Enhancing Bioactivity Prediction via Spatial Emptiness Representation of Protein-ligand Complex and Union of Multiple Pockets
Authors: Zhiyuan Zhou
Yueming Yin
Yiming Yang
Yuguang Mu
Hoi-Yeung Li
Adams Wai-Kin Kong
Venue: NeurIPS 2025 poster ()
Keywords: bioactivity prediction
drug discovery
target-ligand interaction
Primary area: machine_learning_for_sciences

Abstract: Predicting the bioactivity of candidate ligands remains a central challenge in drug discovery. Ligands and endogenous substrates often compete for the same binding sites on target proteins, and the extent to which a ligand can modulate protein function depends not only on its binding but also on how effectively it occupies the relevant pocket. However, most existing methods focus narrowly on local interactions within protein–ligand complexes and neglect spatial emptiness—the unoccupied regions within the binding site that may permit endogenous molecules to engage or interfere. Such unfilled space can diminish the ligand’s functional impact, regardless of binding affinity. To overcome this key limitation in protein–ligand modeling, we propose LigoSpace, a novel method integrating three core components. LigoSpace introduces GeoREC (Geometric Representation of Spatial Emptiness in Complexes) to quantify atomic-level empty space and Union-Pocket to unify multiple protein pockets, providing a global view of binding sites. Additionally, LigoSpace employs a pairwise loss instead of commonly used MSE loss, to better capture relative relationships critical for drug discovery. Extensive experiments on multiple datasets with diverse bioactivity types demonstrate that LigoSpace significantly improves performance when integrated into state-of-the-art models, highlighting the effectiveness of its novel components.

Enhancing Bioactivity Prediction via Spatial Emptiness Representation of Protein-ligand Complex and Union of Multiple Pockets
Zhiyuan Zhou
Yueming Yin
School of Biological Sciences Nanyang Technological University
College of Computing and Data Science Nanyang Technological University
Singapore 637551 zhou04570e ntu edu.sg sg
Singapore 639798
yueming. winontu.dnuuuu edu.
Yiming Yang School of Biological Sciences Nanyang Technological University
Yuguang Mu School of Biological Sciences Nanyang Technological University Singapore 637551 ygmuōntu. edu.
Singapore 637551 yiming0140e..o ntu. edu.sg
Hoi-Yeung Li School of Biological Sciences
Adams Wai-Kin Kong' College of Computing and Data Science Nanyang Technological University
Nanyang Technological University Singapore 637551 hyli@ntu. edu..ntuuedu.g.......
Singapore 639798
adamskong@ntu.c edu. sg
Abstract
Predicting the bioactivity of candidate ligands remains central challenge in drug discovery. Ligands and endogenous substrates often compete for the same binding sites target proteins, and the extent to which ligand can modulate protein function depends not only on its binding but also on how effectively occupies the relevant pocket. However, most existing methods focus narrowly local interactions within protein-ligand complexes and neglect spatial emptiness-the unoccupied regions within the binding site that may permit endogenous molecules to engage or interfere. Such unfilled space can diminish the ligand's functional impact, regardless of binding affinity. To overcome this key limitation in pro- tiin-ligand modeling, we propose LigoSpace, a novel method integrating three components. LigoSpace introduces GeoREC (Geometric Representation of Spatial Emptiness in Complexes) to quantify atomic- empty space and Union- Pocket unify multiple protein pockets, providing global view of binding sites. Additionally, LigoSpace employs a pairwise loss instead of commonly used MSE loss, to better capture relative relationships critical for drug discovery. Extensive experiments on multiple datasets with diverse bioactivity types demonstrate that LigoSpace significantly improves performance when integrated into state-of-the-art models, highlighting the effectiveness of its novel components.
'Equal contribution, may either first. "orresspn author.
39th Conference on Neural Information Processing Systems (NcurIPS 2025).

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Introduction
Bioactivity is the measurable effect compound exerts on a biological system, usually by modulating the functional activity of specific molecular target (e.g,, a protein or nucleic acid). can be quantified experimentally through enzymatic kinetics (Vmax, K kicat Km) or functional and binding assays
that yield parameters such as EC,o, IC5o, Emax and K2) |MarBchal, 2011 Mendez et al. 2019].
Accurate measurement- increasingly, in-silico prediction in drug discovery, chemical biology, and pharmacology to identify the most promising compounds early, reducing the cost and duration of large-scale experimental screens [Kapetanovic 2008). With the growing size of chemical libraries and biological data, there is increasing demand for efficient and accurate computational methods to predict bioactivity. Developing robust bioactivity prediction methods has therefore become key focus in both academic research and industrial applications Ramsundar et al.) 2019].
these effects allows researchers
Recently, machine learning approaches have shown great potential in modeling biological molecules and their interactions, dramatically accelerating the drug discovery process [Rifaioglu et al., 2019 Chen et al. 20188. There have also been some machine learning methods for bioactivity prediction, aiming at etrly-stage screening of the potential active molecules [Prajapati et al., 2025 Ishfaq et al..
2022 Cáceres et al. [2020] Lee et al., [201]] Conventional approaches rely the intrinsic properties of small molecules as features to model ligands, aiming to uncover the relationship between molecular structure and bioactivity. A traditional strategy is to quantitative prructure-actvvig relationship (QSAR) models [Cherkasov et al., 2014 Tropsha et al. 2024]. which primarily utilize molccular descriptors derived from the physicochemical and structural properties of small molecules. While this approach is reasonable and widely adopted, it may overlook the fact that bioactivity fundamentally arises from specific biological interactions, which are critical for thoroughly modeling and under- standing bioactivity. A compound cannot function biologically without its target and environment. Furthermore, unlike other single-target prediction tasks, bioactivity is often evaluated using multiple measurement types, such as IC5o. ECsa. Ka, and K; making the task more challenging. In response to these challenges, recent studies have shifted toward developing models based on curated pocket- ligand interaction datasets that provide more comprehensive information, including abundant bound conformations with proteins and multiple bioactívity measurements (Yin et al., 2024 Huang et al. 2025]. Among these methods designed for ligaad interaction, graph neural networks (GNNs) have become particularly prevalent, as graph-based representations offer a natural and powerful
way to capture molecular properties and relational structures (Zhang et al. 2023
Wang et al. 2024
Mastropietro et al. 2023
Liet al. (02T].
While recent studies increasingly focus on bioactivity prediction using protein information and constructing protein-ligand interaction graphs, they often concentrate on local binding region but overlook the global geometric context of the entire pocket, missing crucial information for accurate bioactivity modeling. Geometric features are known to be important for representing binding status
and have shown effectiveness in modeling molecular interactions [Wei et al. 2024 Han et al.) [024]] Song et al. 2024 Zhang et al., 2022). For instance, geometric representations in Ee))vaquiari
GNNs have demonstrated strong performance in capturing local spatial relationships on protein surfaces, significantly improving binding site prediction (Wei et al. 2024). However, most existing approaches emphasize detailed descriptions of local binding region and structural complementarity between interacting molecules. None of the previous work considers locket-ligand interactions from the perspective of spatial emptiness within the docked conformation. This aspect, which remains underexplored. holds practical importance and corresponds closely with the principle of competitive inhibition [Fun] 1996. Baici 2015). where drug molecules bind to the active site of protein and block access for endogenous substrates (illustrated in Figure D For example, protein kinase inhibitors bind to the enzyme's is ATP-binding pocket, blocking ATP access and thereby suppressing kinase activity.
Previous methods tend to focus on how well the ligand fits the pocket, but often overlook the inverse questions: once binding occurs, how much empty space remains, and to what extent does the ligand occupy the pocket?
Furthermore, current methods for bioactivity prediction typically focus on the local binding pocket in complex with a ligand, which limits access to global pocket information that biologically significant. Additionally, in many prior works, each pocket-ligand pair is treated as an independent data point [Lee et al. 2019, Caceres et al., 2020), overlooking the realistic scenario in which multiple potential drug compounds may interact with different pockets of the same protein. Recent findings underscore
2

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Vaciant space the pociall small
edge
$ Endogenous substrate trocked
Successful infibiiio
LL- Drug Ioands
substrala
Target
Vacant space the pocket is large
Endogenous
substrate
eas outcompetes the drug
Unsuccessful intibiiion
Interactio
Drug out
Figure I: An example of competitive inhibition.
the importance of evaluating bioactivity across diffeerent ligands acting on a common protein, enabling more meaningful and fair comparisons. In response, new methods and datasets (in al. 2024 Huang et al. 2025 have been developed to incorporate multiple ligands per protein and to perform evaluation at the protein level, allowing for more robust and context-awar assessments. However, even with a fixed protein, these approaches often involve distinct binding sites within the same protein, introducing variability that may compromise the consistency bioactivity predictions.
Additionally, a major distinction between drug discovery and other regression tasks lies in the importance of prediction order. The most common training loss, mean-square error (MSE), is symmetric and treats each data point independently. For example, given two ground- bioactivities, 81 and y/2 1, gives the same loss value for the predictions (0) 1.5, 02 1.5) and (ύ1 1.5, /22 = 0.5). The order of the former is wrong, but the order of the latter aligns with the ground truths.
