Protein Model Quality Assessment Using Graph Convolutional Network

Submitted as a conference paper at ICLR 2020

GRAPHQA:PROTEIN MODEL QUALITY ASSESSMENT USING GRAPH CONVOLUTIONAL NETWORK

Federico Baldassarre1, Hossein Azizpour1, David Menendez´ Hurtado2, Arne Elofsson2 1 KTH - Royal Insitute of Technology 2 Stockholm University, Science for Life Laboratory and Dep. of Biochemistry and Biophysics

ABSTRACT

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. Al- ternatively, 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 over the state-of- the-art for both hand-engineered and representation-learning approaches, as well as carefully evaluating the individual contributions of GRAPHQA components.

1 INTRODUCTION

Protein molecules are predominantly present in biological forms, responsible for their cellular functions. Therefore, understanding, predicting and modifying proteins in biological processes are essen- tial 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; Pages` 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. 1 Submitted as a conference paper at ICLR 2020

ENCODER MESSAGE PASSING READOUT CASP

{,}

→ →

ℓ {} { }

→

native

Figure 1: Protein Quality Assessment. 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.

1.1 RELATED WORKS

Protein Quality Assessment (QA) methods are evaluated in CASP (Moult et al., 1995) since CASP7 (Cozzetto et al., 2007). Current techniques can be divided into two categories: single- model methods which operate on a single protein model to estimate its quality (Wallner & Elofsson, 2003), and consensus methods that use consistency between several candidates to estimate their quality (Lundstrom et al., 2001). Single-model methods are applicable to a single protein in isolation and in the recent CASP13 performed comparable to or better than consensus methods for the first time (Cheng et al., 2019). Recent single-model QA works are based on deep learning, except VoroMQA that takes a statistical approach on atom-level contact area (Olechnovic & Ven- clovas, 2017). 3DCNN adopts a volumetric representation of proteins (Derevyanko et al., 2018). Ornate improves 3DCNN by defining a canonical orientation (Pages` et al., 2018). ProQ3D uses a multi-layer perceptron on fixed-length protein descriptors (Uziela et al., 2017). ProQ4 adopts a pre-trained 1D-CNN that is fine-tuned in a siamese configuration with a rank loss (Hurtado et al., 2018). VoroMQA and ProQ3D are among the top performers of CASP13 (Won et al., 2019). Graph Convolutional Networks (GCNs) bring the representation learning power of CNNs to graph data, and have been recently applied with success to multiple domains, e.g. physics (Gonzalez et al., 2018), visual scene understanding (Narasimhan et al., 2018) and natural language understanding (Kipf & Welling, 2017). Molecules can be naturally represented as graphs and GCNs have been proven effective in several related tasks, including molecular representation learning (Duvenaud et al., 2015), protein interface prediction (Fout et al., 2017), chemical property prediction (Niepert et al., 2016; Gilmer et al., 2017; Li et al., 2018a), drug-drug interaction (Zitnik et al., 2018), drug- target interaction (Gao et al., 2018) molecular optimization (Jin et al., 2019), and generation of proteins, molecules and drugs (Ingraham et al., 2019a; You et al., 2018; Liu et al., 2018; Li et al., 2018b; Simonovsky & Komodakis, 2018). However, to the best of our knowledge, GCNs have never been applied to the problem of protein quality assessment.

1.2 CONTRIBUTIONS • This work is the first to tackle QA with GCN which bring several desirable properties over previous methods, including representation learning (3DCNN, Ornate), geometric invariance (VoroMQA, Ornate), sequence learning (ProQ4, AngularQA), explicit modeling of 3D structure (3DCNN, Ornate, VoroMQA) and computational efficiency. • Thanks to these desirable properties, a simple GCN setup achieves improved results compared to the more sophisticated state-of-the-art methods such as ProQ4. This is demonstrated through extensive experiments on multiple datasets and scoring regimes. • Novel representation techniques are employed to explicitly reflect the sequential (residue separation) and 3D structure (angles, spatial distance and secondary structure) of proteins. • Enabled by the use of GCN, we combine the optimization of local and global score for QA, improving over the performance of a global-only scoring method. • Through an extensive set of ablation studies, the significance of different components of the method, including architecture, loss, and features, are carefully analyzed. PyTorch implementation, datasets and experiments: github.com/baldassarreFe/protein-quality-gn.

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2 METHOD

We start describing our method by arguing for representation of protein molecules as graphs in learning tasks, then we deﬁne the problem of protein quality assessment (QA), and ﬁnally we present the proposed GRAPHQA architecture.

2.1 PROTEIN REPRESENTATION AS GRAPHS

Proteins are large molecular structures that perform vital functions in all living organisms. At the chemical level, a protein consists of one or more chains of smaller molecules, which we interchange- ably refer to as residues for their role in the chain, or as amino acids for their chemical composition. The sequence of residues S = { ai } that composes a protein represents its primary structure, where ai is one of the 22 amino acid types. The interactions between neighboring residues and with the environment dictate how the chain will fold into complex spatial structures that represent the protein’s secondary structure and tertiary structure. Therefore, for learning tasks involving proteins, a suitable representation should reﬂect both the identity and sequence of the residues, i.e. the primary structure, and geometric information about the protein’s arrangement in space, i.e. its tertiary structure. Some works use RNN or 1D-CNN to model proteins as sequence with the spatial structure potentially embedded in the handcrafted residue features (Hurtado et al., 2018; Conover et al., 2019). Other recent works explicitly model proteins’ spatial structure using 3D-CNN but ignore its sequential nature (Derevyanko et al., 2018; Pages` et al., 2018). We argue that a graph-based learning can explicitly model both the sequential and geometric structures of proteins. Moreover, it accommodates proteins of different lengths and spatial extent, and is invariant to rotations and translations. In the simplest form, a protein can be represented as a linear graph, where nodes represent amino acids and edges connect consecutive residues according to the primary structure. This set of edges, which represent the covalent bonds that form the protein backbone, can be extended to include the interactions between non-consecutive residues, e.g. through Van der Waals forces or hydrogen bonds, commonly denoted as contacts. By forming an edge between all pairs of residues that are within a chemically reasonable distance of each other, the graph becomes a rich representation of both the sequential and geometric structure of the protein (ﬁgure 2). We refer to this representation, composed of residues, bonds and contacts, as the protein graph:

bond contact P = { vi } , ei,j |i − j| = 1 ∪ ei,j |i − j| > 1, kCi − Cjk ≤ dmax , (1) where i, j = 1,..., |S| are residue indices, C = { (x, y, z)i } represents the spatial arrangement of the residues, i.e. the protein’s conformation, and dmax is a cutoff distance for contacts. With the protein’s structure encoded in the graph, additional residue and relationship features can be encoded as nodes and edges attributes, vi and ei,j respectively. Section 3.2 describes, in detail, an attribution that preserves the sequence information and 3D geometry while remaining invariant to rotation.

A1 C5 Contact B2 A3

C4 B4 A B Bond B2 B5 A1 C (a) Sequential (b) Spatial (c) Graph

Figure 2: Protein representations for learning. Sequential representations for LSTM or 1D-CNN fail to represent spatial proximity of non-consecutive residues. Volumetric representations for 3D- CNN fail instead to capture sequence information and is not rotation invariant. Protein graphs explicitly represent both sequential and spatial structure, and are geometrically invariant by design.

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2.2 PROTEIN QUALITY ASSESSMENT

Experimental identiﬁcation of a protein’s native structure can be time consuming and prohibitively expensive. Alternatively, computational folding methods are used to generate decoy conformations for a speciﬁc target protein. Since no single method is consistently best, a Quality Assessment (QA) step is used to identify the decoys that most correctly represent the native structure. If the native structure Cnative is experimentally determined, the quality of a decoy can be measured by comparison, e.g., in the CASP challenge, decoys submitted for a target are scored against the unreleased native structure. Some comparative algorithms compute global (per decoy) scores, which can be used for ranking and represent the principal factor for CASP, while others produce local (per residue) scores which help identify incorrect parts of a decoy (Uziela et al., 2018). In most scenarios, however, the native structure is not available and quality must be estimated based on physical and chemical properties of the decoy, e.g. in drug development, it would be unpractical to synthesize samples of novel proteins and researchers rely on computational folding and quality assessment instead.

