cNMA: a framework of encounter complex-based normal mode analysis to model conformational changes in protein interactions

Motivation: It remains both a fundamental and practical challenge to understand and anticipate motions and conformational changes of proteins during their associations. Conventional normal mode analysis (NMA) based on anisotropic network model (ANM) addresses the challenge by generating normal modes reflecting intrinsic flexibility of proteins, which follows a conformational selection model for protein-protein interactions. But earlier studies have also found cases where conformational selection alone could not adequately explain conformational changes and other models have been proposed. Moreover, there is a pressing demand of constructing a much reduced but still relevant subset of protein conformational space to improve computational efficiency and accuracy in protein docking, especially for the difficult cases with significant conformational changes. Method and results: With both conformational selection and induced fit models considered, we extend ANM to include concurrent but differentiated intra-and inter-molecular interactions and develop an encounter complex-based NMA (cNMA) framework. Theoretical analysis and empirical results over a large data set of significant conformational changes indicate that cNMA is capable of generating conformational vectors considerably better at approximating conformational changes with contributions from both intrinsic flexibility and inter-molecular interactions than conventional NMA only considering intrinsic flexibility does. The empirical results also indicate that a straightforward application of conventional NMA to an encounter complex often does not improve upon NMA for an individual protein under study and intra-and inter-molecular interactions need to be differentiated properly. Moreover, in addition to induced motions of a protein under study, the induced motions of its binding partner and the coupling between the two sets of protein motions present in a near-native encounter complex lead to the improved performance. A study to isolate and assess the sole contribution of intermolecular interactions toward improvements against conventional NMA further validates the additional benefit from induced-fit effects. Taken together, these results provide new insights into molecular mechanisms underlying protein interactions and new tools for dimensionality reduction for flexible protein docking.