To address these issues, we propose LigoSpace, which integrates three key modules for enhanced bioactivity prediction. We make the following key contributions:
We propose Geometric Representation of spatial Emptiness in protein-ligand Complex (GeoREC) to deseribe the surroundings of each node in the protein-ligand graph represen- tation. This surrounding space quantifies the emptiness within the docking conformation. incorporating a broader global perspective into the overall interaction graph representation. Furthermore, this concept of emptiness holds practical significance, in assessing whether the pocket space is sufficiently tight to hinder the entry of other small molecules into the binding site area, thereby contributing to a more accurate prediction of the compound's bioactivity.
plays pivotal role
We introduce the concept of the Union-Pocket (Figure 3 into the bioactivity prediction task ensure that the entire pocket space can be accessible, facilitating GeoREC measure the empty space inside. Moreover, it provides a broader structural context during the GNN processing, contributing more effective global information integration. Additionally, when evaluating different ligands binding to the same protein, keeping the protein information consistent encourages the model to focus the ligand, the only changing part, enhancing the ability of the model to capture subtle conformational differences within consistent protein context.
We also incorporate pairwise loss alongside the conventional squared error (MSE) loss as the final training objective for bioactivity prediction. This combined loss encourages the model preserve the relative order among samples by emphasizing pairwise differences in their bioactivity labels.
Experimental results demonstrate that LigoSpace leads to substantial improvements in bioactivity prediction across multiple datasets, label types, and GNN architectures. In

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particular. the addition of GeoREC results in significant performance gains, highlighting the critical role of geometric information in accurately modeling protein -igand interactions.
2 Related work and preliminaries
2.1 Bioactivity prediction
Predicting bioactivities is a crucial step in drug discovery, as plays a central role enabling efficient and accurate drug screening [Ishfaq et al. 2022 Yin et al. 2024]. Early empirical approaches [Gohike] et al. 2000, Wang et al., 2002] rely on manually designed scoring functions tailored for specific tasks, requiring substantial expert knowledge to encode underlying biochemical interactions. Subsequently. statistical and traditional machine learning methods [Ballester and Mitchell 2010 Kinnings et al.
2011] are developed to model bioactivity in a data-driven manner by extracting protein and ligand features and applying classical regression algorithms. However, these methods heavily depend on the quality of handerafted features and often suffer from limited generalizability when applied to larger or more diverse datasets. With the rising popularity of deep learning in recent years, sequence- based bioactivity prediction methods have emerged, which directly extract features from the SMILES (Simplified Molecular Input Line Entry System) strings of ligands and the amino acid sequences of proteins, bypassing the need for manual feature engineering. For example, DeepDTA (Öztürk et al. 2018] employs two independent convolutional neural networks to capture latent representations from ligand SMILES and protein sequences. Building upon this, MT-DTI (Shin al. 2019] incorporates attention mechanisms to enhance the model's 's interpretability and capture long-range dependencies.
Inspired by the effectiveness of graph neural networks (GNNs) in handling structured data, recent efforts (Vfghi et al.] 2025) have extended bioactivity prediction to incorporate molecular graph representations. These approaches consider 3D structural information of protein-ligand complexes to varying degrees. GIGN (Yang et al.] 2023] introduces a heterogeneous interaction layer that integrates both covalent and non-covalent interactions into the nessage-passing framework, thereby facilitating more effective node representation learning. DTIGN (Yin et al. 2024] enhances upon this by incorporating intra-moleculat bond features and explicitly modeling non-covalent interactions, including Coulomb and London dispersion forces, and further combining molecular docking with self-attention mechanisms to capture information from diverse binding poses. However, existing models represent protein-ligand complexes as purely topological graphs, thereby underutilizing rich biomolecular structural information and neglecting the spatial interactions between proteins and ligands. To address these limitations, we propose incorporating comprehensive spatial information to better capture the geometrie nature of molecular interactions.
2.2 Task definition
We consider the task of predicting continuous-valin bioactivity based on a set of possible binding poses of ligand across multiple available protein pockets. Let L denote the set of ligands and P the set of protein pockets. Each ligand E L is associated with a set of N₂ possible binding poses:
Xi = {I1,1, 21,, Nh I1es Rdd
(I)
where æy, represents the i-th pose of the ligand/ associated with one of the available protein pockets, and d is the dimensionality of the input representation (e.g., 3D coordinates, graph embeddings, or voxel grids). Let Pi C P be the subset of candidate pockets associated with ligand l. Let y E R denote the experimentally measured bioactivity value of ligand | (e.g., EC5o. ICso), which may not be pocket-specific. The objective is to learn a predictive model f such that:
f(2, Pt),
which aggregates information from the poses across all candidate pockets to estimate in. In practice, pose-level representations can computed and then aggregated using a permutation-invante function:
= Agg (Upune Pt.)))
where Pt. E Pi denotes the pocket corresponding to pose X1.i, fpose is a shared neural network applied to each pose-pocket pair, and Agg a permutation-invarian aggregation function such as mean, sum, iieettionbbacee pooling.

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Identify the closest atom within each discretized directional bin.
14
Cone Rl
Cone
k
C Pocket
Cone 14
@ Ligand
Figure 2: An example of the geometric edges defined in this paper.
3 Methods
3.1 Geometric representation of spatial emptiness in protein-ligand complex
To characterize the spatial configuration inside the pocket within docked protein-ligand complex, we design Geometric Representation of spatial Emptiness in protein-ligand Complex (GeoREC) for each node that captures global information about the spatial emptiness of the structure. Let Vp and Vi denote the sets nodes representing the pocket and the ligand, respectively, within a pocket-ligand complex. The complex graph is defined as G, (Ver E,), where V. V, U Vi, and E, denotes the set of all types of the connection within the complex, usually corresponding to physicochemical interactions such covalent bonds, hydrogen bonds, van der Waals contacts and on.
For each node v; E Ve, we define a local spherical coordinate system centered at v, and uniformly partition the surrounding space into S cones. This spatial decomposition enables the extraction of relative positional features. For each cone E {1,2,... S}. we collect set pocket-ligand nodes
located within it and denote it by (=x) Next, for each cone whose corresponding node set v(s) is non-empty, we identify the node closest to U; and include in the surrounding node set V-(i) This set provides a compact yet informative representation of the spatial emptiness around In this study, GeoREC is incorporated by introducing geometric edges: for each fg sun add an edge (u;, my), forming set of geometric edges denoted as Egeu- An example of the geometric edges is shown Figure 2 The enhanced graph is then defined as: G', (Ve, Ee, Egeu), which incorporates both the original Interaction edges and the newly introduced geometric edges. These geometric edges enhance the graph's 's capacity to perceive spatial emptiness, particularly within the pocket cavity, and also provide alternative pathways for global and local information flow beyond conventional chemical bonds.
3.2 Global interaction model with Union-Pocket
The structure-based bioactivity prediction task can be generally formulated as
G1 f'(11))
where E P is a candidate binding pocket, x denotes the representation of the ligand 1, f' is generic bioactivity prediction model, and ÿt is the predicted bioactivity. this setting, each data point corresponds to local pocket-ligang pair, e.g.. "Data point 1" or "Data point 2" in Figure 3A. Conventional approaches |Wallach al. 2015) Tanebe and Ishida 2021 Yang et al. 2023] predict bioactivity on single local pocket-ligand pair for single ligand. However, a given ligand may engage multiple local pockets on the protein, each potentially contributing differently to the overall bioactivity.
5

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To better reflect the biological context, recent work (Yin et al., 2024] has shifted toward aggregating multiple local pocket-ligand pairs for the same ligand. The prediction task then becomes:
D1 = f(A, PP):
(5)
where Pf C P is the subset of local pockets associated with the ligand poses Xr within the same protein. This setting reflects the biological scenario more closely, as single protein may engage the same ligand through distinct local pockets. Furthermore, set of distinct ligands, denoted as L. may generate numerous fragmented local pockets, introducing variability that hinders the model from capturing a global view of how all ligand peses-regardless of whether they come from the same or different ligands-relate on the same protein.
To mitigate this issue, we propose the concept of the Union-Pocket, defined as the union of all atoms from the candidate pockets associated with given protein. Let P/ {pí ph.... .......P.. J be the set of pockets associated with ligand I. For each p' E P// let A(p') denote the set of atoms comprising pocket p'. The Union-Pocket then defined as:
A(Punion)
U U A(P).. IEC P'EP
(6)
where L is the set of ligands docked to the given protein. The resulting Punion aggregates all atoms from all relevant pockets across ligands and thereby encompasses the full binding region probed by the ligand set C. An example of the formation and data representation of the proposed Union-Pocke are shown in Figure 33 and 3C, respectively. Accordingly, the bioactivity prediction task for each protein can now be reformulated as:
j = funica (Ai, Punion).
where Sunion is the prediction model utilizing the Union-Pocket.
By replacing many local pocket representations with the Union-Pocket, a model can capture richer global interaction information while maintaining spatial consistency across ligands binding to the same protein. When integrated with GeoREC, this strategy improves the geometric representation's s expressiveness and allows the model to more effectively distinguish fine-grained differences ligand poses and spatial emptiness. The shared spatial context provided by the Union-Pocket is crucial for accurate and robust bioactivity prediction.