Here we introduce GRAPHQA, a graph-based QA neural network that learns to predict local and global scores, with minimal feature and model engineering, using existing datasets of scored proteins. In this paper, we train GRAPHQA on two widely-used scoring algorithms: the Global Distance Test Total Score (Zemla, 2003), which is the ofﬁcial CASP score for decoy-level quality assessment, and the Local Distance Difference Test (Mariani et al., 2013), a residue-level score. We denote them g d native ` d native as q := GDT TS(C ,C ) and { qi } := LDDT(C ,C ). ` g With GRAPHQAi (P) and GRAPHQA (P) denoting the network’s local and global predictions for an input P, the learning objective is to minimize the following Mean Squared Error (MSE) losses:

|S| 2 X h ` `i g g 2 L` = GRAPHQAi (P) − qi Lg = [GRAPHQA (P) − q ] . (2) i Note that, for the sole purpose of sorting decoy according to ground-truth quality, training with a ranking loss would be sufﬁcient (Derevyanko et al., 2018). Instead, MSE forces the output to match the quality score, which is a harder objective, but results in a network can be more easily inspected and possibly used to improve existing folding methods in an end-to-end fashion (section 4.2).

2.3 GRAPHQAARCHITECTURE

GRAPHQA is a graph convolutional network that operates on protein graphs using the message- passing algorithm described in Battaglia et al. (2018). The building block of GRAPHQA, a graph layer, takes a protein graph as input (with an additional global feature u), and performs the following propagation steps to output a graph with updated node/edge/global features and unchanged structure: 0 e 0 e→u 0 ei,j = φ (ei,j, vi, vj, u) Update edges e¯ = ρ { ei,j } Aggregate all edges 0 e→v 0 0 v→u 0 e¯i = ρ { ej,i } Aggregate edges v¯ = ρ ({ vi }) Aggregate all nodes 0 v 0 Update nodes 0 u 0 0 Update global features vi = φ (e¯i, vi, u) u = φ (e¯ , v¯ , u) where φ represent three update functions that transform nodes/edges/global features (e.g. a MLP), and ρ represent three pooling functions that aggregate features at various levels (e.g. sum or mean). Similarly to CNNs, multiple graph layers are stacked together to allow local information to propagate to increasingly larger neighborhoods (i.e. receptive ﬁeld). This enables the network to learn quality-related features at multiple scales: secondary structures in the ﬁrst layers, e.g. α-helices and β-sheets, and larger structures in deeper layers e.g. domain structures and arrangements.

The GRAPHQA architecture is conceptually divided in three stages (ﬁgure 1). At the input, the encoder increases the node and edge features’ dimensions through 2×(Linear-Dropout-ReLU) trans- formation and adds a global bias. Then, at its the core, L message-passing layers operate on the encoded graph, leveraging its structure to propagate and aggregate information. The update functions φ consist of Linear-Dropout-ReLU transformations, with the size of the linear layers progressively decreasing. We use average pooling for the aggregation functions ρ, since preliminary experiments with max/sum pooling performed poorly. Finally, the readout layer outputs local and global quality scores by applying a Linear-Sigmoid operation to the latest node and global features, respectively.

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3 EXPERIMENTS

3.1 EXPERIMENTAL SETUP

Following the common practice in Quality Assessment, we use the data from past years’ editions of CASP, encompassing several targets with multiple scored decoys each. Removing all sequences with ` g t,d |S| < 50 from CASP 7-10 results in a dataset of ∼100k scored decoys (P, { qi } , q ) , which we randomly split into a training set (402 targets) and a validation set for hyper-parameter optimization (35 targets). CASP 11 and 12 are set aside for testing against top-scoring methods (table 3).

We evaluate the performances of GRAPHQA on the following standard metrics. At the global level, we compare the predicted and ground-truth GDT TS scores and compute: Root Mean Squared Er- ror (RMSE), Pearson correlation coefficient computed across all decoys of all targets (R), and Pear- son correlation coefficient computed on a per-target basis and then averaged over all targets (Rtarget). At the local level, we compare the predicted and ground-truth LDDT scores and compute: RMSE, Pearson correlation coefficient computed across all residues of all decoys of all targets (R), and Pearson correlation coefficient computed on a per-decoy basis and then averaged over all decoys of all targets (Rmodel). Of these, we focus on Rtarget and Rmodel, which respectively measure the ability to rank decoys by quality and to distinguish the correctly-predicted parts of a model from those that need improvement. A detailed description of these and other metrics can be found in appendix E.

3.2 FEATURES

Node features The node attributes vi of a protein graph P represent the identity, statistical, and structural features of the i-th residue. We encode the residue identity using a one-of-22 encoding of the corresponding amino acid. Following Hurtado et al. (2018), we also add two residue-level statistics computed using Multiple Sequence Alignment (MSA) (Rost et al., 1994), namely self- information and partial entropy, each described by a 23-dimensional vector. Finally, we add a 14-dimensional vector of 3D spatial information including the dihedral angles, surface accessibility and secondary structure type as determined by DSSP (Kabsch & Sander, 1983). Edge features An edge represents either a contact or a bond between two residues i and j w.r.t. to the conformation C = { (x, y, z)i }. An edge always exists between two consecutive residues, while non-consecutive residues are only connected if ||Ci − Cj|| < dmax, with dmax optimized on the validation set. We further enrich this connectivity structure by encoding spatial and sequential distances 2 as an 8D feature vector ei,j. Spatial distance is encoded using a radial basis function exp(−di,j/σ), with σ determined on the validation set. Sequential distance is deﬁned as the number of amino acids between the two residues in the sequence and expressed using a separation encoding, i.e. a one-hot encoding of the separation |i − j| according to the classes { 0, 1, 2, 3, 4, 5 : 10, > 10 }.

3.3 OPTIMIZATION AND HYPERPARAMETER SEARCH

The MSE losses in equation 2 are weighted as Ltot = λ`L` + λgLg and minimized using Adam Optimizer (Kingma & Ba, 2014) with L2 regularization. GRAPHQA is signiﬁcantly faster to train than LSTM or 3D-CNN methods, e.g. 35 epochs takes ∼2 hours on one NVIDIA 2080Ti GPU with batches of 200 graphs. This allows us to perform extensive hyper-parameter search. Table 4 reports the search space, as well as the parameters of the model with highest Rtarget on the validation set.

4 EVALUATION

We compare GRAPHQA with the following methods, chosen either for their state-of-the-art performances or because they represent a class of approaches for Quality Assessment. ProQ3D (Uziela et al., 2017) computes fixed-size statistical descriptions of the decoys in CASP 9-10, including Rosetta energy terms, which are then used to train a Multi Layer Perceptron on quality scores. In ProQ4 (Hurtado et al., 2018), a 1D-CNN is trained to predict LDDT scores from a vectorized representation of protein sequences, a global score is then obtained by averaging over all residues. ProQ4 is pretrained on a large dataset of protein secondary structures and then fine tuned on CASP 9-10 using a siamese configuration to improve ranking performances. Their results are reported on both CASP 11, which is used as a validation set, and CASP 12. 3DCNN (Derevyanko et al., 2018) trains

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Table 1: Comparison of state-of-the-art QA methods. At the residue level we compare LDDT scores and report Pearson correlation and Pearson correlation per model. At the global level we compare GDT TS scores and report Pearson correlation and Pearson correlation per target.

CASP 11 CASP 12 GDT TS LDDT GDT TS LDDT RRtarget RRmodel RRtarget RRmodel ProQ3D .772 .452 .84 .61 .806 .609 ProQ4 .77 .56 .772 .516 VoroMQA .651 .457 .605 .559 Rwplus .206 -.096 .417 AngularQA .651 .439 3D CNN .629 .421 .607 Ornate .637 .386 .670 .491 GRAPHQA .910 .740 .855 .610 .843 .745 .843 .573 GRAPHQARAW .836 .609 .799 .529 .816 .673 .796 .507 a CNN on a three-dimensional representation of atomic densities to rank the decoys in CASP 7-10 according to their GDT TS scores. Notably, no additional feature is used other than atomic structure and type, however, the ﬁxed-size volumetric representation of this method is sensitive to rotations and does not scale well with protein size. Ornate (Pages` et al., 2018) applies a similar 3D approach to predict local CAD-scores (Olechnovic & Venclovas, 2017) and achieves rotation invariance by specifying a canonical residue-centered orientation. Although optimized for local scoring, the average of the predicted scores is shown to correlate well with GDT TS. AngularQA (Conover et al., 2019) feeds a sequence-like representation of the protein structure to an LSTM to predict GDT TS scores. The LSTM network is trained on decoys from 3DRobot and CASP 9-11, while CASP 12 is used for model selection and testing. VoroMQA and RWplus (Olechnovicˇ & Venclovas, 2017; Zhang & Zhang, 2010) are two statistical potential methods that represent an alternative to the other machine-learning based methods.

