Combinatorial subset selection

The chapter begins with a discussion of similarity and diversity measures and how they can be applied in a virtual screening context. The various computational filters in use are also discussed. The rest of the chapter is concerned with different approaches to combinatorial library design, beginning with reagent-based methods followed by product-based approaches of cherry picking and combinatorial subset selection. Finally, approaches to designing libraries optimized on multiple properties simultaneously are discussed. 

Taking account of the combinatorial constraint requires methods that are able to select a combinatorial subset directly from within product space, as illustrated in Fig. 4b. Combinatorial subset selection represents an enormous search space and is typically implemented using an optimization technique such as a GA or SA. For example, there are ... 

It is relatively easy to include additional library properties such as druglike physicochemical property profiles in the product-based approaches to combinatorial subset selection. For example, several groups have handled multiobjectives through the use of weighted-sum fitness functions. In the SELECT program [89], multiple objectives are handled via a fitness function such as the one shown below ... 

Combinatorial chemistry is applying a multitude of approaches such as diversity libraries, dirig-like libraries and combinatorial subset selection. 

The ability of MoSELEGT to simultaneously optimize molecular weight and diversity was tested in the selection of 30 x 30 combinatorial subsets of a 10000-member virtual amide library. It was shown that as the selection progressed, there was an improvement in both the molecular weight and diversity, as well as a spread of nondominated solutions across the Pareto frontier. The 17 nondominated solutions found after 5000 iterations emphasized the competing nature of these two objectives - those with lower... 

In product-based selection, the properties of the resulting product molecules are taken into account when selecting the reactants. Typically this is done by enumerating the entire virtual library that could potentially be made. Any of the subset selection methods described previously could be used to select a diverse subset of products, however the resulting subset is very unlikely to represent a combinatorial subset. This process is known as cherry-picking and is synthetically inefficient as far as combinatorial synthesis is concerned. Synthetic efficiency is maximized by taking the combinatorial... 

Library-based methods attempt to optimise a combinatorial subset directly. Although the computational complexity of the subset selection problem is reduced owing to the combinatorial constraint, the fitness functions employed in library-based methods are more demanding than those used in molecule-based... 

Product-based selection is much more computationally demanding than reagent-based selection. Typically, it requires the computational enumeration of the full virtual combinatorial library and calculation of the descriptors for all possible products, prior to the application of a subset selection method. Consider a three-component reaction with 100 reagents available at each substituent position and assume that the aim is to build a 10 x 10 x 10 combinatorial library. In reagent-based selection, this requires the calculation of descriptors for 300 compounds (100 + 100 + 100). In product-based design, however, the full library of 1 million compounds (100 x 100 x 100) must be enumerated and descriptors must be calculated for each product molecule. 

For any synthetic scheme, the key issue in combinatorial library design is monomer selection, the objective of which is to identify those monomers which when combined together provide the optimal combinatorial library. By optimal we mean that Uhrary which best meets the prescribed objectives it might be the most diverse, have the maximum number of molecules that could fit a 3D pharmacophore or a protein binding site, best match a particular distribution of some physicochemical property, or some combination of these or other criteria. An important consideration when designing a combinatorial Uhrary is the subset selection constraint. In a true combinatorial Ubrary of the form A x B x C, every molecule from the set of reagents A reacts with every molecule from B and every molecule from C to generate n xn x c product structures, where are the numbers of... 

Figure 14.7 An illustration of library optimisation and selection using a multiobjective Pareto algorithm. The virtual library of 20000 compounds has a large number of compounds similar to existing molecules in the GSK collection, and the library is not structurally diverse, containing many close analogues. Selections of a 1920 combinatorial subset yield multiple solutions that have better complementarity to the GSK collection and are not made up of large numbers of close analogues. However, each library has certain advantages, as they are from the non-dominated set of solutions.

Evaluation of Alternative Subsets Selected from Reagent Building Block Libraries for Combinatorial Chemistry. 

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