3.3 The pairwise loss
To better preserve relative order information during optimization, we introduce a pairwise loss Zhu
(et al. 2024 Tynes et al.] 2021] into the bioactivity prediction task. Although recent studies have
explored diverse metries such as Kendall Tau [Fernández-Llanezaa et al. [002]. Top-K precision (Yin
jet al. 2021], and enrichment factors [Yin et al.) 2022] for evaluation, few have improved the loss
function directly into model training. Most existing Al-based methods for bioactivity prediction and
other biological regression tasks still rely on MSE loss to train their models. However, is ineffective
for drug discovery because it considers each prediction independently, neglecting the relative orders of the samples.
Consider the conventional MSE loss, which is also called L2 loss, used for training the bioactivity prediction model:
L2
1
1 1 11
(8)
where N is the total number of training samples (protein-liganl ligand pairs) a batch, ÿl is the predicted bioactivity score for the 1-th ligand, is the ground truth bioactivity label for the 1-th ligand and 11-112 denotes the squared L2 norm. Standard loss functions such as L2 (MSE) and L,, (MAE) simply measure the absolute numerical differences between predicted and true values, ignoring relative order. This limitation poses challenges when capturing correlations among samples. We exploit the pairwise loss as follows:
2
Cpairiise
[1 vU) (0. 1)
(9)
N(N 1)

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A
Binding region
Binding region
Data point
Data point with Union-Pocket
point
Union Pocket
point Union-PPccie Packet
Figure 3: Union-Pocker Pocket. The protein is shown in wheat color. The stick models in green and magenta represent the same ligand, which binds to different regions the protein. The green and magenta surfaces correspond to the surfaces of the ligand molecules in their respective binding conformations. (A) Current methods incorporate pocket-ligand interactions but focus on local regions, treating a small ligand-containing pocket
single data point, thus losing global pocket information. (B) By taking the union of all the local binding regions within the protein, we get the Union-Pocket, indicated by the red dashed line. (C) New data points with our Union-Pocket, which keeps the complete global geometry of the binding region.
Here, N is the number of protein-ligand pairs in batch. and yj are the ground truth bioactivity values for ligand and lj. respectively. V; Sunson (Ri, Punion) and Ú; = Sunson (Ai,, Puriion)) are the predicted bioactivity scores obtained from the model funion. The pairwise difference (y: yj) reflects the relative bioactivity difference in ground truth, while (0: Ú;) is the corresponding prediction difference. The pairwise loss function employs an L2 norm to penalize discrepancies in predicted relative differences (g: ú, compared to the true differences (v) y/ The normalization factor N[N-I] computes the mean over all unique sample pairs, making the loss invariant to batch
size. Ultimately, adopt hybrid loss function Lnyhrid that combines both pointwise and pairwise losses:
Lhybrid >1 L2 + A2 Lpairwise.
(10)
Here, L2 measures the pointwise error between predicted and bioactivity values, and pairwise emphasizes the preservation of the correct difference between the predications. The coefficients Å and A2 are hyperparameters that control the relative contribution of the two components in the overall objective.
4 Experiments
4.1 Datasets and testing settings
DTIGN dataset. We first adopt the dataset constructed in DTIGN (Yin et al. 2024]. This dataset is derived from ChEMBL [Gaulton et al.) [2012], widely used database drug discovery that contains extensive information on chemical compounds, their biological activities, and related properties. The DTIGN dataset comprises protein targets (I1, 12, 13, 14, 15, EI, E2, and E3), each considered as an individual subset containing several binding pockets. Within each subset, hundreds to thousands of ligands are associated with the protein, labeled by IC5o or F.Csp, and each ligand represented by multiple docking poses.

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SIU dataset. We also validate our method on large-scale docking dataset proposed in [Huang al. 2025]. This dataset contains 201.458 and 56,485 small molecule-port pocket pairs with K; and Ka bioactivity labels, respectively, which complement the bioactivity categories in the DTIGN dataset. The K; subset was generated by docking 34,881 unique small molecules to 4,317 protein conformations derived from 764 proteins, whereas the Ka subset was generated by docking 5,201 unique small molecules to 3,682 protein conformations derived from 584 proteins.
The dataset includes two variants, SIU-0.9 and SIU-0.6, sharing the same test set. The numeric suffix denotes the sequence similarity threshold between the training and test data. In this study, we use four subsets of the SIU dataset: SIU-0.9/Ka. SIU-0.9/K,, SIU-0.6/Ka, and SIU-0.6/K,
Evaluation metrics. To ensure fair comparison with previous works, adopt widely used evaluation metrics in bioactivity prediction, including root mean square error (RMSE), Pearson correlation coefficient (r), and Kendall's 's correlation coefficient (r) for DTIGN dataset. We also compare mean absolute error (MAE) and Spearman correlation coefficient for SIU dataset. The details of the definition can be found in Appendix A.6.
Baseline models. To evaluate the effectiveness of the proposed representations and loss function, we adopt DTIGN (Yin et al. 2024), GIGN (Yang et al. 2023], and Graph Attention Network (GAT) (Veličković et al.) 2017 as the baselines. DTIGN is one of the latest GNN based methods designed for bioactivity prediction. It uses multiple local pocket-ligande complexes input. GIGN is also GNN- based method that incorporates 3D structures and physical interactions for predicting protein- ligand binding affinities. GAT is a foundational GNN model that uses attention to focus on relevant nodes. Additional baseline models and more details are demonstrated in Appendix A.2.
4.2 Results
We first compare the baselines with LigoSpace, which integrates GeoREC, Union-Pocket within the GNN, and the hybrid loss function on the DTIGN dataset. As shown in Table our proposed method consistently enhances the DTIGN baseline across all subsets and metrics, demonstrating robust improvements by 9.93%, increases r by 18.39%, and improves T by 19.09%. On the GIGN and GAT baselines, our method also achieves noticeable gains on 7 out of 8 and 6 out of 8 datasets, respectively. These results highlight the consistent effectiveness of our proposed method. Table T also shows that the proposed method achieves more improvement on stronger baselines.
diverse protein targets. On average, our proposed method reduces RMSE
Furthermore, we evaluate the performance of our proposed method on the SIU dataset, which includes broader set of protein targets and ligands. The results are presented in Table with the Uni-Mol [Zhou et al. [023] benchmark taken from (Huang et al. 2025]. The results demonstrate that our LigoSpace-enhanced models outperform their respective baselines in 43 out of 48 dataset-metric com- binations and achieve state-of-the thetheeart performance. Notably, our method achieves substantial gains in some subsets. For example, in SIU-0.9/K, DTIGN+LigoSpace achieves
0.3213 and Spearman correlation of 0.3259. In contrast, the bascline methods struggle to learn meaningful relationships, as reflected by near-zero correlation scores. These results demonstrate the superior capability of our method on more complex datasets, further illustrating its robustness and generalizability. Additional experimental results and comparisons with more baseline models are provided in Appendix A.4.
4.3 Ablation study
To assess the contribution of each individual component in our proposed method, we perform an ablation study by systematically removing one module at a time from the complete configuration on the DTIGN model. The setups are as follows: 1) DTIGN-GUL includes GeoREC (G), Union-Pocket (U), and hybrid loss (L); 2) DTIGN-GU(L) includes GeoREC (G) and Union-Pocket (U), excluding
the hybrid loss (L); 3) (GIL includes the Union-Pocke (U) and hybrid loss (L), excluding
GeoREC (G), and 4) DUIG includes GeoREC (G) and hybrid loss (L), excluding the Union-Pocked (U). The results of the ablation study are shown in Table 3 By comparing these ablation settings with the full enhanced method (DTIGN-GUL) we draw the following conclusions:
The proposed geometric feature GeoREC (G) makes a substantial contribution to performance. When comparing DG)LL- to DTIGN-GUL, we observe a reduction in RMSE by 9.3%, an increase in by 14.4%, and an elevation in 7 by 19%.
