PRINCIPAL COORDINATE MAPS OF MOLECULAR-POTENTIAL ENERGY SURFACES

Obtaining useful representations of molecular conformation spaces and visualizing the associated potential energy surfaces is a complex task , mainly due to the high dimensionality of these spaces. Principal com ponent analysis (PCA), which projects multidimensional data on low-dim ensional subspaces, is thus becoming a common technique for studying s uch spaces. Three issues, relating to the use of principal component t echniques for mapping molecular potential energy surfaces, are discuss ed in this study: the effectiveness of the projection; its accuracy; a nd the mapping procedure. The effectiveness of PCA is demonstrated thr ough detailed analyses of principal component projections of several p eptides. In these cases PCA projected conformation space into a subspa ce smaller even than that defined by the peptide's backbone dihedral a ngles. The average accuracy as well as the distribution of errors in t he projection (i.e., the errors in reproducing individual distances) a re studied as a function of the dimensionality of the projection. The wide variation in accuracy between different systems suggests that it is imperative to indicate the accuracy of the projection whenever PCA projections are used. Furthermore, when projecting potential energy su rfaces on the principal two-dimensional (2D) plane, the projection err ors result in artificial roughening of the surface. A new mapping proc edure, the ''minimal energy envelope'' procedure, is introduced to ove rcome this problem. This procedure yields relatively smooth ''energy l andscapes,'' which highlight the basin structure of the real multidime nsional energy surface. It is demonstrated that the projected potentia l energy maps can be used for charting conformational transitions or d ynamic trajectories in the system. (C) 1998 John Wiley & Sons, Inc.