Cross-Protein Wasserstein Transformer for Protein-Protein Interactions
Authors: Gongping Xu
Tong Zhang
Wenting Zhao
Zhen Cui
Jian Yang
Venue: Submitted to ICLR 2023 (2023)

Abstract: Previous studies reveal intimate relationships between the structure and function of proteins. Motivated by this, for protein-protein interactions (PPIs), we hypothesize that cross-protein structural correspondence, including both global correlation and local co-occurrence, poses a great influence. Accordingly, a novel deep learning framework named Cross-Protein Wasserstein Transformer (CPWT) is proposed to predict PPI sites through fine-grained cross-graph structural modeling. Considering the irregular architecture of acid sequences, for a pair of proteins, graphs are constructed to describe them. Then, a core Cross-Graph Transformer (CGT) module of two branches (e.g. ligand and receptor branches) is proposed for cross-protein structural modeling. Specifically, in this module, Wasserstein affinity across graphs is calculated through cross-graph query (i.e. ligand (query) - receptor (key) or the converse), based on which the multi-head attention is derived to adaptively mine fine-grained cues of PPI sites. By stacking CGT modules, the two branches in CGT are co-evolved in a deep architecture during forward inference, hence being powerful and advantageous in cross-protein structural representation and fine-grained learning. We verify the effectiveness of our CPWT framework by conducting comprehensive experiments on multiple PPI datasets, and further visualize the learned fine-grained saliencies for intuitive understanding.

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CROSS-PROTEIN WASSERSTEIN TRANSFORMER FOR PROTEIN-PROTEIN INTERACTIONS
Paper ID: 3822
ABSTRACT
Previous studies reveal intimate relationships between the structure and function of proteins. Motivated by this, for protein protein-protein protein interactions (PPIs), we hypothesize that cross-protein structural correspondence, including both global correlation and local co-occurrence, poses a great influence. Accordingly, a novel deep learning framework named Cross-Protein Wasserstein Transformer (CPWT) is proposed to predict PPI sites through fine- ine-grained cross-graph structural modeling. Considering the irregular architecture of acid sequences, for a pair of proteins, graphs constructed describe them. Then, a core (CGT) module of two branches (e.g. ligand and receptor branches) is proposed for cross-protein structural modeling. Specifically, in this module, Wasserstein affinity across graphs is calculated through cross-graph query (i.e. ligand (query) receptor (key) or the converse), based on which the multi-head attention is derived adaptively mine fine-gratt lineggrined cues of PPI sites. By stacking CGT modules, the two branches in CGT are co-evolved in a deep architecture during forward inference, hence being powerful and advantageous in cross ppotten structural representation and fine-ge one-grained learning. We verify the effectiveness of our CPWT framework by conducting comprehensive experiments multiple PPI datasets, and further visualize the learned fine-grained saliencies for intuitive understanding.
Graph Transformer
INTRODUCTION
Proteins are chains of amino acids, and physical interaction between proteins is essential to life. The protein-protein interaction (PPI) (Figure shows an example) determines molecular and cellular mechanisms, and thus plays crucial role in biological processes including the gene expression, pro- liferation of cells, etc. Moreover, as proteins are predominant drug targets, characterizing PPIs the fine-grained level, e.g. identifying protein interaction sites for PPIs, would provide significant insight into biological mechanisms, and has important application in drug design, disease treatment (Ryan) & Matthews 2005), and target discovery. For this reason, the research on PPI prediction has drawn increasing attention.
In the early stage, sundry experimental assays have been widely applied to PPI identification, such as nuclear magnetic resonance(NMRR) (Wuthrich] 1989), X-ray crystallography (Svergun et al. (00T) and high- tightthroughhut screening methods (Song et al. 2011). lp. However, identifying the binding sites based on these methods is often consuming and sesource-expensivee Then, with more and more protein structure data available (Berman et al. 2000), computational methods developed to predict protein-protein interaction sites, which can be divided into two categories, i.e. protein docking and data-driven methods. For the protein prretinn- docking (Porter al. 2019 Halperin et al.) 2002), the fundamental principle is the steric complementarity at protein-proter interfaces. However, suffers from the tremendous search space and requirement of expert-defined scoring functions in the searching and scoring processes for predicting complex structures.
For data-driven methods, number of machine learning algorithms with shallow structures are first proposed for PPIs in the early stage. Generally, they can be divided into three categories, i.c. sequence- based methods (Murakami & Mizuguchi] 2010 [Zhang et al.. 2019 Jurtz al.) 2017 Haberal & Ogul
2017,Zheng et al.. (0188), structure- based methods (Du et al.] [ Bradford & Westhead 2005 Neuvirth et al. and those ones based on mixed information (Afsar Minhas et al. [014]] Li et al.
2012|Northse al. 2018 Porollo & Meller 2007). Then, inspired by the success of deep learning in
vision tasks, deep neural networks are employed for protein science, e.g. the success Deep'ind's Alphafold2 (Jumper et al. (222)) for structure prediction. Specifically for PPIs, to utilize the powerful
structure modeling ability, recent works (Bryant et al. 2022 Gao et al. [022 Evans et al.) 202T)
including AF2Complex (Gao al. 2022) and AlphaFool-WMlltimee (Evans al. 202 propose to

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Figure 1: Ball and stick view of the protein complex named 2HRK, bound from a receptor protein (green) and a ligand protein (cyan). The interactive residues are marked as pink in the receptor and orange in the ligand. The zoomed-up area in the red box shows detailed interactions (red dotted lines) of amino acids between asparagine in the receptor (pink) and arginine in the ligand (orange).
predict the structure of multimeric protein complexes through the Alphafold model (Jumper et al.
