Recent advances in sequencing technologies mean there are now thousands of sequenced human genomes, revealing millions of single nucleotide variants (SNVs). For non-synonymous SNVs present in proteins the difficulties of the problem lie in first identifying those nsSNVs that result in a functional change in the protein among the many non-functional variants and in turn linking this functional change to phenotype. Here we present VarMod (Variant Modeller) a method that utilises both protein sequence and structural features to predict nsSNVs that alter protein function. VarMod develops recent observations that functional nsSNVs are enriched at protein–protein interfaces and protein–ligand binding sites and uses these characteristics to make predictions. In benchmarking on a set of nearly 3000 nsSNVs VarMod performance is comparable to an existing state of the art method. The VarMod web server provides extensive resources to investigate the sequence and structural features associated with the predictions including visualisation of protein models and complexes via an interactive JSmol molecular viewer. VarMod is available for use at  The ability to sequence genomes has resulted in the identification of millions of genetic variants, particularly single nucleotide variants (SNVs), within the human population as highlighted by the 1000 genomes project . AdditioThere is therefore a need to develop methods to identify SNVs, in our case non-synonymous SNVs (nsSNVs), that are likely to affect the function of the protein in which they are present and are more likely to be associated with a change in phenotype. A number of methods have been developed previously (reviewed in ), with tHere we have developed VarMod a new method for identifying functional nsSNVs. VarMod develops our recent research in which we demonstrated that disease associated nsSNVs are enriched at protein–protein interfaces . AdditioVarMod obtains features from multiple analyses, which are combined using a support vector machine (SVM)  to make To perform the structural analysis, a structural model of the query protein is generated. To do this, template structures in the protein databank (PDB)  are idenProtein–protein interface sites are modelled using an approach based on Interactome3D . The Intet al. . The sequence features include residue conservation (the Jensen–Shannon convergence) and three features that represent the change of amino acid properties of size/mass, charge and functional group. The size/mass change of the amino acid is represented by the ratio of the mass of the two amino acids. To consider the change in charge between the two amino acids, the 20 amino acids are grouped according to charge (Supplementary Table S2). The feature representing the change in the charge of the amino acid considers changes between these charge groups, with values set in Supplementary Table S3. A further feature represents the change of chemical functional group present in the amino acid side chain. The amino acids are grouped as described by Innis et al.   to predict whether each variant is functional or non-functional. The outputs from each of the SVM models are converted to probabilities as described in Platt . An enseDataset 5 from VariBench  was usedThe SVMs were generated by SVMlight  using a To compare VarMod performance with PolyPhen-2, the final test set of nsSNVs was run on the PolyPhen-2 web server (on 1 March 2014). Predictions were made using the two different classifiers available (HumDiv and HumVar) with default settings. The ROC and Precision–Recall analyses of PolyPhen-2 were performed by varying the ‘pph2_prob’ score.The performance of VarMod was assessed using the set of sequences from VariBench that were not used in cross-validation. The performance of VarMod on the test set of sequences was assessed using the measures of specificity, sensitivity , precision and a Receiver Operator Characteristic (ROC) analysis. The ROC curve and Precision–Recall graph in Figure http://www.wasslab.org/varmod. Users are required to submit a protein sequence (raw sequence or FASTA formatted) or a UniProt accession, and a list of variant positions . A UniProt accession is required to perform the protein–protein interface analysis . Processing time for each submission varies from 5 min to a few hours. Structural data has been pre-computed for all of the UniProt human principal protein isoforms, so submissions using these sequences are processed in a few minutes. Where other sequences are submitted, the structural models and binding sites need to be modelled thereby increasing the running time to a few hours.The VarMod web server is available at The display of VarMod results is split into multiple sections Figures  and 3. TThe sequence and structure sections display the main analyses. The sequence section displays the protein sequence, colour coded to highlight multiple features including residue conservation, ligand binding sites and protein–protein interfaces. The summary results and sequence view can be downloaded as a PDF file.www.jmol.org) molecular viewer forms the main part of the structural section and initially displays the model with the highest confidence . The JSmol viewer enables visualisation of the modelled protein and by default is coloured to highlight the functional regions of the protein (ligand-binding and protein–protein interface sites) and the nsSNVs (red). A control panel to the right of the display enables the user to investigate the nsSNVs by displaying a different model, or modifying the display style (cartoon/spacefill or sticks representations) and colour of the whole protein, nsSNVs or functional sites. The user is able to generate high quality images of the displayed model by clicking on the ‘generate image’ button, enabling the analysis to be used for reports or publications.The structural section first displays the details of the structural templates and models of the protein that have been generated (one for each region/domain for which a template was identified). A JSmol . The VarMod server provides a resource for users to identify functional nvSNVs and to investigate the individual features associated with these variants. Plans for future improvements to the server include increasing the number of interface and binding site features such as considering how variants may alter binding energies and options to submit variants in alternative formats such as Variant Call Files (VCF), which will facilitate high throughput analysis of nsSNVs identified from sequencing studies.Supplementary Data are available at NAR Online.


One very important functional domain of proteins is the protein-protein interacting region (PPIR), which forms the binding interface between interacting polypeptide chains. Post-translational modifications (PTMs) that occur in the PPIR can either interfere with or facilitate the interaction between proteins. The ability to predict whether sites of protein modifications are inside or outside of PPIRs would be useful in further elucidating the regulatory mechanisms by which modifications of specific proteins regulate their cellular functions.Using two of the comprehensive databases for protein-protein interaction and protein modification site data , we created new databases that map PTMs to their locations inside or outside of PPIRs. The mapped PTMs represented only 5 % of all known PTMs. Thus, in order to predict localization within or outside of PPIRs for the vast majority of PTMs, a machine learning strategy was used to generate predictive models from these mapped databases. For the three mapped PTM databases which had sufficient numbers of modification sites for generating models , the resulting models yielded high overall predictive performance as judged by a combined performance score (CPS). Among the multiple properties of amino acids that were used in the classification tasks, hydrophobicity was found to contribute substantially to the performance of the final predictive models. Compared to the other classifiers we also evaluated, the SVM provided the best performance overall.http://sysbio.chula.ac.th/PtmPPIR).These models are the first to predict whether PTMs are located inside or outside of PPIRs, as demonstrated by their high predictive performance. The models and data presented here should be useful in prioritizing both known and newly identified PTMs for further studies to determine the functional relationship between specific PTMs and protein-protein interactions. The implemented R package is available online (The online version of this article (doi:10.1186/s12859-016-1165-8) contains supplementary material, which is available to authorized users. Post-translational modification (PTM) of proteins is a key mechanism for cellular regulation including protein-protein interactions, protein functions, protein turnover, protein localization, cell signaling, and proteomic diversity , 2. MoreBecause of advances in high-throughput technologies especially in protein mass spectrometry, enormous amounts of data related to PTMs have been obtained. At the present, there are multiple databases available for studying PTMs such as UniProt , dbPTM , PTMCuraPPIRs can only be confidently identified from protein structures that were determined using high resolution techniques such as X-ray crystallography, NMR spectroscopy, and/or cryo-electron microscopy. The Protein Data Bank (PDB) is a rapidly expanding resource consisting of a large number of structures for protein-protein complexes, including detailed information of PPIRs at the amino acid residue level . These sWe began this study with a simple question: For any detected protein modification, can we predict whether that modification is inside or outside of a PPIR? To address this question, we first integrated the information from the PDB and PhosphoSitePlus databases to generate new supervised datasets indicating which PTM sites are experimentally confirmed to be inside or outside of PPIRs (mapped PTMs). Subsequently, we used several conventional features including hydropathy index, secondary structure, PSSM (Position-Specific Scoring Matrix), and sequence conservation (surrounding the modified site), along with existing web-based applications, to perform the prediction. However, these features and applications proved to be insufficient to accomplish the task. Therefore, a different approach was required.One strategy that has been used successfully to make predictions based on pattern recognition is “machine learning”. In fact, this strategy has been recently employed to predict