Average RMSE differences for different types of mutations, prediction methods and their combinations with ENCoM.

<p>We calculate the RMSE difference (<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003569#pcbi.1003569.e049" target="_blank">Eq. 8</a>) for different subsets of the data (columns) and different methods (rows). Methods followed by a ‘+’ denote linear combinations of the named method with ENCoM. The heatmap values (shown within cells) denote the bootstrapped (10000 iterations) average RMSE difference with respect to random and are color coded according to the map on the upper left (lower values in red signify better predictions). For example the values in the leftmost column representing all data comes from the subtraction of the averages in the corresponding box plots in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003569#pcbi-1003569-g004" target="_blank">Figure 4</a> for the non-combined methods and the random model. Different subsets of types of mutations are show according to certain properties of the amino-acids or residues involved: buried (less than 30% solvent-exposed surface area) or exposed (otherwise), small (A,N,D,C, G, P,S, and V) or big (otherwise), polar (R,N,D,E,Q,H,K,S,T and Y) or non-polar including hydrophobic and aromatic (otherwise). Both methods and subsets of the data are clustered according to similarities in the RMSE difference profiles. Cases where the combination of a method with ENCoM is beneficial, i.e., the RMSE difference is lower than either method in isolation are denoted by a ‘*’ next to their values within the cell.</p

Prediction of domain motions.

<p>The best overlap found within the 10 slowest internal motion modes for different NMA models on domain movements. Legend: All (all cases, N = 248), I (Independent movements, N = 130), C (Coupled movements, N = 117), A (apo form, N = 124) and H (holo form, N = 124). AI (apo form independent, N = 130), HI (holo independent, N = 130), AC (apo coupled, N = 116) and HC (holo coupled, N = 116). Box plots generated from 10000 resampling bootstrapping iterations. ENCoM/ENCoM_ns outperform ANM and STeM on all types of motion.</p

Prediction of loop conformational change.

<p>The best overlap found within the 10 slowest internal motion modes for different NMA models on loop movements. Acronyms are the same as in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003569#pcbi-1003569-g002" target="_blank">Figure 2</a>. Number of cases: All (488), I (252), C (236), A (244) and H (244). AI (126), HI (126), AC (118) and HC (118). Box plots generated from 10000 resampling bootstrapping iterations. ENCoM/ENCoM_ns outperform ANM and STeM on all types of motion. The prediction of loop motions is much harder and here the difference between ENCoM and ENCoM_ns are more pronounced.</p

Self-consistency error.

<p>The error calculated the magnitude of the biases in the prediction of forward and back mutations. Box plots were generated from 10000 resampling bootstrapping iterations for the 57 proteins pairs in the Thiltgen dataset. ENCoM/ENCoM_ns are the methods with lowest self-consistency errors.</p

Illustration of the representation of inter-residue interactions by the different NMA methods.

<p>The figure shows three amino acids (D11, D45 and R141) from the <i>M. tuberculosis</i> ribose-5-phospate isomerase (PDB ID = 2VVO). The distances between alpha carbons are shown with the yellow dotted lines and labeled in black. Interaction strengths relative to ANM (in red) are shown for STeM (green) and ENCoM (yellow). ANM treats all pairs as equal while STeM treat equally D11 and R141 with respect to D45 even though the interaction between D45 and R141 is much stronger by virtue of side-chain interactions, as correctly described in ENCoM.</p

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

<div><p>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.</p></div

Performance of different parameter sets on the prediction of mutations, b-factors and motions.

<p>We present as a parallel plot the bootstrapped median RMSE for stabilizing and destabilizing mutation, average best overlap for domains and loop movements as well as self-consistency bias and errors. In the right-most four columns with include the logarithm of the 4 alpha variables. Different parameter sets are colored based on b-factors correlations (red gradient) or domain movement overlaps (blue gradient). The black line represent the specific set of parameters used in ENCoM while the dashed line represents the values for ENCoM using the set of alpha parameters employed in STeM. There is a dichotomy in parameter space such that most sets of parameters are either good at predicting b-factors or overlap and mutations.</p

Correlation between predicted and experimental b-factors for different ENM models.

<p>Box plots represent the average correlations from a non-redundant dataset containing 113 proteins generated from 10000 resampling bootstrapping iterations. ANM and ENCoM have comparable correlations but lower than GNM and STeM.</p

Root Mean Square Error (RMSE) on the prediction of the effect of destabilizing mutations.

<p>RMSE of the linear regression through the origin between experimental and predicted variations in free energy variations (ΔΔG). Box plots generated from 10000 resampling bootstrapping iterations on the subset of destabilizing mutations (experimental ΔΔG>0.5 kcal/mol) in the PoPMuSiC-2.0 dataset (N = 174). The results for destabilizing mutations mirror to a great extent those for the entire dataset given that they represent 57% of the entire dataset.</p

Root Mean Square Error (RMSE) on the prediction of the effect of stabilizing mutations.

<p>RMSE of the linear regression through the origin between experimental and predicted variations in free energy variations (ΔΔG). Box plots generated from 10000 resampling bootstrapping iterations on the subset of stabilizing mutations (experimental ΔΔG<−0.5 kcal/mol) in the PoPMuSiC-2.0 dataset (N = 45). With the exception of DMutant and ENCoM, most methods are not substantially better than random and some are substantially worst for stabilizing mutations.</p