2021). based on which interactions between protein sequences can be further identified. Moreover.
multiple deep learning methods (Amidi et al.) 2018 Torng & Altman 2017 Jiménez et al. 2017]
Skalic al. 2019) attempt to map irregular atomic coordinates to regular representations of 3D grids,
or just to 2D images which are then fed into Convolutional Neural Networks (Gainza et al.
2020). Recently, graph neural networks (GNNs) (Fout et al. 2017 Liu et al.) 2020 Morehead et al. 2022 are applied to deal with PPI prediction and achieve state-of- performance.
Considerable progress has been made in PPI prediction, especially by GNNs. However, considering the intimate structure- funuution relationship, two main issues are remaining to be solved: (1) insuffi- cient cross-protein structural modeling: the often used post-fusion of vectorized protein features fails to well characterize the cross-protein structural correlation; (2) unsophisticated fine-grained learning for PPI sites: interactive pairs of sites always take a pretty small proportion of residues (as shown in Figure in proteins that fine-gu ene-grained modeling is rather necessary for PPI prediction, which is not adequately investigated in the previous study.
To tackle these issues, we propose a deep learning framework named Cross-Protein Wasserstein Transformer (CPWT) for PPI prediction. For a given pair of proteins, e.g. ligand and receptor, the target is to detect those interactive pairs of sites. Considering the irregular architecture of proteins and intrinsic relations among residues, graphs are constructed to describe proteins with residues as nodes and spatial relationship for defining edges, then fed to corresponding graph encoders for feature learning. Furthermore, a core Cross- Graph Transformer (CGT) module, consisting of two branches (e.g. ligand and receptor branches), is proposed to model structural correlation across proteins with fine-grained learning PPI sites. In this process, cross-graph modeling is required, which is rather non-trivial. Theoretically, as irregular graphs don't 't lie in the Euclidean space, the common metric like cosine similarity, cannot well describe the cross- poos--gapph structural relationship. To address this issue, the Wasserstein metric is specifically introduced, based on which pross-protein query operations (i.e. ligand (query)- receptor (key) or the converse) first. conducted in the CGT by calculating Wasserstein affinities across graphs. Furthermore, multi-head attention is derived based on Wasserstein affinities to adaptively highlight salient pairs of sites and update the Transformer values. With the optimal transport principle of Waserstein affinity, the CGT advantagous in characterizing two irregular (cross-graph) point/residue sets and exploring both global and local cross- graph structural information. Moreover, the CGT can be stacked in multiple layers so that its two branches can be effectively co-evolved in a deep architecture, hence being powerful in cross-protein structural expression and advantageous in fine-grained learning. We verify the effectiveness of our CPWT framework by conducting comprehensive experiments on PPI datasets, then visualize the fine-grained saliencies and compare them with the ground truth interaction for intuitive understanding.
The contributions are summarized as follows: (I) We propose new Cross-Protein Wasserstein Transformer framework to promote the PPI prediction from the perspective of sophisticated cross- protein structural modeling based Wasserstein affinities; (2) We propose novel CGT module in which the multi-hean head attention is derived to mine fine- -raiied cues of PPI sites. Moreover, this module can be stacked into deep architecture with branches co-evolved, which are powerful
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in eross pross-protein structural expression with sophisticated fine- grained learning; (3) We report the state-of-the-art performance on multiple PPI datasets with comprehensive experiments.
RELATED WORK
The PPI prediction problem has two flavors (Muraami Mizuguchi 2010, Zhang et al., 2019 Jurtz et al., 2017; Haberal& & Ogul 2017; Zheng et al. 2018 Afsar Minhas et al. 2014] Li et al. 2012, Northey et al. 2018: Porollo & Meller 2007): the partner-independent prediction and the partner-specific one. The former is to predict whether single residue of protein could interact with residues from any other protein, while the latter to detect interaction between residues from two proteins. Here, we focus on those works of partner-specific prediction, which is more relevant to task. Generally, they can be roughly divided into two categories named surface geometry- -based and graph-based methods, respectively.
Surface geometry-based methods. In order to encode and exploit surface geometry and interface complementarity in deep learning framework, several methods have been proposed (Townshend
et al.
2019 [Behler& & Parrinello] 2007, Sverrisson et al., 2021; Gainza et al. 2020 [verrisson et al.
2021). Townshend et al. (Townshend et al., 2019) employs voxelization method which voxelizes
local atomic environments or "surface patches", surrounding each of them, and then applies
3D convolutional neural network extract its latent features. Sverrisson et al. (Sverrisson al.