individual sites of protein modification with high performance –18, althIn this study, the integrated PDB/PTM-specific datasets were analyzed and modeled using machine learning algorithms. Our predictive models showed high performance measures, and important features contributing to predictive power were identified. These predictive models are available online and may be useful in providing additional insight related to the functional relationship between specific PTMs and protein-protein interactions.Figure Although the number of data points required for machine learning is a function of the variability and complexity of the datasets and research problems being addressed, at least 75–80 data points have been reported as the minimum necessary for achieving acceptable performance levels , 23. ThiInitially, we focused on the phosphorylation dataset and performed position-specific sequence analysis surrounding the phosphorylation sites found either within or outside of PPIRs using PhosphoLogo .Using this conventional approach, a few general conclusions were possible: 1) there was a rather strong preference for tyrosine as the phosphorylation site within PPIRs Fig. ; 2) the Next, we used individual conventional features  in a machine learning strategy in an attempt to develop models for predicting whether modification sites are inside or outside of PPIRs  were individually encoded into numerical arrays using 102 indices of AAindex1  and thenn, AUC, and MCC were low (<0.5), while Sp could reach the maximum at 1 , Random Forest (RF), C4.5, KStar, and Multilayer Perceptron (MLP). Table Except for RF (see below), the SVM provided the best performance overall , and the best individual performance for two of the three PTM-specific datasets, namely acetylation and ubiquitylation. For the phosphorylation-specific dataset, the k-NN and C4.5 classifiers  provided slightly better performance than the SVM. Despite the latter results, since the SVM was used to obtain the optimized lists of indices and features for subsequent modeling by the other classifiers, some biases may have been introduced  that compromised the performance of the other classifiers. To address this issue, the phosphorylation-specific dataset was re-evaluated using either k-NN or C4.5 exclusively as the classifiers (instead of the SVM) for all feature selection and classification tasks. As shown in Table http://sysbio.chula.ac.th/PtmPPIR.In order to maximize performance and minimize the number of features required, the final PTM-specific predictive models were generated using the optimized lists of indices and features as described Tables  and 4, eThe final models were evaluated using 10 independent iterations of 5-fold cross-validation, and the resulting calculated performance measures for the models were high Table . NeverthFinally, the overall performance of our predictive models was compared with that of NPS-HomPPI , a more Finally, we applied our predictive models to the large number of sequences from the PhosphoSitePlus database that have no corresponding 3D structure in the PDB database . Table In this study, we developed machine learning models for predicting whether post-translationally modified sites in proteins are inside or outside of PPIRs (protein-protein interacting regions). We combined data from two of the most comprehensive databases currently available, namely 3D structural and protein-protein interaction data from the PDB, and protein modification site data from the PhosphoSitePlus database. After the filtering and mapping processes Fig. , only thDuring the initial generation of the predictive models, the imbalance between the total numbers of interacting and non-interacting sites caused misclassifying during the learning process, as indicated by poor performance measures  should not be directly extrapolated to the other class of PTMs (located inside PPIRs). Nevertheless, when the models were applied to the large number of PTM sequences with no PDB structure information , between 1–4 % of the modification sites were predicted to be located inside PPIRs , it will be necessary to prioritize which individual PTMs will be selected for further studies of their roles in regulating protein functions. The prediction for any newly identified PTMs as being localized inside PPIRs would help with this prioritization, since PTMs located inside PPIRs are likely to significantly impact (promote or disrupt) protein-protein interactions. However, we should note one caveat to this generalized approach in predicting the importance of specific PTMs for their effects on protein-protein interactions: some PTMs located outside of PPIRs could also affect protein-protein interactions , but such PTMs would not be identified using our approach. As a second potential use for the data generated by these models, investigators can search the lists provided here of known PTMs either determined or predicted to be located inside PPIRs , based on the existing structural and PTM databases. Our models show relatively high predictive performance measures. As more data become available, the performance of these models should be even better. Specifically, discovery of new PPIRs as a result of rapidly increasing 3D structure determinations should increase the accuracy of the predictive models. These predictive models are available online and may be useful in providing additional insight related to the functional relationship between specific PTMs and protein-protein interactions.ftp://ftp.wwpdb.org/). Because a significant number of PDB files remain uncurated, it was necessary to use filtering software (written in-house) to remove files with unusable formats . Subsequently, an additional filtering software module  was employed to remove those PDB files for proteins with no interacting protein partners. Next, the dataset containing the remaining PDB files was analyzed using the “contact” function of Jmol [The protein-protein interacting region (PPIR) map was generated based on the PDB database . First,  of Jmol  to detecDatasets of protein post-translational modifications (PTMs) were downloaded from PhosphoSitePlus 3/29/2015) . These d/2015 . Thttps://hpcwebapps.cit.nih.gov/PhosphoLogo/) was used for the phosphorylation dataset, and Motif-x [http://motif-x.med.harvard.edu/motif-x.html) was employed for the acetylation and ubiquitylation datasets. Please note that PhosphoLogo is not compatible with phosphorylated histidine input [http://www.cbs.dtu.dk/services/NetSurfP/); conservation of the modified site and its surrounding residues was calculated by CPhos [https://hpcwebapps.cit.nih.gov/CPhos/).PTM–specific datasets were subjected to analysis using different existing algorithms to calculate position-specific amino acid preferences for the modified site and its surrounding residues: PhosphoLogo   was markedly smaller than that of non-interacting residues. Therefore, the chance for a modified site to be located inside an interacting region was correspondingly lower than that for localization outside an interacting region, thus creating a class imbalance which introduces a computational bias. Such an imbalance causes misclassification during the learning process of predictive model generation –45. In tOne solution to deal with this imbalance problem is an approach called under-sampling –48, usinAfter the balancing process, sequences contained in each of the seven PTM-specific datasets were then encoded into numerical data using AAindex1 , a databA total of 102 indices (out of 544) were selected for use in the encoding step , sensitivity (Sn) or true positive rate (TPR), specificity (Sp) or true negative rate (TNR), and area under receiver operating characteristic curve (AUC). ACC, MCC, PPV, F1, Sn, and Sp are defined asThe support vector machine (SVM) has been widely applied in computational biology fields due to its high predictive performance –53 compaTo improve the performance of the predictive models, optimal subsets of indices (from AAindex1) were identified for encoded PTM-specific datasets using a “greedy-based” algorithm. First, individual encoded dataset arrays were divided into 102 14-column blocks of features , each block representing an individual index. The classification functions were fitted to these index-specific sub-datasets, and indices were then ranked based on multiple performance measures. While AUC is the most frequently used performance measure, alternative performance measures could also be used, each of which could potentially yield different results. Thus, to minimize biases arising from any individual measure, we employed an approach based on the highest summation of three different performance measures , designated as the Combined Performance Score (CPS). After initial ranking of indices using CPS, classification tasks were performed sequentially by including the index-specific sub-datasets one by one in order of their individual rank. As a result, the optimal set of indices that led to the maximum CPS value for each PTM-specific dataset was identified. Finally, encoded PTM-specific datasets were reduced to contain only sub-datasets corresponding to indices in the optimal sets.For each reduced PTM-specific dataset, the Relief-F  and InfoThe reduced feature subsets for encoded PTM-specific datasets were evaluated in the classification tasks using the k-nearest neighbors , KStar, Random Forest (RF), C4.5, and Multilayer Perceptron (MLP) classifiers implemented in the machine learning software Weka . The defhttp://sysbio.chula.ac.th/PtmPPIR.The classifier that led to the highest performance measures was used to generate final predictive models that were specific to each PTM type. The R language was used to implement the models. We host the R package in our server at AUC, area under receiver operating characteristic curve; CPS, combined performance score; k-NN, k-nearest neighbors; MCC, Matthew’s correlation coefficient; MLP, multilayer perceptron; PPIR, protein-protein interacting region; PTM, post-translational modification; RF, random forest


