Abstract
Elastic network models (ENMs) are valuable tools for investigating collective motions of proteins, and a rich variety of simple models have been proposed over the past decade. A good representation of the collective motions requires a good approximation of the covariances between the fluctuations of the individual atoms. Nevertheless, most studies have validated such models only by the magnitudes of the single-atom fluctuations they predict. In the present study, we have quantified the agreement between the covariance structure predicted by molecular dynamics (MD) simulations and those predicted by a representative selection of proposed coarse-grained ENMs. We then contrast this approach with the comparison to MD-predicted atomic fluctuations and comparison to crystallographic B-factors. While all the ENMs yield approximations to the MD-predicted covariance structure, we report large and consistent differences between proposed models. We also find that the ability of the ENMs to predict atomic fluctuations is correlated with their ability to capture the covariance structure. In contrast, we find that the models that agree best with B-factors model collective motions less reliably and recommend against using B-factors as a benchmark.
Highlights
Elastic network models (ENMs) provide a greatly simplified perspective on collective protein motions, and ever since Tirion’s pioneering work[1] a variety of different models have been suggested
ENMs are motivated by the statistical properties of interaction averages in collective motions,[1] and we find it important to use methods that can compare the inter-residue positional covariances describing this collectivity, rather than just single-atom variances
To learn which of the investigated ENMs are better suited to model the inter-residue covariances of compact folded proteins, we calculated the Bhattacharyya coefficient for the comparison of each ENMpredicted covariance matrix to the covariance matrix obtained from molecular dynamics (MD) simulations
Summary
Elastic network models (ENMs) provide a greatly simplified perspective on collective protein motions, and ever since Tirion’s pioneering work[1] a variety of different models have been suggested. The success of coarse-grained ENMs has to some extent been surprising, and their simplicity has provided novel insights into diverse protein mechanisms. Tirion computed thermodynamical statistics for proteins using an intrinsic dynamics model with a greatly simplified harmonic potential.[1] The potential was constructed to have its minimum at the equilibrium coordinates reported from experimentally determined structures. This work demonstrated the feasibility of predicting collective motions from ENMs, and how computationally expensive structure minimization can be avoided. Bahar et al.[9] proposed an isotropic model employing a potential which restrains angular deviations of contacts.[19]
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