2021) operates directly on the large set of atoms that compose the protein, generates a point cloud representation for the protein surface, learns task-specific geometric and chemical features on the surface point cloud and finally applies new convolutional operator that approximates geodesic coordinates in the tangent space. Dai et al. (Dai & Bailey-Kellogg 202T) constructs pairs of point clouds encoding the structures of two partner proteins, in order to predict their structural regions mediating interaction. It extracts local surface features and global protein features and then concatenated them predict the interface regions on both interacting protein.
Graph-based methods. As one of the geometric deep learning methods, Graph Neural Networks (GNN) have been enthusiastically sought and have been proposed for protein interface region prediction (Fout et al. 2017; Duvenaud et al.] 2013
Liu et al.) 2020) SSchit et al., [017]] Pittalla & (Biley-Kellogg 20200. Font al. (Fout al. 2017 represents the protein as graph, which amino acids as nodes and affinities between nodes as edges. Then it employs GNN to learn node features, and classify each amino acid pair by a classifier. For better incorporating more informations. Liu et al. (Liu et al. 2020) proposes high-order interactions for protein interface. Same as (Fout et al. 2017). it learns node features by GNN. proposes the sequential modeling method to incorporate the sequential information. Then it incorporates high-order pairwise interactions to generate 3D tensor containing different pairwise interactions, and employs Convolutional Neural Cetworks(CNNs,, to perform 2D dense predictions. Pittala et al. (Pittala & Kielly-Kellogg/// 2020) combines the advantages of GNN and attention mechanisms an integrated model for predicting both epitopes and paratopes. The former aggregate properties across local regions in protein and the latter explicitly encode the context of the partner. Recently, Morehead et al. (Morehead et al.) 2022) proposes the geometric transformer for rotation-invariant protein interface contact prediction. Moreover, the PepNN (Abdin et al. 2022) framework is proposed for protein-peptide interaction, where the reciprocal attention is employed for cross-graph measurement.
Different from all previous works, we propose a new CPWT framework from the perspective of cross-protein structural modeling. Specifically, we propose novel CGT module consisting of two branches with multi-head attention based on the Wasserstein affinity, which is advantageous in cross-protein structural expression and fine-graine -raiined learning on PPI sites.
THE PROPOSED FRAMEWORK
3.1 OVERVIEW
The architecture of our CPWT framework with a one-layer CGT is shown in Figure which takes pair of ligand and receptor proteins as the input. Generally, the CPWT framework consists of three main learning processes including graph encoding, cross-graph transform, and PPI site prediction. Considering the irregular structure of proteins, graphs are constructed to describe them by taking residues nodes with corresponding edges defined according to the spatial relationship. To learn robust features from these graphs, graph encoders such as GNNs are then applied. Furthermore, these encoded graphs are fed into the specifically designed CGT module characterize structural
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Cmuss Graph Transfommer
Ligand Protein
Ligand Graph
Encoded Ligand Graph
Ligand Graph Embeddingg
asserstein A fffiniyy
Graph Encoder
Lettur
Kg
Vi
Loss
Sampling
Prediction
Strategy
Complex Protein
Combinsted Representatiin
V
Graph
fourpu
Recoder
W Wasserstein A Affintyy
Encoded Receptor Craph
Receptor Graph Embedding
Receptor Protein
Receptor Graph
Cross-Gruph Transfommer
Figure 2: The architecture of our CPWT framework. Three main learning processes involved in the CPWT framework, including graph encoding, cross- Sess-Wassrsstein transformer, and prediction. The input pairs of receptor and ligand proteins are first modeled as graphs, which takes residues in amino acid sequences as nodes with edges existed in the k-nearest neighbors. Then, multi-layer GNN can be stacked the encoder for robust feature learning. The encoded graphs are both fed into the CGT module for further fine-grained cross-protein learning. In this process, multiple CGT layers can be stacked into a deep architecture (only one layer shown here) with the two branches in CGT co-evolved. More details could be found in Section Finally, the learned features of residues from two input proteins are combined for PPI site prediction.
correlation across two proteins and meantime achieve fine- ine-grained learning. As shown in Figure 2 the CGT module consists of two branches that are mutually interacted and thus co-evolved. For each branch, two main operations, i.e. cross-graph query and multi-head attention, are involved. Specifically, the cross-gras moss-graph query calculates the Wasserstein affinity across proteins where the sinkhorn algorithm is applied for cross-graph structural optimization. Based on query-resulted Wasserstein affinities, the multi-head attention is derived update CGT values detect salient pairs of sites. Finally, the learned features of residues in ligand and receptor proteins are combined fulfill the prediction of those PPI sites. In the following parts, we descibe the learning processes in detail.
to adaptively
3.2 GRAPH ENCODING
For an input pair of ligand and receptor proteins, we first construct graphs for them which are denoted as Gi {(V,, E V", cly E E and G, {(V",""))) Ex] E V", V", .e'y E"), respectively. Here, yl and V" are the node sets ligand and receptor graphs, while and g are the edge sets. x denotes the feature vector of the i-th node while e/y denotes the relationship (edge) feature between the i-th and j-th nodes in the ligand graph.
We adopt GNNs to learn nodes' representation based on its local neighbors. Considering that neighbours always contribute differently to the center node, different weights are distributed to them according to their distances from the center node, with larger weights for closer neighbors. Taking a node x in the ligand graph example, the graph encoding process is follows:
h = o ( + Whel + +b'), a, = softmar(h/pp),
(1)
z = = + W Σ hy,
(2)
where N! is neighbour of the i-th node and WW denotes neighbour node number, W!, W.. W are leamable projection matrices, b' is the learnable bias, and p' is optimiz- able projection vector. (-)) is a non-linear activation function, e.g. Relu, which results in the encoded feature denoted as z/.
