
==== Front
Brief Bioinform
Brief Bioinform
bib
Briefings in Bioinformatics
1467-5463
1477-4054
Oxford University Press

10.1093/bib/bbae455
bbae455
Problem Solving Protocol
AcademicSubjects/SCI01060
PGBind: pocket-guided explicit attention learning for protein–ligand docking
https://orcid.org/0009-0001-1937-6855
Shen Ao Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, 131 Dong’an Road, Shanghai 200032, China
Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention, Fudan University, 131 Dong’an Road, Shanghai 200032, China

https://orcid.org/0000-0003-1322-7530
Yuan Mingzhi Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, 131 Dong’an Road, Shanghai 200032, China
Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention, Fudan University, 131 Dong’an Road, Shanghai 200032, China

https://orcid.org/0009-0004-7335-785X
Ma Yingfan Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, 131 Dong’an Road, Shanghai 200032, China
Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention, Fudan University, 131 Dong’an Road, Shanghai 200032, China

Du Jie Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, 131 Dong’an Road, Shanghai 200032, China
Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention, Fudan University, 131 Dong’an Road, Shanghai 200032, China

https://orcid.org/0000-0002-9255-3897
Wang Manning Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, 131 Dong’an Road, Shanghai 200032, China
Shanghai Key Laboratory of Medical Image Computing and Computer Assisted Intervention, Fudan University, 131 Dong’an Road, Shanghai 200032, China

Corresponding author. Digital Medical Research Center, School of Basic Medical Sciences, Fudan University, Shanghai 200032, China. E-mail: mnwang@fudan.edu.cn
Ao Shen and Mingzhi Yuan contributed equally to this work.

9 2024
18 9 2024
18 9 2024
25 5 bbae45524 4 2024
07 8 2024
31 8 2024
© The Author(s) 2024. Published by Oxford University Press.
2024
https://creativecommons.org/licenses/by-nc/4.0/ This is an Open Access article distributed under the terms of the Creative Commons Attribution Non-Commercial License (https://creativecommons.org/licenses/by-nc/4.0/), which permits non-commercial re-use, distribution, and reproduction in any medium, provided the original work is properly cited. For commercial re-use, please contact journals.permissions@oup.com

Abstract

As more and more protein structures are discovered, blind protein–ligand docking will play an important role in drug discovery because it can predict protein–ligand complex conformation without pocket information on the target proteins. Recently, deep learning-based methods have made significant advancements in blind protein–ligand docking, but their protein features are suboptimal because they do not fully consider the difference between potential pocket regions and non-pocket regions in protein feature extraction. In this work, we propose a pocket-guided strategy for guiding the ligand to dock to potential docking regions on a protein. To this end, we design a plug-and-play module to enhance the protein features, which can be directly incorporated into existing deep learning-based blind docking methods. The proposed module first estimates potential pocket regions on the target protein and then leverages a pocket-guided attention mechanism to enhance the protein features. Experiments are conducted on integrating our method with EquiBind and FABind, and the results show that their blind-docking performances are both significantly improved and new start-of-the-art performance is achieved by integration with FABind.

protein–ligand docking
drug discovery
protein–ligand blind docking
AI for science
Science and Technology Innovation Plan Of Shanghai Science and Technology Commission 10.13039/501100018625 23S41900400 Fudan University Science Intelligence Special Fund FD-AI4S04183
==== Body
pmcIntroduction

Protein–ligand docking plays a crucial role in drug discovery, facilitating drug design [1], target identification [2], and virtual screening [3]. It simulates interactions between proteins and potential drugs, improving efficiency and reducing costs in the discovery and optimization of new drugs [4]. Compared with docking to a given protein pocket, blind protein–ligand docking is more challenging, where the binding sites of the protein are unknown [5]. Currently, ¡5% of human coding genes can be used as commercial drug targets, and huge disease targets look forward to being explored [6]. A large number of new drug R&D are crowded on the same target track, so there is an urgent need to discover more new drug targets [7]. Blind docking can be a valuable tool to discover new drug targets, which offers novel perspectives and directions in drug development [8]. In addition, with the flourishing development of techniques predicting protein structures [9], proteins without pocket information are anticipated to be more and more applied in drug discovery and blind docking technology is essential for virtual screening based on these protein structures [10].

Traditional blind docking methods are usually based on massive sampling of molecule orientations and conformation and the scoring of each candidate, which makes them very time-consuming and impractical for large libraries [11–13]. With the advancement of geometric deep learning methods for protein and ligand representation [14, 15], deep learning-based scoring methods have been proposed to accelerate the scoring process [16, 17], but the constraints of massive sampling cannot be overcome. Recently, regression-based deep learning methods have shown good promise for blind docking since they achieve equivalent or higher docking accuracy while being two to three orders of magnitude faster, e.g. EquiBind [18], TankBind [19], E3Bind [20], and FABind [21]. Given a ligand and a fixed protein structure, regression-based models can directly predict the final docking conformation of the ligand without sampling its conformation space. They usually first model both the protein and the ligand as graphs and then utilize deep neural networks to extract features for both graphs with intra- and inter-graph message passing. Finally, the docking conformation is directly regressed from the extracted features [18]. Regression-based blind-docking approach has shown its advantages in speed and the current research focus is on how to improve its accuracy.