Docking Approach using Ray Casting), operates by comparing the topography of the protein surface when “viewed” from a vantage point inside the protein against the topography of a bound ligand when “viewed” from the same vantage point. Here, we present five key enhancements to DARC. First, we use multiple vantage points to more accurately determine protein-ligand surface complementarity. Second, we describe a new scheme for rapidly determining optimal weights in the DARC scoring function. Third, we incorporate sampling of ligand conformers “on-the-fly” during docking. Fourth, we move beyond simple shape complementarity and introduce a term in the scoring function to capture electrostatic complementarity. Finally, we adjust the control flow in our GPU implementation of DARC to achieve greater speedup of these calculations. At each step of this study, we evaluate the performance of DARC in a “pose recapitulation” experiment: predicting the binding mode of 25 inhibitors each solved in complex with its distinct target protein (a protein interaction site). Whereas the previous version of DARC docked only one of these inhibitors to within 2 Å RMSD of its position in the crystal structure, the newer version achieves this level of accuracy for 12 of the 25 complexes, corresponding to a statistically significant performance improvement (p < 0.001). Collectively then, we find that the five enhancements described here – which together make up DARC 2.0 – lead to dramatically improved speed and performance relative to the original DARC method.Over the past decade, protein-protein interactions have emerged as attractive but challenging targets for therapeutic intervention using small molecules. Due to the relatively flat surfaces that typify protein interaction sites, modern virtual screening tools developed for optimal performance against “traditional” protein targets perform less well when applied instead at protein interaction sites. Previously, we described a docking method specifically catered to the shallow binding modes characteristic of small-molecule inhibitors of protein interaction sites. This method, called DARC ( Protein-protein interactions underlie most biological processes –3, and aUnlike enzymes and other traditional drug targets, protein surfaces evolved to bind other proteins typically lack the deep pockets used as small-molecule binding sites –19. SurvDocking Approach using Ray-Casting) [To address this, we recently developed an alternative screening approach called DARC (Casting) , a dockiCasting)  that we Casting) . To idenIf a ligand docked into this surface pocket is indeed shape-complementary, the surface of this ligand when “viewed” from this vantage point (the origin) should have a very similar topography to that of the pocket. To map the topography of the ligand, we cast a collection of rays from the origin point, with each of the angles  used to map the pocket topography. For each ray, we determine the distance of its first intersection with the ligand (if indeed the ray intersects the ligand). We express the difference in the “observed” surface topographies of the pocket and ligand as follows:Conceptually, each of the four conditions above represents a distinct type of deviation between the two surfaces. In the first case (c1), a ray hits the surface pocket before reaching the ligand: this indicates underpacking in the protein-ligand interface. In the second case (c2), a ray intersects the ligand before reaching the pocket: this indicates that the ligand’s volume overlaps that of the protein, and thus points to a steric clash. In the third case (c3), a ray that intersects the pocket does not intersect the ligand at all: this indicates that the ligand is too small for the pocket. Finally, in the fourth case (c4), a ray that intersects the ligand does not intersect the pocket: this indicates that the ligand extends outside the binding pocket.Beyond simply evaluating the shape complementary of a protein-ligand complex, this “shape score” can also be used as an objective function for optimization. By adjusting the ligand position and orientation to minimize this score, one can use DARC to rapidly dock a ligand into a surface pocket. In practice, we use a particle swarm optimization (PSO) scheme  to minimExtending the approach further, by sequentially docking a large number of compounds in this manner one can use DARC to carry out a virtual screen to identify compounds that complement the shape of some surface pocket on a protein of interest. Previously, we found that DARC could be used in virtual screening benchmarks to pick out known small-molecule inhibitors of Bcl-xL and XIAP that were hidden amongst pools of “decoy” compounds. Despite its relatively simple implementation, DARC outperformed other popular virtual screening tools at this task—tools that have been developed in the context of “traditional” target classes, rather than for inhibitors of protein interactions. We then used DARC to carry out a computational screen of 65,000 compounds to identify those that would best complement a pocket on the surface of Mcl-1, an anti-apoptotic member of the Bcl-2 protein family. We tested the top 21 DARC hits in biochemical assays, and found that indeed 10 of these are inhibitors of Mcl-1, with Ki values ranging from 1.2 to 21 μM for the best 4 compounds. Collectively these results validated DARC for virtual screening at protein interaction sites, and demonstrated its usefulness for identifying new inhibitors acting at these sites .(1) We refined the ray-casting approach, such that rays emanate from multiple origin points to better map the shapes of the surface pocket and the ligand. (2) We developed a new strategy for parameterizing DARC in a faster and more robust way, thus enabling a broader and more representative set of protein complexes to be included in training. (3) We introduced a new scheme to efficiently sample small-molecule conformers “on-the-fly” in a single docking trajectory, rather than sequentially consider each conformer in a separate trajectory. (4) We incorporated electrostatics into the DARC scoring function, allowing simultaneous optimization of both shape- and electrostatic-complementarity. (5) We identified the computational performance bottleneck in our previous implementation of GPU-DARC [We have drawn upon experiences and observations from our early applications of DARC to enhance its performance through the five key ways we describe in this study: GPU-DARC , and adjcollective effect of these enhancements results in a notable increase in the number of testcases that are correctly docked to within 2 Å RMSD, with an overall performance improvement that does rise to the level of statistical significance (p < 0.001). Thus, we can conclude that together, these individual enhancements lead to dramatic improvements in DARC’s robustness, accuracy, and speed.As described below, we examine the effect of each of these enhancements in a “pose recapitulation” benchmark. Due to the unfortunate dearth of examples of small-molecule inhibitors bound at a protein interaction sites, the size of our benchmark set is necessarily limited. This, in turn, limits the observed statistical significance of performance improvements stemming from individual enhancements. As will be demonstrated below, however, the Previously, we assembled a set of unique proteins for which a crystal structure was available in complex with a small-molecule inhibitor of a protein-protein interaction site . At the As described above, the topography of the protein surface is mapped from a vantage point inside the protein, using an “origin” point from which rays emanate. The placement of this origin point is critical to ensuring that the resulting topography map gives an accurate and complete view of the surface pocket—in an intuitive sense, it should be centered “behind” the pocket. For an ideal scenario, in which the surface pocket is a purely concave “dimple” on the surface of a near-spherical protein, the protein’s center of mass can serve as a natural choice for the origin’s location. In practice, however, the pocket shapes are never purely concave, and any ruggedness means that some parts of the protein surface cannot be “seen” from a given vantage point. An incomplete description of the protein surface, in turn, limits the ability of DARC to identify truly complementary ligands.In order to map the protein surface topography more accurately, we therefore modified the ray casting approach such that rays emanate from multiple origins: we expected this strategy would better “illuminate” all regions of the protein surface. To do so, we begin from a single origin centered 30 Å behind the pocket see . RotatinAs before, the topography of the protein surface is mapped by casting rays at each of the “pocket” gridpoints that directly contact the protein. Rather than retain the distances at which rays from all five origins hits a given protein surface point, we only store the distance from the closest origin: each origin is thus “responsible” only for those regions of the protein surface pocket that are closest to it, and for which that origin is therefore likely to have an optimal vantage point .Having mapped the protein surface pocket using rays cast from multiple origins, we then evaluate ligand complementarity exactly as described earlier: we simply cast the rays that emanate from each origin towards the ligand, and compare the distances at which these intersect with the ligand to the distances at which they intersected the protein surface . This stTo examine the effect of using multiple origins, we used DARC to dock each of the 25 protein-ligand pairs in our test set . In eachWe also carried out this “pose recapitulation” experiment using the previously described version of DARC , which oWe note that before inclusion of this new feature in DARC, only one complex in our set was docked to within 2 Å RMSD of the crystal structure; using multiple origins, there are now three such cases. Examination of the crystallographic complexes for these improved cases reveals that many share a binding mode in which the ligand (or part of the ligand) faces directly into the protein . In suchThere are four parameters (c1/c2/c3/c4) used by DARC when evaluating shape complementarity . Since sIn our original parameterization of DARC , we usedTo speed up weight fitting, we adapted our approach such that explicit docking at every step would no longer be required. We also took this opportunity to parameterize DARC not for its ability to simply recapitulate the bound pose of a known ligand, but rather for its ability to optimally distinguish a known ligand from among a pool of “decoy” compounds. The latter represents a virtual screening scenario, such that the resulting weights may exhibit improved performance for this task.We started by first reformulating DARC’s shape complementarity score as follows:Relative to our previous formulation , we haveWe again turned to our non-redundant set of 25 complexes in which a small-molecule inhibitor is bound at a protein interaction