ABSTRACT
Using Normal Modes ............................................................................................ 259 17.3 Results ................................................................................................................................. 261
17.3.1 Modi ed eNMA in Internal Coordinates without Tip Effect ............................... 261 17.3.2 Re nement of X-ray Anisotropic Thermal Parameters
Using Normal Modes ............................................................................................ 261 Acknowledgments ..........................................................................................................................264 References ......................................................................................................................................265
Normal mode analysis (NMA) is a powerful method that has been used to model the harmonic vibrations of protein structures [1-4], especially large-scale deformational motions of supramolecular complexes [5,6]. However, due to the construction and diagonalization of the Hessian matrix, the normal mode calculation can become computationally intractable as the size of the structure increases. One effective way to address this problem is with the recent development of elastic normal mode analysis (eNMA) [7,8], which makes a coarse-grained approximation of the complex atomic structure with a much simpler elastic network and reduces the complex all-atom potential to a simpler Hookean potential. The coarse-grained approximation can be based on either the Cα atoms [8], a subset of Cα atoms [9], a lattice representation of the protein [10], or even nodes placed within low-resolution electron cryomicroscopy maps (cryo-EM) [11,12] that have no correlation to the positions of any real atoms. Even with such a simpli cation of the structure and potential, eNMA preserves the low-frequency eigenvectors predicted by more accurate molecular mechanics force elds and is as effective as and sometimes more powerful than the standard NMA procedure [5]. An additional bene t to these approximations is that the initial structure