All regression-based methods adopt a pocket prediction strategy explicitly or implicitly. Taking EquiBind [18] as an example, the blind docking process begins with the generation of residue-level features for the protein and atom-level features for the ligand through a graph network. Subsequently, attention weights between the ligand feature and all residues are computed based on their extracted features. By leveraging these weights along with the coordinates of the residues, keypoints of the protein and ligands are both identified where the region around the keypoints on the protein can be considered as a pocket. As illustrated in Fig. 1(a), the problem with existing methods is that some non-pocket features are mixed with pocket features, making the coordinates of keypoints influenced by the non-pocket areas, thereby leading to wrong docking. The lack of guidance by prior information of the pocket position leads to redundant and unreasonable intra- and inter-graph information interactions, resulting in feature distribution that is not conducive to docking.

Figure 1 Feature distribution and weight for ligand coordinate regression before and after pocket guidance; (a) before pocket guidance, the estimated ligand coordinate is interfered with non-pocket points as some non-pocket point features are mixed with pocket point features; (b) after pocket guidance, the pocket point features gather together, avoiding the influence of non-pocket regions in ligand coordinate regression.

In this paper, we design a plug-and-play pocket-guided (PG) strategy to embed pocket prior into protein features during blind docking. The first step of our strategy is to estimate the pocket region on a protein [19–21]. Though there are many pocket prediction methods available [22–25], most of them are voxel-based methods, making it challenging to achieve plug-and-play because existing regress-based blind-docking methods model proteins as residue graphs [18, 21]. Therefore, we design a simple yet effective graph-based pocket prediction module to predict the pocket region. Then, with the predicted pocket prior information, we develop an explicit PG attention mechanism to enhance the protein features to focus on the estimated pocket regions. As depicted in Fig. 1(b), through the proposed PG strategy, the influence of the non-pocket region is greatly weakened and the regressed coordinates of the keypoints become more accurate. We design a plug-and-play PG module to enhance the graph-based protein features, which can be seamlessly integrated into existing blind docking methods to improve their performances. Experiments are conducted on two existing blind docking models, EquiBind and FABind, and their performances are both significantly improved. New start-of-the-art (SOTA) performance is achieved by integrating our PG module with FABind. Our contributions can be summarized as follows:

We introduce the PG strategy in the field of blind protein–ligand docking. Our approach improves blind docking accuracy by enhancing the protein features with the guidance of estimated pockets.

We design a plug-and-play PG module, which can be seamlessly integrated into existing blind docking models to improve their performances. Experiments show that the proposed module significantly improves the performance of EquiBind and FABind and new SOTA performance is achieved by integrating the proposed PG module into FABind.

We give several examples to show that the integrated framework can explore new potential binding sites, which may inspire the discovery of new potential pockets.

Related work

Blind protein–ligand docking. The purpose of blind protein–ligand docking is to predict the binding conformation of protein–ligand complexes, essentially involving predicting the relative coordinates of each atom on the ligand when fixing protein pose. Traditional approaches involve iteratively deriving the final docking conformation by minimizing physics energy functions, which takes a heavy computation burden, and recent deep-learning based methods are usually much faster. Deep-learning docking methods can be divided into two categories: sampling-based methods and regression-based methods. Sampling-based methods sample a large number of ligand conformations and choose one from them by deep learning-based scoring functions [16, 17]. Regression-based methods directly calculate the binding conformation without sampling [18–21]. Our approach falls in the category of regression-based methods, aiming to enhance blind docking performance by introducing pocket priors. The structure of regression-based models can be further categorized into two types: the direct models, exemplified by EquiBind [18], which predict the final binding conformation directly from features of both protein and ligand; and the two-step models, which first predict the approximate pocket region, followed by docking only the ligand to the predicted pocket rather than the entire protein. TankBind [19], E3Bind [20], and FABind [21] belong to the latter types, among which FABind is the current SOTA model.

Pocket prediction. Pocket prediction involves identifying potential binding sites on a protein, enabling a better understanding of protein function and the development of new drugs[26]. Traditional methods for protein pocket prediction primarily depend on geometric, template, and energy-based approaches. Exemplary methods in each category include Fpocket [23], 3DLigandSite [24], and AutoSite [25], respectively. Recently, deep learning has been widely used for pocket prediction. Most of these methods, including DeepSite [27], DeepPocket [28], RecurPocket [29], and RefinePocket [30], voxelize proteins and utilize networks like convolutional neural network [31] and 3D U-Net [32] to extract protein features. MaSIF [33] and dMaSIF [34] process protein surface to meshes and point clouds, respectively, and utilize models dedicated to mesh and point cloud for feature extraction [35]. Because of the substantial difference in protein modeling between the above pocket prediction methods and existing blind docking approaches, it is difficult to integrate these pocket prediction methods into blind docking. P2Rank [36], as an open-source tool for partitioning potential functional blocks in proteins, has been applied in some deep blind docking methods, such as TankBind [19] and E3Bind [20], but the functional blocks it divides are relatively fragmented, which limits its performance.