site ; to setuThe key to the reformulation of DARC’s shape complementarity score above  is that Collectively, we generated more than 16 million “decoy poses” (25 proteins x 650 ligands x 1000 randomly docked poses for each protein-ligand combination). Rather than store these decoy poses explicitly, we instead simply stored the four “component energies”  was typically completed in minutes (it took under a minute to run 100 iterations). To objectively examine the performance that could be expected from the weights obtained by this method, we used leave-one-out cross-validation. For each of the 25 proteins in our test set, we developed a unique set of weights trained only on the other 24 proteins; we then used this custom weight set to dock the native ligand of interest back into its cognate receptor, and evaluated the ligand RMSD relative to the crystal structure of this protein-ligand complex. The mean of the custom weight sets used in this experiment are reported in We compared the RMSD of these 25 DARC-docked examples, using our previous DARC weights  or usingExamination of the crystallographic complexes for these improved cases reveal that indeed the previous weight set may have insufficiently penalized poses that are slightly underpacked .in silico libraries, the speed of virtual screening is likely to be of paramount importance for the foreseeable future. It is important to note that the speed of modern docking approaches generally scale not only with the size of the screening library, but also with the number of conformations considered for an average ligand in the library.Efficiently sampling the potential positions, orientations, and conformations of each compound is critical to virtual screening. As the size of “purchasable” chemical space continues to increase , and thein situ during docking [in situ during docking with “anchor-and-grow” incremental construction, or alternatively a set of rigid conformers can be pre-generated and screened sequentially [Modern docking / virtual screening tools address the problem of ligand conformational sampling in different ways. Some programs, such as FRED, pre-generate a collection of low-energy ligand conformations (“conformers”), then sample each of these individually in separate docking trajectories . Other p docking . In the entially , 35. In entially .DARC makes use of particle swarm optimization (PSO)  to minimTo increase the efficiency of our sampling, we adapted our approach such that the set of (pre-generated) conformers would instead be considered on-the-fly during docking . We reasAt the start of the simulation, we assigned each of the pre-generated conformers a unique index. During the PSO, seven parameters would be included in the optimization: one to indicate which ligand conformation should be used, and six to transform the atoms of this ligand to the appropriate position and orientation with respect to the protein. This approach is particularly suited to PSO optimization, which simultaneously maintains multiple solutions (“particles”) during a docking trajectory; separate populations that make use of different “promising” conformers can each explore their own local clusters of solution space, whereas conformers that are not used in any productive poses are sampled less frequently. This, in turn, could reduce the overall time required to run the optimization.Given that the search space for a given trajectory is now much larger (there is an extra degree of freedom), we anticipated that using “on-the-fly” conformer sampling would lead to slower convergence than a trajectory in which only a single conformer was considered. To test this, we first used “sequential” conformer docking with very intensive sampling (1000 particles and 1000 steps) to identify the optimal score that could be obtained when docking the native ligand back into its cognate receptor, for each of the 25 complexes in our set . Next, tper trajectory, however, the advantage of on-the-fly sampling lies in the fact that only a single trajectory is needed. Since we use an average of 163 conformers for the ligands in our test set  , 43 and While DARC was originally predicated on matching the surface shapes of the ligand and the protein surface, we quickly noted (by inspection of mis-docked structures) that a number of ligands exhibited pseudo-symmetry when examined purely on the basis of their shapes. In other words, docking without consideration of chemical complementarity very quickly highlighted the limitations of docking on the basis of shape complementarity alone.To address this, we built into DARC the ability to capture electrostatic complementarity using the most common approach employed by other modern docking tools. Given the (fixed) receptor conformation, we solve the Poisson-Boltzmann equation to calculate the electrostatic potential at a series of gridpoints that span the surface pocket of interest . For conGiven the electrostatic potential, we evaluate the electrostatic complementarity by summing over atomic partial charges in the traditional manner as follows:ϕi) at the location of a given ligand atom (i), we use trilinear interpolation of the closest gridpoints that encapsulate the center of the atom. Atomic partial charges (qi) for the ligand were determined using the “molcharge” program from OpenEye (see -1).To determine the electrostatic potential (nEye see . To ensuEnhancement #2) to develop a new set of weights for DARC, this time including electrostatic complementarity as follows:We then used the strategy described above  applies equally well here; this allowed us to use the same approach to derive a new set of weights that includes this electrostatic term. For the results presented below, we again used the same leave-one-out cross-validation described earlier.not previously docked to within 2 Å RMSD, however, five new complexes were now “correctly docked” upon inclusion of this electrostatics term . Examination of such cases showed that these were typically ligands bound to flat regions of the protein surface; while shape alone was insufficient to correctly dock the ligand, inclusion of electrostatics enabled the native pose to be identified  were originally designed to process multithreaded 3D graphics through ray-tracing makes them extremely well-suited for the ray-casting that underlies DARC. Previously, we adapted DARC such that the ray-casting step would be carried out on the GPU; meanwhile, the central processing unit (CPU) would be responsible for updating the ligand coordinates and repeatedly passing these to the GPU. This GPU implementation proved extremely useful, because it led to a speedup of about 27-fold in typical-use cases, as compared to the time required to carry out the analogous calculations using the CPU alone .Upon more recent examination of the speedup observed when carrying out various calculations in DARC, we found that the size of the ligand and the number of particles both contributed to the bottleneck in the speedup that could be achieved. As noted earlier, DARC uses particle swarm minimization to optimize the ligand’s displacement and rotation  relative to a saved “reference” position. While the ray-casting step was taking place on the GPU, applying the transformation to translate and rotate the ligand to its new coordinates was carried out on the CPU, and was required for every particle (at every step of the docking trajectory). Our observations of the scaling with respect to ligand size and number of particles led us to hypothesize that the performance bottleneck in the GPU-enabled calculation was either due to the time required for the CPU to apply the appropriate transformation to every ligand atom of every particle, or because of the amount of data transferred from the CPU to the GPU.To address this bottleneck, we devised a new scheme for splitting control flow between the CPU and the GPU . During To evaluate the speedup achieved by this new strategy we determined the time needed for docking each of the 25 complexes in our test set , either Our scheme also proved naturally amenable for using the GPU to calculate the electrostatic part of the DARC score as well : at setuone of the ligands in our test set to within 2 Å RMSD of its position in the crystal structure, “DARC 2.0” achieves this level of accuracy for 12 of the 25 complexes. The dramatic improvement in the RMSD of these docked complexes is reflected through the Wilcoxon signed-rank test, which confirms a statistically significant performance improvement from these collective enhancements (p < 0.001).Here, we present a number of enhancements to the robustness, speed and accuracy of DARC; each enhancement builds upon the previous one. These include introduction of multiple origins from which rays can emanate, a new scheme for rapidly determining optimal weights in the scoring function, the ability to rapidly screen conformers “on-the-fly” during docking, inclusion of electrostatic complementarity in the scoring function, and improved control flow for GPU computing. As a result of the linear narrative by which we have describe these enhancements, however, the overall improvement from this collection of improvements is less apparent. In Even with these enhancements, the performance of DARC on this benchmark is worse than that reported for benchmarks comprised of “traditional” drug targets such as enzymes and hormone receptors: pose prediction experiments find that several methods can successfully reproduce the bound pose for these targets to within 2 Å RMSD upwards of 70% of the time , though none of the  ligands generated by OMEGA were within 2 Å RMSD of the crystallographic ligand. In such cases, even a perfectly docked conformer could not have achieved our goal of docking to within 2 Å RMSD of the crystallographic ligand. In We also note that our benchmark included the crystallographic (protein-bound) ligand conformers among those sampled: in a “true” application, such a structure would not be available. In this experiment, we included the “correct” ligand conformer in order to avoid apparently negative results for cases in which no ligand conformer at all was available within 2 Å RMSD of the crystallographic ligand. As shown in Nonetheless, the ability to achieve such a dramatic collective improvement in DARC 2.0 relative to DARC 1.0 is striking in part due to the success of DARC 1.0 for virtual screening. As noted earlier, our initial deployment of DARC in a screen against Mcl-1 allowed us to identify 4 new inhibitors with Ki values ranging from 1.2 to 21 μM ; given tsome hits are