In product-based selection, the properties of the resulting product molecules are taken into account when selecting the monomers. Having enumerated the virtual library any of the subset selection methods introduced in Chapter 6 could then in principle be applied. This process is generally referred to as cherry-picking but it is synthetically inefficient insofar as combinatorial synthesis is concerned. Synthetic efficiency is maximised by taking the combinatorial constraint into account and selecting a combinatorial subset such that every reagent selected at each point of variation reacts with every other reagent selected at the other positions.
Product-based selection is much more computationally demanding than monomer-based selection. The number of combinatorial subsets in this case is given by the following equation:
where R is the number of positions of variability and there are ni monomers to be selected from a possible Ni at each substitution position. Thus, there are almost 1040 different 10 x 10 x 10 libraries that could be synthesised from a 100 x 100 x 100 virtual library. The selection of combinatorial subsets has been tackled using optimisation techniques such as simulated annealing and genetic algorithms as will be discussed in detail below.
Despite the greater computational complexity of performing product-based selection compared to monomer-based selection it can be a more effective method when the aim is to optimise the properties of a library as a whole, such as diversity or the distribution of physicochemical properties. For example, it has been shown that more diverse libraries result if selection is performed in product-space rather than in monomer-space [Gillet et al. 1997; Jamois et al. 2000]. In addition, product-based selection is usually more appropriate for focussed libraries which require consideration of the properties of the product structures.
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