Methods

As a plug-and-play network module, our PG module can be seamlessly integrated into any blind docking models only if they model whole protein as graph. Here we use EquiBind [18] as an example to introduce how the PG module works together with a direct regression model, and the integrated model is denoted as EquiBind-PG. Section 3.1 provides an overview of EquiBind-PG. Details about how to obtain pocket priors and how to process prior pocket features are given in Section 3.3. The EquiBind module is briefly introduced in Section 3.2 for completeness. At last, we explain how to insert the proposed PG module into the current SOTA model FABind in Section 3.4.

Overview

As shown in Fig. 2(a), a PG module is plugged into the original EquiBind [18] to form the EquiBind-PG. The PG module is utilized to enhance the protein features under the guidance of pocket estimation before they are further processed by EquiBind, so that the docking can be improved. We will first briefly introduce EquiBind for completeness and then present how the PG module enhances the protein features.

Figure 2 Overview of PGBind; (a) EquiBind-PG: the protein and the ligand are constructed as graphs; the PG module is plugged in to process the features of protein residues; then, the processed protein graph and the ligand graph are input together into IEGMN to accomplish feature interaction between them; subsequently, the docking module regresses several keypoints to achieve matching between the protein and the ligand; finally, it outputs the docking conformation based on keypoints matching; (b) PG module: the protein graph is input into the pocket prediction network to estimate the pocket region;using the estimated pocket region, the PG-attention module achieves feature interaction using geometric self-attention and explicit cross-attention to generate new enhanced protein features; (c) FABind-PG: it is a two-step regression method, which first predicts pocket region and then docks the ligand to the predicted pocket region; we insert PG module between the FABind layer and Gumbel-softmax in the first step to enhance the protein features.

EquiBind module

Both proteins and ligands are represented as graphs when they are inputted into EquiBind. Concretely, the protein graph is constructed using its residues as nodes and using the connections between each node to its 10 closest neighbors with a distance of 30 Å as edges. The ligand graph is constructed by utilizing its atoms as nodes and an edge is established between each atom pair within a distance of 4 Å. The detailed features of nodes and edges can be found in Supplementary Material (B). Firstly, the constructed protein graph and ligand graph are inputted into the independent equivariant graph matching network (IEGMN) [37] so that the protein features and ligand features can interact with each other. In IEGMN, both features and coordinates in protein and ligand are transformed by performing intra- and inter-graph message passing. Given the protein node features \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{P}$\end{document}, the protein coordinates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{P}$\end{document}, the ligand node features \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{L}$\end{document}, and the ligand coordinates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{L}$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\textrm{IEGMN}\left (H^{P}, X^{P}, H^{L}, X^{L}\right ) = H^{P}{\prime },X^{P}{\prime },H^{L}{\prime },X^{L}{\prime }$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{P}{\prime }$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{P}{\prime }$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{L}{\prime }$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{L}{\prime }$\end{document} are transformed protein node features, protein node coordinates, ligand node features, and ligand node coordinates, respectively. Subsequently, the docking module takes as input and a multi-head attention network is used to calculate the attention weights, which is utilized to regress the keypoints on protein and ligand from the residue coordinates and atom coordinates. Through rigid transform on the ligand, the keypoints on protein and ligand are binding correspondingly to perform the predicted ligand binding pose. To reduce non-existent ligand conformations, EquiBind docking module incorporates additional geometric conformation constraints, i.e. the local atomic structures (bond lengths and adjacent bond angles) [16] are rigid. For fairness, we use the same loss including ligand RMSD and Kabsch-RMSD as EquiBind to train EquiBind-PG.

Pocket-guided module

Instead of directly inputting a protein graph into the IEGMN module in EquiBind, a protein graph is first processed by the PG module for feature enhancement. The PG module injects pocket prior knowledge into protein features so that EquiBind can perform better ligand docking. As shown in Fig. 2(b), the PG module consists of two parts: the pocket prediction module and the PG-attention module.

Pocket prediction module: Following the data processing approach in EquiBind [18], our pocket prediction module takes a protein graph as input and predicts whether a residue is located in the easily bindable active region, i.e. the pocket. The pocket prediction module includes a simple graph neural network (GNN) and a pocket prediction head. Firstly, the protein graph is input into a simple GNN to update node features by aggregating information from neighboring nodes. We define the graph’s node features as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{P}=\{h_{i}\in \mathbb{R}^{64}|i=1,\ldots ,N\}$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $N$\end{document} is the number of protein nodes, and the feature dimension is encoded to 64 through a multilayer perceptron (MLP). The GNN updates the node features through several layers of feature propagation. Each node’s feature is updated by aggregating features from its neighboring nodes. The feature propagation from node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $j$\end{document} to node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} in layer \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $(l+1)$\end{document} is

(1) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& m_{j\rightarrow i}=\varphi\left(h_{i}^{l},h_{j}^{l},t_{j\rightarrow i},f_{j\rightarrow i}\right),\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $h_{i}^{l}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $h_{j}^{l}$\end{document} are the features of node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} and node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $j$\end{document} in later \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $l$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\varphi $\end{document} is a shallow neural network, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $t_{j\rightarrow i}$\end{document} is the distance between node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} and node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $j$\end{document}, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $f_{j\rightarrow i}$\end{document} is the edge feature between node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} and node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $j$\end{document}.