Table 1 compares the performances of GRAPHQA and other state-of-the-art methods on CASP 11 and 12, while ﬁgure 3 contains a graphical representation of true vs. predicted scores for all target in CASP 12, and an example funnel plot for the decoys of a single target. A more in-depth evaluation on the stage 1 and stage 2 splits of CASP 11, 12, 13 and CAMEO can be found in appendix F.

Of all methods, only GRAPHQA and ProQ4 co-optimize for local and global predictions, the former thanks to the graph-based architecture, the latter thanks to its siamese training conﬁguration (the results reported for ProQ3D refer to two separate models trained for either local or global scores). At the local level, our method proves to be on par or better than ProQ3D and ProQ4, demonstrating the ability to evaluate quality at the residue level and distinguishing correctly predicted parts of the protein chain. At the global level, signiﬁcantly higher R and Rtarget metrics indicate than GRAPHQA is more capable than other state-of-the-art methods at ranking decoys based on their overall quality. As shown in our ablation studies (section 5), hand-engineered features like MSA and DSSP contribute to the performances of GRAPHQA, yet we wish to prove that our method can learn directly from raw data. GRAPHQARAW is a variant that relies uniquely on the one-hot encoding of amino acid identity, similarly to how 3D-CNN and Ornate employ atomic features only. The results for GRAPHQARAW show that, even without additional features, our method outperforms purely representation-learning methods.

4.1 ABLATION STUDIES

In this section we analyse how various components of our method contribute to the final performance, ranging from optimization and architectural choices to protein feature selection. Unless stated otherwise, all ablation studies follow the training procedure described in section 3.3 for a lower number of epochs. We report results on CASP 11 as mean and standard deviation of 10 runs. Local and global co-optimization We investigate the interplay between local and global predictions, specifically whether co-optimizing for both is beneficial or detrimental. At the global level, models trained to predict only global scores achieve a global RMSE of 0.129±.007, whereas models trained to predict both local and global scores obtain 0.117±.006, suggesting that local scores can

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provide additional information and help the assessment of global quality. At the local level instead, co-optimization does not seem to improve performances: models trained uniquely on local scores achieve a local RMSE of 0.121±.002, while models trained to predict both obtain 0.123±.004. Connectivity and Architecture In this study, we test the combined effects of the depth of the network L and the cutoff value dmax. On the one hand, every additional message-passing layer allows to aggregate information from a neighborhood that is one hop larger than the previous, effectively extending the receptive field at the readout. On the other hand, the number of contacts included in the graph affects its connectivity and the propagation of messages, e.g. low dmax correspond to a low average degree and long shortest paths between any two residues, and vice versa (section B.2). Thus, an architecture that operates on sparsely-connected graphs will require more message-passing layers to achieve the same holistic view of a shallow network operating on denser representations. However, this trade off is only properly exposed if u, φu, ρu are removed from the architecture. In fact, this global pathway represents a propagation shortcut that connects all nodes in the graph and sidesteps the limitations of shallow networks. With the global pathway disabled, global predictions are computed in the readout layer by aggregating node features from the last MP layer. Figure 4 reports the RMSE obtained by networks of different depth with no global path, operating on protein graphs constructed with different cutoff values. As expected, the shallow 3-layer architecture requires more densely-connected inputs to achieve the same performances of the 9-layer network. Surprisingly, local predictions seem to be more affected by these factors than global predictions, suggesting that a large receptive field is important even for local scores. Node and Edge Features We evaluate the impact of node and edge features on the overall prediction performances (figure 5). For the nodes, we use the amino acid identity as a minimal representation and combine it with: a) DSSP features, b) partial entropy, c) self information, d) both DSSP and MSA features. All features improve both local and global scoring, with DSSP features being marginally more relevant for LDDT. For the edges, we evaluate the effect of having either: a) a binary indicator of bond/contact, b) geometric features, i.e. the euclidean distance between residues, c) sequential features, i.e. the categorical encoding of the separation between residues, d) both distance and separation encoding. Progressively richer edge features seem to be benefit LDDT predictions, while little improvement can be seen at the global level.

4.2 VISUALIZATION AND EXPLAINABILITY

The design of GRAPHQA makes it suitable not only for scoring, but also to identify refinement opportunities for computationally-created decoys. Figure 6 shows a decoy that correctly models the native structure of its target for most of the sequence, but one extremity to which both GRAPHQA and LDDT assign low local scores. Unlike LDDT, however, GRAPHQA is fully differentiable and the trained model can be used to explain the factors that influenced a low score and provide useful feedback for computational structure prediction. A simple approach for explaining predictions of a differentiable function f(x) is Sensitivity Anal- ysis (Baehrens et al., 2010; Simonyan et al., 2014), which uses k∇xfk to measure how variations in the input affect the output. In figure 6 we consider the scores predicted for two different residues and compute the magnitude of the gradients w.r.t. the edges of the graph. Interestingly, GRAPHQA

GDT-TS LDDT .17 .16 Layers 3 .15 .16 9 .14 .15

.13 RMSE .14

.12 .13 .11 .12

0 6 8 10 12 14 0 6 8 10 12 14 Cutoff Cutoff (a) (b) (c)

Figure 3: Histograms of true vs. predicted LDDT Figure 4: Trade-off between number of (a) and GDT TS (b) scores on CASP 12, (c) funnel message-passing layers and connectivity plot of the decoys of target T0944 (PDB 5ko9). of the protein graph.

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Rmodel (LDDT) Rtarget (GDT-TS) Rmodel (LDDT) Rtarget (GDT-TS)

Residues Edge Type

Res + DSSP Distance Res + Part Entr Sep Enc Res + Self Info

All Dist + Sep Enc

0.50 0.55 0.60 0.55 0.65 0.75 0.58 0.60 0.70 0.75

Figure 5: Ablation study of node and edge features. All node features improve both local and global scoring, with DSSP features being marginally more relevant for LDDT (left). Richer edge features beneﬁt LDDT predictions, while little improvement can be seen at the global level (right). is able to capture quality-related dependencies not only in the neighborhood of the selected residues, but also further apart in the sequence.

Finally, we measure whether the global predictions of GRAPHQA could be used to improve the contact maps used by computational methods to build protein models. If the network has learned a meaningful scoring function for a decoy, then the gradient of the score w.r.t. the contact distances should aim in the direction of the native structure. Considering all decoys of all targets in CASP 11, g we obtain an average cosine similarity cos (∂GRAPHQA /∂d, ddecoy − dnative) of 0.14±.08, which suggests that gradients can be used as a coarse feedback for end-to-end protein model prediction.

(a) Predicted (b) True (c) Native (d) (e)

Figure 6: One decoy of T0773 in CASP11. Both GRAPHQA (a) andLDDT (b) assign low local scores to a segment of the decoy (in red), highlighting a discrepancy w.r.t. the native structure (c). The gradient magnitude w.r.t. the edges of the predicted LDDT score for residues 20 (d) and 60 (e) reveal long range dependencies inside the protein graph.

5 CONCLUSION

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.

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11 Submitted as a conference paper at ICLR 2020

APROTEIN QUALITY ASSESSMENT

For the interested reader, we describe here in more detail how the Global Distance Test Total Score (Zemla, 2003) and the Local Distance Difference Test (Mariani et al., 2013) are computed. Further- more, we provide an intuition over what the benefits and downsides of each method are and motivate why a better quality assessment should consider both a global measure and a local measure. 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).

Figure 7: GDT TS

Table 2

d native i kCi − Ci k < 1 < 2 < 5 < 10 1 0.6 A˚ x x x x 2 1.2 A˚ x x x 3 1.9 A˚ x x x 4 2.5 A˚ x x 5 6.3 A˚ 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.