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3.3 THE CROSS-GRAPH TRANSFORMER
The CGT module models structural correlation across proteins and meantime achieves fine- tne-grained learning on PPI sites. consists two branches, i.e. ligand and receptor branches, that are co-evolved during forward inference. For each branch, two main operations named cross-graph query and multi-head attention are involed. Specifically, the Wasserstein affinity based on the optimal transport is used for cross goss-graph modeling in the cross-graph query. We introduce them in detail below.
Cross-graph query. The cross-query operation aims to measure the structual relationship between two graphs. Considering that irregular graphs don't Io lie in the Euclidean space, apply the Wasser- stein affinity to characterize cross-graph structural information through the optimal transport. Here, taking the ligand branch features of the ligand graph while Z, |zj .z...... _ E RT, for the receptor graph, then the Wasserstein affinity of the cross ligand-receptor query, denoted as A1, E Ruxx,, can be written as:
example, let Z [z]. _n,11 R represent the encoded
A q: (Z, Z, 0, Tú, M,
where Tir is the optimal transport matrix, @ represents elementwise production, and O2 denotes the parameter set involved. M,, E [R is a pairwise affinity matrix with the element in the i-th row and j-th column calculated as:
Mi. = cosine W WoZ. 24 W2Z
(4)
W Q. Wi E θ are learnable matrices corresponding to the ligand and receptor.
Simlar with the cross ligand-receptor query, the cross receptor- ligand query 9, (Z,, Zi, θ,) calculates the Wasserstein affinity A,, E R",."" using with corresponding parameters, e.g. W W K.
Multi-head attention. Based on those cross-grapp query- resulted Wasserstein affinities Ai,r: Ay. we further derive the multi-head attetion to adaptively highlight those salient pairs of residues. For simplication, we take the ligand branch with one-head attention example, which can be easily extended to the multi-head case. Formally, for the ligand branch:
Fi = [i Zy, Db) = soʃ soflmar(( (imox(A1.)) V
(5)
Here, 4 denotes the parameter set involved in the multi-head attention, sof soflmax()) applies softmax operation along the rows of A,,, and results in ny x nh. dimension matrix for adaptively weighting the nodes in the value graph V, Z, W/ Vi E R xd'. Fi E IR= is the output.
The above cross-graph query and Multi-head attention operations fulfill the cross-graph tranformer with one-head attention. And the multi- heal attention F F can be achieved by conducting parallel multi-channel transformation f (:", (-) based on Eqn. (3--5) 5 and then aggregating all those channels. Moreover, multi-layer CGT modules can be stacked in a deep architecture with the ligand and receptor branches co-evoled, where the output features of the previous layer are concatenated with those of the current layer. The whole process is shown in Algorithm [
f.m(()
The optimal transport. In the learning process above, one crucial step is to learn the matrix T in Eqn. (3) for calculating the Wasserstein affinity between two cross-graph node sets. Formally, TA e RT x is the solution of an mntropy-smoother optimal transport problem:
T argmin À (Tr,,, M,,) ((Tr,)).
where B) trA" ((T,r)) is discrete joint probability distribution calculating the entropy of Ti, Specifically, the optimization problem in (6) can be efficiently solved through Sinkhorn's fixed point iterations(Cutur) 2013), and the solution can be written as:
T = diag(u, Ki,g (i,,ddgggvi)))) vi.r) = ur, c Kir c 1n, VT,
where K,, is calculated based on the distance matrix Mr with K,,- = e AM... In Sinkhorn iterations, urr and Vt.r are kept alternately update. Taking the k-th iteration as an example, the update takes the following form:
/n R-1
1m/mm
u
(8)
KP u
Kf.
with uf.r- = 1,, as an initialization.
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Algorithm 1: Stacking multi-layer CGT modules.
Input: Encoded ligand and receptor graph features Z, Z, number of stacked layers
for k f- 1 to K do
// Conducting cross-graph query according to Eqn. then
calculating multi-head attention through applying ng the
multi-channel version of Eqn. (5) based A (1) then
A
if
F(K) (Z) Z,, P:): F(A) = fr (Zr Zi, P,);
else
[(K) (0 k- 0 Pi); F(K) f.m
end
// node feature update;
O (k) Jausspee (Concalenatel 0 (k-1) F
(k) Souspus (Coneattnnateeeeee 0 (k-1) FF(())
10
11
end
Output: The output graph features 0 (k) 00hh of the K K-layer CGT module
EXPERIMENT
In this section, we first introduce the used datasets and experiment setup including the implemen- tation details, parameter setting and the evaluation metires. Then we compare our model with other baseline methods. Finally, we analyze our method through ablation experiments.