Each node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} receives feature propagation from its surrounding nodes \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\mathcal{N}(i)$\end{document}, the updated feature of node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} is defined as

(2) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& h_{i}^{(l+1)}=\frac{1}{|\mathcal{N}(i)|} \sum_{j \in \mathcal{N}(i)} m_{j \rightarrow i}\end{align*}\end{document}

and the final node feature is calculated after \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $N_{L}$\end{document} layers of propagation and transformation. After the simple GNN processing, we get the updated node features \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{Ps}=\{s_{i}\in \mathbb{R}^{64}|i=1,\ldots ,N\}$\end{document}.

Then we input \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{Ps}$\end{document} into the pocket prediction head to obtain pocket estimation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\hat{Y}=\{\hat{y}_{i}\in \mathbb{R} |i=1,\ldots ,N \}$\end{document}. To overcome the issue of imbalanced positive and negative labels caused by the low proportion of pockets on proteins, we perform a biased sampling on non-pocket regions to achieve a balance in the number of positive and negative tags. The samples are then used to calculate the binary entropy loss with the true binary labels:

(3) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& \mathcal{L}(y_{i}^{*},\hat{y}_{i})=-(y_{i}^{*}log(\hat{y}_{i})+(1-y_{i}^{*})log(1-\hat{y}_{i})),\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\hat{y}_{i}$\end{document} is the predicted feature, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $y_{i}^{*}$\end{document} is the ground-truth label of the pocket for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document}th residue. We calculate the closest protein residue to each ligand atom and consider residues within 30 Å as the pocket and their corresponding label \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $y^{*}_{i}=1$\end{document}, and vice versa. The label of the protein node is ultimately calculated as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Y=\{\text{bool}(\hat{y}_{i}>0) |i=1,\ldots ,N \}$\end{document}.

PG-attention module: As shown in Fig. 2(b), we input node features \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{Ps}$\end{document} and corresponding predicted binary pocket labels \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Y$\end{document} to the PG-attention module to further enhance protein features by interaction between pocket region and non-pocket region. The combination of geometric self-attention module and explicit cross-attention module is stacked \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $N_{pg}$\end{document} blocks to form our PG-attention module. We define protein node coordinates as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{P}=\{x_{i}^{P}\in \mathbb{R}^{3}|i=1,\ldots ,N\}$\end{document}.

The geometric self-attention module involves two stages: attention score calculation and aggregation. Given the protein node features \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{Ps}$\end{document} and coordinates \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $X^{P}$\end{document}, the attention score between node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} and node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $j$\end{document} is denoted as

(4) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& e_{i,j}=\frac{h_{i}W^{Q}\left(h_{j}W^{K}+d_{i,j}W^{R}\right)^{T}}{\sqrt{D}},\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $d_{i,j}\in \mathbb{R}^{64}$\end{document} is the geometric embedding based on \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $x^{P}_{i}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $x^{P}_{j}$\end{document}, which consists of a pair-wise distance embedding and a triplet-wise angular embedding [38], \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $D$\end{document} is the dimension of embedded node feature, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{Q}$\end{document}, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{K}$\end{document},\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{R}\in \mathbb{R}^{64\times 64}$\end{document} are projection layers for queries, keys, and geometric embeddings.

The output feature \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $z_{i}$\end{document} of node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $i$\end{document} is obtained according to the following formulas:

(5) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& z_{i}=\sum_{j=1}^{N}\text{softmax}\left(e_{i,j}\right)\left(h_{j}W^{V}\right),\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{V}\in \mathbb{R}^{64\times 64}$\end{document} is a projection layer for values. After that, we get geometric self-attention features of protein nodes, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Z=\{z_{i}\in \mathbb{R}^{64}|i=1,\ldots ,N\}$\end{document}.

To avoid redundant and unreasonable feature interactions, we incorporate estimated pocket as an explicit inductive bias to enhance node features. In our explicit cross-attention module, the protein node features are further processed based on whether they belong to the estimated pocket region. According to pocket binary labels \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Y$\end{document}, the pocket nodes features and non-pocket nodes features are, respectively, represented as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Z_{N}=\{z_{n}\in \mathbb{R}^{64}|n=1,\ldots ,P\}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Z_{M}=\{z_{m}\in \mathbb{R}^{64}|m=1,\ldots ,N-P\}$\end{document}, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $P$\end{document} is the numbers of pocket nodes. The feature correlation from non-pocket node to pocket node is the key to better learning the difference between pocket features and non-pocket features, which is essential to keep the geometric consistency for docking. In this process, the features of pocket nodes remain unchanged and the features of non-pocket nodes are updated.

Similar to geometric self-attention, the cross-attention score \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $a_{m,n}$\end{document} from non-pocket node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $m$\end{document} to pocket node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n$\end{document} is represented as

(6) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& a_{m,n}=\frac{(z_{m}W^{Qn})\left(z_{n}W^{K}\right)^{T}}{\sqrt{D}},\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $W^{Qn}\in \mathbb{R}^{64\times 64}$\end{document} is a projection layer for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $Z_{N}$\end{document}.

