A

Figure 3. Diverse or not diverse? The three selected figures are a highly diverse selection from set A, but a low diversity selection from set B.

chemical space comprises a huge number of compounds. Only a very small fraction of these compounds is known and characterized (see Table 4).

Table 4. Size of the chemical space to which the diversity of a combinatorial library refers [10].

Number of molecules Chemical space

Table 4. Size of the chemical space to which the diversity of a combinatorial library refers [10].

Number of molecules Chemical space

10l«o

Possible drugs

1018

Likely drugs

107

Known compounds

106

Commercially available compounds

106

Compounds in a corporate database

104

Compounds in drug databases

103

Commercial drugs

102

Profitable drugs

Diversity is therefore always regarded as a local phenomenon and limited to a certain part of the structural space. Extent and localization of the region covered has to be defined previously - otherwise it is impossible to define the diversity of a subset.

In order to obtain a pragmatic and useful base for diversity computations, diverse chemical structures are compared with a known part of chemical space. This approach is applicable when the library described in terms of diversity is a small fraction of the entire dataset.

Consequently, the generation of huge virtual libraries is necessary in order to define the visible chemical space and form a virtual mesh in this space. Distances, similarities, or even diversity can be measured by referring to this virtual mesh.

7.2 How Do We Compute Diversity? 7.2.1 An Overview

As explained in Section 7.1.3, a universal definition of similarity or diversity of a set of molecules is not possible. For this reason, the diversity computation algorithm is split into several computational steps, and every step must be adapted to the given problem (see Fig. 4). The major steps are:

• Choice of descriptors.

• Calculation of descriptor values.

• Calculation of similarities in the descriptor space.

• Mapping or classifying the descriptors.

• Selection of compounds.

Every particular study looks at just some of the structural properties and neglects others. To ensure that the initial aim of the library design is achieved, a critical interpretation of the results is essential.

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