12 12 5 5 11 4 2 4 2 6 11 6

3 1 3 1

7 10 7 10

2 2 8 8

9 1 1 9

Figure 8: Example of LDDT scoring for residue 7: the residues within a radius R1 are { 6, 8, 10 } the native structure (left) and { 6, 8 } for the decoy (right); at a radius R2 we have { 3, 6, 8, 9, 10, 11 } the native structure (left) and { 3, 6, 8, 9, 10 } for the decoy (right).

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BDATASETS AND STATISTICS

B.1 DATASETS

We consider all decoys of all target included in CASP 7-13, excluding proteins whose sequence is shorter than 50 residues and targets that have been canceled by the organizers. In addition to CASP datasets, we test our method on all targets published in CAMEO (Haas et al., 2013) between July and December 2017.

Table 3: Datasets from previous CASP editions

Dataset Targets Models Usage CASP 7 95 19591 CASP 8 122 34789 Train/Val CASP 9 117 34946 CASP 10 103 26254 CASP 11 83 16094 CASP 12 40 6924 Test CASP 13 20 7838 CAMEO 676 20891

B.2 PROTEIN GRAPHS STATISTICS

The cutoff value dmax determines which edges are included in the graph and, consequentially, its connectivity. A low cutoff implies a sparsely connected graph, with few edges and long paths between nodes. A higher cutoff yields a denser graph with more edges and shorter paths. In ﬁgure 9 we report some statistics about number of edges, average degree and average shortest paths, evaluated at different cutoff values on 1700 decoys from CASP 11.

Number of edges Avg Degree Avg Shortest Path 12000 40 80 10000

8000 30 60

6000 20 40 4000 10 20 2000

0 0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14

Cutoff dmax Cutoff dmax Cutoff dmax Figure 9: Number of edges, average degree, and average shortest paths at different cutoff values (sample size: 1700 decoys from CASP 11)

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CGRAPHQA ARCHITECTURE

In this section, we illustrate in more detail the structure of the GRAPHQA architecture, as well as the hyperparameter space that was explored to optimize performances on the validation set.

C.1 MESSAGE-PASSING LAYERS

Within GRAPHQA, a protein structure is represented as a graph whose nodes correspond to residues and whose edges connect interacting pairs of amino acids. At the input, the features of the i-th residue are encoded in a node feature vector vi. Similarly, the features of the pairwise interaction between residues i and j are encoded in an edge feature vector ei,j. A global bias term u is also added to represent information that is not localized to any speciﬁc node/edge of the graph. With this graph representation, one layer of message passing performs the following updates.

1. For every edge i → j, the edge feature vector is updated using a function φe of adjacent nodes vi and vj, of the edge itself ei,j and of the global attribute u: 0 e ei,j = φ (ei,j, vi, vj, u)

0 2. For every node i, features from incident edges { ej,i } are aggregated using a pooling function ρe→v: 0 e→v 0 e¯i = ρ { ej,i } 3. For every node i, the node feature vector is updated using a function φv of aggregated 0 incident edges e¯i, of the node itself vi and of the global attribute u: 0 v 0 vi = φ (e¯i, vi, u) 4. All edges are aggregated using a pooling function ρe→u: 0 e→u 0 e¯ = ρ { ei,j } 5. All nodes are aggregated using a pooling function ρv→u: 0 v→u 0 v¯ = ρ ({ vi }) 6. The global feature vector is updated using a function φu of the aggregated edges e¯0, of the aggregated nodes v¯0 and of the global attribute u: u0 = φu (e¯0, v¯0, u)

In GRAPHQA, all intermediate updates are implemented as Linear-Dropout-ReLU functions, and all aggregation functions use average pooling. The encoder and readout layers do not make use of message passing, effectively processing every node/edge in isolation. Message passing is instead enabled for the core layers of the network and enables GRAPHQA to process information within progressively expanding neighborhoods. The number of neurons in the core message-passing layers decreases from the input to the output. Speciﬁcally it follows a linear interpolation between the input and output numbers reported below, rounded to the closest power of two. In preliminary experiments, we noticed that a progressive increase of the number of layers results in convergence issues, which is in contrast to the practice of increasing the number of channels in Convolutional Neural Networks.

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C.2 HYPERPARAMETER OPTIMIZATION

We perform a guided grid search over the following hyper parameter space. The ﬁnal model is chosen to be the one with the highest Rtarget on the validation set. The following considerations were made:

• The values for dmax are chosen on the base that the typical bond length is ∼ 5A˚ and residue- residue interactions are negligible after ∼ 10A.˚ • The values for σ are chosen so that the RBF encoding of the edge length is approximately linear around ∼ 5A.˚ • The values for L are chosen to approximately match the average length of the shortest paths in the protein graphs at different cutoffs. • In addition to what described in section 2.3, we also tested an architecture with BatchNorm layers between the Dropout and ReLU operations, but apart from a signiﬁcant slowdown we did not notice any improvement.

Table 4: Hyper parameter space and best values

Hyper parameter Values Best MP Layers L 3, 4, 5, 6, 7, 8, 9 6 MP input size e 32, 64, 128 128 MP input size v 64, 128, 256, 512 512 MP input size u 64, 128, 256, 512 512 MP output size e 8, 12, 16, 32 16 MP output size v 8, 16, 32, 64 64 MP output size u 8, 12, 16, 32 32 Cutoff dmax 6, 8, 10, 12 8 Sigma σ 10, 15, 20 15 Dropout rate 0, 0.1 0.2, 0.3, 0.4 0.2 Learning rate 10−2, 10−3 10−3 Weight decay 10−4, 10−5 10−5 Local weight λ` 1, 5, 10 1 Global weight λg 1, 5, 10 1

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DADDITIONAL STUDIES

To complement the analysis reported in the main text, we perform additional studies on the effect of feature representation and on the generalization ability of the trained model.

D.1 DISTANCE AND SEPARATION ENCODING

The feature vectors associated to the edge of the graph represent two types of distances between residues, namely spatial distance and separation in the sequence. In this study we evaluate the effect of different representations on validation performances. Spatial distance is the physical distance between ammino acids, measured as the euclidean distance between their β carbon atoms. We consider three possible encodings for this distance:

• Absent: spatial distance is not provided as input; • Scalar: spatial distance is provided as a raw scalar value (in Angstrom);˚ • RBF: spatial distance is encoded using 32 RBF kernels, with unit variance, equally spaced between 0 and 20.

Figure 10 reports the aggregated performances on CASP 11 of ten runs for each of the above. The rich representation of the RBF kernels seem to improve both LDDT and GDT TS scoring performances, even though the effect is rather limited.

Rmodel (LDDT) Rtarget (GDT-TS)

Absent

Scalar

RBF

0.58 0.59 0.60 0.61 0.68 0.70 0.72 0.74 0.76

Figure 10: Spatial distance: absent, encoded as a scalar, encoded using RBF kernels.

Separation is the number of residues between to amino acids in the sequence, we consider three possible encodings:

• Absent: sequential separation is not provided as input; • Scalar: sequential separation is provided as a raw scalar value (positive integer); • Categorical: sequential separation is encoded as a one-hot categorical variable, according to the classes { 0, 1, 2, 3, 4, 5 : 10, > 10 }, which are based on typical interaction patterns within a peptidic chain.

Figure 11 reports the aggregated performances on CASP 11 of ten runs for each of the above. For local scoring, the choice of encoding plays little difference as long as separation is present in the input. On the other hand, the choice of categorical encoding over scalar encoding results in higher global scoring performance.

Rmodel (LDDT) Rtarget (GDT-TS)

Absent

Scalar

Categorical

0.56 0.58 0.60 0.68 0.70 0.72 0.74 0.76

Figure 11: Sequential separation: absent, encoded as a scalar, encoded as a categorical variable.