8

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Table 1: Comparison of model performance baselines and their LigoSpace-enhancel versions with the proposed methods across multiple datasets
Model
Metric
Dataset
11
12
13
15
E1
E2
E3
Avg
Avg Imp%
RMSE
1.1977
0.7952
1.1443
0.9396
0.9518
0,9086
0.7765
1,0869
0,9751
DTIGN baseline
0.3547
0.7128
0.7839
0.6177
0.6227
0,3363
0.6946
0.4825
0.5757
T1
0.2445
0.4922
0.5991
0.4691
0.2139
0.4917
0.3786
0,4183
RMSE
1.0344
0.6507
1,0245
0.8124
0.8966
0.8645
0.7262
1,0150
0.8783
9.93%
DYIGNN-LigoSace
0.5895
0.7888
0.8251
0.7334
0.6986
0.4969
0.7275
0.5924
0.6315
18. 18.39%
0.4239
0.5454
0.5205
0.3705
0.5243
0.4563
19.09%
RMSE
1.2365
0.7487
1,0677
0.8560
0.8700
0,9563
0.7545
0,9704
0,9325
GIGN baseline
0.4357
0.7234
0.8080
0,6888
0.7302
0.4435
0.7246
0.6285
0.6478
0.3216
0.5083
0.6310
0.4920
0.5439
0.3443
0.5043
0.4664
0.4765
RMSE
0.9515
0.6880
0.9403
0.8111
0.8302
0.8733
0.8737
0.9161
0.8605
7.72%
GiGNeeigoSpace
0.6861
0.7735
0.7450
0.7513
0,4912
0.6637
0.6860
0.7063
0.4899
0.5378
0.6673
0,5439
0.5591
0.3786
0.5511
0,5228
0.5313
11,51
RMSE
1,1801
0.9270
1. 1.3433
1 1,0200
1.0547
0.8962
0.8579
1.1716
1.0564
GAT haseline
0.4147
0.4771
0,6663
0.5091
0.5035
0.3771
0.5836
0.3468
0,4848
T
0.2267
0.3115
0.4618
0,3685
0.3428
0.2451
0.3917
0.2938
0,3302
1.1767
1.0037
1.0322
0.9252
0.8587
GAT-LigoSpace
0,4511
0,5437
0.6813
0.5570
0.5302
0,3604
0,5838
0.4060
0.5142
6.07%
0,2922
0.3593
0.4823
0.4075
0.3690
0.2497
0.3819
0.3330
0.3594
8.82%
Table 2: Comparison of model performance on SIU dataset
Dataset / label
Method
RMSEL
MAE,
rt
Spearman
Unimol
1.364
1.141
-0.033
-0.082
DTIGN
1.839
1.490
-0.001
-0.042
DTIGN=LigoSSace
1.304
1.060
0.321
0.326
STU-0.9 Ka
GIGN
1.708
1.367
0.070
0.038
GIGNaLigoSpace
1.455
1.139
0.296
0.261
GAT
1.545
1.240
0.092
0.082
GAT+LigoSpace
1.473
1.166
0.261
0.254
Unimol
1.235
1.017
0.485
0.452
DTIGN
1.607
1.276
0,360
0.329
DTIGN+LigoSpace
1.296
1.054
0,485
0.441
SIU-0.9 K;
GIGN
1.597
1.337
0.223
0.167
GIGN+LigoSpace
1.487
1.240
0.371
0.338
GAT
1.706
1.386
0,301
0,262
GAT+LigoSpace
1.625
1.339
0.316
0.294
Unimol
1.389
1.192
-0.149
-0,206
GIGN
1.371
1.115
0.265
0.281
GIGN+LigoSpace
1.326
1.078
0.280
0.227
STU-0.6 Ka
DTIGN
1.349
1.079
0.329
0.329
DTIGNNLigoSpace
1,332
1.069
0.327
0,248
GAT
1.521
1.285
0,233
0.157
GAT+LigoSpace
1.424
1.182
0.107
0.133
Unimol
1.255
1.034
0.472
0.452
GIGN
1.789
1.503
0.225
0.230
GIGN+LigoSpace
1.404
1.165
0.498
0.463
SIU-0.6/ K;
DTIGN
1.993
1.653
0.123
0.091
DTIGN+LigoSpace
1.321
1.079
0.472
0.452
GAT
1.976
1.690
-0.060
-0.096
GAT+LigoSpace
1.694
1.381
0.303
0.263
The Union-Pocket also confers consistent advantages in the majority of cases. Compared to DTIGN- G(U)L,, which excludes the Union-Pocket (U), it reduces the RMSE by 5.8%, increases by 7%, and improves 7 by 9% on average. Notably, GeoREC and Union-Pocker sometimes exhibit mutually reinforcing relationship; when utilized in isolation, their influence may be restricted. For instance,

---

dataset EI, DGJL and DTIGN-G(U)) yield r of approximately 0.31 and 0.32, whereas the DTIGN-GUL boosts to 0.5, marking a nearly 60% improvement. This demonstrates that excluding either GeoREC (G) or Union-Pocker (U) results in substantial performance degradation, whereas their integration leads to a reinforced effect.
Integrating the hybrid loss (L) enhances the training process, particularly in terms of order consistency, This is evidenced by comparing DTIGN-GUL with DTIGN-GU(L); across 8 datasets, improves in 7 cases. On average, compared to DTIGN-GU(L), it reduces the RMSE by 3.1 %. increases r by 4%, and improves by 4.6%. This validates the effectiveness of incorporating the pairwise loss in bioactivity prediction.
Table 3: Ablation study on DTIGN baseline (each variant excludes one component)
Dutasct
DTTIG-GUU
DTIGN-GU(L) rt
DTIGN-(G)UL
DTTIGN-GUU)
RMSE/
rf
7 RMSE
r
RMSEI
rf
r
RMSEL
II
1.0364
0.5895
0.42339
1.1163
0.5259
0.3494
1.1341
0.4721
0.3249
1.0739
0.5941
0.4128
12
0.6507
0,7888
0.5454
0.7292
0.7284
0.5081
0.7724
0.7077
0.4665
0.7395
0.7331
0.5265
1.0245
0.8251
0.6360
1.0557
0.8153
0.6175
0.8196
0.6348
1,2061
0.7486
0.5446
I4
0.8124
0.7334
0,5205
0.8550
0.7072
0,5023
0.9149
0,6666
0.4725
0.8364
0.7149
0.5067
0.8966
0.6986
0.5083
0.8625
0.7127
0.5225
0,9591
0.6343
0.4561
0.9017
0.6928
0.4994
EI
0,8645
0.4969
0.3705
0.8586
0.4513
0.3498
0,9513
0.3064
0.1727
0.9243
0.3176
0.1983
E2
0,7262
0.7275
0.5243
0.7600
0.7083
0,5066
0.8263
0.6384
0.4300
0.7323
0.7314
0.5332
1.0150
0.5924
0.4563
1.0119
0.5955
1,0679
0.519%
0.3917
1.0438
0.5656
0.4332
Avg
0.8783
0.6815
0,4982
0.9062
0.6556
0.4761
0,9679
0.5956
0.4187
0.9323
0.6373
0.4568
5
Conclusion
Bioactivity prediction a crucial task in computational drug discovery. In this work, we introduced GeoREC, a geometric representation of spatial emptiness in protein-ligand complexes, and the Union- Pocket, a unified structural context for multiple pockets, to enhance bioactivity prediction in drug discovery. By measuring unoccupied space and integrating global pocket information, our approach captures critical aspects of competitive binding that were previously overlooked. Additionally, we exploited pairwise loss function to better preserve the relative order among samples. Extensive experiments across diverse datasets and bioactivity measurements demonstrate that LigoSpace significantly improves prediction accuracy. Specifically, the substantial performance gains achieved by GeoREC highlight the critical importance of the proposed geometric feature in ligand interactions modeling.
Acknowledgments and Disclosure of Funding
This work was partially supported by Singapore Ministry of Education (MOE) Tier 1 RG97/22.
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Reviews:
[{"review_id": "4cl1h7Hddu", "reviewer": "Reviewer_U3wC", "summary": "This paper proposes a new approach to structure-based bioactivity prediction by incorporating spatial information beyond traditional binding interactions. The authors introduce GeoREC, a method that models the unoccupied space around atoms in a protein-ligand complex, and Union-Pocket, which combines multiple pockets from the same protein to provide a consistent structural context across ligands. A hybrid loss function is also used to improve the preservation of bioactivity rankings. The method shows improved performance over some baselines on the DTIGN and SIU datasets, and an ablation study confirms that each component contributes to the overall gain.", "questions": "1. Union-Pocket appears effective on datasets like DTIGN and SIU, where multiple pockets per protein are available. However, how does the method apply to standard benchmarks like PDBbind [1], where proteins typically have only one known binding site? Can the authors comment on the generalizability of their approach in such single-pocket settings?\n2. What specific criteria were used to define individual pockets before forming Union-Pocket? The effectiveness of Union-Pocket depends on how the individual pockets are initially defined. Could the authors clarify how pockets are constructed during data preprocessing—for example, what criteria or radius are used? Since these pocket definitions may rely on heuristic rules or docking-based priors, to what extent does the Union-Pocket strategy introduce new information, rather than simply aggregating existing sampling bias?\n3.  While the three proposed components—GeoREC, Union-Pocket, and hybrid loss—are each shown to improve performance, the conceptual motivation for combining them is not clearly articulated. What is the biological or modeling rationale for combining GeoREC, Union-Pocket, and the pairwise loss in a single framework? Were they motivated together, or added independently for empirical gain?\n\n[1] Wang, Renxiao, et al. \"The PDBbind database: Collection of binding affinities for protein− ligand complexes with known three-dimensional structures.\" Journal of medicinal chemistry 47.12 (2004): 2977-2980.", "limitations": "Yes. The authors acknowledge certain limitations in Appendix A.9, specifically the potential increase in computational cost due to the use of Union-Pocket.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 3, "significance": 3, "originality": 3, "strengths_and_weaknesses": "*Strength*\n- The model introduces three well-defined components—GeoREC, Union-Pocket, and hybrid loss—and each is shown through ablation to provide a consistent improvement.\n- The paper is generally well-structured and clearly presented.\n- This research focuses on a core issue in the field of computational drug discovery: accurately predicting bioactivity based on protein-ligand complex structures.\n\n*Weakness*\n1. While the method performs well on certain SIU subsets, the results for Ki 0.9, Ki 0.6, and Kd 0.6 in the appendix are clearly below state-of-the-art levels. This raises concerns about the model's generalizability across different label types and dataset settings.\n2. The paper includes only a limited set of baselines. The lack of comparison with more diverse or competitive methods makes it difficult to judge how strong the proposed model is in a broader context.\n3. The abstract implies that stronger binding directly translates to stronger bioactivity. This is scientifically inaccurate. While binding affinity is a necessary component of bioactivity, it is not sufficient—many ligands bind tightly without eliciting a biological response, or even elicit off-target effects.