The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $z_{m}$\end{document} of node \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $m$\end{document} is updated according to the following formulas:

(7) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*}& z{\prime}_{m}=\sum_{n=1}^{P}\text{softmax}\left(a_{m,n}\right)\left(z_{n}W^{V}\right).\end{align*}\end{document}

The processed features of protein nodes are ultimately represented as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $H^{Pn}=Z_{M} \cup Z_{N}$\end{document}.

Plugging the PG module into FABind

To validate the plug-and-play capability of our proposed PG module, we also plug it into the SOTA blind docking method FABind [21], which is a two-step regression method. FABind first predicts the docking region and then docks the ligand to the docking candidate regions.

As shown in Fig. 2(c), FABind-PG consists of two steps: pocket prediction and docking. In the first step, it extracts protein and ligand features through FABind layer and then utilizes Gumbel-softmax to predict the center point of the pocket, around which a region within 20 Å is selected as the docking candidate region. Considering the relatively large area of the docking candidate region compared to the final docking region, which still includes a significant portion of non-pocket region in the protein. We insert our PG module between the FABind layer and Gumbel-softmax in the FABind prediction step to process the whole protein features, distinguishing better pocket region features from non-pocket region features. Then, the updated protein features are fed into the docking module, and based on these updated features, more robust ligand pose estimation can be achieved.

Experiments

Implementation details

Dataset: Similar to previous studies on blind protein–ligand docking, we conduct our protein–ligand docking experiments on the PDBBind v2020 [39] dataset which provides structural information of protein–ligand complexes along with determined binding affinity information. For a fair comparison, we use the processed data in EquiBind [18] when experimenting with EquiBind-PG, and the processed data in FABind [21] when experimenting with FABind-PG. Following recent works [19–21], we also evaluate the performances of our methods on proteins that have not been encountered in the training set.

Competitors: We compare our models with traditional methods and recent deep learning models, in which QVina-W [11], GNINA [40], SMINA [13], and GLIDE [12] are score-based methods. EquiBind [18], TankBind [19], DiffDock [41], E3Bind [20], and FABind [21] are recent deep learning-based methods.

Training details: We first utilize the training dataset to train the pocket prediction module in PG module, and then train whole models including PG module. For EquiBind-PG training, we train our model 500 epochs using an Adam optimizer with a rate of 5e-5 and four batch sizes on a single A40 GPU. As shown in Fig. 3, we can see that the training loss is significantly reduced after incorporating PG module. For FABind-PG training, due to the high computational demands of FABind, we adopt a fine-tuning strategy to the given model parameters. Initially, we freeze the officially provided weight of FABind and only fine-tune our PG module at a rate of 1e-4 for 120 epochs. Subsequently, the original model parameters are unfrozen, the PG module is trained at a rate of 1e-5, and the original FABind model is trained at a rate of 1e-7 for 20 epochs. Model training is implemented on a single A40 GPU with batch size set to 3. For more detailed experimental settings, please see Supplementary Material (A and B).

Figure 3 Training loss on the valid set comparison.

Metrics: Following EquiBind, we use two types of metrics to evaluate the predicted ligand pose: (1) Ligand RMSD, which is the Root Mean Square Deviation (RMSD) of the predicted atomic Cartesian coordinates of the ligand, serving to evaluate the model’s ability to predict the ligand pose at the atomic level. (2) Centroid Distance, which is the Euclidean distance between the predicted average ligand coordinates and the ground-truth average ligand coordinates, measuring the model’s capability to explore the binding site.

Performance in flexible self-docking

In flexible blind self-docking tasks, the protein structure remains fixed, while the conformation of the docking ligand is unknown. The model needs to predict the coordinates of each atom in ligand, equivalent to both its conformation and its translation and orientation. As shown in Table 1, we observe a significant improvement in the performance after incorporating the PG module. In the comparison between EquiBind-PG and EquiBind, we observe large improvements in every metric after inserting the PG module whether the conformation is optimized or not (-U). The mean ligand RMSD and the percentage of centroid distance <5Å of EquiBind-PG are close to the current SOTA method FABind. When the PG module is inserted into FABind, we observe improvements in performance across most metrics. The mean RMSD decreases by 14.1%, and the 75th percentile of centroid distance values decreases by 14.3%, outperforming all previous methods by a large margin. Moreover, there are significant improvements in the <5Å metrics of both ligand RMSD and centroid distance. Overall, the pocket guidance significantly reduces the prediction of off-target conformations and improves prediction performance, as evidenced by the 75th percentile values, mean values, and the percentage below 5 Å. FABind-PG outperforms DiffDock(1) in all metrics and surpasses the performance of DiffDock(10) and DiffDock(40) in most metrics. Although FABind-PG does not outperform DiffDock(10) and DiffDock(40) in terms of <2Å metric, it does offer a speed advantage, being two orders of magnitude faster.

