A coarse-grained elastic network atom contact model and its use in the simulation of protein dynamics and the prediction of the effect of mutations

Abstract Normal mode analysis (NMA) methods are widely used to study dynamic aspects of protein structures. Two critical components of NMA methods are coarse-graining in the level of simplification used to represent protein structures and the choice of potential energy functional form. There is a trade-off between speed and accuracy in different choices. In one extreme one finds accurate but slow molecular-dynamics based methods with all-atom representations and detailed atom potentials. On the other extreme, fast elastic network model (ENM) methods with C α -only representations and simplified potentials that based on geometry alone, thus oblivious to protein sequence. Here we present ENCoM, an Elastic Network Contact Model that employs a potential energy function that includes a pairwise atom-type non-bonded interaction term and thus makes it possible to consider the effect of the specific nature of amino-acids on dynamics within the context of NMA. ENCoM is as fast as existing ENM methods and outperforms such methods in the generation of conformational ensembles. Here we introduce a new application for NMA methods with the use of ENCoM in the prediction of the effect of mutations on protein stability. While existing methods are based on machine learning or enthalpic considerations, the use of ENCoM, based on vibrational normal modes, is based on entropic considerations. This represents a novel area of application for NMA methods and a novel approach for the prediction of the effect of mutations. We compare ENCoM to a large number of methods in terms of accuracy and self-consistency. We show that the accuracy of ENCoM is comparable to that of the best existing methods. We show that existing methods are biased towards the prediction of destabilizing mutations and that ENCoM is less biased at predicting stabilizing mutations. Author Summary Normal mode analysis (NMA) methods can be used to explore the ensemble of potential movements around an equilibrium conformation by mean of calculating the eigenvectors and eigenvalues associated to different normal modes. Each normal mode represents one particular set of global collective, correlated and complex, form of motion of all atoms in the system. Any conformation around equilibrium can be represented as a linear combination of amplitudes associated to each normal mode. Differences in the magnitudes of the set of eigenvalues between two structures can be used to calculate differences in entropy. Coarse-grained NMA methods utilize a simplified potential and representation of the protein structure and thus decrease the computational time necessary to calculate eigenvectors and their respective eigenvalues. Here we present ENCoM the first coarse-grained NMA method to consider side-chain atomic interactions and thus able to calculate the effect of mutations on eigenvectors and eigenvalues. Such differences in turn are related to entropic differences and can thus be used to predict the effect of mutations on protein stability. ENCoM performs better than existing NMA methods with respect to different traditional applications of NMA methods (such as conformational sampling) or comparably for the prediction or crystallographic b-factors. ENCoM is the first NMA method that can be used to predict the effect of mutations on protein stability. Comparing ENCoM to a large set of dedicated methods for the prediction of the effect of mutations on protein stability shows that ENCoM performs better than existing methods considering a combination of prediction ability (particularly on stabilizing mutations) and bias (how does the prediction of a forward or back mutations differ). ENCoM is the first entropy-based method developed to predict the effect of mutations on protein stability.

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