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D.2 TRANSMEMBRANEVS. SOLUBLEPROTEINS

In this study, we evaluate how the natural environment of a protein affects the predictive performances of our method. Targets from CASP 11 and 12 are classiﬁed as transmembrane and soluble according to Peters et al. (2015) and scored separately using GRAPHQA. Transmembrane proteins behave differently from soluble proteins as a consequence of the environment they are placed in. The former expose non-polar residues to the cellular membrane that surrounds their structure. On the contrary, the latter tend to present polar amino acids to the surrounding water-based solvent. Since this information is not explicitly provided to the model, we can compare the predictive performances between the two sets and check that it has actually learned a ﬂexible protein representation. The outcome of this evaluation is shown in table 5. While it is evident that GRAPHQA performs better on soluble proteins, which are more numerous in the training set, it also scores transmembrane proteins to an acceptable degree.

Table 5: Performances of GRAPHQA on transmembrane and soluble targets from CASP 11 and 12.

GDT TS LDDT FRL RRtarget RMSE ρ ρtarget τ τtarget RRmodel RMSE Transmembrane 0.092 0.714 0.538 0.209 0.714 0.463 0.523 0.328 0.679 0.487 0.170 Soluble 0.076 0.790 0.627 0.177 0.796 0.500 0.594 0.361 0.770 0.532 0.155

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EADDITIONAL METRICS

The Quality Assessment literature is rich of metrics to measure the performances of a scoring method. In the main text we tried to keep the exposition uncluttered by only reporting ﬁgures for the most important metrics. Here we present a more extensive set of metrics, that further describe our method and can serve as future benchmark. In the following, we use: t = 1,...,T Target proteins d = 1,...,Dt Decoys of a target t i, j = 1,..., |S | Residue indexes of a target qg,t,d = GDT TS(Ct,d,Ct,native) Global quality score (true) `,t,d t,d t,native Local quality scores (true) qi = LDDT(C ,C ) g t,d Global quality score (predicted) GRAPHQA (P ) ` t,d Local quality scores (predicted) GRAPHQAi (P )

Root Mean Squared Error (RMSE) We compute RMSE between all true and predicted scores, for both LDDT and GDT TS. For LDDT, it it the square root of:

t |St| T D 2 1 X 1 X 1 X `,t,d ` MSE = q − GRAPHQA (Pt,d) T Dt |St| i i t=1 d=1 i=1

For GDT TS, it it the square root of:

T Dt 1 X 1 X g,t,d g t,d 2 MSE = q − GRAPHQA (P ) T Dt t=1 d=1

Correlation coefﬁcients We compute the Pearson (R), Spearman (ρ) and Kendall (τ) correlation coefﬁcients between all true and predicted scores. Since all scores are treated equally, with no dis- tinction between different decoys or different targets, a high value for these scores can be misleading. Thus, their per-model and per-target versions should be also checked. For LDDT:

`,t,d ` t,d R = PEARSON { qi } , { GRAPHQAi (P ) }

`,t,d ` t,d ρ = SPEARMAN { qi } , { GRAPHQAi (P ) }

`,t,d ` t,d τ = KENDALL { qi } , { GRAPHQAi (P ) }

For GDT TS: g,t,d g t,d R = PEARSON { q } , { GRAPHQA (P ) } g,t,d g t,d ρ = SPEARMAN { q } , { GRAPHQA (P ) } g,t,d g t,d τ = KENDALL { q } , { GRAPHQA (P ) }

Correlation coefficients per-model For every decoy of every target, we compute the Pearson (Rmodel), Spearman (ρmodel) and Kendall (τmodel) correlation coefficients between true and predicted residue-level scores (LDDT). We then report the average correlation coefficients across all decoys of all targets. The per-model correlation coefficients estimate the performance of the network to rank individual residues by their quality and distinguish correctly vs. incorrectly folded segments.

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Per-model correlation coefﬁcients are computed only for LDDT:

T Dt 1 X 1 X `,t,d ` R = PEARSON { q } , { GRAPHQA (Pt,d) } model T Dt i i t=1 d=1 T Dt 1 X 1 X `,t,d ` ρ = SPEARMAN { q } , { GRAPHQA (Pt,d) } model T Dt i i t=1 d=1 T Dt 1 X 1 X `,t,d ` τ = KENDALL { q } , { GRAPHQA (Pt,d) } model T Dt i i t=1 d=1

Correlation coefficients per-target For every target, we compute the Pearson (Rtarget), Spearman (ρtarget) and Kendall (τtarget) correlation coefficients between true and predicted decoy-level scores (GDT TS). We then report the average correlation coefficients across all targets. With reference to the funnel plots, this would be the correlation between the markers in every plot, averaged across all plots. The per-target correlation coefficients estimate the performance of the network to rank the decoys of a target by their quality and select the ones with highest global quality. Per-target correlation coefficients are computed only for GDT TS:

T 1 X g,t,d g t,d R = PEARSON { q } , { GRAPHQA (P ) } target T t=1 T 1 X g,t,d g t,d ρ = SPEARMAN { q } , { GRAPHQA (P ) } target T t=1 T 1 X g,t,d g t,d τ = KENDALL { q } , { GRAPHQA (P ) } target T t=1

First Rank Loss (FRL) For every target, we compute the difference in GDT TS between the best decoy according to ground-truth scores and best decoy according to the predicted scores. We then report the average FRL across all targets. This represents the loss in (true) quality we would suffer if we were to choose a decoy according to our rankings and can is represented in the funnel plots by the gap between the two vertical lines indicating the true best (green) and predicted best (red). FRL measures the ability to select a single best decoy for a given target. In our experiments, however, we noticed that FRL is extremely subject to noise, as it only considers top-1 decoys. Therefore, we consider NDCG to be a superior metric for this purpose, though we have not seen it used in the QA literature. FRL is only computed for GDT TS:

T 1 X g,t,d g,t,d∗ FRL = max { q } − q , T t=1

g t,d where d∗ = arg maxd { GRAPHQA (P ) } for every target t. Recall at k (REC@k) We can describe Quality Assessment as an information retrieval task, where every target represents a query and its decoys are the documents available for retrieval. If we consider the best decoy to have a score of 1 and all others to have zero score, we can compute the average REC@k as the percentage of queries for which the best decoy is retrieved among the top-k results. This metric, however, is subject to the same pitfalls of FRL, since it only considers the best decoy of every target and ignores the relevance of the others. As described below, NDCG offers a better perspective over the decoys retieved by a QA method. Normalized Discounted Cumulative Gain at k (NDCG@k) For a given query we consider the top-k decoys ranked according to their predicted global scores. Discounted Cumulative Gain at k

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(DCG@k) is computed as the cumulative sum of their ground-truth GDT TS scores (gain), discounted however according to the position in the list. A high DCG@k is obtained therefore by a) selecting the k-best decoys to be part of the top-k predictions, and b) sorting them in order of decreasing quality (the higher in the list, the lower the discount). Dividing DCG@k by DCGideal@k (obtained by ranking according to the ground-truth scores), yields the Normalized Discounted Cumulative Gain NDCG@k ∈ [0, 1], which can be compared and averaged across targets.

FADDITIONAL RESULTS

In this section we present additional results for datasets, dataset splits, methods, and metrics that are excluded from the main text for sake of brevity. The datasets considered in the following pages are: CASP 11, CASP 12, CASP 13, CAMEO. The CASP 11 and 12 datasets are conventionally divided into: stage 1, containing 20 randomly- selected decoys per target, and stage 2, containing the top-150 decoys of each target. In the QA literature, some papers report results either on the dataset as a whole, or on the stage 1 and stage 2 splits. Furthermore, some papers report performances of other methods that differ from the original papers for reasons that are left unspeciﬁed. In the main text, we adhere to the following rules to summarize the metrics we collected:

• Metrics computed on stage 1 are considered noisy and ignored, since stage 1 splits contain only 20 randomly-selected decoys per target • Metrics computed on stage 2 and on the whole dataset are considered equally valid, allow- ing to ”merge” results from papers with different scoring strategies • If multiple values are reported from multiple sources for the same (method, dataset) pair, only the best one is reported

