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 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.

1. INTRODUCTION

Proteins are chains of amino acids, and physical interaction between proteins is essential to life. The protein-protein interaction (PPI) (Figure 1 shows an example) determines molecular and cellular mechanisms, and thus plays a crucial role in biological processes including the gene expression, proliferation of cells, etc. Moreover, as proteins are predominant drug targets, characterizing PPIs at 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(NMR) (Wuthrich, 1989) , X-ray crystallography (Svergun et al., 2001) and high-throughput screening methods (Song et al., 2011) . However, identifying the binding sites based on these methods is often time-consuming and resource-expensive. Then, with more and more protein structure data available (Berman et al., 2000) , computational methods are developed to predict protein-protein interaction sites, which can be divided into two categories, i.e. protein-protein docking and data-driven methods. For the protein-protein docking (Porter et al., 2019; Halperin et al., 2002) , the fundamental principle is the steric complementarity at protein-protein interfaces. However, it 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, a 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.e. sequencebased methods (Murakami & Mizuguchi, 2010; Zhang et al., 2019; Jurtz et al., 2017; Haberal & Ogul, 2017; Zheng et al., 2018 ), structure-based methods (Du et al., 2016; Bradford & Westhead, 2005; Neuvirth et al., 2004) and those ones based on mixed information (Afsar Minhas et al., 2014; Li et al., 2012; Northey et 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 of DeepMind's Alphafold2 (Jumper et al., 2021) for structure prediction. Specifically for PPIs, to utilize the powerful structure modeling ability, recent works (Bryant et al., 2022; Gao et al., 2022; Evans et al., 2021) including AF2Complex (Gao et al., 2022) and AlphaFold-Multimer (Evans et al., 2021) propose to Considerable progress has been made in PPI prediction, especially by GNNs. However, considering the intimate structure-function relationship, two main issues are remaining to be solved: (1) insufficient 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 1 ) in proteins so that fine-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 on PPI sites. In this process, cross-graph modeling is required, which is rather non-trivial. Theoretically, as irregular graphs don't lie in the Euclidean space, the common metric like cosine similarity, cannot well describe the cross-graph structural relationship. To address this issue, the Wasserstein metric is specifically introduced, based on which cross-protein query operations (i.e. ligand (query) -receptor (key) or the converse) are 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 is 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: (1) We propose a new Cross-Protein Wasserstein Transformer framework to promote the PPI prediction from the perspective of sophisticated crossprotein structural modeling based on Wasserstein affinities; (2) We propose 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



Figure1: 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).

