Autocorrelation of 3D Molecular Properties

Spatial autocorrelation coefficients can be used to produce a 3D-QSAR that does not require alignment of the structures. The user must choose the conformation to be compared, however. The physical basis of the autocorrelation vector is the observation that properties at one point in space are often correlated with those at another point in space for example, adding a methyl group to a carbon atom typically changes the steric energy at several CoMEA lattice points and/or the distances between several surface points. The autocorrelation vector for enantiomers will be identical, because the autocorrelations are based on distances between points, and enantiomers have the same distances between atoms and properties based on them. Hence, the user must decide which is the bioactive enantiomer after the analysis. 

The original 2D autocorrelation analysis calculates a vector based on the distances between all atoms of a structure and any property of these atoms.205 206 For each pair of atoms, the distance between the atoms (number of bonds between them) and the product of the properties is noted. Each element of the autocorrelation vertor is the sum of these products for one particular distance. A separate autocorrelation vector is calculated for each property of interest—typically, volume, electronegativity, hydrogen bonding character, hydrophobicity. As a final step a principal components analysis reduces the number of variables to consider. 

For a 3D-QSAR autocorrelation matrix, the distances are calculated from the 3D structures of the molecules. Both points on a CoMFA-like lattice and points on the molecular surface have been used for these distance calcula-tions.2 7 208 Similarly, the 3D autocorrelation properties are based on properties at these points (e.g., electrostatic or hydrophobic potential). Wagener et al. used a point density of 10 points/A on the van der Waals surface for the property calculation for the autocorrelation matrix, they considered distances from 1 to 13 A and a distance interval of 1 A to produce an autocorrelation vector of length 12.2° These 12 properties were then analyzed by principal components analysis, a Kohonen map, and a feed-forward multilayer neural 

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