\n4. The figures, particularly Figure 1, are not visually effective. Fonts are too small, and the graphical elements are not intuitive. Given that the method is fundamentally geometric, better visualizations are essential.\n5. There are some writing and LaTeX formatting issues. For example, terms like IC₅₀ and EC₅₀ are incorrectly written in italics or math mode. Similarly, the Pearson correlation coefficient should be denoted as lowercase r, not uppercase R.", "was_revised": true, "final_justification": "After considering the rebuttal, additional experiments, and clarifications, I am increasing my score to 4. The paper introduces a meaningful geometric perspective for structure-based bioactivity prediction (GeoREC and Union-Pocket) and a hybrid loss formulation, and the expanded evaluation now includes more competitive baselines, showing consistent improvements across most metrics. The authors clarified the applicability to single-pocket benchmarks, defined pocket construction explicitly (5 Å criterion), and revised the abstract to avoid conflating binding affinity with bioactivity, addressing several key concerns. However, some issues remain partially resolved: certain SIU subsets still show modest gains, suggesting sensitivity to label types; Union-Pocket depends on docking-derived priors, with no sensitivity analysis; the conceptual motivation for combining all components is still somewhat empirical; and generalizability to datasets like PDBbind is argued but not demonstrated experimentally. Overall, the work presents a technically solid and novel approach with improved clarity and broader evaluation after rebuttal, but residual concerns about robustness, scalability, and empirical breadth prevent a higher recommendation, leading to a borderline accept (score 4).", "rebuttal": "Thank you for your comments. We sincerely appreciate your recognition of the significance of our work and the paper writing. Here are the responses to the comments.\n\n### **In response to Weakness 1**\n\nWe have completed comprehensive experiments across all SIU subsets for both Kd and Ki tasks, evaluating three baseline models (GAT, GIGN, DTIGN) and their enhanced versions. Our results demonstrate that the enhanced models outperform their respective baselines in 43 out of 48 dataset-metric combinations and achieve state-of-the-art performance on 10 out of 16 dataset-level metrics. We also note that the SIU benchmark, introduced in [1], is a rigorous and up-to-date standard for evaluating ligand binding affinity. We believe these stable and competitive results across varied settings demonstrate the robustness and generalizability of our method.\n\n|Dataset/label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|:-|:-|:-|:-|:-|:-|\n|SIU0.9/Kd|Unimol|1.364|1.141|-0.033|-0.082|\n||DTIGN|1.839|1.490|-0.001|-0.042|\n||DTIGN enhanced|**1.304**|**1.060**|**0.321**|**0.326**|\n||GIGN|1.708|1.367|0.070|0.038|\n||GIGN enhanced|**1.455**|**1.139**|**0.296**|**0.261**|\n||GAT|1.545|1.240|0.092|0.082|\n||GAT enhanced|**1.473**|**1.166**|**0.261**|**0.254**|\n|SIU0.9/Ki|Unimol|1.235|1.017|0.485|0.452|\n||DTIGN|1.607|1.276|0.360|0.329|\n||DTIGN enhanced|**1.296**|**1.054**|**0.485**|**0.441**|\n||GIGN|1.597|1.337|0.223|0.167|\n||GIGN enhanced|**1.487**|**1.240**|**0.371**|**0.338**|\n||GAT|1.706|1.386|0.301|0.262|\n||GAT enhanced|**1.625**|**1.339**|**0.316**|**0.294**|\n|SIU0.6/Kd|Unimol|1.389|1.192|-0.149|-0.206|\n||GIGN|1.371|1.115|0.265|0.281|\n||GIGN enhanced|**1.326**|**1.078**|**0.280**|0.227|\n||DTIGN|1.349|1.079|0.329|0.329|\n||DTIGN enhanced|**1.332**|**1.069**|0.327|0.248|\n||GAT|1.521|1.285|0.233|0.157|\n||GAT enhanced|**1.424**|**1.182**|0.107|0.133|\n|SIU0.6/Ki|Unimol|1.255|1.034|0.472|0.452|\n||GIGN|1.789|1.503|0.225|0.230|\n||GIGN enhanced|**1.404**|**1.165**|**0.498**|**0.463**|\n||DTIGN|1.993|1.653|0.123|0.091|\n||DTIGN enhanced|**1.321**|**1.079**|**0.472**|**0.452**|\n||GAT|1.976|1.690|-0.060|-0.096|\n||GAT enhanced|**1.694**|**1.381**|**0.303**|**0.263**|\n\n\n### **In response to Weakness 2**\n\nWe have expanded our experiments to include additional competitive baselines: the explainable heterogeneous interaction graph neural network (EHIGN) [2], the structure-aware interactive graph neural network (SIGN) [3], and the multi-task bioassay pre-training (MBP) approach [4]. Results (attached below) show that the proposed method consistently improves performance over these models across most metrics (39/43) on a representative benchmark subset.\n\nTogether with the existing GAT, GIGN, and DTIGN, these additional methods form a diverse and competitive baseline set that includes heterogeneous, attention-based, and multi-task learning approaches. This broader comparison provides a more comprehensive assessment of the proposed model's effectiveness.\n\n|Dataset / Label|Method|RMSE(↓)|Pearson(↑)|Tau(↑)|\n|:-|:-|:-|:-|:-|\n|DTIGN I1/ IC50|EHIGN|1.215|0.146|0.052|\n||EHIGN Enhanced|1.239|**0.193**|**0.108**|\n||SIGN|0.911|0.681|0.492|\n||SIGN Enhanced|**0.909**|**0.712**|**0.539**|\n||MBP|1.280|0.148|0.036|\n||MBP Enhanced|**1.152**|**0.466**|**0.325**|\n|DTIGN I2 / IC50|EHIGN|1.089|0.042|0.011|\n||EHIGN Enhanced|**0.999**|**0.053**|**0.045**|\n||SIGN|0.582|0.848|0.632|\n||SIGN Enhanced|**0.569**|0.848|**0.641**|\n||MBP|1.071|0.073|0.081|\n||MBP Enhanced|**0.977**|**0.449**|**0.258**|\n|DTIGN E1 / EC50|EHIGN|0.994|-0.050|-0.026|\n||EHIGN Enhanced|1.006|**0.010**|**-0.009**|\n||SIGN|0.887|0.464|0.393|\n||SIGN Enhanced|**0.861**|**0.506**|**0.446**|\n||MBP|0.972|0.028|0.005|\n||MBP Enhanced|**0.913**|**0.334**|**0.241**|\n\n|Dataset / Label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|:-|:-|:-|:-|:-|:-|\n|SIU 0.6 / Kd|EHIGN|1.404|1.180|-0.015|0.020|\n||EHIGN Enhanced|**1.325**|**1.110**|**0.159**|**0.213**|\n||MBP|1.693|1.418|-0.195|-0.189|\n||MBP Enhanced|**1.406**|**1.194**|**0.082**|**0.041**|\n|SIU 0.6 / Ki|EHIGN|1.450|1.222|0.118|0.106|\n||EHIGN Enhanced|**1.394**|**1.164**|**0.256**|**0.169**|\n||MBP|1.748|1.483|0.304|0.253|\n||MBP Enhanced|**1.699**|**1.434**|**0.317**|0.225|\n\n\n### **In response to Weakness 3**\n\nWe fully agree that strong binding affinity alone does not guarantee bioactivity. While binding is a prerequisite for bioactivity, it is not sufficient on its own—many tightly binding ligands fail to produce the desired biological effect. We will revise the abstract as follows to more accurately reflect this distinction.\n\n> **Abstract**: Predicting the bioactivity of candidate ligands remains a central challenge in drug discovery. Ligands and endogenous substrates often compete for the same binding sites on target proteins, and the extent to which a ligand can modulate protein function depends not only on its binding but also on how effectively it occupies the relevant pocket. However, most existing methods focus narrowly on local interactions within protein–ligand complexes and neglect spatial emptiness—the unoccupied regions within the binding site that may permit endogenous molecules to engage or interfere. Such unfilled space can diminish the ligand’s functional impact, regardless of binding affinity. In this paper,  ... (The rest remains unchanged.)\n\n\n### **In response to Weakness 4**\n\nDue to submission constraints, we are unable to upload revised figures here. However, we will improve the figures in the final version by increasing font sizes and making the graphical elements more intuitive to better convey the geometric nature of our method.\n\n\n### **In response to Weakness 5**\n\nWe will correct the formatting issues in the final version by using the proper LaTeX conventions—ensuring that terms like IC₅₀ and EC₅₀ are written in non-italic text and that the Pearson correlation coefficient is correctly denoted as lowercase $r$.\n\n\n### **In response to Question 1**\n\nThe concept of Union-Pocket is indeed applicable to single-pocket settings like those in PDBbind. In our method, we consider not just the local pocket surrounding a specific ligand pose, but the union binding region estimated by all ligand poses docked around known active sites. This includes all possible functional active sites and their surrounding environments that could contribute to bioactivity upon ligand binding. In single-pocket benchmarks, if the pocket is defined broadly enough—e.g., by enlarging the docking box—it effectively serves the same role as a Union-Pocket. Thus, our method remains generalizable and effective in such settings.\n\n\n### **In response to Question 2**\n\nIndividual pockets are defined as the set of protein residues with at least one atom located within 5 Å of any ligand atom [5-7]. This definition follows a commonly used proximity-based criterion that reflects potential physical interactions.\n\nThe Union-Pocket strategy introduces two key types of new information beyond simply aggregating existing docking poses. First, instead of using one large docking box that covers the entire protein surface, we define multiple smaller docking boxes around each cluster of functional sites. This approach forces ligands to explore and generate binding poses specifically within these localized regions, reducing sampling bias and ensuring more thorough and uniform coverage of all potential binding sites. Second, by taking the union of all such individual pockets, the resulting Union-Pocket–ligand graph captures the global spatial context of the ligand, including its relative location and the overall geometry of empty regions around potential binding sites. This holistic view of binding topography is not available in any single pose or local pocket, thereby providing richer structural information for bioactivity prediction.