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WIREs Comput Mol Sci
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Computing protein dynamics from protein structure with elastic network models

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Elastic network models ENMs allow to analytically predict the equilibrium dynamics of proteins without the need of lengthy simulations and force fields, and they depend on a small number of parameters and choices. Despite they are valid only for small fluctuations from the mean native structure, it was observed that large functional conformation changes are well described by a small number of low frequency normal modes. This observation has greatly stimulated the application of ENMs for studying the functional dynamics of proteins, and it is prompting the question whether this functional dynamics is a target of natural selection. From a physical point of view, the agreement between low frequency normal modes and large conformation changes is stimulating the study of anharmonicity in protein dynamics, probably one of the most interesting direction of development in ENMs. ENMs have many applications, of which we will review four general types: (1) the efficient sampling of native conformation space, with applications to molecular replacement in X‐ray spectroscopy, cryo electro‐miscroscopy, docking and homology modeling; (2) the prediction of paths of conformation change between two known end states; (3) the comparison of the dynamics of evolutionarily related proteins; (4) the prediction of dynamical couplings that allow the allosteric regulation of the active site from a distant control regions, with possible applications in the development of allosteric drugs. These goals have important biotechnological applications that are driving more and more attention on the analytical study of protein dynamics through ENMs. WIREs Comput Mol Sci 2014, 4:488–503. This article is categorized under: Molecular and Statistical Mechanics > Molecular Dynamics and Monte-Carlo Methods
Sketch of the derivation of the elastic network model ENM force field, which is often also called Go model or Structure‐based protein model. For each pair of atoms in contact in the native structure, the real energy landscape (blue), which is unknown, is approximated with a function that has its minimum at the observed native distance (red), and this in turn is approximated as a parabola (green), which is valid in a neighborhood of the minimum.
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Conformation changes are studied with the elastic network models ENM by generating two ENM potentials centered at the start and end structures A and B, respectively (red and green curve), and interpolating between them in the multidimensional space of the ENM degrees of freedom as UAB(r, λ) = (1 − λ)UA(r) + λUB(r). When λ is varied between zero and one, the minimum of the potential for given λ allows estimating the energy landscape along the reaction coordinate and the energy barrier that opposes to the conformation change.
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Torsional normal modes of the Leucine transporter (left, PDB code 1usg) and Adenylate kinase (right, PDB code 4ake). Lowest frequency normal modes are on the right side of each plot. The black circles represent the effective number of Cartesian degrees of freedom displaced by the mode, the red squares represent the number of torsion angles displaced by the mode, and the green triangle represent the contribution of the mode to the conformation change (PDB codes 1usk for LeuT and 1ank for ADK). One can see that low frequency modes tend to have large, although not largest Cartesian collectivity, small torsional collectivity, i.e., they are hinge‐like, and yield the largest contributions to conformation changes, although the extent of their contribution can vary a lot from one conformation change to another.
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Left: The types of elastic network models ENMs depend on a small number of choices and parameters. Right: Torsion angles used as degrees of freedom in ENMs in internal coordinates.
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