4.1 DATASET
The employed datasets are DB3 (Hwang et al. 2008), DB4 (Hwang et al. 2010), DB5 Vrrvenn et al. 2015), and DB5.5 from the family of Docking Benchmark (DB) datasets. Each dataset is split into training and test sets. DB5.5 is the latest and largest dataset consisting of totally 271 complexes, which provides the bound state of two given proteins well the unbound state of each protein. The DB5 is the subset of the DB5.5 with 230 complexes, which is most widely used. The DB3 and DB4 are subsets of DB5, which are relatively small. Specially, the DB3 contains 119 complexes and DB4 has 171 complexes totally.
4.2 EXPERIMENT SETUP
Data Preprossing Considering the irregular structure of proteins, graphs are constructed to describe them by taking residues as nodes with their edges defined according to the spatial relationship. all datasets, we extract the same features and labels by following the work in (Fout al. 2017). Generally, the features are divided into two types, i.c. sequence features and structural features. Specially, the Position Specific Scoring Matrix(PSSM) is extracted from amino acid sequence as sequence features. For structural features, we extract Relative Accessible Surface Area(rASA), residue depth, protrusion index, hydrophobicity and half sphere amino acid composition. Finally, we combine all the aforementioned features, which result in 70-dimension features for nodes. Edge features composed of average atomic distance and the angle between two residues (Fout et al. 2017). To define the label, pair of amino acids are treated to be interactive if any two non-hydrogen atoms, each from one amino acid, are within 6,, which is also adopted by (Fout et al. 2017 Townshend et al. 2019).
Implementation Details For inputs of higand-receple pairs, we employ graph encoders of siamese-
like networks and each graph encoder is a two-layer GNN module, resulting in features of 512. For the CGT module, we stack it into two-layer architecture, and foutput in Algorithm i set lllayer GNN. The output 512-dimension features of the two-layer CGT are further passed through two layers of MLP for prediction. For protein, the number of positive is far less than that of negative
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samples, so we employ the weighted cross-entropy loss to train our model in end-to end manner. Specially, the weight for positive samples is 0.1 while for negative ones. We train our model with stochastic gradient descent optimizer (SGD) for 200 epochs on 2080Ti GPU cards, where the learning rate is 0.1.
Protocol For the Docking Benchmark (DB) datasets, training sets are generally complexes from previous version dataset and test sets are those updated in the current version. For example, we split DB5.5 into a training set corresponding to DB5 and test set composed of the complexes added in the update from DB5 to DB5.5. We use the same training set and test set as in all baseline methods (Fout ct al. 2017: Townshend et 2019 Liu al. 2020 Schütt al., 2017 Duvenaud et al. (2015) for the DB5 dataset. For the DB3, DB4 and DB5.5 datasets, we use the fixed training examples and test examples shown on the websitell Following the previous works (Fout et al. 2017 Townshend et al. 2019; Liu et al. 2020), we evaluate the performance by median area under the receiver operating characteristic curve (MedAUC) across all complexes the test set. The experiments are repeated 10 times and we use the average of the ten runs the final performance. For each method we report the mean and standard deviation of MedAUC across 10 runs.
4.3 EXPERIMENTAL RESULTS
We compare the CPWT framework with ttate-of-the-arts methods. including Node Average (NA) (Fout et al. 2017). Node and Edge AVEA) (Fout et al.] (017). Deep Tensor Neu- ral Networks (DTNNs) (Schütt et al. 2017), Single Weight Matrix (MFN) (Duvenaud et al. 20015),
Siamese Atomic Surfacelet Network (SASNet) (Townshend et al. 2019) and High-Order Pairwise Interactions (HOPI) (Liu et al. 2020). The results are shown in Table I Specifically on the DB5
dataset, we compare our performance with all baseline methods reported in (Fout et al. 2017: Town shend et al. 2019 Liu al., 2020), while the results on DB3 and DB4 datasets of the work (Liu et al. 2020) are not compared here because different protocols are used. According to the results in Table I our proposed CPWT method outperforms all baselines all DB datasets. Specifically, in the most widely used DB5 dataset, our method achieves approximately 0.041 performance gain comparing with the previous work (Fout et al. 2017). is worth noting that the recent work (Liu et al. 2020) reports relatively high performance among those compared methods on the DB5 dataset. However, it conducts additional data augmentation by incorporating in in-protein pairwise interactions as positive pairs of samples. Comparing with this method, we still obtain better performance without the data augmentation. On the DB3 and DB4 datasets with less protein complexes, SASNet and several graph- based methods get poor performance. However, our method still achieve good performance. For the DB5,5 dataset, which is the largest one, our method still get the best result, with the performance gain of 0.013 comparing with NA (Fout et al. 2017). All the results above demonstrate the effectiveness of our proposed CPWT framework and the robustness against variation of dataset size.
Table I: Comparsion with hate-oo-thhe-rt-mmthee
Methods
DB3
DB4
DB5
DB5.5
NA (Fout et al. 2017)
0.895 (0.015)
0.902 (0.005)
0.882 (0.007)
0.931 (0.007)
NEA Fout et al. 2017
0,881 (0.009)
0.898 (0.005)
0.898 (0.005)
0.917 (0.008)
DTNNS (Schütt al. 2017
0.853 (0.017)
0.870 (0.015)
0.880 (0.007)
0.924 (0.013)
MFN (Duvenaud et al. 2015)
0.875 (0.019)
0.878 (0.009)
0.871 (0.013)
0.929 (0.012)
SASNet ( (lwwnshend al.