Table 1 Flexible blind self-docking performance; EquiBind-U represents the EquiBind method without optimization of the regression result by point cloud ligand fitting; the green denotes improvement after plugging our PG model and models with (*) are re-inferred on our same machine

Method	Ligand RMSD	Centroid distance		
	Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}	Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}		
	25%	50%	75%	Mean	2Å	5Å	25%	50%	75%	Mean	2Å	5Å	Average runtime(s)	
QVina-W	2.5	7.7	23.7	13.6	20.9	40.2	0.9	3.7	22.9	11.9	41.0	54.6	49	
GNINA	2.8	8.7	22.1	13.3	21.2	37.1	1.0	4.5	21.2	11.5	36.0	52.0	146	
SMINA	3.8	8.1	17.9	12.1	13.5	33.9	1.3	3.7	16.2	9.8	38.0	55.9	146	
GLIDE	2.6	9.3	28.1	16.2	21.8	33.6	0.8	5.6	26.9	14.4	36.1	48.7	1405	
Vina	5.7	10.7	21.4	14.7	5.5	21.2	1.9	6.2	20.1	12.1	26.5	47.1	205	
TankBind	2.6	4.2	7.6	7.8	17.6	57.8	0.8	1.7	4.3	5.9	55.0	77.8	0.87	
E3Bind	2.1	3.8	7.8	7.2	23.4	60.0	0.8	1.5	4.0	5.1	60.0	78.8	0.44	
DiffDock(1)	2.4	4.9	8.9	8.3	20.4	51.0	0.7	1.8	4.5	5.8	54.1	76.8	2.72	
DiffDock(10)	1.6	3.8	7.9	7.4	32.4	59.7	0.6	1.4	3.6	5.2	60.7	79.8	20.81	
DiffDock(40)	1.5	3.5	7.4	7.4	36.0	61.7	0.5	1.2	3.3	5.4	62.9	80.2	82.83	
EquiBind*	4.0	6.4	10.5	8.4	3.0	38.3	1.3	3.0	7.2	5.7	37.2	68.3	0.01	
EquiBind-PG(ours)	3.3(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.7)	5.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.8)	8.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.4)	6.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.5)	8.3(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}5.3)	48.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}10.2)	1.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.2)	1.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.1)	3.8(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.4)	4.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.7)	51.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}13.8)	79.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}11.6)	0.02	
EquiBind-U*	3.5	5.8	10.2	8.0	4.1	44.6	1.3	3.0	7.2	5.7	37.2	68.3	0.01	
EquiBind-U-PG(ours)	2.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.6)	4.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.9)	7.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.3)	6.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.5)	12.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}8.0)	51.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}6.9)	1.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.2)	1.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.1)	3.8(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.4)	4.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.7)	51.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}13.8)	79.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}11.6)	0.02	
FABind(*)	1.7	3.3	6.8	6.4	31.7	63.9	0.7	1.4	3.5	4.7	61.4	79.6	0.14	
FABind-PG(ours)	1.7(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.0)	3.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.2)	5.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.2)	5.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.9)	31.7(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}0.0)	70.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}6.1)	0.7(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.0)	1.3(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.1)	3.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.5)	3.7(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.0)	63.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}1.7)	86.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}6.9)	0.19	

Performance in blind self-docking for unseen proteins

We further evaluated our model’s ability on the unseen protein test set, testing whether the PG module can still produce more prominent feature extraction for the docking regions of unseen proteins. The results are shown in Table 2. When incorporating PG to EquiBind, we can observe a significant improvement in the performance of every metric, with far fewer predictions deviating from the target (RMSD >5Å), and a two times increase in the number of high-quality conformations (RMSD <2Å). FABind-PG outperforms FABind and achieves new SOTA results in most metrics. Particularly, the <5Å metrics are significantly improved for both ligand RMSD and centroid distance, achieving 64.6% and 81.3%, respectively. In general, there are substantial improvements in mean values, the 75th percentile values, and the metrics below 5Å, indicating our pocket guidance performs well even in unseen proteins. Furthermore, FABind-PG surpasses DiffDock in both all metrics and speed.

Table 2 Flexible blind self-docking performance on unseen proteins; EquiBind-U represents the EquiBind method without optimization of the regression result by point cloud ligand fitting; the green denotes improvement after plugging our PG model and models with (*) are re-inferred on our same machine

