Evaluation of Protein Elastic Network Models Based on an Analysis of Collective Motions

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.

From Sequence to Function: Coevolving Amino Acids Encode Structural and Functional Domains

“…Specifically, the DDs were obtained by an elastic network (ENM) analysis [66,67] of the reference structure for each MSA [32]. The structure-based character of the DD analysis is an apt complement of the sequence-based one of EDs.…”

Comparing the intrinsic dynamics of multiple protein structures using elastic network models

“…This practice does not come without assumptions, however, as neither of these are direct observations of thermal motion, and in the case of B-factors, the experimental conditions do not reflect the solvent environment for which its application might be intended. In recent years attempts have been made to carefully quantify how these assumptions affect the parameterisation [53][54][55][56]. Notably, a wide range of cut-off values (from 8 to 15 Å) has been used in cut-off based models to represent the interatomic interactions.…”

“…This might explain the apparent robustness of the ENMs to the choice of cut-off, as even very long cut-offs can discriminate protein surface from protein interior. In order to also predict the energetic separation between normal modes, a narrower range of parameters are found to be appropriate [53,56]. The lack of uniformity in ENM parameterisation is partly a consequence of differing opinions on benchmarking procedures.…”

“…Validation against detailed molecular mechanics force fields performed on large protein datasets has shown that ENMs reproduce the slow dynamics obtained from molecular simulations well (see references [11][12][13][14]39,40,44,56,61]). …”

“…In many such studies, the normal mode analysis is validated by comparing with conformational change, or by testing the insights obtained by independent means [36,[63][64][65]. Comparison of predictions from ENMs with molecular dynamics simulations has also been used to validate and benchmark models [12,39,40,44,56,61].…”