\n\n\n### **In response to Question 3**\n\nThe proposed GeoREC and Union-Pocket were motivated together because the Union-Pocket provides the global geometry of protein-ligand interaction graphs. The pairwise loss is an add-on to let the model perceive both the relative error (direction-based) and the absolute error (distance-based) between its predictions and labels.\n\n\n### **References**  \n[1] Redefining the task of Bioactivity Prediction, ICLR, 2025\n\n[2] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024\n\n[3] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021\n\n[4] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, BIB, 2024\n\n[5] Geometric interaction graph neural network for predicting protein–ligand binding affinities from 3d structures (GIGN), Journal of physical chemistry letters, 2023\n\n[6] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024\n\n[7] SiteFerret: beyond simple pocket identification in proteins, JCTC, 2023"}, {"review_id": "b2YxP1HrCS", "reviewer": "Reviewer_KYpi", "summary": "This paper proposes a method to improve bioactivity prediction by combining three components: a novel geometric representation (GeoREC) designed to model the \"spatial emptiness\" within a binding site; a unified \"Union-Pocket\" that provides a consistent global context for the protein; and a pairwise-enhanced loss function to better preserve the relative ranking of bioactivities. Experiments are performed on \nDTIGN and SIU dataset to valid performance.", "questions": "**Suggestions/Questions**:\n1. The central motivation of the paper rests on the importance of \"spatial emptiness\" for predicting bioactivity. However, the intuition behind this needs further development.  Could you please provide a more detailed explanation?\n2. Adding more powerful baselines, such as SIGN, GET, MBP, and so on.\n3. What is the main difference of the pairwise losses between GeoREC and previous work listed above?\n4. It's better to detail the advantages of predicting affinity based on docked conformations rather than co-crystal structures.\n\nI'm willing to raise my socre is these suggestions/questions are solved.", "limitations": "Yes", "rating": 4, "confidence": 5, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 3, "significance": 2, "originality": 3, "strengths_and_weaknesses": "**Strengths**\n1. The paper is generally well-written and clearly structured.\n\n2. The central motivation of modeling \"spatial emptiness\" is conceptually interesting.\n\n**Weaknesses**\n1. The claim of novelty for the pairwise loss function is overstated. Ranking-based or pairwise losses are well-established in computational chemistry and drug discovery, particularly for binding affinity prediction and virtual screening tasks. [1][2]\n\n2. The connection between the proposed GeoREC method and the concept of \"spatial emptiness\" is not sufficiently justified. The paper argues that GeoREC captures emptiness by connecting a central atom to the nearest neighboring atoms within predefined spatial cones. However, it is not immediately clear how these new edges, which connect existing atoms, directly represent or quantify the volume of \"unoccupied space\". A more rigorous explanation, perhaps with visualizations or a stronger biophysical argument, is needed to convince the reader that this geometric construction is a valid and effective proxy for spatial emptiness.\n\n3.  The experimental validation raises concerns about the generalizability and practical utility of the method. The primary DTIGN dataset consists of only 8 protein targets. This is a very small number and may not be representative of the vast chemical and structural space of protein targets. \n\n4. The set of baseline models is somewhat limited. While including DTIGN and GIGN is appropriate, several more recent and powerful state-of-the-art geometric deep learning models for protein-ligand interaction are missing, such SIGN[3], GET[4], MBP[2], and so on.\n\n[1]. A bioactivity foundation model using pairwise meta-learning, Nature Machine Intelligence,  2024\n\n[2]. Multi-task bioassay pre-training for protein-ligand binding affinity prediction, Briefings in Bioinformatics, 2024\n\n[3]. Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021\n\n[4]. Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning, ICML, 2024", "was_revised": true, "final_justification": "My concerns have been solved.", "rebuttal": "Thank you for your interest in our work and your insightful suggestions. Below are our responses to your questions.\n\n###  **In response to Weakness 1**\n\nWe appreciate the point and acknowledge that several related works have adopted ranking or pairwise loss. In our work, the pairwise loss complements the primary objective by explicitly modeling relative differences between samples. A detailed comparison with [1] and [2] is provided in the response to the corresponding question below.\n\nWhile the core idea of employing pairwise loss is similar, the problem settings differ. We have reviewed related literature and cited several works in our original submission, including [3] and [4]. We will additionally cite these newly mentioned references and revise the manuscript to clarify our contribution more precisely.\n\n### **In response to Weakness 2**\n\nGeoREC captures *spatial emptiness* implicitly via geometric edge construction. For each atom, the surrounding space is partitioned into $K$ cones of equal solid angle. Each cone connects the central atom to its nearest neighbor, and the **distance $s$ to the nearest atom** in each cone provides a lower bound on unoccupied volume in that direction.\n\nConsider:\n\n- A surrounding sphere of radius $r$ is partitioned into $K$ cones.\n- Volume per cone:  \n  $$\n  V_{\\text{cone}} = \\frac{4}{3} \\pi \\frac{r^3}{K}\n  $$\n- If the nearest atom in a cone lies at distance $s$, the **empty volume** in that direction is at least:  \n  $$\n  V_{\\text{empty}} \\ge \\frac{4}{3} \\pi \\frac{s^3}{K}\n  $$\n\nThus, longer distances imply more emptiness, and this grows with $s^3$. GeoREC encodes the distance to the nearest atom in each cone, providing a compact and physically meaningful proxy for local spatial emptiness.\n\n### **In response to Weakness 3**\n\nThe two datasets used in this study, DTIGN and SIU, represent distinct scenarios in bioactivity learning. DTIGN includes 8 protein targets, with diverse and sufficient numbers of bioactivity assays (see paragraph 2, page 2, and Table 1 in [5]). In this case, models were trained independently for each target to evaluate target-specific performance. In contrast, the SIU dataset includes 1,720 protein targets (Figure 2, page 4 in [6]) and is designed to assess model generalizability across a wide chemical and structural space, where a single model is trained jointly on all targets. We now completed a comprehensive set of experiments on the SIU dataset. The results show that our method consistently improves performance across multiple metrics, demonstrating that our method enhances baseline models even in large-scale, diverse bioactivity prediction tasks.\n\n\n|Metrics|RMSE|MAE|Pearson r|Spearman r|\n|:-|:-|:-|:-|:-|\n|Baseline avg|1.667|1.368|0.180|0.152|\n|Enhanced avg|**1.429**|**1.163**|**0.336**|**0.308**|\n\n|Dataset/label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|:-|:-|:-|:-|:-|:-|\n|SIU0.9/Kd|Unimol|1.364|1.141|-0.033|-0.082|\n||DTIGN|1.839|1.490|-0.001|-0.042|\n||DTIGN enhanced|**1.304**|**1.060**|**0.321**|**0.326**|\n||GIGN|1.708|1.367|0.070|0.038|\n||GIGN enhanced|**1.455**|**1.139**|**0.296**|**0.261**|\n||GAT|1.545|1.240|0.092|0.082|\n||GAT enhanced|**1.473**|**1.166**|**0.261**|**0.254**|\n|SIU0.9/Ki|Unimol|1.235|1.017|0.485|0.452|\n||DTIGN|1.607|1.276|0.360|0.329|\n||DTIGN enhanced|**1.296**|**1.054**|**0.485**|**0.441**|\n||GIGN|1.597|1.337|0.223|0.167|\n||GIGN enhanced|**1.487**|**1.240**|**0.371**|**0.338**|\n||GAT|1.706|1.386|0.301|0.262|\n||GAT enhanced|**1.625**|**1.339**|**0.316**|**0.294**|\n|SIU0.6/Kd|Unimol|1.389|1.192|-0.149|-0.206|\n||GIGN|1.371|1.115|0.265|**0.281**|\n||GIGN enhanced|**1.326**|**1.078**|**0.280**|0.227|\n||DTIGN|1.349|1.079|**0.329**|**0.329**|\n||DTIGN enhanced|**1.332**|**1.069**|0.327|0.248|\n||GAT|1.521|1.285|0.233|0.157|\n||GAT enhanced|**1.424**|**1.182**|0.107|0.133|\n|SIU0.6/Ki|Unimol|1.255|1.034|0.472|0.452|\n||GIGN|1.789|1.503|0.225|0.230|\n||GIGN enhanced|**1.404**|**1.165**|**0.498**|**0.463**|\n||DTIGN|1.993|1.653|0.123|0.091|\n||DTIGN enhanced|**1.321**|**1.079**|**0.472**|**0.452**|\n||GAT|1.976|1.690|-0.060|-0.096|\n||GAT enhanced|**1.694**|**1.381**|**0.303**|**0.263**|\n\n\n### **In response to Weakness 4**\n\nWe have expanded our experiments to include additional competitive baselines: EHIGN [7], SIGN [8], and MBP [2]. Results (attached below) show that the proposed method consistently improves performance over these models across most metrics (39/43) on a representative benchmark subset.