in structural databases (see Note 5). Subsequently, properties and descriptors to be used in the selection process are to be calculated. As there are limitations in terms of file size etc., such virtual libraries cannot hold more than a few million products. This makes it necessary to filter out reagents (see Subheading 1.3.) prior to construction of the virtual library. 

Mixtures containing up to several thousand distinct chemical entities are often synthesized and tested in mix-and-split combinatorial chemistry. The descriptor representation of a mixture may be approximated as the descriptor average of its individual component molecules, e.g., using atom-pair and topological torsion descriptors. 

Chemoinformatics (or cheminformatics) deals with the storage, retrieval, and analysis of chemical and biological data. Specifically, it involves the development and application of software systems for the management of combinatorial chemical projects, rational design of chemical libraries, and analysis of the obtained chemical and biological data. The major research topics of chemoinformatics involve QSAR and diversity analysis. The researchers should address several important issues. First, chemical structures should be characterized by calculable molecular descriptors that provide quantitative representation of chemical structures. Second, special measures should be developed on the basis of these descriptors in order to quantify structural similarities between pairs of molecules. Finally, adequate computational methods should be established for the efficient sampling of the huge combinatorial structural space of chemical libraries. 

Representation. The solution space is composed of discrete combinatorial alternatives of batch production schedules. For example, in the permutation flowshop problem, where the batches are assumed to be executed in the same order on each unit, there are A number of solutions, where N is the number of batches. We must find a way to compactly represent this solution space, in such a way that significant portions of the space can be characterized with respect to our objective as either poor or good without explicitly enumerating them. 

To solve the problems of representation and control, we will employ the framework of the branch-and-bound algorithm, which has been used to solve many types of combinatorial optimization problems, in chemical engineering, other domains of engineering, and a broad range of management problems. Specifically, we will use the framework proposed by Ibaraki (1978), which is characterized by the following features ... 

Theoretically it has been shown (Thayse, 1988) that the DDP formalism is closely related to a simpler form of horn clause logic, i.e., the propositional calculus. This would suggest that we could use the horn clause form to express some of the types of knowledge we are required to manipulate in combinatorial optimization problems. The explicit inclusion of state information into the representation, necessitates the shift from the simpler propositional form, to the first-order form, since we wish to parsimoniously represent properties that can be true, or take different values, in different states. By limiting the form to horn clauses, we are striving to retain the maximum simplicity of representation, whilst admitting the necessary expressive power. 

Ibaraki, T., Branch and bound procedure and state-space representation of combinatorial optimization problems. Inf. Control 36,1-27 (1978). 

Sanmartf, E., Friedler, E, Puigjaner, L., 1998. Combinatorial technique for short term scheduling of multipurpose batch plants based on schedule-graph representation. Comput. Chem. Eng., 22(Suppl.) S847-S850... 

Figure 8.15 Schematic representation of resin-bound dynamic combinatorial chemistry and structures of the family of intercalating DNA binding agents M, [54],...

Having the desired reactant lists, the chemist can now create a virtual library by enumerating the product structures in a fully combinatorial manner. Enumeration instructions are prevalidated for all PGVL registered reactions for a user-specified reaction, PGVL Hub enables enumeration via the Markush representation of the reaction scheme. Once the products are... 

Very generally, the identification of a molecule of interest by a combinatorial strategy requires (i) the random synthesis of a balanced library in which the different candidates are statistically equi-represented, (the over-representation of some compounds and the under-representation of others will bias the population and subsequently may affect the outcome of the selection) (ii) the efficient partitioning of candidates which display the desired property depends upon a carefully adjusted selection pressure combined with an effective procedure allowing the physical separation of the winners, and (iii) the identification of these winning molecules and their defined synthesis at high yield and low cost for further use. This means either a very sensitive analytical method to determine the chemical structure of the selected molecules must be used... 

The necessity of introducing a combinatorial contribution to the chemical potential is a result of the neglect of size effects in the thermodynamics of pairwise interacting surface models. It also appears in lattice models that do not allow for a realistic representation of molecular sizes and are often simplified to models of equally sized lattice objects. The task of the combinatorial contribution is to represent the chemical potential of virtually homogeneous interacting objects of different size in 1 mol of a liquid mixture of a given composition with respect to the size and shape of the molecules. 

Figure 7.2 Schematic representation of target-tempiated in situ dynamic combinatorial chemistry.

The Oriented Substituent Pharmacophore PRopErtY Space (OSPPREYS) approach, introduced by Martin and Hoeffel [6], is in software terms an extension of CCG s MOE package, written using SVL. The 3D oriented substituent pharmacophores are aimed towards better representation of diversity and similarity in combinatorial libraries in the 3D pharmacophore space. Combinatorial library design often operates only on substituents rather than on the final products as the complications related to the conformational coverage in the 3D space and the scaffold dependency limit the product-based approaches to smaller libraries. The 3D oriented substituent pharmacophores add two more points and the corresponding distances to each substituent pharmacophore which represent the relationship of the substituents in the product with only little additional information. The fingerprints permit the creation of property space by multidimensional scaling (MDS) and, since scaffold independent, can be stored separately and applied to different libraries [6],... 

A lot of effort has been invested over the past 20 years in the optimization of the different steps of pharmacophore generation molecular editing and 3D representation, combinatorial enumeration, conformational expansion and pharmacophore perception methodologies for small drug-like data sets. However, we note that today there are still some areas with potential for improvement in the field of ligand-based pharmacophore modeling ... 

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