Metrics diversity

A diversity metric is a function to aid the quantification of the diversity of a set of compounds in some predefined chemical space. Diversity metrics fall into three main classes (1) Distance-based methods, which express diversity as a function of the pairwise molecular dissimilarities defined through measurement. (2) Cell-based methods, which define diversity in terms of occupancy of a finite number of cells that represent disjoint regions of chemical space. (3) Variance-based methods, which quantify diversity based on the degree of correlation between a compound s important features. 

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W., Mills, J. E., Withka, J. M. (2010) Design of a multi-purpose fragment screening library using molecular complexity and orthogonal diversity metrics. / Comput-Aided Mol Des. Manuscript in preparation. 

The diversity of a library of compounds denotes the degree of heterogeneity, structural range or dissimilarity within the set of compounds. A number of different diversity metrics have been suggested and all are based, either directly or indirectly, on the concept of intermolecular similarity or distance. Determining the (dis)similarity between two molecules requires firstly that the molecules are represented by appropriate structural descriptors and secondly that a quantitative method of determining the degree of resemblance between the two sets of descriptors exists. 

Many different structural descriptors have been developed for similarity searching in chemical databases [4] including 2D fragment based descriptors, 3D descriptors, and descriptors that are based on the physical properties of molecules. More recently, attention has focused on diversity studies and many of the descriptors applied in similarity searching are now being applied in diversity studies. Structural descriptors are basically numerical representations of structures that allow pairwise (dis)similarities between structures to be measured through the use of similarity coefficients. Many diversity metrics have been devised that are based on calculating structural (dis)similarities, some of these are described below. 

The diversity metric can then be the distance to the nearest object, or the degree of overlap between the two distributions. The second metric has to be calculated on the fly, as it is dependent on the membership of the distribution, which will vary according to which library subset is selected. Diversifying metrics based on molecular properties have been used to cluster corporate databases [34], and so are available to balance out the representative metric. 

This section discusses the different strategies used to select a subset of the library. It should be remembered that the best subset selection is neither arbitrarily nor maximally diverse [49], because we cannot guarantee a direct and strong link between the SAR and the diversity metrics used. 

Some descriptors are best described by diversity metrics that focus on the distance between objects. The precise functional form of the metric varies, but a useful example is ... 

The dimensionality of chemical structure space exceeds that of known biological functional space. The dimensionality of biological functional space has increased in recent years due to the discovery of a multitude of genes, largely from the Human Genome Project. This chapter, however, will focus on chemical diversity rather than functional diversity. Quantification of chemical diversity involves two areas first, the predefmition of a chemical space, accomplished by selection of a diversity metric and a compound representation (i.e., molecular descriptors) and second, a rational subset selection, or classification, method dependent on efficient dimensionality reduction. Here, we describe these methods, prerequisites for a definition... 

The most intuitive cell-based diversity metric is simply the number of cells occupied by a design defined in (11) where 5, is one if the ith cell is occupied and zero if it is not, M the total number of cells. 

CONFORT performs an exhaustive conformational analysis of a molecule [71]. Two different search modes either generate a user-defined number of conformations, or output a maximally diverse set of conformations, which was used in this study. The diversity metric is based on interconformational distances that circumvent the generation of duplicate structures. The conformations are relaxed and optimized by applying only internal coordinates and analytic gradients and by the Tripos force field package. 

Several diversity and space coverage measurements have also been considered in the combinatorial optimization process (15). Diversity and space coverage can be evaluated using a number of cell-based methods. These methods, implemented as diversity metrics (23), evaluate how much of the space occupied by the complete library is filled by the subset. For example, the cell-based fraction metric attempts to select one compound from each cell in order to cover as many cells as possible. However, owing to the combinatorial constraint, the objective to cover all occupied cells can seldom be achieved. The cell-based Chi metric attempts to level out the distribution so as to provide an even allocation of compounds to cells. Cell-based entropy and cell-based density metrics attempt to select more than one compound from the most populated cells, in order to respect the level of occupancy of each cell. The following metrics can be used as target functions in the combinatorial optimization process ... 

These numbers are so vast that, even with the most optimistic projections of combinatorial synthesis capabilities and optimum chemical diversity metrics, only a minute fraction of this chemical space could conceivably be explored by... 

Although their methods were similar, the motivations of the two groups appear to be rather different. Hassan et al. wanted to compare the performance of different diversity metrics, while Agrafiotis was interested in a much more general method that could encode any desirable selection criterion (similarity, predicted activity, cost and availability of starting materials, reaction block design, etc.) and would allow... 

Lin [58] has proposed a diversity metric based upon the premise that maximizing the diversity of a subset of molecules is equivalent to maximizing its information content. The crux of the approach is the postulate that every collection of molecules is composed of a finite number of distinct species, or classes, of molecules, and that the ability to distinguish among these species can be described as a function of their mutual dissimilarity. The more distinguishable the species, the greater their information content of the collection. The diversity of the collection may then be quantified using Shannon s entropy formalism ... 

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