Normalizing normal mode analysis.

Few would disagree, but a generation later, the statement remains a prophecy rather than fact. Although 41,000 protein structures are known, there are none for which there is a complete description of the dynamics that is often key to understanding functional mechanism. Despite keen interest in protein dynamics, studies have remained the purview of computer simulation while the challenges of experimental characterization are only slowly being overcome. Methods, such as molecular dynamics, are based on sound chemical physics but require approximations for application to large biomolecular systems (Karplus and McCammon, 2002). With each new methodology, a tension has emerged between the desire to characterize uncharted systems and the fear of the unknown impact of inherent assumptions and approximations on the simulations’ results. A firmer footing can be established by comparing computed and experimental results when possible (Karplus and McCammon, 2002). Until recently, experimental validations of normal mode calculations were largely qualitative. Since its introduction to biomolecules in the early 1980s, normal mode analysis (NMA) has allowed reduction in the dimensionality of simulations, and their extension to larger motions and longer timescales than hitherto accessible (Ma, 2005). NMA’s simplifying assumptions are that, as a structure is perturbed from equilibrium, the energy increase is parabolic, and that atoms move within the structure as coupled harmonic oscillators. Solutions of the Hamiltonian (energy) equation yield normal mode vectors describing the directions of collective atomic motions, their amplitudes and frequencies—at least in principle. The molecule’s dynamics can then be approximated by a sum of normal mode vibrations. Excitement was heightened with the finding that the directions of known conformational changes often correlate with the sum of a few dominant modes, suggesting that NMA might be predictive of not just small oscillations, but of functionally relevant conformational dynamics (Figure 1). NMA’s application to large biomolecular systems requires crude approximations. Chief among these are elastic network model (ENM), and coarse-grained approximations that group several atoms into a single oscillator (Ma, 2005). In dynamics simulations, atoms are moved by forces calculated from the distortion of local stereochemistry. In ENM simplifications, the dependence of these forces on the types of atoms and chemical bonding is mostly ignored. With uncertainty as to the impact of the approximations, interpretations of NMA results have been largely qualitative, focusing on relative amplitudes and directions, but not frequencies. Three recent publications start to address these concerns through comparison of NMA to experimental B factors of known structures (Eyal et al., 2006; Hamacher and McCammon, 2006;