## Comparison of Molecular Conformation CATS3D

Like many 2D descriptors, CATS has a counterpart in 3D space: the CATS3D descriptor. While the topological pharmacophore approach has the advantage that the time-consuming calculation of conformations can be avoided, the binding event is nevertheless a three-dimensional interaction between a ligand and its receptor. Accordingly, it should be advantageous to exploit such information if available.

The main difference in the correlation vector representation of a 3D conformation in comparison with a topological representation of a molecule is that the distances between the atoms are no longer shortest paths. Instead, Euclidean distances between all atoms are used. Distances between atoms are not restricted to integer values, so the distances have to be partitioned into a set of distance bins. Several such binning schemes have been proposed [9, 16, 17]. For CATS3D we generally employ 20 distance bins that cover distances from 0 to 20 A in steps of 1 A.

For CATS3D we used the modified PATTY atom types [23] available with the pH4_aType function in MOE [24]. Other PPP assignment schemes could also be employed. PATTY provides six PPP types: cation, anion, hydrogen-bond acceptor, hydrogen-bond donor, polar (hydrogen-bond acceptor and hydrogen-bond donor) and hydrophobic. Whereas the topological CATS descriptor allows assignments of more than a single PPP type to one atom, the CATS3D descriptor employs a single PPP type per atom.

Using 20 distance bins for each of the 21 possible combinations of PPP pairs resulted in a descriptor of 420 dimensions. The value stored in each bin is scaled by the added incidences of the two respective features. Each dimension ("bin") of the CATS3D CV is calculated according to the equation cvj=—1—yy14d (2)

where i and j are atom indices, d is a distance range, T is the pair of PPP types of atoms i and j, N1 and N2 are the total number of atoms of types of i and j present in a molecule and (Kronecker delta) = 1 for all pairs of atoms of type T within the distance range d. The factor of 0.5 in the sum avoids double counting of pairs. Pairs of atoms with themselves are not considered.

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