Normal-mode analysis (NMA) is a computational exploration of the "natural" motion of a structure given as a set of coordinates (Brooks and Karplus, 1983; Tama et al., 2002) or as a low-resolution density map (Chacon et al., 2003). In both cases the structure is represented as an elastic network, and the dynamical properties of the resulting object are investigated near its equilibrium. The analysis results in a set of principal motions or flexing of entire domains. A few low-energy modes are often typically represent motions or flexing of entire domains. A few low-energy modes are often sufficient to arrive at a satisfactory description of the experimentally observed dynamic behavior of large molecules, as demonstrated for some functionally relevant conformational changes of large macromolecular assemblies, such as virus swelling (Tama and Brooks, 2002) and the ribosomal ratchet motion (Tama et al., 2003; Wang et al., 2004; see also Ma, 2005). The demonstrated ability of NMA to predict coarse (i.e., relation to motions of large domains) dynamic features of a molecule has been exploited by the development of a new fitting method (Tama et al., 2004a,b), termed normal-mode flexible fitting (NMFF). While fitting by real-space refinement, described in the previous section, starts out with a representation of the atomic structure as a set of flexibly connected rigid components, fitting by NMFF leaves the atomic structure intact and attempts to explain the observed density map by deforming the X-ray structure using a superimposition of suitably weighted normal modes. In a process of refinement, the cross-correlation coefficient between the experimental map and the deformed simulated map is maximized. Application to cryo-EM maps of RNA polymerase and elongation factor G as bound to the ribosome lead to excellent fits (Tama et al., 2004b).
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