20 Submitted as a conference paper at ICLR 2020

F.1 CASP 11

GDT TS LDDT TestSet Method Source FRL R Rtarget RMSE ρ ρtarget τ τtarget R Rmodel RMSE ProQ3D ProQ4 0.84 0.61 0.125 ProQ4 ProQ4 0.77 0.56 0.147 CASP 11 GRAPHQARAW Ours 0.082 0.836 0.609 0.146 0.837 0.49 0.637 0.354 0.799 0.516 0.14 GRAPHQA Ours 0.071 0.91 0.74 0.117 0.918 0.622 0.747 0.461 0.852 0.602 0.122 3D CNN 0.046 0.755 0.673 0.529 ProQ3D Ornate 0.066 0.795 0.691 0.782 0.606 0.58 0.462 3D CNN 0.087 0.637 0.521 0.394 VoroMQA Ornate 0.085 0.689 0.617 0.682 0.482 0.483 0.361 3D CNN 0.122 0.512 0.402 0.303 RWplus stage 1 Ornate 0.128 0.08 0.467 0.003 0.371 -0.016 0.274 3D CNN 0.064 0.535 0.425 0.325 3D CNN Ornate 0.104 0.532 0.442 0.614 0.369 0.437 0.28 Ornate Ornate 0.077 0.635 0.465 0.634 0.372 0.44 0.275 GRAPHQARAW Ours 0.09 0.829 0.63 0.135 0.81 0.514 0.609 0.393 0.79 0.475 0.131 GRAPHQA Ours 0.035 0.923 0.788 0.09 0.924 0.647 0.755 0.515 0.861 0.57 0.108 3D CNN 0.066 0.452 0.433 0.307 ProQ3D Ornate 0.053 0.772 0.444 0.796 0.432 0.594 0.304 3D CNN 0.063 0.457 0.499 0.321 VoroMQA Ornate 0.066 0.651 0.419 0.688 0.412 0.505 0.291 3D CNN 0.089 0.206 0.248 0.176 RWplus stage 2 Ornate 0.088 0.056 0.167 0.033 0.192 0.011 0.137 3D CNN 0.064 0.421 0.409 0.288 3D CNN Ornate 0.074 0.629 0.375 0.655 0.363 0.433 0.254 Ornate Ornate 0.055 0.637 0.386 0.673 0.371 0.475 0.259 GRAPHQARAW Ours 0.071 0.82 0.379 0.149 0.82 0.357 0.618 0.251 0.787 0.529 0.142 GRAPHQA Ours 0.063 0.899 0.539 0.123 0.905 0.507 0.729 0.363 0.839 0.61 0.126

GDT-TS LDDT 1 1 R: 0.910 R 0.852 Rtarget: 0.740 Rmodel 0.602 Predicted Predicted

0 0 0 True 1 0 True 1 GDT-TS GDT-TS

50% 0.87

40% 0.86

30%

0.85 Average nDCG @ k Average Recall @ k 20%

0.84

10%

0.83 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 k k

Figure 12: CASP 11: Histograms of true vs. predicted LDDT and GDT TS scores, average recall @ k, average NDCG @ k

21 Submitted as a conference paper at ICLR 2020

T0759 T0760 T0761 T0762 T0763 T0764

T0765 T0766 T0767 T0768 T0769 T0770

T0771 T0772 T0773 T0774 T0776 T0777

T0778 T0780 T0781 T0782 T0783 T0784

T0785 T0786 T0787 T0788 T0789 T0790

T0791 T0792 T0794 T0796 T0797 T0798

T0800 T0801 T0803 T0805 T0806 T0807

T0808 T0810 T0811 T0812 1 Predicted Best decoy Predicted True 0 0 True 1

Figure 13: CASP 11: funnels (continues)

22 Submitted as a conference paper at ICLR 2020

T0813 T0814 T0815 T0816 T0817 T0818

T0819 T0820 T0821 T0822 T0823 T0824

T0825 T0827 T0829 T0830 T0831 T0832

T0833 T0834 T0835 T0836 T0837 T0838

T0840 T0841 T0843 T0845 T0847 T0848

T0849 T0851 T0852 T0853 T0854 T0855

T0856 T0857 T0858 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 14: CASP 11: funnels (continued)

23 Submitted as a conference paper at ICLR 2020

F.2 CASP 12

GDT TS LDDT TestSet Method Source FRL R Rtarget RMSE ρ ρtarget τ τtarget R Rmodel RMSE ρ ρmodel ProQ3D 3D CNN 0.164 0.609 0.602 0.451 ProQ4 Ours 0.772 0.516 0.776 0.498 VoroMQA 3D CNN 0.161 0.557 0.515 0.38 RWplus 3D CNN 0.192 0.313 0.355 0.257 CASP 12 3D CNN 3D CNN 0.146 0.607 0.521 0.381 AngularQA AngularQA 0.138 0.651 0.439 GRAPHQARAW Ours 0.092 0.816 0.673 0.149 0.814 0.606 0.624 0.448 0.796 0.501 0.139 GRAPHQA Ours 0.089 0.843 0.745 0.137 0.834 0.66 0.684 0.503 0.843 0.565 0.124 ProQ3D Ornate 0.086 0.671 0.705 0.478 0.636 0.335 0.482 VoroMQA Ornate 0.085 0.456 0.611 0.381 0.554 0.263 0.414 RWplus Ornate 0.132 -0.272 0.479 -0.538 0.465 -0.381 0.344 stage 1 Ornate Ornate 0.113 0.551 0.566 0.484 0.504 0.339 0.374 AngularQA AngularQA 0.148 0.502 GRAPHQARAW Ours 0.068 0.721 0.679 0.127 0.623 0.596 0.451 0.448 0.661 0.413 0.118 GRAPHQA Ours 0.043 0.814 0.789 0.085 0.755 0.684 0.589 0.541 0.718 0.474 0.105 ProQ3D Ornate 0.06 0.806 0.6 0.8 0.54 0.601 0.388 VoroMQA Ornate 0.106 0.605 0.559 0.604 0.501 0.445 0.362 RWplus Ornate 0.103 -0.096 0.417 -0.096 0.378 -0.067 0.265 stage 2 Ornate Ornate 0.072 0.67 0.491 0.657 0.458 0.472 0.322 AngularQA AngularQA 0.128 0.377 GRAPHQARAW Ours 0.094 0.807 0.614 0.151 0.807 0.545 0.618 0.395 0.793 0.507 0.141 GRAPHQA Ours 0.08 0.832 0.707 0.141 0.828 0.61 0.679 0.456 0.842 0.573 0.125

GDT-TS LDDT 1 1 R: 0.843 R 0.843 Rtarget: 0.745 Rmodel 0.565 Predicted Predicted

0 0 0 True 1 0 True 1 GDT-TS GDT-TS

0.84 50%

0.83 40%

0.82 30%

0.81 Average nDCG @ k Average Recall @ k 20%

0.80 10%

0.79 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 k k

Figure 15: CASP 12: Histograms of true vs. predicted LDDT and GDT TS scores, average recall @ k, average NDCG @ k

24 Submitted as a conference paper at ICLR 2020

T0859 T0860 T0861 T0862 T0863 T0864

T0865 T0866 T0868 T0869 T0870 T0871

T0872 T0873 T0879 T0886 T0889 T0891

T0892 T0893 T0896 T0897 T0898 T0900

T0902 T0903 T0904 T0911 T0912 T0918

T0920 T0921 T0922 T0928 T0941 T0942

T0943 T0944 T0945 T0947 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 16: CASP 12: funnels

At a close analysis, it appears that the model completely fails to score decoys of target T060 and defaults to predicting a small constant value. To help pinpointing the problem, we compare the predictions made by GRAPHQA and GRAPHQARAW (available in the repository). It turns out that the model trained on amino acid identity only does not output the same degenerate predictions as its fully-featured counterpart (the predictions are not perfect, but deﬁnitely better than a constant). We suspect that an error in the preprocessing pipeline might have produced misleading features for T060, e.g. the multiple sequence alignment program that extracts self information and partial entropy, or the DSSP program that computes secondary structure features.

25 Submitted as a conference paper at ICLR 2020

F.3 CASP 13

CASP 13 is the most recent edition of CASP and, at the moment, only few targets are available for public evaluation, i.e. their decoy structures are fully characterized, submitted predictions and ground-truth GDT TS scores can be downloaded from the website. Here we present an evaluation on publicly available targets, while waiting to update these results as more data is released.

Also, it is important to note that GRAPHQA is only trained on CASP 7-10, while other participants have likely (re)trained their models on all previous CASP datasets as well as other datasets. How- ever, even without retraining, we achieve performances that are in line with the results presented for CASP 11 and 12.

