ABSTRACT
CONTENTS 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112 6.2 Theory and Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
6.2.1 Normal Mode Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113 6.2.2 Multi-Scale Energy Functions Using Elastic Networks . . . . . . 114 6.2.3 Rotation-Translation Block Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . 115 6.2.4 Multi-Scale NMAUsing Elastic Network Hamiltonians
and the RTB Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.2.5 Mapping the Pathway of Conformational Change Using
NMA.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.2.5.1 Linear Interpolation between Endpoints Using
Normal Mode Directions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 6.2.5.2 Nonlinear/Iterative Approach . . . . . . . . . . . . . . . . . . . . . . . . 118
6.3 Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 119 6.3.1 Unveiling Molecular Mechanisms of Conformational
Changes of Large Macromolecular Assemblies . . . . . . . . . . . . . . . 120 6.3.1.1 The Mechanism and Pathway of pH Induced
Swelling in Cowpea Chlorotic Mottle Virus. . . . . . . . . 120 6.3.1.2 Dynamic Reorganization of the Functionally
Active 70S Ribosome. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123 6.3.1.3 Myosin II ATPase Inhibition . . . . . . . . . . . . . . . . . . . . . . . . . . . 126
6.3.2 Exploration of Global Distortions and Interpretation of Low-Resolution Structural Information . . . . . . . . . . . . . . . . . . . . . . . . 128 6.3.2.1 Global Distortions of Biological Molecules from
Low-Resolution Structural Information . . . . . . . . . . . . . 128
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6.3.2.2 Flexible Fitting of Atomic Structures into Low-Resolution Electron Density Maps . . . . . . . . . . . . . 129
6.4 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
It is now well established that large-scale rearrangements in proteins are important for a variety of protein functions including catalysis and regulation of activity. The recent developments in experimental methods, especially cryo-electron microscopy (cryo-EM), have revealed that largemolecular assemblies are also highly dynamic.While experiment can provide a tremendous source of information on these dynamical properties, computationalmethodsmust be employed to complement experimental observations. Indeed, by using theory to explore (at near-atomic levels of detail) functionally important rearrangements observed in experiments at low-resolution it is possible to gain new insights into the mechanism of these transformations that are presently inaccessible to experiments. The exploration of molecular motions of biological molecules and their
assemblies by simulation approaches such as molecular dynamics has provided significant insights into structure-function relationships for small biological systems. However, the study of large-scalemacromolecular assemblies by this technique is limited to relatively short timescales due to the computational complexity of brute-force simulation methods. Normalmode analysis (NMA)provides an alternative tomolecular dynam-
ics for the study of motions of macromolecules. The timescale accessible to theoretical work is extended with NMA, and this approach has been proven extremely useful for studying collective motions of biological systems [1-3]. Exploration of the normal modes of a molecular system can yield insights, at the atomic level, on the mechanism of large-scale rearrangements of proteins-proteins complexes that occur upon ligand-protein binding [4-11]. Studies employing NMA have generally focused on a few largeamplitude/low-frequency normal modes, which are expected to be relevant to function. Theoretical studies of dynamical properties of biological systems by NMA
have been limited to small proteins (up to 300 residues) [12], mainly due to the size of the biological system. The protein model used in such calculations consists of classical point masses, with typically one point per atom, and the energy terms for interactions between atoms are defined by semiempirical force-fields. The use of such force-fields requires an energetically precise
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all-atom description of the equilibrium configuration of the macromolecule, which becomes computationally difficult to achieve as the system size increases. However, multi-scale approaches that retain the atomic detail have also seen some success. Elastic network models can also be used to address these issues [13]. In
the elastic network model approach a simplified potential is used to represent the molecule as a set of pseudo-particles that capture the molecule mass distribution. These particles are coupled via harmonic springs to provide a description of the system as an elastic net. This model does not necessitate preliminary energy minimization, thereby permitting direct analysis of crystal and NMR coordinates, or even low-resolution structures obtained from electron microscopy [14-17]. Moreover, the reduced representation of the molecule, whereby a single coordinate is used to represent several atoms (e.g., using Cα atoms to represent each residue of a protein) provides a multiscale description that can significantly reduce the computational expense. The elastic network model, in concert with methods that facilitate large diagonalization problems such as the rotation-translation block (RTB) method [18,19] or DIMB [20], have extended studies of dynamics via NMA to very large biological assemblies. In the following pages, we will review the elastic network model and RTB-
based diagonalization techniques used in NMA as well as methods based on NMA for the generations of feasible conformational change pathways between different conformations of biological systems. We will illustrate recent successes of NMAapplied to large macromolecular assemblies. Particular focus will be on recent studies of viruses, the ribosome and myosin. In addition, the application of elastic network normal mode analysis to low-resolution structures obtained from cryo-EM will also be presented.