identified then a screening campaign is considered successful: missing out on additional active compounds in the library does not detract from this success. In other words, provided that the number of “true” hits in a library is not exceedingly small, false positives limit the perceived performance of virtual screening much more than false negatives. This is deceptive in some ways, however, since these additional hit compounds that were (incorrectly) excluded may have superior potency than the compounds that were ultimately prioritized for further characterization (i.e. in “wetlab” assays).In a virtual screening experiment, two types of errors can limit performance: false negatives  and false positives . In practice, as long as In a pose recapitulation benchmark, such as the one used in this study, the ligand to be used for each testcase is pre-determined, and there is a single “right answer” . This is a far more stringent test than a virtual screen; when screening, failing to correctly dock an individual (active) compound from the library would simply lead to exclusion of this compound from among the hits , and would go unnoticed.In retrospect, DARC 1.0 exhibited impressive performance for virtual screening because a number of active compounds were identified—but many other compounds more potent than those we chose to characterize may have been present in our library. Because of the improved performance demonstrated by DARC 2.0 in pose recapitulation, we anticipate fewer false negatives in screening applications—leading, in turn, to improved potency of initial screening hits from DARC 2.0 relative to DARC 1.0.www.rosettacommons.org), with the new features described here included in official releases 2015.05 and beyond. The Protocol Capture accompanying this manuscript  to a spherical coordinate file; we call this a “ray-file”. To generate this ray-file we need to input the protein (in PDB format), and specify one or more target residue(s). The command to run DARC is as follows:Rosetta/main/source/bin/make_ray_files.macosclangrelease-protein 4ERF.pdb-central_relax_pdb_num 54,99To use multiple origins, we use:Rosetta/main/source/bin/make_ray_files.macosclangrelease-protein 4ERF.pdb-central_relax_pdb_num 54,99 –multiple_originIn the second step, we are actually running the docking calculations using the pre-generated ray-file. Here we give the input ligand(s) for screening against the ray-file, as follows:Rosetta/main/source/bin/DARC.macosclangrelease-protein 4ERF.pdb-ligand 0R3_0001.pdb-extra_res_fa 0R3.params-ray_file eggshell_rosetta_4ERF_54,99.txtTo search conformers on-the-fly:Rosetta/main/source/bin/DARC.macosclangrelease-protein 4ERF.pdb-ligand 0R3_0001.pdb-extra_res_fa 0R3.params-ray_file eggshell_rosetta_4ERF_54,99.txt–search_conformers trueRather than center the pocket grid at the target residue(s), we can instead center it using a bound ligand (primarily for benchmarking purposes):Rosetta/main/source/bin/make_ray_files.macosclangrelease-protein 4ERF.pdb-central_relax_pdb_num 54,99 -bound_ligand 0R3_0001.pdb-extra_res_fa 0R3.params –lig_gridThe output of the DARC run is a docked model of the protein-ligand complex; in this case it would be named “DARC_4ERF_0R3.pdb”Fullatom minimization of the DARC models can either be carried out separately in Rosetta, or immediately after completion of the DARC. To minimize the DARC models immediately after docking we add the flag “-minimize_output_complex” as follows:Rosetta/main/source/bin/DARC.macosclangrelease-protein 4ERF.pdb-ligand 0R3_0001.pdb-extra_res_fa 0R3.params-ray_file eggshell_rosetta_4ERF_54,99.txt–minimize_output_complexThis gives an additional output file named “mini_4ERF_0R3.pdb”.-origin_cutoff 9-atom_radius_scale 0.9 -num_particles 100 -num_runs 100-missing_point_weight 13.3-steric_weight 3.12-extra_point_weight 8.13–esp_weight 0.03 –use_connolly_surfaceOther optional flags to use when running DARC include:1) at a distance 30 Å from the center of the pocket, and at a location centered “behind” the pocket. When using a single origin, we noted that the location of the origin is key for suitably defining the topography of the protein surface. The protein center of mass can work well for globular proteins, but can be “off-center” for many proteins that are not nearly-spherical. Below we describe several ways to define O1: their applicability depends in part on the geometry of the pocket itself. We note, however, that the use of multiple origins provides more robust results with respect to the location of O1.Whether using a single origin or multiple origins, we begin by placing the first origin point (O1 should simply be placed in the direction of the protein’s center of mass (this is default). If so, we place O1 30 Å away from the center of the pocket (P) along the P→Q direction, where Q is the center of the protein. If not, we offer three distinct methods to set O1: (1) We make use of the fact that pockets at protein-interaction sites are broad and flat, and thus we find the plane that best fits the pocket points (by minimizing the least-squares distance of points to the plane). We then place O1 along the normal to the plane passing through P, so that distance P–O1 = 30 Å, yielding two solutions (one “above” the plane of the pocket and one “below” the plane of the pocket). We then select the solution for which the O1–Q distance is less (i.e. the rays will emanate from within the protein rather than from far above the pocket). (2) Alternatively, for pockets that are deeper and narrower, we define a series of vectors si, each of which defines the distance and direction from the ith surface point to P. We then carry out a vector summation of all these vectors si, such that we determine the direction of the pocket which most faces away from solvent. We place O1 in this direction at a distance of 30 Å. (3) Finally, we offer the user fine control over the location of the origin by placing O1 30 Å away from P along the P→R direction, where R is a user-specified residue.As a first step, the user can choose whether O1 is defined, four more origin points (O2–O5) are then defined. We add O2–O5 as follows: O2 and O3 are obtained by rotating O1 by ±45° around vector w = u×v, where u is the vector from P to O1, v is the vector from P to a randomly chosen point, and × denotes vector product; O4 and O5 are obtained by rotating O1 by ±45° around vector z = u×w.Once OTo prepare the protein, we begin by using Rosetta to fill in any missing atomic coordinates and add hydrogen atoms. We then use OpenEye’s “molcharge” program to add amber99 partial charges to each atom.To generate the electrostatic potential grid, we use OpenEye’s ZAP toolkit   to match the size of the interface pocket grid. This step can be carried out while generating the ray file:Rosetta/main/source/bin/make_ray_files.macosclangrelease-protein 4ERF.pdb-central_relax_pdb_num 54,99-bound_ligand 0R3_0001.pdb-add_electrostatics –espGrid_file 4ERF.agd-extra_res_fa 0R3.paramsThe output from this command will be a ray-file named “eggshell_4ERF_54,99.txt” and an electrostatic potential grid file named “DARC_4ERF.agd” which we will use as input for running docking using DARC.Then we call DARC for running the docking calculations using the pre-generated ray-file and corresponding electrostatic potential grid as follows:-extra_res_fa 0R3.params-ray_file eggshell_rosetta_4ERF_54,99.txtRosetta/main/source/bin/DARC.macosclangrelease-protein 4ERF.pdb-ligand 0R3_0001.pdbTo include electrostatics score:Rosetta/main/source/bin/DARC.macosclangrelease-protein 4ERF.pdb-ligand 0R3_0001.pdb-extra_res_fa 0R3.params-ray_file eggshell_rosetta_4ERF_54,99.txt–add_electrostatics -espGrid_file DARC_4ERF.agdFor each ligand in our test set, we used the OMEGA software –29 to geThe statistical significance of the comparisons presented here was evaluated using Wilcoxon signed-rank test, as implemented in the R statistical computing environment .S1 DatasetThe protocol capture contains all the example input and output files, and representative command-lines and flags required for running DARC.(GZ)Click here for additional data file.S1 Figgreen, while the docked model is shown in cyan. (A) In this example  Among examples for which performance was slightly deteriorated when using multiple origins , the pockets were typically relatively flat and featureless; both docked poses appear to have equivalent shape complementarity, and the difference is presumably due simply to slight shifts in the relative ranking of these mis-docked poses when the origin is altered.In all cases, the crystallographic ligand is shown in (TIFF)Click here for additional data file.S2 Figgreen, while the docked model is shown in cyan. (A) In this example (2YEL), the previous weight set may have insufficiently penalized underpacking at the protein-ligand interface. The new weights increase this penalty, leading to a much-improved pose (RMSD goes from 6.0 Å to 0.4 Å). (B) Among examples for which performance was slightly deteriorated when using the newer weight set , the based for the diminished performance is not clear; both docked poses appear to have equivalent shape complementarity, and the difference is presumably due simply to slight shifts in the relative ranking of these mis-docked poses.In all cases, the crystallographic ligand is shown in (TIFF)Click here for additional data file.S3 Figgreen, while the docked model is shown in cyan. (A) In this example , the crystallographic ligand binds to a flat region of the protein surface. Using shape alone, the correct pose is not clear; upon inclusion of the electrostatics term, the correct pose can be identified based on interactions around the (charged) phosphate group . (B) Among examples for which performance was slightly deteriorated when including electrostatics , we find relatively non-polar protein surfaces with nearly symmetric binding pockets. While the sulfonamide group makes favorable electrostatic interactions in the native pose, the incorrect pose selected upon inclusion of electrostatics includes alternate  electrostatic interactions involving this group.In all cases, the crystallographic ligand is shown in (TIFF)Click here for additional data file.S4 FigAs in (EPS)Click here for additional data file.S1 TableWe compiled a set of 25 unique protein interaction sites for which a crystal structure has been solved in complex with a small-molecule inhibitor. This set is based upon our previous set of 21 complexes that were available at the time (drawn in part from the 2P2I  and TIMB(DOCX)Click here for additional data file.