GDT TS LDDT TestSet Method Source FRL R Rtarget RMSE ρ ρtarget τ τtarget R Rmodel RMSE ProQ3D Ours 0.160 0.849 0.671 0.129 0.810 0.619 0.625 0.458 ProQ4 Ours 0.147 0.671 0.733 0.182 0.645 0.668 0.492 0.508 VoroMQA Ours 0.024 0.767 0.665 0.177 0.765 0.606 0.571 0.443 CASP 13 3D CNN Ours 0.135 0.661 0.753 0.192 0.632 0.662 0.457 0.487 Ornate Ours 0.283 0.533 0.646 0.352 0.522 0.642 0.360 0.467 GRAPHQARAW Ours 0.122 0.767 0.727 0.167 0.774 0.701 0.573 0.524 0.723 0.475 0.154 GRAPHQA Ours 0.093 0.846 0.834 0.123 0.840 0.799 0.647 0.616 0.764 0.539 0.142

GDT-TS LDDT 1 1 R: 0.846 R 0.764 Rtarget: 0.834 Rmodel 0.539 Predicted Predicted

0 0 0 True 1 0 True 1 GDT-TS GDT-TS

10% 0.840

8% 0.835

6% 0.830

0.825 4% Average Recall @ k Average nDCG @ k 0.820 2%

0.815 0%

0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 k k

Figure 17: CASP 13: Histograms of true vs. predicted LDDT and GDT TS scores, average recall @ k, average NDCG @ k

26 Submitted as a conference paper at ICLR 2020

T0950 T0951 T0953s1 T0953s2 T0954 T0957s1

T0957s2 T0958 T0960 T0963 T0966 T0968s1

T0968s2 T1003 T1005 T1008 T1009 T1011

T1016 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 18: CASP 13: funnels

27 Submitted as a conference paper at ICLR 2020

F.4 CAMEO

GDT TS LDDT TestSet Method Source FRL R Rtarget RMSE ρ ρtarget τ τtarget R Rmodel RMSE ProQ3D ProQ4 0.79 0.64 0.137 ProQ4 ProQ4 0.65 0.56 0.201 VoroMQA 3D CNN 0.099 0.456 0.427 0.346 CAMEO RWplus 3D CNN 0.162 0.122 0.095 0.068 3D CNN 3D CNN 0.06 0.586 0.532 0.426 GRAPHQARAW Ours 0.046 0.725 0.585 0.17 0.675 0.505 0.497 0.379 0.699 0.56 0.169 GRAPHQA Ours 0.044 0.747 0.598 0.197 0.666 0.525 0.495 0.399 0.748 0.616 0.161

GDT-TS LDDT 1 1 R: 0.747 R 0.748 Rtarget: 0.598 Rmodel 0.616 Predicted Predicted

0 0 0 True 1 0 True 1 GDT-TS GDT-TS 100%

0.950

80% 0.945

0.940 60%

0.935 Average nDCG @ k Average Recall @ k 40% 0.930

0.925 20%

0.920 0 5 10 15 20 25 1 2 3 4 5 6 7 8 9 10 k k

Figure 19: CAMEO: Histograms of true vs. predicted LDDT and GDT TS scores, average recall @ k, average NDCG @ k

28 Submitted as a conference paper at ICLR 2020

2ML1_A 2ML2_A 2ML3_A 2MNT_A 2MP6_A 2MP8_A

2MPH_A 2MPK_A 2MPW_A 2MQ8_A 2MQB_A 2MQC_A

2MQD_A 2MQH_A 2MQM_A 2MR6_A 2MRC_A 2MRL_A

2MSV_A 2MU0_A 2MUI_A 2MVB_A 2MW1_A 2MXD_A

2MXX_A 2MZZ_A 2N00_A 2N03_A 2N0P_A 2N1D_A

2RTT_A 3WCG_D 3WD6_D 3WDX_B 3WE5_B 3WE9_A

3WFX_B 3WGQ_B 3WH9_B 3WJ1_A 3WJ2_D 3WJO_B

3WMJ_A 3WNV_B 3WOY_A 3WOZ_D 3WSU_B 3WSW_D 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 20: CAMEO: funnels (continues)

29 Submitted as a conference paper at ICLR 2020

3WTB_H 3WTC_B 3WV6_B 3WV9_D 3WVA_B 3WW1_B

3WWV_A 3WX5_B 3WXV_A 3WXW_A 3WXW_H 3WY7_D

3WYB_B 3WYD_B 3WYH_B 3X1B_B 3X2E_D 4BWH_A

4CG4_F 4CIT_A 4CJX_B 4CL2_A 4CNE_B 4CNF_B

4CNJ_D 4CRQ_B 4CRR_A 4CSI_B 4CUK_D 4CUO_A

4CVH_A 4CVK_A 4CW9_B 4CWC_C 4CWE_C 4CX8_B

4D2K_D 4D40_B 4D4Z_B 4D6V_A 4D79_D 4D7S_B

4JJJ_A 4L22_A 4L7V_A 4LDZ_B 4LID_B 4LM6_C 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 21: CAMEO: funnels (continues)

30 Submitted as a conference paper at ICLR 2020

4LM6_D 4LMS_A 4LMS_C 4LMX_C 4LMX_K 4LMX_L

4LPL_A 4LQR_A 4LUG_B 4LUR_A 4LVC_D 4LWL_A

4LX4_D 4LZL_A 4M0X_B 4M1X_D 4M3K_B 4MAG_A

4MFI_A 4MH1_B 4MHL_A 4MHU_B 4MMO_B 4MMP_A

4MNP_A 4MTR_B 4MXG_D 4MYI_A 4MYJ_A 4N1H_D

4N1L_A 4N1V_A 4N81_A 4NCP_F 4NEX_B 4NF7_A

4NJ8_B 4NKN_F 4NKR_E 4NL9_B 4NL9_D 4NOV_A

4NR0_D 4NXY_A 4O4O_B 4O6Z_D 4O89_B 4O8Q_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 22: CAMEO: funnels (continues)

31 Submitted as a conference paper at ICLR 2020

4O8V_B 4O9H_L 4OB1_A 4OB7_A 4OD6_A 4OGD_B

4OIB_A 4OJU_D 4OJX_A 4OKZ_D 4OLO_D 4OLP_D

4ONY_B 4ORA_A 4OSP_D 4OTP_A 4OUA_B 4P29_B

4PAC_A 4PDE_A 4PEN_A 4PKM_A 4PLP_B 4PNF_H

4PNG_B 4PQH_B 4PQI_A 4PQX_D 4PRS_B 4PSD_A

4PTZ_D 4PU3_B 4PU7_A 4PUG_B 4PUI_B 4PUX_A

4PV3_C 4PV3_D 4PW1_B 4PW3_D 4PW9_B 4PWU_D

4PYS_B 4Q0Y_C 4Q16_D 4Q1K_C 4Q28_D 4Q2B_F 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 23: CAMEO: funnels (continues)

32 Submitted as a conference paper at ICLR 2020

4Q32_D 4Q34_A 4Q3U_D 4Q47_B 4Q4T_A 4Q53_B

4Q5T_A 4Q69_B 4Q6K_D 4Q6U_B 4Q76_B 4Q7A_D

4Q97_B 4Q9A_B 4Q9B_B 4Q9C_A 4Q9D_B 4Q9O_B

4QAF_B 4QAN_B 4QAW_H 4QB1_A 4QB5_D 4QB7_A

4QBA_B 4QBD_C 4QBD_D 4QCC_B 4QD8_F 4QDG_B

4QDY_A 4QE0_B 4QEA_G 4QEY_J 4QEZ_C 4QF3_B

4QFH_B 4QFU_L 4QG5_D 4QGM_A 4QGN_A 4QGR_B

4QHB_D 4QHQ_A 4QHX_A 4QHZ_D 4QKU_D 4QL5_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 24: CAMEO: funnels (continues)

