Geometric versus topological clustering: an insight into conformation mapping.

Clustering molecular conformations into "families" is a common procedure in conformational analysis of molecular systems. An implicit assumption which often underlies this clustering approach is that the resulting geometric families reflect the energetic structure of the system's potential energy surface. In a broader context we address the question whether structural similarity is correlated with energy basins, i.e., whether conformations that belong to the same energy basin are also geometrically similar. 'Topological mapping' and principal coordinate projections are used here to address this question and to assess the quality of the 'family clustering' procedure. Applying the analysis to a small tetrapeptide it was found that the general correlation that exists between energy basins and structural similarity is not absolute. Clusters generated by the geometric 'family clustering' procedure do not always reflect the underlying energy basins. In particular it was found that the 'family tree' that is generated by the 'family clustering' procedure is completely inconsistent with its real topological counterpart, the 'disconnectivity' graph of this system. It is also demonstrated that principal coordinate analysis is a powerful visualization technique which, at least for this system, works better when distances are measured in dihedral angle space rather than in cartesian space.