Why are large conformational changes well described by harmonic normal modes?

Low-frequency normal modes generated by elastic network models tend to correlate strongly with large conformational changes of proteins, despite their reliance on the harmonic approximation, which is only valid in close proximity of the native structure. We consider 12 variants of the torsional network model (TNM), an elastic network model in torsion angle space, that adopt different sets of torsion angles as degrees of freedom and reproduce with similar quality the thermal fluctuations of proteins but present drastic differences in their agreement with conformational changes. We show that these differences are related to the extent of the deviations from the harmonic approximation, assessed through an anharmonic energy function whose harmonic approximation coincides with the TNM. Our results indicate that mode anharmonicity is more strongly related to its collectivity, i.e., the number of atoms displaced by the mode, than to its amplitude; low-frequency modes can remain harmonic even at large amplitudes, provided they are sufficiently collective. Finally, we assess the potential benefits of different strategies to minimize the impact of anharmonicity. The reduction of the number of degrees of freedom or their regularization by a torsional harmonic potential significantly improves the collectivity and harmonicity of normal modes and the agreement with conformational changes. In contrast, the correction of normal mode frequencies to partially account for anharmonicity does not yield substantial benefits. The TNM program is freely available at https://github.com/ugobas/tnm. SIGNIFICANCE The functional mechanisms of most proteins originate from their dynamical behavior in the native state. Improving our ability to model and predict protein dynamics is thus essential in a variety of applications, including the docking of proteins with other proteins, macromolecules, or ligands. Elastic network models provide simple analytical predictions in the form of normal modes, which are based on a harmonic approximation that is only valid for small displacements from the native conformation. We investigate how such predicted native dynamics may yet hold valuable information about larger-scale functional motions. In particular, we show that low-frequency modes that are collective (displace many atoms) remain harmonic even for large displacements and correlate better with experimentally observed conformational changes.

Automated summary

This study investigates the correlation between low-frequency normal modes in elastic network models and large conformational changes in proteins, finding that mode anharmonicity is more strongly related to collectivity than amplitude. Strategies such as reducing degrees of freedom or regularization by torsional harmonic potentials significantly improve the collectivity and harmonicity of normal modes.