33 Submitted as a conference paper at ICLR 2020

4QLO_A 4QMF_B 4QMG_E 4QN8_C 4QNI_A 4QNS_D

4QNU_H 4QNY_B 4QOA_A 4QOX_A 4QPD_B 4QPG_C

4QPI_A 4QPI_B 4QPO_D 4QPV_B 4QPY_C 4QQ7_B

4QRI_B 4QRJ_B 4QRK_A 4QRL_A 4QRZ_A 4QS4_A

4QT8_A 4QT9_B 4QTP_D 4QTZ_A 4QU7_D 4QVG_D

4QVK_B 4QVR_A 4QVS_A 4QVU_A 4QWO_B 4QX6_D

4QYO_A 4QYR_A 4R01_B 4R03_A 4R0C_D 4R0G_D

4R0J_A 4R0M_A 4R0Z_A 4R1H_B 4R1K_B 4R27_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 25: CAMEO: funnels (continues)

34 Submitted as a conference paper at ICLR 2020

4R2B_B 4R2F_A 4R31_F 4R33_B 4R37_B 4R4B_F

4R4G_A 4R4H_A 4R4N_V 4R5O_D 4R60_B 4R6H_A

4R6K_A 4R6Y_A 4R7E_A 4R7F_A 4R7K_D 4R7O_G

4R7Q_A 4R7R_A 4R7S_A 4R7T_C 4R80_B 4R86_B

4R8O_B 4R99_D 4R9M_C 4R9N_A 4R9X_B 4R9Z_B

4RAA_A 4RAS_C 4RBM_A 4RC1_I 4RCK_B 4RCO_B

4RD7_A 4RD8_B 4RDB_A 4REI_A 4REV_B 4REW_B

4RFA_A 4RG1_B 4RGB_B 4RGI_A 4RGK_A 4RGP_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 26: CAMEO: funnels (continues)

35 Submitted as a conference paper at ICLR 2020

4RHC_L 4RHL_B 4RHO_B 4RHT_D 4RK2_B 4RK5_A

4RK9_B 4RKQ_D 4RL6_B 4RL9_B 4RLB_B 4RLC_A

4RM7_A 4RMM_A 4RN3_B 4RN7_A 4RNF_A 4RNJ_B

4RNL_D 4RO3_B 4RO6_A 4ROP_A 4ROQ_A 4ROR_A

4ROT_A 4RP5_B 4RPC_B 4RPF_C 4RPO_D 4RQA_A

4RQO_B 4RQQ_D 4RQT_A 4RRP_F 4RS2_B 4RS3_A

4RSH_C 4RSL_A 4RT5_B 4RTF_D 4RU0_B 4RU1_L

4RUW_A 4RV1_F 4RWE_A 4RWF_A 4RWG_C 4RWH_A 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 27: CAMEO: funnels (continues)

36 Submitted as a conference paper at ICLR 2020

4RWR_B 4RXL_A 4RXM_B 4RXT_A 4RXU_A 4RY0_A

4RY1_B 4RY8_D 4RY9_B 4RYA_A 4RYB_B 4RYK_A

4RZP_B 4S13_H 4S1R_H 4S1S_H 4S2T_Q 4TPU_A

4TPV_B 4TQJ_B 4TQX_A 4TRT_B 4TZH_B 4U00_A

4U06_A 4U08_B 4U09_B 4U7A_A 4U9W_D 4UAO_B

4UDK_F 4UDP_B 4UE0_C 4UEG_B 4ULV_B 4UMK_D

4UMS_A 4UOH_C 4UOX_D 4URJ_D 4URP_B 4USS_A

4UU4_A 4UUC_A 4UVQ_A 4UWW_A 4UX7_B 4UXJ_H 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 28: CAMEO: funnels (continues)

37 Submitted as a conference paper at ICLR 2020

4UY4_B 4UY5_A 4UYB_A 4UYI_A 4UYP_D 4UYQ_A

4UYQ_B 4UZ8_B 4UZG_A 4UZM_A 4UZZ_A 4UZZ_B

4V06_B 4V0P_A 4V1G_C 4V2A_A 4V2B_B 4V2E_B

4V2X_A 4V3H_B 4V3I_A 4W8L_C 4WA0_A 4WD1_A

4WGX_D 4WHB_H 4WHN_D 4WIP_C 4WMF_C 4WOE_B

4WPZ_A 4WRI_A 4WRP_B 4WSZ_B 4WXJ_B 4WZX_A

4X0K_A 4X36_A 4X3H_A 4X3X_A 4X54_A 4X5S_B

4X6G_H 4X8F_P 4X8K_A 4XCW_F 4XDI_B 4XDY_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 29: CAMEO: funnels (continues)

38 Submitted as a conference paper at ICLR 2020

4XDZ_B 4XEA_A 4XED_A 4XEL_B 4XEQ_D 4XEU_A

4XFE_A 4XFK_A 4XFR_B 4XFV_A 4XGJ_A 4XGL_A

4XGU_F 4XHC_B 4XHM_B 4XI2_A 4XI5_D 4XIJ_A

4XIN_B 4XJ6_A 4XK1_B 4XK2_C 4XKZ_A 4XL8_C

4XLL_B 4XLT_A 4XOX_B 4XP7_A 4XPO_A 4XQ1_A

4XQ3_G 4XQ7_A 4XRP_D 4XRP_E 4XRP_F 4XS5_D

4XTT_B 4XUP_F 4XUT_C 4XUV_B 4XV0_A 4XVH_A

4XVO_C 4XVV_B 4XWI_B 4XX6_B 4XXF_A 4XXL_A 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 30: CAMEO: funnels (continues)

39 Submitted as a conference paper at ICLR 2020

4XXP_A 4XXT_A 4XYK_D 4Y0B_B 4Y0C_A 4Y61_B

4Y7D_B 4Y85_C 4Y8W_C 4Y97_G 4Y97_H 4Y9J_B

4Y9T_A 4YAY_A 4YBG_A 4YC6_G 4YC7_B 4YCS_F

4YDH_C 4YDI_L 4YDJ_A 4YDJ_B 4YDK_H 4YDK_L

4YDL_B 4YE2_B 4YE5_B 4YEP_B 4YEQ_U 4YER_B

4YF1_D 4YFE_B 4YFG_A 4YFL_F 4YFY_B 4YGQ_A

4YGT_A 4YGU_D 4YH7_A 4YH7_B 4YHE_B 4YHS_A

4YIC_B 4YJ0_C 4YJW_A 4YJZ_L 4YK8_A 4YK8_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 31: CAMEO: funnels (continues)

40 Submitted as a conference paper at ICLR 2020

4YKC_A 4YKE_B 4YL5_A 4YLE_A 4YLT_A 4YME_A

4YMR_B 4YMW_A 4YMW_C 4YMX_B 4YN1_A 4YN2_A

4YNA_D 4YNW_B 4YO7_A 4YOD_A 4YOK_A 4YOO_A

4YPJ_B 4YQY_B 4YQZ_D 4YS6_A 4YS8_D 4YUB_B

4YV7_A 4YVD_A 4YWE_H 4YWH_B 4YWJ_B 4YWN_B

4YX1_B 4YX5_A 4YXC_B 4YY8_B 4YYC_A 4YYF_C

4YZ8_A 4YZH_A 4YZS_B 4YZY_A 4Z04_A 4Z0N_A

4Z1H_A 4Z24_B 4Z29_B 4Z34_A 4Z36_A 4Z48_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 32: CAMEO: funnels (continues)

41 Submitted as a conference paper at ICLR 2020

4Z7X_B 4Z8X_C 4Z8Z_A 4ZA2_D 4ZBG_A 4ZCH_B

4ZFN_B 4ZG1_F 4ZGF_A 4ZHB_A 4ZJF_D 4ZJM_A

4ZJN_C 4ZJP_A 4ZJS_E 4ZJU_A 4ZN6_B 4ZNM_B

4ZO4_D 4ZPJ_A 4ZQB_B 4ZR7_D 4ZR8_B 4ZRX_A

4ZTI_B 4ZTK_A 4ZV3_C 5A0G_F 5A0L_B 5A0N_A

5A1F_A 5A2L_H 5AF7_B 5AFF_C 5AGA_A 5AGQ_A

5AH2_D 5AIE_A 5AJ8_B 5AJA_B 5AJT_D 5AL7_B

5AMO_B 5B8F_C 5B8H_B 5B8I_A 5B8I_B 5B8I_C 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 33: CAMEO: funnels (continues)

42 Submitted as a conference paper at ICLR 2020

5BMQ_A 5BNZ_B 1 Best decoy Predicted True Predicted

0 0 True 1

Figure 34: CAMEO: funnels (continued)