AUTOMATED CONFORMATIONAL-ANALYSIS FROM CRYSTALLOGRAPHIC DATA .1. A SYMMETRY-MODIFIED SINGLE-LINKAGE CLUSTERING-ALGORITHM FOR 3-DIMENSIONAL PATTERN-RECOGNITION

Single-linkage cluster analysis is used to identify discrete conformational subgroups for a chemical fragment from crystal structure data. Fragment conformations are defined by N(t) torsion angles for N(f) occurrences of the fragment in the Cambridge Structural Database. Conformational analysis is complicated by (a) the 2D topological symmetry of the fragment, giving rise to permutations of torsion-angle sequences, and (b) by the presence of 3D enantiomers in the original crystal structures. All steps in the single-linkage algorithm are modified to use fragment symmetry to obtain the optimum torsional overlap of all fragments. Thus, all symmetry equivalents of a given conformation are grouped into the same cluster and the final set of clusters represents an asymmetric unit of conformational space. Principal-component analysis is used to provide a visual mapping of the clustering process. The complete procedure is shown to be effective when applied to a test data set of 222 six-membered carbocycles of known conformational complexity.