(2199)
0.800 (0.012)
0.802 (0.014)
0.876 (0.037)
0.910 (0.008)
NeiA+HOPI (Liu et al. 2020)
0,919 (0.015)
NeiWA+HOPI (Liu et
2020
0.930 (0.016)
CPWT
0.917 (0.001)
0.913 (0.005)
0.939 (0.002)
0.944 (0.008)
4.4 ABLATION STUDY
As our CPWT framework has achieved promising performance compared to the existing state-of-the- art methods, it is interesting and meaningful to make clear how the modules or parameters setting, e.g. the number of CGT layers and graph encoder layers, influence the performance of protein interaction prediction. For this purpose we conduct several additional experiments to explore our framework based on the DB5 dataset as follows.
Influence of the CGT layer number. To investigate the impact of CGT module on our framework, stack multiple CGT layers and compare the performance between them. The results are shown in
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NDALOC
NMNOCC
240
200
047
340
053
N
2
(a)
(b)
(c)
Figure 3: The evaluation of hyperparameters.cd (a) the number of CGT layers (denoted N), (b) À in Wasserstein affinity, (c) in Wasserstein affinity)
Fig. 3 (a). When the number of CGT layers is set 0, means no CGT module in our framework. It can be observed that our designed CGT module effectively promote the performance, as 1.3% performance gain is obtained by using one-layer CGT module comparing with the framework without any CGT module. Moreover,the performance varies with the number of CGT layers. And the best result obtained when the number set to 2.
Effectiveness of multi-head attention module. We compare the performance between model with or without multi healt-head attention. We remove multi-head attention module and use just the Wasserstein affinity (named CPWT no MH) to implement cross-graph function. For comprehensive evaluations, we evaluate the result in multiple setting with different GNN layers used in the graph encoder. The results are shown in Table 3 It is observed that the multi-head attention also improves performance because the performance decreases from 93.9% to 92.3% without using the multi-head attention, which demonstrates the meaningness of conducting uineggrined learning on residues.
Comparsion with the cross-protein reciprocal attention. We compare the performance between the models using the Wasserstein affinity and reciprocal attention in PepNN (Abdin et al.) 2022). where the cosine similarity employed for cross-graph measurement. We replace the Wasserstein affinity with the reciprocal attention in our model, which is named as CPRA. The performaces are evaluated on all datasets and the results are shown Table 2 As it is shown, performance improvement is obtained on all datasets, which verifies the effectiveness of our CPWT by introducing the Wasserstein affinity.
Table 2: Comparsion with reciprocal attention.
Datasets
DB3
DB4
DB5
DB5.5
CPRA
0.887 (0.003)
0.900 (0.007)
0.928 (0.003)
0.935 (0.009)
CPWT
0.917 (0.001)
0.913 (0.005)
0.939 (0.002)
0.944 (0.008)
Influence of the hyperparameter in Wasserstein affinity. Wasserstein affinity module, there are two key hyperparameter À and K. X is the regularization coefficient, which controls the strength of the regularization and K controls the iterative update steps. We set different values and compare them. The results shown in Fig. (c) and Fig. 3 (d). Specifically, À controls local information between the nodes across two graphs. For too large values of X, the OT matrix would become little graphs and therefore would degrade the ability of capturing patterns of protein complex. Even though two parameters are varied in pretty large range of values, the performance of the model stays above 90%.
sensitive to the local correlation between
Influence of multiple GNN layers in graph encoder. For comprehensive comparison, conduct experiments with multiple numbers of GNN layers in the graph encoder, and compare the results with those baselines based graph. The results are shown in Table As shown, more GNN layers lead to the performance reduction because of the over-smoothing. Moreover, we can observe that our proposed CPWT framework always achieve the best performance even though the number GNN layer varies, which demonstrates the effectiveness of our proposed method.
Visualization of salient pairs of residues. To intuitively understand the effect of our fine- ine-grained learning, further visualize the factor values of multi-head attention using protein complex 3V6Z as an example in Figure 4 According to Figure g intuitively, our proposed CGT module can endow large weights most interactive pairs comparing with the ground truth. Specifically, compared with
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Under review as a conference paper at ICLR 2023
GroundTidhh
(t) CheedThhhhinnttor
Waseestennfftttt
Redigroci dltntion
(1) Reciprool atvedioninnattoonn
Figure 4: The visualization of the ground truth(a), (b), learned saliencies (c), (d) and reciprocal attention (c), (f) separately in the heatmap and protein cartoon model upon protein complex 3V6Z. The red parts in (b) are the binding sites of the ground truth in the complex and the red parts in (d) and (f) denotes the learned salient pairs of sites.
Table Comparsion with graph- methods on the DB5 dataset.
GNN Layers
2
NA
(Fout et al. 2017
0.864 (0.007)
0.882 (0.007)
0.891 (0.005)
0.889 (0.005)
NEA (Fout et al. 2017
0.876 (0.005)
0.898 (0.005)
0.895 (0.006)
0.889 (0.007)
DTNNs (Schutt et al. 2017)
0.867 (0.007)
0.880 (0.007)
0.882 (0.008)
0.873 (0.012)
MFN (Duvenaud al.