Method	Ligand RMSD	Centroid distance		
	Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}	Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}		
	25%	50%	75%	Mean	2Å	5Å	25%	50%	75%	Mean	2Å	5Å	Average runtime(s)	
QVina-W	3.4	10.3	28.1	16.9	15.3	31.9	1.3	6.5	26.8	15.2	35.4	47.9	49	
GNINA	4.5	13.4	27.8	16.7	13.9	27.8	2.0	10.1	27.0	15.1	25.7	39.5	146	
SMINA	4.8	10.9	26.0	15.7	9.0	25.7	1.6	6.5	25.7	13.6	29.9	41.7	146	
GLIDE	3.4	18.0	31.4	19.6	19.6	28.7	1.1	17.6	29.1	18.1	29.4	40.6	1405	
Vina	7.9	16.6	27.1	18.7	1.4	12.0	2.4	15.7	26.2	16.1	20.4	37.3	205	
TankBind	3.4	5.7	10.8	10.5	3.5	43.7	1.2	2.6	8.4	8.2	40.9	70.8	0.87	
E3Bind	3.0	6.1	10.2	10.1	6.3	38.9	1.2	2.3	7.0	7.6	43.8	66.0	0.44	
DiffDock(1)	4.1	7.2	18.2	12.5	8.1	33.1	1.4	3.7	16.7	10.0	33.6	58.3	2.72	
DiffDock(10)	3.2	6.4	16.5	11.8	14.2	38.7	1.1	2.8	13.3	9.3	39.7	62.6	20.81	
DiffDock(40)	2.8	6.4	16.3	12.0	17.2	42.3	1.0	2.7	14.2	9.8	43.3	62.6	82.83	
EquiBind*	5.9	9.5	15.1	11.5	0.0	14.6	3.0	7.0	13.5	9.0	9.0	46.5	0.01	
EquiBind-PG(ours)	4.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.0)	6.4(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.1)	11.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}4.0)	9.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.4)	2.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}2.1)	26.4(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}11.8)	1.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.4)	3.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.8)	7.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}6.4)	6.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.8)	34.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}25.0)	67.4(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}20.9)	0.02	
EquiBind-U*	5.5	9.0	15.1	11.2	0.0	17.4	3.0	7.0	13.5	9.0	9.0	46.5	0.01	
EquiBind-U-PG(ours)	4.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.9)	6.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.9)	10.7(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}4.4)	8.8(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.4)	4.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}4.2)	31.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}14.5)	1.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.4)	3.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.8)	7.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}6.4)	6.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}2.8)	34.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}25.0)	67.4(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}20.9)	0.02	
FABind*	2.3	3.9	9.3	7.8	17.4	56.9	1.0	1.5	5.4	6.0	56.3	73.6	0.14	
FABind-PG(ours)	2.2(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.1)	3.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.3)	6.3(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}3.0)	6.1(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.7)	18.8(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}1.4)	64.6(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}7.7)	0.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.1)	1.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}0.0)	4.0(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.4)	4.5(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}1.5)	56.9(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}0.6)	81.3(\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}7.7)	0.19	

Ablation study

We perform ablation experiments on EquiBind. As shown in Table 3, we ablate different settings of our PG-attention module which consists of geometric self-attention module and explicit cross-attention module. To explore the effectiveness of our explicit cross-attention module, we delete this module and the result is shown in ”without cross” row. Considering the number of model parameters, we replace this module with the self-attention module as another strategy, depicted in the ”replace with self” row. It can be observed that our PG-attention module outperforms these two variant strategies, among which replacing the explicit cross-attention module with the self-attention module is better than deleting it directly. To further verify the superiority of the special attention mechanism, we set up two other experimental variants: one is to conduct self-attention mechanism through implicit encoding to study the effectiveness of the explicit self-attention mechanism, and the other is to conduct attention mechanism from pocket region to non-pocket region. The results are displayed in rows ”implicit” and ”pocket to non,” respectively, which indicate that explicit cross-attention from non-pocket region to pocket region is more effective. Overall, our explicit cross-attention can better characterize the docking region features.

Table 3 Ablation study on flexible blind self-docking performance; “-U” represents the method without optimization of the regression result by point cloud ligand fitting as in EquiBind and models with (*) are re-inferred on our same machine

Method	-U	Ligand RMSD	Centroid distance	
		Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}	Percentiles\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\downarrow $\end{document}	%Below\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\uparrow $\end{document}	
		25%	50%	75%	Mean	2Å	5Å	25%	50%	75%	Mean	2Å	5Å	
EquiBind*	✓	3.5	5.8	10.2	8.0	4.1	44.6	1.3	3.0	7.2	5.7	37.2	68.3	
		4.0	6.4	10.5	8.4	3.0	38.3	1.3	3.0	7.2	5.7	37.2	68.3	
EquiBind-PG(ours)	✓	2.9	4.9	7.9	6.5	12.1	51.5	1.1	1.9	3.8	4.0	51.0	79.9	
		3.3	5.2	8.1	6.9	8.3	48.5	1.1	1.9	3.8	4.0	51.0	79.9	
- without cross	✓	3.0	5.7	9.5	7.7	8.0	44.6	1.1	2.3	6.0	5.3	43.5	70.5	
		3.7	6.0	10.0	8.1	4.7	40.2	1.1	2.3	6.0	5.3	43.5	70.5	
- replace with self	✓	2.9	5.3	9.0	7.3	9.6	47.1	1.2	2.2	5.3	4.9	45.7	73.3	
		3.5	5.7	9.3	7.6	5.2	40.8	1.2	2.2	5.3	4.9	45.7	73.3	
- implicit	✓	3.0	5.0	8.1	7.0	10.7	49.6	1.1	2.1	4.5	4.4	48.5	78.2	
		3.5	5.4	8.2	7.3	6.1	45.5	1.1	2.1	4.5	4.4	48.5	78.2	
- pocket to non	✓	3.0	5.5	8.2	6.9	9.9	44.6	1.1	2.0	4.6	4.2	48.8	78.2	
		3.6	5.8	8.7	7.2	6.1	42.2	1.1	2.0	4.6	4.2	48.8	78.2	
- with FA	✓	2.9	5.7	9.4	9.6	11.3	43.5	1.2	2.3	4.7	5.4	46.3	75.5	
		3.4	6.0	9.4	8.3	6.3	41.6	1.2	2.3	4.7	5.4	46.3	75.5	

Moreover, we experiment on different numbers of blocks of the self-attention module and the explicit cross-attention module and the results are shown in Fig. 4. We can find stacking three blocks is best in generating good conformations (RMSD <2Å), whether the model is optimized or not (-U). Other detailed indicators can be found in Supplementary Material (E). Through the above metrics, the number of blocks is designed to be 3.