Our analysis of λ in Escherichia coli, Saccharomyces cerevisiae, and Homo sapiens sequences reveals how co- and post-translationally acting chaperones differentially promote non-conservative substitutions in their substrates, likely through buffering of their destabilizing effects. We further find that λ serves well to quantify the evolution of intrinsically disordered proteins even though the unstructured, thus generally variable regions in proteins are often flanked by very conserved sequences. Crucially, we show that both intrinsically disordered proteins and highly re-wired proteins in protein interaction networks, which have evolved new interactions and functions, exhibit a higher λ at the expense of enhanced chaperone assistance. Our findings thus highlight an intricate interplay of molecular chaperones and protein disorder in the evolvability of protein networks. Our results illuminate the role of chaperones in enabling protein evolution, and underline the importance of the cellular context and integrated approaches for understanding proteome evolution. We feel that the development of λ may be a valuable addition to the toolbox applied to understand the molecular basis of evolution.Evolution is driven by mutations, which lead to new protein functions but come at a cost to protein stability. Non-conservative substitutions are of interest in this regard because they may most profoundly affect both function and stability. Accordingly, organisms must balance the benefit of accepting advantageous substitutions with the possible cost of deleterious effects on protein folding and stability. We here examine factors that systematically promote non-conservative mutations at the proteome level. Intrinsically disordered regions in proteins play pivotal roles in protein interactions, but many questions regarding their evolution remain unanswered. Similarly, whether and how molecular chaperones, which have been shown to buffer destabilizing mutations in individual proteins, generally provide robustness during proteome evolution remains unclear. To this end, we introduce an evolutionary parameter  Evolutionary innovation through mutation is important for adaptation, thus ultimately survival of all species. Proteins, the main actors of cellular life, are generally only marginally stable in the cell and sensitive to mutations. This raises the question how the emergence of new functions is balanced with the destabilizing effect of mutations. Here, we incorporate biophysical knowledge on the stability effect of mutations into an extended model of protein evolution to better understand at the proteome level factors that promote non-conservative, more likely destabilizing mutations. Our analyses reveal a central role of molecular chaperones, specialized quality control enzymes that are known to promote protein evolvability by buffering the destabilizing effect of mutations in individual substrates. We find that chaperones support non-conservative mutations at the proteome level both directly, and through stabilizing intrinsically disordered proteins. We demonstrate how the main co- and post-translationally acting chaperones distinctly promote the same non-conservative mutations that characterize the re-wiring of protein interactions. Our results thus suggest how energetically costly protein quality control pathways can systematically promote the evolution of protein networks, and highlight the importance of considering the cellular context for understanding protein and proteome evolution. Protein evolution is central to adaptation and ultimately survival of all species dN, and synonymous or silent substitutions, dS. Their rate ratio ω = dN/dS is widely used to detect the strength of positive or purifying selection on protein sequences dNThe evolution of protein coding genes is commonly described by the rates of non-synonymous substitutions, or amino acid changes, ω = dN/dS to understand broad evolutionary selective pressures, it is more limited in quantifying how proteins evolve. Recent efforts to carefully integrate structural information have revealed distinct modes of evolution in buried and exposed residues Leu to Ile, often have very little effect on a protein, whereas a non-conservative (NC) mutation is more likely to affect protein stability and function dN, ω does not discriminate between the disparate effects of different amino acid mutations on protein structure and function, which is important for gaining further insight into the forces that shape protein evolution. Importantly, proteins are only marginally stable Despite the usefulness of λ, that directly infers the rate ratio of NC and C substitutions. Our rationale for λ is the demonstration in many experimental systems and biophysical analyses that NC mutations are generally more likely destabilizing than C mutations see ω, λ can capture known instances of rapid and distinct evolution, namely, those of intrinsically disordered proteins and those acting as re-wired nodes in protein-protein interaction networks. In these cases, NC mutations appear to drive new protein interactions and thus novel functions. Importantly, analyses of λ in the proteomes of E. coli, S. cerevisiae, and H. sapiens revealed higher λ values in chaperone substrates, suggesting that chaperones globally promote the acceptance of NC substitutions. Taken together, our analysis suggests that the mutations that are both on average more destabilizing and more likely leading to novel protein interactions are also preferentially found in chaperone substrates. These findings obtained at a systems-level for three different organisms agree with individual biochemical studies indicating a capacitor role of specific chaperones in evolution We hypothesized that incorporating the stability effect of mutations into an extended model of protein evolution may shed light onto how cellular factors influence the evolution of protein coding sequences. To this end, we developed an evolutionary parameter, dN are needed to better describe the forces shaping protein evolution. Initial classifications into “conservative” substitutions between more similar, and “radical” substitutions between more dissimilar amino acids focused for instance on charge and polarity in vivo is highly contextual, depending on the local and global protein fold, and is not easily measurable in high-throughput, we predicted the stability effect of a large set of mutations for the S. cerevisiae proteome in silicoΔΔG for different amino acids pairs . Because a hard classification into C or NC substitution is of necessity an approximation that neglects the detailed structural context of mutations for that particular protein, we sought to define only the most frequently destabilizing mutations as NC . Disordered regions in proteins maintain a distinct composition of polar and charged amino acids, and IDPs are under tight cellular regulation to prevent their aggregation λ based on the more general classification of NC and C defined above, to describe the evolution of IDPs.An interesting correlate and test case for our new evolutionary parameter S. cerevisiae proteome into three classes based on the percentages of residues that were predicted to be disorder, as described in ω, we found that ω is not well suited to detect differences in the evolution of proteins of different levels of structuredness . Evolving a novel protein interaction has been suggested to present one of the easiest routes to acquiring a novel protein function λ might characterize the evolvability of protein interactions.We next used λ and the evolution of novel PPIs, we extracted the consensus most highly re-wired proteins from the protein networks (PN) of S. cerevisiae and S. pombe , the weak substrates evolved at significantly higher relative rates of NC substitutions  and conservative (C) amino acid changes. Because NC substitutions are more likely to affect protein stability, which is a major biophysical constraint on function λ allows to characterize several aspects of protein evolution that are inaccessible to the established evolutionary rate ratio ω. In support of our rationale, we found that λ can quantify known instances of rapid protein evolution. For instance, λ captures the distinct evolutionary patterns of intrinsically disordered proteins, which paradoxically ω does not detect. Of note, not all disordered regions are equally variable, and distinct functional roles have been attributed to conserved and flexible disorder λ will become a useful tool to examine the evolution of proteins. The classification used here may be adapted and optimized using additional criteria to improve its usefulness to different problems. Thus, while some non-synonymous mutations will always be non-conservative and destabilizing, there may be species or compartment-specific aspects to consider in the classification of NC vs. C. Further refinements of the concept and implementation of λ may help capture specific aspects of protein evolution, for instance within specific organisms or organelles or even within classes of proteins, such as IDPs.To better understand λ we could capture the role of chaperones in conferring robustness against NC mutations, as well as the role of NC mutations in re-wiring of protein networks. Our findings that proteins most critical in protein interaction networks are both highly re-wired despite strong purifying selection, and preferentially supported by chaperones, suggests a general