Analyzing large-scale structural change in proteins: Comparison of principal component projection and sammon mapping

Effective analysis of large-scale conformational transitions in macromolecules requires transforming them into a lower dimensional representation that captures the dominant motions. Herein, we apply and compare two different dimensionality reduction techniques, namely, principal component analysis (PCA), a linear method, and Sammon mapping, which is nonlinear. The two methods are used to analyze four different protein transition pathways of varying complexity, obtained by using either the conjugate peak refinement method or constrained molecular dynamics. For the return-stroke in myosin, both Sammon mapping and PCA show that the conformational. change is dominated by a simple rotation of a rigid body. Also, in the case of the T -> R transition in hemoglobin, both methods are able to identify the two main quaternary transition events. In contrast, in the cases of the unfolding transition of staphylococcal nuclease or the signaling switch of Ras p21, which are both more complex conformational transitions, only Sammon mapping is able to identify the distinct phases of motion.