Dynamic properties of oligomers that characterize low-frequency normal modes

Dynamics of oligomeric proteins (one trimer, two tetramers, and one hexamer) were studied by elastic network model-based normal mode analysis to characterize their large-scale concerted motions. First, the oligomer motions were simplified by considering rigid-body motions of individual subunits. The subunit motions were resolved into three components in a cylindrical coordinate system: radial, tangential, and axial ones. Single component is dominant in certain normal modes. However, more than one component is mixed in others. The subunits move symmetrically in certain normal modes and as a standing wave with several wave nodes in others. Secondly, special attention was paid to atoms on inter-subunit interfaces. Their displacement vectors were decomposed into intra-subunit deformative (internal) and rigid-body (external) motions in individual subunits. The fact that most of the cosines of the internal and external motion vectors were negative for the atoms on the inter-subunit interfaces, indicated their opposing movements. Finally, a structural network of residues defined for each normal mode was investigated; the network was constructed by connecting two residues in contact and moving coherently. The centrality measure "betweenness" of each residue was calculated for the networks. Several residues with significantly high betweenness were observed on the inter-subunit interfaces. The results indicate that these residues are responsible for oligomer dynamics. It was also observed that amino acid residues with significantly high betweenness were more conservative. This supports that the betweenness is an effective characteristic for identifying an important residue in protein dynamics.