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Figure 11. Distance matrices of drug molecules based on pharmacophore pseudo atom types. Distances are calculated from three-dimensional structures and given in nm. Such matrices can be used to obtain a uniform description of a diverse set of molecular structures (see legend of Fig. 9 for the definition of pharmacophore types).

obtain the three-dimensional structure of the molecule. For molecules with high flexibility, a conformation analysis must be performed to arrive at a set of molecular conformations that are all included into the dataset [60,61].

Descriptors can be computed from atom coordinates, from the molecular surface [62-64], or from molecular interaction potentials [15,65,66].

7.3.12 Distance Matrix

The distance matrix describes the distances between all atoms (or functional groups) of a molecule. It is the three-dimensional counterpart of the molecular topology. A direct comparison of distance matrices is normally not possible because of size and appearance of the matrix depends on the atom numbering in the molecules.

If the matrix is restricted to a subset of atoms, functional groups or pharmacophore centers shared by all molecules considered the matrices can be compared automatically by computer programs [67] (Fig. 11). However, this implies an atom-by-atom superposition of all atoms (or groups, or PCs) that are part of the matrix.

7.3.13 Autocorrelation Coefficients

Autocorrelation descriptors (ACDs) based on spatial data are a preferred way of describing drug molecules. Classification of autocorrelation descriptors arrives at a high level of pharmacophore recovery.

Major advantage of autocorrelation coefficients are:

1. Pharmacophore-like representation of molecular properties such as charge distribution, pattern of hydrogen bonding acceptors or donors, etc.

2. Invariance to rotation and translation of the molecules. Therefore it is not necessary to superimpose structures to be compared.

A major disadvantage is the time required for the computation. The entire algorithm (generation of 3-D structure, conformation analyses, property calculation, property mapping on surface or field and autocorrelation transformation) needs between 100 and 100 000 s for one molecule. With today's computer technology, using multi-processor compute servers and highly vectorized software, it is possible to calculate up to several thousand three-dimensional autocorrelation descriptors within a day (Table 7).

Another important disadvantage is the insufficient representation of stereochemistry: enantiomers show exactly the same autocorrelation descriptor values.

7.3.13.1 Based on Atom Coordinates

The most simple way is using the same single atom properties, as for the topological autocorrelation descriptors. The distance now is not measured as the number of bonds between the two atoms in consideration, but as the real distance between the atoms. The distances are as signed to classes (e.g., distance between 0.1 nm and 0.2 nm) in order to get a limited number of descriptors (e.g., 20), and the coefficient is calculated for each class [68].

7.3.13.2 Based on Surface Properties

More time-consuming computations are needed to obtain autocorrelation coefficients based on molecular surface properties [69,70]. Atom properties (such as charge, lipophilicity, etc.) or interaction potentials (electrostatic interaction, van der Waals interactions, hydrogen bonding donor or acceptor sites, etc.) are mapped to the surface of the molecule. In the next step, autocorrelation coefficients are calculated to represent the patterns of these properties on the surface. The descriptor includes information like: "two negative regions with a distance of 0.9 nm" or "a hydrogen bond acceptor and a lipophilic group with 0.6 nm diameter in 1.8 nm distance", etc.

7.3.13.3 Based on Potential Fields

Autocorrelation coefficients are also calculated on the basis of three-dimensional molecular interaction fields (e.g., MIP, CoMFA-field or CoMSIA-field). These fields are generated by mapping of atom properties to the spatial neighborhood of the molecule [21]. Distances between grid points located in the space around the molecules are used as input for the autocorrelation algorithm.

Because potential fields describe the pharmacophore of a molecule rather than its topology, they are applicable to sets of molecules with diverse chemical scaffolds.

The invariance to translation and rotation is achieved by integration over all five independent modes of motion (i.e., translational movement in the x, y or z directions and rotation around two independent axes). The autocorrelation coefficient F(r) is calculated from all pairs of points x and y with a distance of r and the properties f(x) or f(y):

. L JL/(*)'[L I ny) de dcp\-dx y, + r- sin0- cos<p y2 = x2 + r- sin0 • simp y3 = x3 + r- cosd

7.3.14 Virtual Screening

Virtual screening or "in-silico" screening is used for the design of targeted libraries. All information about the target or known active compounds can be used to remove unfavorable structures from the library [71,72].

Three-dimensional structural constraints are derived from analyses of structure-activity relationships or from high-throughput screening results. However, the best starting point for a three-dimensional 'in-silico' screening is a three-dimensional target structure from X-ray or NMR-analysis. All compounds of the virtual library are screened against this target structure and the results are used as a binary filter or for scoring of the compounds [8,73].

Table 7. Computation times for autocorrelation descriptors, using the fastest and most precise methods.

Task

Time (s) (simple method)

Time (s) (best method)

Generation of three-dimensional structure

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