Proteins are ubiquitous molecules whose function in biological processes is determined by their 3D structure.
 Experimental identification of a protein's structure can be time-consuming, prohibitively expensive, and not always possible. 
 Alternatively, protein folding can be modeled using computational methods, which however are not guaranteed to always produce optimal results.
 GraphQA is a graph-based method to estimate the quality of protein models, that possesses favorable properties such as representation learning, explicit modeling of both sequential and 3D structure, geometric invariance and computational efficiency. 
 In this work, we demonstrate significant improvements of the state-of-the-art for both hand-engineered and representation-learning approaches, as well as carefully evaluating the individual contributions of GraphQA. Protein molecules are predominantly present in biological forms, responsible for their cellular functions. Therefore, understanding, predicting and modifying proteins in biological processes are essential for medical, pharmaceutical and genetic research. Such studies strongly depend on discovering mechanical and chemical properties of proteins through the determination of their structure. At the high level, a protein molecule is a chain of hundreds of smaller molecules called amino acids. Identifying a protein's amino-acid sequence is nowadays straightforward. However, the function of a protein is primarily determined by its 3D structure. Spatial folding can be determined experimentally, but the existing procedures are time-consuming, prohibitively expensive and not always possible. Thus, several computational techniques were developed for protein structure prediction (Arnold et al., 2006; Wang et al., 2017; Xu, 2019) . So far, no single method is always best, e.g. some protein families are best modeled by certain methods, also, computational methods often produce multiple outputs. Therefore, candidate generation is generally followed by an evaluation step. This work focuses on Quality Assessment (QA) of computationally-derived models of a protein (Lundstrom et al., 2001; Won et al., 2019) . QA, also referred to as model accuracy estimation (MAE), estimates the quality of computational protein models in terms of divergence from their native structure. The downstream goal of QA is two-fold: to find the best model in a pool of models and to refine a model based on its local quality. Computational protein folding and design have recently received attention from the machine learning community (Wang et al., 2017; Xu, 2019; Jones & Kandathil, 2018; Ingraham et al., 2019b; Anand & Huang, 2018; Evans et al., 2018; AlQuraishi, 2019) , while QA has yet to follow. This is despite the importance of QA for structural biology and the availability of standard datasets to benchmark machine learning techniques, such as the biannual CASP event (Moult et al., 1999) . The field of bioinformatics, on the other hand, has witnessed noticeable progress in QA for more than a decade: from earlier works using artificial neural networks (Wallner & Elofsson, 2006) or support vector machines (Ray et al., 2012; Uziela et al., 2016) to more recent deep learning methods based on 1D-CNNs, 3D-CNNs and LSTMs (Hurtado et al., 2018; Derevyanko et al., 2018; Pagès et al., 2018; Conover et al., 2019) . In this work, we tackle Quality Assessment with Graph Convolutional Networks, which offer several desirable properties over previous methods. Through extensive experiments, we show significant improvements over the state-of-the-art, and offer informative qualitative and quantitative analyses. GRAPHQA predicts local and global scores from a protein's graph using message passing among residues with chemical bond or spatial proximity. CASP QA algorithms score protein models by comparison with experimentally-determined conformations. For the first time we applied graph convolutional networks to the important problem of protein quality assessment (QA). Since proteins are naturally represented as graphs, GCN allowed us to collect the individual benefits of the previous QA methods including representation learning, geometric invariance, explicit modeling of sequential and 3D structure, simultaneous local and global scoring, and computational efficiency. Thanks to these benefits, and through an extensive set of experiments, we demonstrated significant improvements upon the state-of-the-art results on various metrics and datasets and further analyzed the results via thorough ablation and qualitative studies. Finally, we wish that Quality Assessment will gain popularity in the machine learning community, that could benefit from several curated datasets and ongoing regular challenges. We believe that richer geometric representations, e.g. including relative rotations, and raw atomic representations could represent an interesting future direction for learning-based Quality Assessment. Global Distance Test Total Score (GDT TS) Global Distance Test Total Score (GDT TS) is a global-level score obtained by first superimposing the structure of a decoy to the experimental structure using an alignment heuristic, and then computing the fraction of residues whose position is within a certain distance from the corresponding residue in the native structure ( figure 7 ). This percentage is computed at different thresholds and then averaged to produce a score in the range [0, 100], which we rescale between 0 and 1 (table 2). Table 2 i 2.5Å x x 5 6.3Å x 20% 60% 80% 100% Local Distance Difference Test (LDDT) Local Distance Difference Test (LDDT), is a residue-level score that does not require alignment of the structures and compares instead the local neighborhood of every residue, in the decoy and in the native structure. If we define the neighborhood of a residue as the set of its contacts, i.e. the set of other residues that lie within a certain distance from it, we can express the quality of that residue as the percentage of contacts that it shares with the corresponding residue in the native structure. Figure 8: Example of LDDT scoring for residue 7: the residues within a radius R 1 are { 6, 8, 10 } the native structure (left) and { 6, 8 } for the decoy (right); at a radius R 2 we have { 3, 6, 8, 9, 10, 11 } the native structure (left) and { 3, 6, 8, 9, 10 } for the decoy (right).
GraphQA is a graph-based method for protein Quality Assessment that improves the state-of-the-art for both hand-engineered and representation-learning approaches
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