\n\n\n|Dataset / Label|Method|RMSE(↓)|Pearson(↑)|Tau(↑)|\n|-|-|-|-|-|\n|DTIGN I1/ IC50|EHIGN|1.215|0.146|0.052|\n||EHIGN Enhanced|1.239|**0.193**|**0.108**|\n||SIGN|0.911|0.681|0.492|\n||SIGN Enhanced|**0.909**|**0.712**|**0.539**|\n||MBP|1.280|0.148|0.036|\n||MBP Enhanced|**1.152**|**0.466**|**0.325**|\n|DTIGN I2 / IC50|EHIGN|1.089|0.042|0.011|\n||EHIGN Enhanced|**0.999**|**0.053**|**0.045**|\n||SIGN|0.582|0.848|0.632|\n||SIGN Enhanced|**0.569**|0.848|**0.641**|\n||MBP|1.071|0.073|0.081|\n||MBP Enhanced|**0.977**|**0.449**|**0.258**|\n|DTIGN E1 / EC50|EHIGN|0.994|-0.050|-0.026|\n||EHIGN Enhanced|1.006|**0.010**|**-0.009**|\n||SIGN|0.887|0.464|0.393|\n||SIGN Enhanced|**0.861**|**0.506**|**0.446**|\n||MBP|0.972|0.028|0.005|\n||MBP Enhanced|**0.913**|**0.334**|**0.241**|\n\n\n|Dataset / Label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|-|-|-|-|-|-|\n|SIU 0.6 / Kd|EHIGN|1.404|1.180|-0.015|0.020|\n||EHIGN Enhanced|**1.325**|**1.110**|**0.159**|**0.213**|\n||MBP|1.693|1.418|-0.195|-0.189|\n||MBP Enhanced|**1.406**|**1.194**|**0.082**|**0.041**|\n|SIU 0.6 / Ki|EHIGN|1.450|1.222|0.118|0.106|\n||EHIGN Enhanced|**1.394**|**1.164**|**0.256**|**0.169**|\n||MBP|1.748|1.483|0.304|0.253|\n||MBP Enhanced|**1.699**|**1.434**|**0.317**|0.225|\n\n### **In response to Question 1**\n\nThe motivation for using spatial emptiness comes from the blocking mechanism: ligands that fully occupy key regions of a binding site can outcompete endogenous substrates and more effectively modulate protein function. Bioactivity depends not only on where atoms are present, but also on where critical voids remain. Incomplete occupancy may leave space for substrate binding, reducing inhibition. By modeling spatial emptiness, we capture how well a ligand blocks substrate access—offering a meaningful proxy for bioactivity.\n\n### **In response to Question 2**\nWe have added more powerful baselines include SIGN, MBP and EHIGN. See tables above.\n\n### **In response to Question 3**\nHere are more details about the difference between ours and other 2 works.\n\n[1]\nIn this work, they use a BCE as their ranking loss. We summarize the difference between their ranking loss and our pairwise loss in the table below:\n|Aspect|Loss in [1]| Loss in our work|\n|-|-|-|\n|Objective|Learns relative order (which is larger/smaller)|Learns relative difference (how much larger/smaller)|\n|Loss type|Binary classification|Regression|\n|Noise Robustness|More robust to absolute value noise|Focuses on precise difference alignment|\n\n[2]\nIn this work, the pairwise loss enables meta-learning for few-shot adaptation. E.g., ligand bioactivity data from the same assay are inherently comparable, allowing the model to learn relative differences even with limited data. This loss also guides the model to refine predictions on new assays using only a few samples.\nIn our work, the pairwise loss is a supplementary term in a hybrid loss for a regression task.\nHere is a table for the summary:\n|Aspect|Loss in [2]|Loss in our work|\n|-|-|-|\n|Objective|Enable few-shot adaptation via meta-learning|Improve static prediction via relative order|\n|Calculation scope|Task-specific subsets|All samples in a batch|\n|Typical Use Case|Low-data,cross-assay adaptation|General bioactivity prediction|\n|Loss Integration|Core to meta-learning loops|Hybrid loss with MSE|\n\n### **In response to Question 4**\nPredicting affinity from docked conformations offers key advantages over using co-crystal structures. Co-crystal structures are scarce and costly to obtain, especially for novel targets, whereas docking provides scalable access to approximate protein–ligand complexes. Most of our training data lack co-crystal structures, so using docked conformations enables broader applicability. Moreover, deep learning can be designed to denoise and learn meaningful patterns, making our approach practical and robust for real-world tasks like virtual screening.\n\n\n### **References**  \n[1] A bioactivity foundation model using pairwise meta-learning, Nature Machine Intelligence, 2024\n\n[2] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, Briefings in Bioinformatics, 2024\n\n[3] Gradient Aligned Regression via Pairwise Losses, arXiv preprint, 2024\n\n[4] Pairwise difference regression: a machine learning meta-algorithm for improved prediction and uncertainty quantification in chemical search, JCIM, 2021\n\n[5] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024\n\n[6] Redefining the task of Bioactivity Prediction, ICLR, 2025\n\n[7] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024\n\n[8] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021\n\n[9] Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning, ICML, 2024"}, {"review_id": "Bv8GqzbdvW", "reviewer": "Reviewer_1izV", "summary": "This paper improves the bioactivity prediction task by considering spatial emptiness, union pockets and pairwise loss. The spatial emptiness aims to identify pockets and ligands atoms without sufficient contact. Union pockets combine pockets of different ligands to generate a more comprehensive view. Pairwise loss provides more precise supervision signal for bioactivity prediction. With these techniques, the authors have achieved substantial improvements on multiple benchmarks.", "questions": "1.\tAdd more baseline methods:\nThere are a lot of strong baseline models for bioactivity prediction, and it’s better to make a more comprehensive comparison. For example, physics-based methods like MM-PB/GBSA, ABFEP or deep learning methods like EHIGN. \n2.\tThe implementation of GeoREC:\nFor neighbors in each cone, are they distinguished by their directions? Is this direction information incorporated into Egeo? If not, what is the difference between GeoREC and neighborhood-based edge construction?\n3.\tWhy can GeoREC model spatial emptiness but other methods cannot?", "limitations": "Yes", "rating": 5, "confidence": 4, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 3, "clarity": 2, "significance": 2, "originality": 3, "strengths_and_weaknesses": "Strengths:\n\n1.\tPairwise loss and union pockets have incorporated important inductive bias into the bioactivity prediction task.\n2.\tThe paper has achieved substantial improvement on multiple benchmarks and has conducted solid ablation tests.\n\nWeaknesses:\n\n1.\tThe authors did not compare their method with some strong baselines, for example, EHIGN that published on TPAMI.\n2.\tMore experiments or explanation should be provided by claiming that GeoREC can model spatial emptiness.", "was_revised": true, "final_justification": "This paper proposes a novel approach to bioactivity prediction through the use of spatial emptiness modeling (GeoREC), union pockets, and pairwise loss. These innovations aim to improve how protein–ligand interactions are represented and learned, and the method demonstrates strong performance across multiple benchmarks.\n\nAfter reviewing the rebuttal and follow-up discussion, I find that the authors have meaningfully addressed my concerns:\n\nStronger Baselines: The authors have significantly expanded the evaluation by adding three high-quality baseline methods: EHIGN, SIGN, and MBP. These additions improve the completeness of the comparison and demonstrate consistent performance gains across a wide range of settings, with the proposed method outperforming baselines in the majority of cases.\n\nSpatial Emptiness via GeoREC: The explanation of how GeoREC captures spatial emptiness through a cone-based geometric edge construction is both physically intuitive and technically sound. The notion of using the minimum distance in each cone as a proxy for unoccupied volume is clever and offers a novel inductive bias in molecular modeling.\n\nDirectionality and Angular Information: While I initially had concerns about the lack of explicit angular encoding, the authors clarified that their model does not aim to explicitly reconstruct angles, but rather relies on sufficient geometric and topological information already present in the graph structure. Their ablation studies show that adding explicit angle features does not improve performance and can even harm it, likely due to redundancy or added complexity. This clarification partially resolves my concern.\n\nOverall, the authors have convincingly demonstrated the methodological soundness and empirical strength of their approach. The work introduces new ideas and inductive biases that are likely to benefit future research in protein–ligand modeling and bioactivity prediction. While some architectural and interpretability aspects could still benefit from further investigation, the paper is well-motivated, technically solid, and significantly strengthened by the rebuttal. I maintain my positive assessment and raise my rating to 5. Nevertheless, the scalability to deeper and larger neural networks like EquiFormer still needs further investigation.", "rebuttal": "Thank you for your kind recognition of our work and for providing valuable suggestions. Our responses are as follows.\n\n### **In response to Weakness 1**\n\nWe have expanded our experiments to include additional competitive baselines: the explainable heterogeneous interaction graph neural network (EHIGN) [1], the structure-aware interactive graph neural network (SIGN) [2], and the multi-task bioassay pre-training (MBP) approach [3]. Results (attached below) show that the proposed method consistently improves performance over these models across most metrics (39/43) on a representative benchmark subset.