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.