2015
0.865 (0.007)
0.871 (0.013)
0.873 (0.017)
0.869 (0.017)
NeiA+HOPT (L.u et al. 2020
0.902 (0.012)
0.919 (0.015)
0.921 (0.009)
0.915 (0.009)
NeiWA+HOPI (Liu et 20200
0.908 (0.019)
0.930 (0.016)
0.924 (0.011)
0.914 (0.013)
CPWT no MH
0.912 (0.006)
0.923 (0.005)
0.921 (0.006)
0.915 (0.005)
CPWT
0.923 (0.003)
0.939 (0.002)
0.932 (0.002)
0.928 (0.005)
the reciprocal attention in (Abdin al. 2022). our framework achieves more fine-grained learning as has less red area but generally covers the ground truth. Hence, Table and Fig, 4ijointly verify the effectiveness of our CPWT framewrok by introducing Wasserstein affinity.
CONCLUTION
In this paper, a novel CPWT framework was proposed for the PPI prediction task. Based on the hypothesis of intimate structure-function relationship. the CPWT framework focuses on cross- cross-protein structural modeling as well as fine-gran fine-grained learning on pairs of residues. Considering the irregular structure of proteins, graphs were constructed describe them, with graph encoders then applied for robust features. Then, core Cross-Graph Transformer (CGT) module was proposed for cross- prosein structural modeling, where the rross-graph query was conducted based on Wasserstein affinities across graphs. Moreover, the multi-head attention was accordingly derived for mining fine-grained cues. For better feature learning ability, the CGT was stacked into multi-layer structure with the ligand and receptor branches co-evolved during forward inference. Comprehensive experiments were conducted for performance evaluation, and the learned fine-gre men-grained saliencies were also visualized. All these above verified the effectiveness of our CPWT framework.

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Under review as a conference paper at ICLR 2023
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12


Reviews:
[{"review_id": "swdH4yCDk9", "reviewer": "Reviewer_sndu", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper propose a cross attention mechanism for classifying protein-protein interactions. The hypothesis is that information from both proteins get mixed during encoding, leading to better predictions. Paper also propose using the Wasserstein distance measure while processing the attention values.", "summary_of_the_review": "I recommend that the authors revise the whole of the method section, keeping in mind reproducibility of this paper. Then resubmit to another conference or journal.\n\nExperiments to show the effects between \"cross attention\" and \"no cross attention\" is needed. Readers may not be convinced that crossing has a significant impact on the prediction until they see good experiments. Keeping everything else unchanged, train two transformers. one with crossing of features (in this paper) and the other transformer without crossing of features.", "strength_and_weaknesses": "Key new ideas are (1) cross transformer (2) Use of Wassertien distance.\nVery good that the authors repeat their experiments 10 times and generate error bars.\n\nThe method description seems incomplete. Elaborations about this is given in the next section of the review", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "3: The contributions are significant and somewhat new. Aspects of the contributions exist in prior work."}, "extra_text": {}}, {"review_id": "iQczfAeIA3", "reviewer": "Reviewer_HBkA", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "The paper proposes Cross-Protein Wasserstein Transformer (CWPT) for protein-protein interaction site detection. For this it proposes an elaborate architecture, composed of three main parts: (i) A graph network as the encoder of the individual proteins, (ii) a (cross-graph) transformer with cross-attention (from one protein to another) using a Wasserstein affinity, and (iii) a final module to operate on the cross-protein embeddings to detect the interaction sites.", "summary_of_the_review": "The work does not have a technical machine learning contribution and hence should be refereed as an application paper. Given that there are quite a few recent works on protein complexes, it is unclear what application benefits the results of this work bring about. Furthermore, the presentation requires important clarifications. These together suggest that the paper may not be ready for publication.", "strength_and_weaknesses": "- The ablation studies with regards to the importance of different components are informative.\n\n- Given the recent advances in protein-complex folding, what is the benefit of PPI site prediction?\n- The results should have been compared with the recent methods that do structure prediction for a pair or a complex of proteins.\n\n", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "3: Some of the paper’s claims have minor issues. A few statements are not well-supported, or require small changes to be made correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "2: The contributions are only marginally significant or novel."}, "extra_text": {}}, {"review_id": "J3YVQpjR_Fu", "reviewer": "Reviewer_jcwb", "summary": "", "questions": "", "limitations": "", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a novel deep learning framework named Cross-Protein Wasserstein Transformer (CPWT) to predict PPI sites through fine-grained cross-graph structural modeling, which promotes the PPI prediction from the perspective of sophisticated cross-protein structural modeling based on Wasserstein affinities. Then, a core Cross-Graph Transformer (CGT) module of two branches (e.g. ligand and receptor branches) is proposed for cross-protein structural modeling. Specifically, in this module, Wasserstein affinity across graphs is calculated through cross-graph query (i.e. ligand (query) - receptor (key) or the converse), based on which the multi-head attention is derived to adaptively mine fine-grained cues of PPI sites. By stacking CGT modules, the two branches in CGT are co-evolved in a deep architecture during forwarding inference, hence being powerful and advantageous in cross-protein structural representation and fine-grained learning. The experimental results show the effectiveness of our CPWT framework by conducting comprehensive experiments on multiple PPI datasets, and further visualize the learned fine-grained saliencies for intuitive understanding.", "summary_of_the_review": "Considering the above pros and cons, my recommendation of the paper is marginally below the acceptance threshold.", "strength_and_weaknesses": "##########################################################################\n\nPros:\n\n- This paper proposes a new Cross-Protein Wasserstein Transformer framework to promote the PPI prediction from the perspective of sophisticated cross- protein structural modeling based on Wasserstein affinities.