Normal mode analysis of proteins: a comparison of rigid cluster modes with C(alpha) coarse graining.

The ability to infer dynamic motions from an equilibrium (static) conformation of a protein can be essential in establishing structure-function relationships. In particular, the low-frequency motions are of functional interest because statistical mechanics predicts these motions will have the largest amplitudes. In this paper, we address the computational cost of normal mode analysis (NMA) applied to a C(alpha)-based elastic network model (C(alpha)-NMA) and present a new coarse-grained rigid-body-based analysis (cluster-NMA). This new method represents a protein as a collection of rigid bodies interconnected with harmonic potentials. This representation produces reduced degree-of-freedom (DOF) equations of motion (EOMs) which, even in the case of large structures (10(3+) residues), enables the computation of normal modes to be done on a desktop PC. We present the complete theory and analysis of cluster-NMA and also include its application to a variety of structures. The results of the new method are compared with C(alpha)-NMA and it is shown that cluster-NMA produces very good approximations to the lowest modes at a fraction of the computational cost.