Spread design

Spread design objective select the maximally dissimilar subset of molecules. This requires maximizing the distance of points within the subset from each other. One analogy for this is electron repulsion. 

The objective of a spread design is to identify a subset of molecules in which the molecules are as dissimilar as possible under a given similarity metric. For a given metric to measure the similarity of a subset, all subsets of size k (plus any molecules previously selected) could be evaluated and the subset that produces the lowest similarity measure chosen. In practice, simple non-optimal sequential algorithms are often used to approximate the maximally dissimilar subset two such algorithms are described below. 

Figure 3. Spread design for fictitious example. (Reproduced from Higgs et al., 1997 with permission.)...

Although not shown in the figures, a random selection is often considered the baseline method of subset selection. Random sampling typically selects many molecules from the dense clusters, and several molecules near the previously selected molecules. Spread designs select the most diverse subset of molecules... 

Figure 6. Combinatorial libraries comparison cumulative number of molecules selected versus the rank of the spread design for each of 10 random orderings of molecules within (a) Library A (b) Library B.

This example shows how spread designs can be used to solve practical problems. There is always a descriptor selection problem, as chemists continue to invent new molecular descriptors. Which should be used Which molecular similarity measure performs best Controlled experiments are expensive. Simulation can be used as a guide. 

Selection of test items so that they are as dissimilar a possible to each other is accomplished by choosing items which are projected far from each other and on the periphery of the plot. Such designs are useful for answering the question of whether or not the properties have an influence. A maximum spread design wa used to determine whether modification of the solvent would increase the endo/exo stereoselectivity in the reduction of an enamine from camphor. The answer was negative [17 a],... 

The reaction showed promising stereoselectivity when it was run without any solvent. As the reaction might involve charged species, it was quite natural to examine whether or not the selectivity could be increased in the presence of a solvent. The solvents used to investigate this were selected according to a "maximum spread" design in their principal properties, see Fig. 16.2. 

The first example of a "uniform spread" design in the study of solvent varation was applied to the Willgerodt-Kindler reaction.[3] It is not reproduced here, since it is very similar to the above example of amine variation. A very clear application of the principle of "uniform spread" is given in an example on the Fischer indole synthesis in the next chapter. 

A similar problem is encountered when a promising solvent has been found in a screening experiment, e.g. by a "uniform spread" design. It is reasonable to assume that the preferred solvent has properties which are similar to those of a promising candidate. The next step is then to explore the solvents projected in the vicinity of the promising candidate in the score plot. This can be accomplished by a small "uniform spread" selection around the winning candidate, or by a simplex search described below. 

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