Abstract
Elastic network models (ENMs) have been widely used in the last decades to investigate protein motions and dynamics. There the intrinsic fluctuations based on the isolated structures are obtained from the normal modes of these elastic networks, and they generally show good agreement with the B-factors extracted from X-ray crystallographic experiments, which are commonly considered to be indicators of protein flexibility. In this paper, we propose a new approach to analyze protein fluctuations and flexibility, which has a more appropriate physical basis. It is based on the application of random forces to the protein ENM to simulate the effects of collisions of solvent on a protein structure. For this purpose, we consider both the Cα-atom coarse-grained anisotropic network model (ANM) and an elastic network augmented with points included for the crystallized waters. We apply random forces to these protein networks everywhere, as well as only on the protein surface alone. Despite the randomness of the directions of the applied perturbations, the computed average displacements of the protein network show a remarkably good agreement with the experimental B-factors. In particular, for our set of 919 protein structures, we find that the highest correlation with the B-factors is obtained when applying forces to the external surface of the water-augmented ANM (an overall gain of 3% in the Pearson’s coefficient for the entire dataset, with improvements up to 30% for individual proteins), rather than when evaluating the fluctuations obtained from the normal modes of a standard Cα-atom coarse-grained ANM. It follows that protein fluctuations should be considered not just as the intrinsic fluctuations of the internal dynamics, but also equally well as responses to external solvent forces, or as a combination of both.
Highlights
The B-factors of a protein, the Debye-Waller factors or temperature factors, are measures of the atomic displacements about their equilibrium position, i.e., atomic fluctuations [1–3], and the effects of multiple conformations as well as errors in the structures
The flexibility of the protein structure will be investigated by using traditional parameter-free anisotropic network model (pfANM) mode-based fluctuations as well as from the outcome of the random force applications to the protein
This means that the average displacements of the protein elastic network due to the force application are well correlated with the experimental B-factors, with a similar agreement as for the traditionally used mode-based fluctuations
Summary
The B-factors of a protein, the Debye-Waller factors or temperature factors, are measures of the atomic displacements about their equilibrium position, i.e., atomic fluctuations [1–3], and the effects of multiple conformations as well as errors in the structures. They are generally accepted to be mostly the result of internal protein dynamics and any static disorder [4]. They have been shown to be associated with protein flexibility and to correspond closely to protein mechanisms [5–9]. It has been shown that the MD-derived atomic fluctuations due to the internal protein motions show some degree of agreement with the experimental
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