Figure 4 Ligand RMSD <2Å values in flexible self-docking predicted by different blocks of PG-attention module; EquiBind-U represents the EquiBind method without optimization of the regression result by point cloud ligand fitting.

Furthermore, we ablate the choice of pocket prediction module. The original intention of our pocket prediction module is to provide guidance for a rough docking region, rather than pursuing a precise docking area. We design an experimental variant that uses the FABind layer [21] with higher accuracy in predicting pocket positions as the GNN encoder of the pocket prediction module. The results are shown in the “with FA” row in Table 3. We can find that the results are roughly the same as using a simple GNN utilized in our model. In summary, the keypoint of our proposed PG model is the pocket guidance strategy, not the accuracy of the pocket prediction module. More details of pocket prediction analysis can be found in Supplementary Material (C).

Case analysis

Pocket guidance can pull back extremely deviated conformations. As analyzed previously in Fig. 1, without explicit prior guidance, some non-pocket features are mixed with pocket features, leading to offset conformations often produced. We show a case to illustrate the effectiveness of our method in pulling back extremely deviated conformations. As shown in Fig. 5, after pocket guidance, the off-target conformation is pulled back a lot, and the RMSD dropped from 11.1752 to 2.0834 Å. From protein feature t-SNE, we can see that the features of nodes in pocket areas cluster together using the pocket guidance strategy.

Figure 5 PDB 6QGF protein features t-SNE and ligand pose changes with and without pocket guidance; upper: the pink dots represent non-pocket region features, while the blue dots represent pocket region features; lower: ligand poses predicted by EquiBind and EquiBind-PG are blue and red, respectively; the ground-truth pose is orange.

Pocket guidance can discover new potential binding sites. In this analysis, we show that EquiBind-PG has the potential of finding new binding sites that do not exist in PDBBind. As shown in Fig. 6(a), the ligand pose generated by EquiBind-PG (red) is far from the ground-truth (orange) provided by PDBBind but the ligand is docked to the region which is the binding site of a ligand (pink) provided by PDB Bank [43]. In this case, Equibind-PG docks the ligand to the pocket of another molecule, whose morgan fingerprint is similar as the ligand as shown in Fig. 6(b). Though our docking result is different from the PDBBind gold standard, it is physically reasonable and potentially possible. Our method shows the ability to explore new potential binding sites, further demonstrating the significance of blind docking and showing promise in addressing drug target congestion. We look forward to further verification through wet experiments in the future.

Figure 6 (a) PDB 5ZK7 protein–ligand docking conformation; the ground-truth pose is orange and the predicted pose by EquiBind-PG is red; the pink ligand is obtained by PDB Bank; the blue ligand is predicted by EquiBind; (b) similarity analysis between docked ligand and the true ligand of the binding site; the pose predicted by EquiBind-PG is treated as the probe molecule and the true ligand of the binding site obtained from PDB Bank serves as the reference molecule; we visualize the similarity between these two molecules by comparing their morgan fingerprints, which represent molecules by considering their local structural information; the similarity score is tanimoto coefficient [42].

Conclusion

In this paper, we propose a PG strategy to enhance the protein features in deep-learning-based blind protein–ligand docking. To this end, we design a plug-and-play PG module to better distinguish pocket and non-pocket regions in protein feature extraction. Experimental results show that our module can be integrated into EquiBind and FABind and improve their performances in flexible blind self-docking. We also give a case report that the integrated model has the ability to explore new potential binding sites.

Key Points

PGBind is a pocket-guided strategy in the field of blind protein–ligand docking, improving blind docking accuracy by enhancing the protein features with the guidance of estimated pockets.

We design a plug-and-play Pocket-Guided module, which can be seamlessly integrated into existing blind docking models to improve their performances. Experiments show that the proposed module significantly improves the performance of EquiBind and FABind and new SOTA performance is achieved by integrating the proposed PG module into FABind.

Case analysis shows that the integrated framework can explore new potential binding sites, which may inspire the discovery of new potential pockets.

Supplementary Material

Supplementary_bbae455

Funding

This work is supported by the Science and Technology Innovation Plan Of Shanghai Science and Technology Commission 23S41900400 and Fudan University Science Intelligence Special Fund FD-AI4S04183. The computations in this research were performed using the CFFF platform of Fudan University.

Data availability

Data and codes in our experiments are released in https://github.com/ShenAoAO/PGBind.
==== Refs
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