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Computer simulations of molecular motions in solution are used to study protein flexibility at atomic detail. For large proteins, molecular dynamics simulations over relevant time scales become unfeasible, and it is common to adopt simplified models based on the Go approximation that derives effective inter-residue interactions from the topology of the native structure. Despite their simplicity, Elastic Network Models (ENM) have been shown to capture collective protein motions, in good agreement with experimental atomic fluctuations from X-ray crystal structures and with all-atoms molecular dynamics simulations.
ENM differ in their choices of degrees of freedom. The simplest choice corresponds to the so called Gaussian Network Model (GNM), which uses just one degree of freedom per residue and is based on the assumption that perturbations from the native structure are isotropic. The Anisotropic Network Model (ANM) adopts three Cartesian coordinates per residue. Here we present the Torsional Network Model (TNM), a new coarse-grained model in torsion angle space. The aim of TNM is to reduce the number of degrees of freedom from Cartesian coordinates to torsion angles while keeping the same EN simplicity in the potential energy. In doing so, rigid-body degrees of freedom that modify bond lengths and bond angles are fixed, and the perturbed structures obtained through this model preserve protein-like covalent structure and secondary structure. Our model is able to reproduce the thermal fluctuations as derived from B-factors in X-ray crystallography experiments. We further investigate the ability of TNM to predict large conformational changes in proteins as a consequence of torsion angle variations, such as hinge and shear movements. |
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