role of chaperones in protein network evolution. Proteins have tightly co-evolved with their cellular environment. By using well-curated sets of chaperone substrates, we find that weak chaperone dependence more strongly promotes protein evolution. Likely, stringently dependent substrates might already have exhausted all chaperone capacity for their normal folding requirements. The evolutionary advantage of weak chaperone dependence thus might also explain the low specificity observed in large and heterogeneous substrates sets for the Hsp70 and Hsp90 chaperone systems. The detailed differentiation between strong vs. weak substrate dependence demonstrates the power of λ to analyze this relationship at proteome level. The global link between the evolution of novel protein functions arising from NC mutations, and the buffering role of chaperones is in remarkable agreement with the analysis of accepted mutations from a directed enzyme evolution experiment focused on the bacterial chaperone GroEL We found the same set of NC substitutions to critically stand out in several independent paradigms: chaperone substrates and intrinsically disordered proteins show elevated rates of NC amino acid changes, and NC substitutions were strongly enriched in proteins that have evolved novel interactions as evident by both the comparison of large-scale protein interaction networks as well as an interaction propensity scale derived from a curated database of protein complexes. Thus, using Our results also fit well in the wider context of related work and theoretical considerations that mutational robustness is central to evolution and adaptation S. cerevisiae proteome, species–optimized metrics may increase the strength and significance of insight gained from λ in other organisms. The current classification into NC and C substitutions may become less accurate with increasing evolutionary distance from S. cerevisiae, raising the question of how λ changes with evolutionary distance. Similarly, optimized classifications may further increase the power of λ in the analysis of specific sets of proteins, such as IDPs or distinct sub-cellular localizations. To this end, we expect clear advances from novel targeted evolutionary approaches that more explicitly take aspects of protein biophysics and cellular processes into account. New technologies such as deep mutational scanning A detailed and mechanistic understanding of protein and proteome evolution will ultimately require contributions from many different approaches at different levels of resolution. Sequence-based evolutionary models will continue providing important insights and assistance in interpreting the increasing amounts of available sequencing data, offering a very efficient indication of distinct selective pressures. Cases of particular interest can be further analyzed with specialized algorithms to predict phenotypic consequences of individual mutations that may achieve higher resolution, especially in well-curated protein families and with available structural information. While in this work the definition of NC and C substitutions is based on predicted stability effects of mutations across the λ allowed us an integrated analysis that revealed a finely tuned interplay of costly protein homeostasis and beneficial evolution at proteome level. The direct relationship between chaperone assistance and the evolvability of protein networks is intriguing, and may explain the link between expanding chaperone systems with increasing proteome size and complexity Cost-benefit trade-offs are ubiquitous in organismal evolution. Our evolutionary parameter ijq is the instantaneous rate from codon i to j (i≠j),Protein evolutionary rates and parameters were estimated by maximum likelihood from a Markov model of codon substitutions t, κ, γ, and λ from pairs of aligned orthologous coding sequences by minimizing the log likelihood functionijn is the number of sites, and πi is set to the average genome codon composition of the species compared, in analogy to the F61 model. t is the relative divergence time estimated from the relative distance of two orthologous input sequences. κ is the transversion-transition ration of all substitutions in the input sequences. λ is the ratio of the rates of non-conservative and conservative substitutions. Thus, λ indicates the relative partitioning between on average more and less likely destabilizing mutations given all amino acid changes. All calculations were implemented in Matlab, and the function fminsearch was used for maximum likelihood estimation. The conventional evolutionary rates dN and dS, and their ratio ω = dN/dS were computed with the Matlab function dndsml. An independent evolutionary count model based on the established approach by Nei and Gojobori The transition probability matrix Generally, the calculation of evolutionary rates is based on counting the number of synonymous, non-synonymous, and here also conservative and non-conservative mutations between aligned orthologs relative to the number of synonymous, non-synonymous, conservative and non-conservative sites in the two sequences, while correcting for multiple substitutions. The maximum likelihood approach explicitly models codon sequence evolution as a stochastic process, and estimates all critical parameters, including the transition/transversion ratio, simultaneously in a probabilistic manner from the sequences. The power of maximum likelihood approaches decreases for small datasets, thus maximum likelihood methods are often applied to larger phylogenies. The count model does not explicitly incorporate transition/transversion biases, but includes mutations that are more than one nucleotide substitution apart by averaging over all possible mutational pathways, and is more robust for small datasets, e.g. low counts of non-conservative mutations. Both approaches produce very similar results .S. cerevisiae proteome. This algorithm predicts the effect of mutations with support vector machines that have been trained on experimental data on protein stability. Predictions of stability effects of mutations achieve an accuracy of about 70%. We ranked all amino acid pairs, combined in both directions , based on how likely there were highly destabilizing . Of note, some mutations exhibit clear anisotropy in their mutational effects. For instance, while Ala to Val mutations is mostly neutral, Val to Ala mutations are very often predicted to be highly destabilizing. Val residues are often found in the tightly packed hydrophobic core of proteins, thus more sensitive to substitutions. Because the direction of the mutation is not normally known, we considered the combined effect between amino acid pairs. Mutations that were in less than 20% of their occurrences highly destabilizing were considered conservative (C), and non-conservative (NC) otherwise. We validated that this is in full agreement with the widely used Blosum62 amino acid substitution matrix in that no NC mutation had a positive Blosum62 score. The conservative and non-conservative substitutions used in this analysis are listed in Protein stability is a major constraint on protein evolution. The stability effect of mutations depends on the local and global protein fold. However, sequence-based evolutionary models require a clear classification of mutations. In addition, detailed evolutionary trajectories are not known from comparing pair-wise sequence alignments of orthologous sequences, i.e. it is generally not known which sequence has incurred the mutation. We thus chose a simple classification into more likely destabilizing  and less likely destabilizing (conservative C) substitutions to approximate the stability effect of mutations and integrate it into sequence-based evolutionary models. The effect of mutations on protein stability was predicted from the amino acid sequences with the I-Mutant3.0 algorithm λ in S. cerevisiae, we started from 5025 known pairs of orthologous sequences between S. cerevisiae and S. paradoxus. We removed all alignments of pairs of orthologs if more than 1/3 of the positions in the alignments contained gaps, and required satisfactory convergence of the maximum likelihood in the computation of evolutionary rates (maxl<−1000). This lead to a curated dataset of 3495 pairs of orthologous sequences. Parameter estimation by maximum likelihood becomes inaccurate at very small sample sizes. To test for the robustness of our results, we analyzed protein evolutionary rates for proteins with at least 3 NC substitutions as estimated by maximum likelihood, and validated our findings by evolutionary rates computed by both the maximum likelihood and the count method of all sequences. Orthologs of E. coli and S. salmonella have diverged less, and we report the evolutionary rates from the count method. Similarly, orthologs of H. sapiens and M. musculus are more distant, and we report the evolutionary rates calculated by the count method, because these include also mutations that are more than one nucleotide substitution apart. Of note, the parameters from the maximum likelihood and count models are very highly correlated (S. cerevisiae (Scer) and S. paradoxus (Spar) were retrieved from the Broad Institute (http://www.broadinstitute.org/regev/orthogroups). We also computed evolutionary rates from aligned orthologs of E. coli and S. salmonella, and of H. sapiens and M. musculus, which were obtained from the Ensembl database (http://ensembl.org/biomart/martview/). For