Procrustean rotation in concert with principal component analysis of molecular dynamics trajectories: Quantifying global and local differences between conformational samples.

Given the principal component analysis (PCA) of a molecular dynamics (MD) conformational trajectory for a model protein, we perform orthogonal Procrustean rotation to "best fit" the PCA squared-loading matrix to that of a target matrix computed for a related but different molecular system. The sum of squared deviations of the elements of the rotated matrix from those of the target, known as the error of fit (EOF), provides a quantitative measure of the dissimilarity between the two conformational samples. To estimate precision of the EOF, we perform bootstrap resampling of the molecular conformations within the trajectories, generating a distribution of EOF values for the system and target. The average EOF per variable is determined and visualized to ascertain where, locally, system and target sample properties differ. We illustrate this approach by analyzing MD trajectories for the wild-type and four selected mutants of the beta1 domain of protein G.