Internal Normal Mode Analysis (iNMA) Applied to Protein Conformational Flexibility

Abstract

We analyze the capacity of normal modes to predict observed protein conformational changes, and, notably, those induced by the formation of protein-protein complexes. We show that normal modes calculated in internal coordinate space (ICS) provide better predictions. For a large test set, using the ICS approach describes the conformational changes more completely, and with fewer low-frequency modes than the equivalent Cartesian coordinate modes, despite the fact that the internal coordinate calculations were restricted to torsional angles. This can be attributed to the fact that the use of ICS extends the range over which movements along the corresponding eigenvectors remain close to the true conformational energy hypersurface. We also show that the PaLaCe coarse-grain protein model performs better than a simple elastic network model. We apply ICS normal-mode analysis to protein complexes and, by extending the approach of Sunada and Go̅, [Sunada, S.; Go̅, N. J. Comput. Chem. 1995, 16, 328-336], we show that we can couple an accurate view of the Cartesian coordinate movements induced by ICS modes with the detection of the key residues responsible for the movements.