orthologs of the more distant H. sapiens and M. Musculus we required at least 80 aligned codons as described in via the corresponding amino acid sequences. Protein abundances for S. cerevisiae were obtained from S. cerevisiae mRNA expression levels were taken from E. coli were retrieved from H. sapiens “whole organism integrated dataset” from the paxdb database (www.pax-db.org). Intrinsic disorder was predicted with Disopred2 S. cerevisiae from H. sapiens from E. coli, S. cerevisiae, and H. sapiens respectively.For our analysis of rrelated . GenomicS. cerevisiae and S. pombe were downloaded from the Biogrid database (http://thebiogrid.org). To circumvent a systematic bias due to the very different coverage of the two networks, we extracted a consensus list of highly re-wired proteins as the consensus top 10% proteins in each network with the most “non-orthologous” interactions, i.e. interactions to proteins that do not have orthologs in the other species. We chose this procedure as a very conservative approach to infer re-wired protein interactions. If both binding partners have orthologous proteins in both species, but the exact edge is not present and both networks have very different depth and coverage, it is difficult to systematically know if this is because the edge is in fact not conserved, or simply because the edge was not detected in the much smaller network. In contrast, interactions to proteins that do not have an ortholog in the other organism must be species-specific, thus re-wired. Hubs are the top 10% most highly connected proteins in our study, and non-hubs the bottom 10% connected proteins. Bottlenecks are critical proteins that show a high betweenness centrality, i.e. concentrate the highest density of shortest paths The protein-protein interaction networks for λ and ω respectively by chaperone dependence, intrinsic disorder, and expression level. Predictor variables that did not improve the overall regression fit were excluded. The regressions of λ generally only relied on the input of chaperone dependence and disorder; we found expression to not explain λ, consistent with the lack of correlation between λ and expression levels. Correlation coefficients of regression fits ranged between R = 0.32 and R = 0.45. Partial regression plots indicate the individual contributions of predictor variables. Error bars were derived from predicting λ and ω respectively only from individual predictor variables. The relatively large error bars for the contributions of chaperone dependence reflect the limited power of predicting a continuous variable (λ or ω) only from a categorical one (chaperone substrate or not). This statistical approach is available from the freely available R package “NP” To systematically evaluate the contribution of chaperone assistance to protein evolutionary rates under consideration of confounding factors, we employed non-parametric regression analyses based on a kernel-smoothing approach that has explicitly been developed to test for the significance of categorical predictor variables. The test is fully data driven and robust to over-fitting through extensive cross-validation for smoothing parameter selection and bootstrapping to obtain the null distribution. We used this non-parametric regression model to predict www.r-project.org).Differences between distributions of evolutionary rates were tested for statistical significance by Wilcoxon rank-sum tests, and significant enrichments of protein categories in hubs and bottlenecks by Fisher's exact test. Next to p-values, we report the standardized mean difference (SMD) as measure of effect sizes between distributions. All statistical analyses were performed in the statistics environment R , 20% (NC20) and 30% (NC30), and compared to mutations that do not have a positive score in the Blosum62 matrix (NC). D Mutation rates of NC substitutions for different thresholds, compared to the rate of non-synonymous mutations (N). E Differences in the distributions of predicted stabilities for NC and C mutations for different thresholds.(EPS)Click here for additional data file.Figure S2NC substitutions have more severe phenotypic or fitness effects.A NC mutations are more damaging than C mutations as indicated by significantly higher PolyPhen scores. B NC mutations have more severe phenotypic consequences than C mutations as indicated by significantly lower SNPs3D scores. C NC mutations exhibit significantly lower experimentally measured fitness values compared to C mutations based on data from (EPS)Click here for additional data file.Figure S3Data curation and model validation.A The evolutionary parameter ω = dN/dS as computed by Maximum Likelihood estimation , and computed by an independent count model dnds) correlate very highly. Evolutionary rates and parameters are calculated for aligned orthologs of S. cerevisiae and S. paradoxus. B We implemented an independent extended count model to verify the evolutionary parameter λ = dNC/dC. The high correlation between λ computed by the ML or count model validates the overall approach and implementation. C The estimation of additional parameters compared to the model implemented by Yang and Nielson D Distributions of the evolutionary rates dS, dN, dC, and dNC. E Expression levels are the strongest determinant of the protein evolutionary rate dN and the rate ratio ω. For S. cerevisiae mRNA expression levels and ω are clearly correlated (Spearman's correlation coefficient Rs = −0.29). F Expression levels are not correlated to λ (RS = 0.04).(EPS)Click here for additional data file.Figure S4λ but not ω links to intrinsic disorder.A To avoid a consistent expression bias, structured , moderately unstructured  and unstructured  proteins were randomly sampled to have the same distributions of mRNA expression levels. We included n = 749 proteins of each category in our analysis . B Intrinsic disorder (% of disordered residues) does not correlate to ω (RS = 0.07), but C correlates to λ (RS = 0.36).(EPS)Click here for additional data file.Figure S5Effect of chaperone assistance and disorder on λ.A Substrates and non-substrates of the chaperonin GroEL in E. coli are both on average highly structured, but substrates evolve at higher λ. B Intrinsic disorder plays a much bigger role in the proteome of the eukaryote S. cerevisiae than in the prokaryote E. coli. C Chaperone networks in eukaryotes are more complex, and split more distinctively into co-translationally acting chaperones that facilitate de novo folding, and post-translationally acting chaperones in response to stress. The main co-translationally acting chaperone in the eukaryote S. cerevisiae is the ribosome-associated Hsp70 SSB. The main post-translationally acting heat shock protein is Hsp90. D Kinases that are strong Hsp90 substrates dN, but are also significantly less abundant than kinases that are not Hsp90 substrates. E Weak SSB substrates evolve at similar λ to non-substrates, but are significantly less disordered. As a result, the effect of SSB to promote λ in weak substrates cannot be explained by higher levels of intrinsic disorder. Significance levels are indicated as n.s. (not significant), * (p<0.05), and *** (p<0.001).(EPS)Click here for additional data file.Figure S6Higher λ in network hubs and bottlenecks. Hubs and bottlenecks as the most critical proteins in protein interaction networks are characterized by low ω, thus strong purifying selective pressure. Despite their generally high degree of conservation, both hubs and bottlenecks exhibit a higher λ. A The top and bottom 5% of proteins with respect to their network degree and betweenness centrality are compared. When considering only the extreme 5%, the statistical significance for λ in the smaller dataset is lost compared to the extreme 10%, but the trends are maintained. B The top 1% of proteins with the highest network degree  or betweenness centrality are compared to the bottom 5% of proteins with the lowest network degree or betweenness centrality respectively. We retain the bottom 5% because these proteins are already characterized by the minimal degree 1 or betweenness centrality 0. Proteins that are part of highly conserved large macromolecular complexes such as the ribosome or proteasome do not exhibit a higher λ despite their high degree in experimentally characterized protein interaction networks. The full proteome is shown for reference.(EPS)Click here for additional data file.Figure S7Chaperones facilitate higher λ in network hubs and bottlenecks.A Significance of the predictor variables explaining the higher λ in hubs compared to non-hubs. Only expression and disorder are significant predictors in the statistical analysis. B Hubs are more disordered, but also more highly expressed and longer-lived. Generally, more disordered proteins are usually less expressed and turned-over more rapidly. It appears that the chaperone SSB allows higher disorder and high, stable expression of its substrates compared to genome wide trends. C Significance of the predictor variables explaining the higher λ in bottlenecks compared to non-bottlenecks. Both disorder and SSB assistance significantly promote λ. D Bottlenecks are more disordered, but turned over more rapidly than non-bottlenecks. Significance levels are indicated as n.s. (not significant), * (p<0.05), and *** (p<0.001).(EPS)Click here for additional data file.Dataset S1Extended evolutionary rates.(XLSX)Click here for additional data file.