\n- This paper also proposes a novel CGT module in which the multi-head attention is derived to mine fine-grained cues of PPI sites. Moreover, this module can be stacked into a deep architecture with two branches co-evolved, which are powerful in cross-protein structural expression with sophisticated fine-grained learning.\n- This paper reports the state-of-the-art performance on multiple PPI datasets with comprehensive experiments.\n##########################################################################\n\nCons:\n\n- The core idea of this paper is CPWT framework and CGT module, however, although the authors achieved SOTA performance on multiple PPI datasets with comprehensive experiments, seems CGT is just combined multi-head attention and Wasserstein affinity, if lacking enough theory support or empirical insight such combination novelty is limited.\n- The authors claim \"To learn robust features from these graphs, graph encoders such as GNNs are then applied.\" Why? What GNNs have to do with robustness?\n- In the experiment section, all experiments are based on Docking Benchmark (DB) datasets, is there any other dataset to support the hypothesis?\n- Missing code link to reproduce experiments.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "4: All of the claims and statements are well-supported and correct.", "technical_novelty_and_significance": "2: The contributions are only marginally significant or novel.", "empirical_novelty_and_significance": "Not applicable"}, "extra_text": {}}, {"review_id": "46i9CpIOp_C", "reviewer": "Reviewer_1voW", "summary": "", "questions": "", "limitations": "", "rating": 3, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "main_review": "", "summary_of_the_paper": "This paper proposes a method for protein interface prediction. In a nutshell, given two proteins (a ligand and a receptor) whose 3D structures are assumed known, the aim is to identify contacts between residues in the receptor and residues in the ligand.\n\nTo this end, the authors propose a simple model that:\n1. Uses GNN layers to independently compute per-residue embeddings for the ligand and the receptor.\n2. Refines these embeddings by applying (possibly several) layers of doubly stochastic cross-attention between the ligand and receptor embeddings.\n3. Uses the resulting refined embeddings to predict residue-residue interactions.\n\nThe authors evaluate the resulting approach on the Docking Benchmark (DB) datasets. \n", "summary_of_the_review": "As it stands, unfortunately I do not believe the manuscript to have a sufficiently significant contribution, neither methodological nor application-related, to warrant publication.\n\nFrom a methodological perspective, the proposed model follows a traditional dual GNN encoder architecture with cross-attention fusion layers. Perhaps the most innovative design choice is the use of doubly stochastic cross-attention by means of the Sinkhorn algorithm in these cross-attention layers, but doubly stochastic attention is also not novel per se (see e.g. [1]).\n\nFrom an application-centric perspective, the reported performance improvements are within the margin of error for the most competitive baselines (e.g. NeiWA+HOPI) whenever these are shown (only one out of four datasets), making it hard to judge the significant of the results. Moreover, in my opinion, the experimental setup itself is too limited for an application-centric manuscript. As potential directions for improvement in this regard, I would suggest all of the following:\n\n1. Reporting NeiA+HOPI and NeiWA+HOPI performance values for all datasets.\n2. Evaluating on larger, newer benchmarks such as DIPS [2] and DIPS-Plus [3].\n3. Including more recent baselines in the comparison.\n\nReferences:\n[1] Sander, Michael E., et al. \"Sinkformers: Transformers with doubly stochastic attention.\" International Conference on Artificial Intelligence and Statistics. PMLR, 2022.\n[2] Savidor, Alon, et al. \"Database-independent protein sequencing (DiPS) enables full-length de novo protein and antibody sequence determination.\" Molecular & Cellular Proteomics 16.6 (2017): 1151-1161.\n[3] Morehead, Alex, et al. \"DIPS-Plus: The Enhanced Database of Interacting Protein Structures for Interface Prediction.\" arXiv preprint arXiv:2106.04362 (2021).", "strength_and_weaknesses": "Strengths:\n+ Despite the recent breakthroughs in protein structure prediction heralded by AlphaFold2, accurately predicting the interface of protein-protein interactions remains an open problem, making the paper's topic very relevant.\n\nWeaknesses:\n+ Experimental results for the most competitive baselines (NeiA+HOPI and NeiWA+HOPE) are lacking for three out of four datasets.\n+ The experiments do not provide compelling evidence that the proposed approach outperforms the baselines by a significant margin.\n+ For an application-focused paper, the experimental results lack breadth in terms of the datasets and metrics under consideration.\n+ The paper lacks a significant methodological contribution.", "limitations_and_societal_impact": "", "review_text": "", "extra_scores": {"correctness": "2: Several of the paper’s claims are incorrect or not well-supported.", "technical_novelty_and_significance": "1: The contributions are neither significant nor novel.", "empirical_novelty_and_significance": "1: The contributions are neither significant nor novel."}, "extra_text": {}}]

Author rebuttal:

Decision: Reject