| Abstract: | 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 component analysis (PCA), which projects multidimensional data on low-dimensional subspaces, is thus becoming a common technique for studying such spaces. Three issues, relating to the use of principal component techniques for mapping molecular potential energy surfaces, are discussed in this study: the effectiveness of the projection; its accuracy; and the mapping procedure. The effectiveness of PCA is demonstrated through detailed analyses of principal component projections of several peptides. In these cases PCA projected conformation space into a subspace smaller even than that defined by the peptide's backbone dihedral angles. The average accuracy as well as the distribution of errors in the projection (i.e., the errors in reproducing individual distances) are 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 surfaces on the principal two-dimensional (2D) plane, the projection errors result in artificial roughening of the surface. A new mapping procedure, the “minimal energy envelope” procedure, is introduced to overcome this problem. This procedure yields relatively smooth “energy landscapes,” which highlight the basin structure of the real multidimensional energy surface. It is demonstrated that the projected potential energy maps can be used for charting conformational transitions or dynamic trajectories in the system. © 1998 John Wiley & Sons, Inc. J Comput Chem 19: 1255–1267, 1998 |