\n\n\n|Dataset / Label|Method|RMSE(↓)|Pearson(↑)|Tau(↑)|\n|:-|:-|:-|:-|:-|\n|DTIGN I1/ IC50|EHIGN|1.215|0.146|0.052|\n||EHIGN Enhanced|1.239|**0.193**|**0.108**|\n||SIGN|0.911|0.681|0.492|\n||SIGN Enhanced|**0.909**|**0.712**|**0.539**|\n||MBP|1.280|0.148|0.036|\n||MBP Enhanced|**1.152**|**0.466**|**0.325**|\n|DTIGN I2 / IC50|EHIGN|1.089|0.042|0.011|\n||EHIGN Enhanced|**0.999**|**0.053**|**0.045**|\n||SIGN|0.582|0.848|0.632|\n||SIGN Enhanced|**0.569**|0.848|**0.641**|\n||MBP|1.071|0.073|0.081|\n||MBP Enhanced|**0.977**|**0.449**|**0.258**|\n|DTIGN E1 / EC50|EHIGN|0.994|-0.050|-0.026|\n||EHIGN Enhanced|1.006|**0.010**|**-0.009**|\n||SIGN|0.887|0.464|0.393|\n||SIGN Enhanced|**0.861**|**0.506**|**0.446**|\n||MBP|0.972|0.028|0.005|\n||MBP Enhanced|**0.913**|**0.334**|**0.241**|\n\n\n|Dataset / Label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|:-|:-|:-|:-|:-|:-|\n|SIU 0.6 / Kd|EHIGN|1.404|1.180|-0.015|0.020|\n||EHIGN Enhanced|**1.325**|**1.110**|**0.159**|**0.213**|\n||MBP|1.693|1.418|-0.195|-0.189|\n||MBP Enhanced|**1.406**|**1.194**|**0.082**|**0.041**|\n|SIU 0.6 / Ki|EHIGN|1.450|1.222|0.118|0.106|\n||EHIGN Enhanced|**1.394**|**1.164**|**0.256**|**0.169**|\n||MBP|1.748|1.483|0.304|0.253|\n||MBP Enhanced|**1.699**|**1.434**|**0.317**|0.225|\n\n\n### **In response to Weakness 2**\n\nGeoREC captures *spatial emptiness* implicitly via geometric edge construction. For each atom, the surrounding space is partitioned into $K$ cones of equal solid angle. Each cone connects the central atom to its nearest neighbor, and the **distance $s$ to the nearest atom** in each cone provides a lower bound on unoccupied volume in that direction.\n\nConsider:\n\n- A surrounding sphere of radius $r$ is partitioned into $K$ cones.\n- Volume per cone:  \n  $$\n  V_{\\text{cone}} = \\frac{4}{3} \\pi \\frac{r^3}{K}\n  $$\n- If the nearest atom in a cone lies at distance $s$, the **empty volume** in that direction is at least:  \n  $$\n  V_{\\text{empty}} \\ge \\frac{4}{3} \\pi \\frac{s^3}{K}\n  $$\n\nThus, longer distances imply more emptiness, and this grows with $s^3$. GeoREC encodes the distance to the nearest atom in each cone, providing a compact, learnable, and physically meaningful proxy for local spatial emptiness.\n\n\n### **In response to Question 1**\n\nOur proposed method is a general and plug-and-play module that can be seamlessly integrated into various GNN-based models for bioactivity prediction. However, it is not directly applicable to physics-based approaches such as MM-PB/GBSA or ABFEP, as these rely on fundamentally different simulation principles. In response to your suggestion of benchmarking against stronger baselines, we have further incorporated three representative deep learning models—EHIGN [1], SIGN [2], and MBP [3]—into our experimental evaluation. We evaluated them on both datasets used in our study. As shown in the table above, our method consistently improves the performance across these baselines, further demonstrating its effectiveness and generalizability.\n\n\n### **In response to Question 2**\n\nIn the current implementation of GeoREC, cones are not explicitly distinguished by their directions. However, the relative spatial orientation is largely captured by the dense network of intra- and inter-molecular edge lengths—including chemical bonds, protein–ligand interface edges, and the shortest atom distances sampled within each cone—which together encode the geometric relationships between atoms.\n\nWe also experimented with explicitly embedding directional angle ranges into the geometric edge features, but this reduced performance, as shown in our ablation results. Our hypothesis is that these explicit directional features introduce additional complexity, making it harder for the model to reconcile them with the directional cues already embedded in the graph through edge lengths. Moreover, since the union pocket structure is fixed and its graph contains sufficient edges to form triangles with common sides and vertices, angular information can be inferred from these edge-based geometric relationships. This makes explicit angle features not only redundant, but potentially disruptive to the model's ability to learn coherent spatial patterns.\n\nAs a result, GeoREC differs from conventional neighborhood-based edge construction by enforcing directional locality through conical constraints, while still relying on implicit directionality captured via edge geometry and connectivity in the 3D graph—without requiring explicit angular encodings.\n\n\n|Method|Metric|I1|I2|E1|Avg.imp(%)|\n|:--|:--|:--|:--|:--|:--|\n|DTIGN|RMSE(↓)|1.1977|0.7952|0.9086|-|\n||Pearsonr(↑)|0.3547|0.7128|0.3363|-|\n||Tau(↑)|0.2445|0.4922|0.2139|-|\n|DTIGN enhanced|RMSE(↓)|**1.0364**|**0.6507**|**0.8645**|**12.16**|\n||Pearsonr(↑)|**0.5895**|**0.7888**|**0.4969**|**41.54**|\n||Tau(↑)|**0.4239**|**0.5454**|**0.3705**|**52.46**|\n|DTIGN enhanced w/ angle ranges|RMSE(↓)|1.1532|0.8363|0.9131|-0.65|\n||Pearsonr(↑)|0.4903|0.6280|0.3509|10.22|\n||Tau(↑)|0.3305|0.4015|0.2258|7.44|\n\n\n### **In response to Question 3**\n\nGeoREC is specifically designed to capture spatial emptiness by introducing geometric edges that connect a central atom to its nearest neighbor in each predefined directional cone. These edges encode the minimum distance required to reach another atom in that direction, thereby providing a lower bound on the unoccupied volume. This is a direct and localized way to represent spatial sparseness—something that standard graph construction methods do not account for.\n\nIn contrast, other methods typically rely on local neighborhoods constructed via chemical bonds or distance thresholds, and their receptive field grows only with the number of GNN layers. As a result, the model may completely miss distant atoms that lie just outside the local neighborhood but are crucial for estimating spatial emptiness in a particular direction. GeoREC addresses this limitation by ensuring that each directional cone is always represented, regardless of the connectivity of the initial graph.\n\nAdditionally, since the union pocket graph is fixed, it contains sufficient edges to form triangles with common sides and vertices, allowing the model to recover angular relationships implicitly through edge lengths and connectivity. This removes the need to explicitly encode angle features. Our ablation study shows that angle features degrade the mode performance—likely due to redundancy and additional complexity.\n\nTaken together, GeoREC provides an efficient, geometry-aware design that captures directional unoccupied space, which is otherwise inaccessible to conventional methods relying solely on bonded or proximity-based edges.\n\n\n### **References**  \n[1] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024\n\n[2] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021\n\n[3] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, BIB, 2024"}, {"review_id": "uSifqjhb9f", "reviewer": "Reviewer_b5PK", "summary": "This paper proposes a method called GeoREC to address the bioactivity prediction problem. GeoREC quantifies the spatial emptiness around each atom within a protein-ligand complex, and introduces two key innovations: (1) the Union-Pocket, which aggregates multiple binding pockets to capture global interaction context, and (2) a pairwise loss function, which preserves relative ordering among predictions. Together, these enhancements improve the accuracy and selectivity of affinity prediction.", "questions": "See Weakness", "limitations": "This prediction method relies on the complex conformation structure. If the docking method generates inaccurate complex conformations, it may negatively affect the performance. Moreover, the method lacks analysis and discussion regarding this limitation.", "rating": 4, "confidence": 3, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": 2, "clarity": 2, "significance": 2, "originality": 2, "strengths_and_weaknesses": "Stengths: \n1. The proposed augmentation strategy consistently improves performance across various baselines, including DTIGN, GIGN, and GAT.\n2. The pair-wise loss complements the regression loss by enhancing the selectivity for specific ligands and mitigating the effects of noise in affinity values.\n\nWeaknesses:\n1. What impact do different aggregation strategies have on the final performance?\n2. Why does this method perform well on the SIU dataset, which contains complexes with a single binding pocket and a single ligand?\n3. How does the method perform on the LBA (Ligand Binding Affinity) task?\n4. If a ligand can bind to multiple positions in a protein with different conformations, how can multiple complex conformations be modeled? Does the method support using multiple complex conformations as input?", "was_revised": true, "final_justification": "Thank you for the authors’ rebuttal. Most of my concerns have been addressed. My remaining concern is that the authors only compare the improvements against certain methods, without including comparisons to other strong binding affinity baselines. Nevertheless, I am happy to raise my score.", "rebuttal": "Thank you for your comments. We are grateful for your acknowledgment that our method has achieved substantial improvements on multiple benchmarks. Here we would like to response to the comments.\n\n\n### **In response to Weakness 1**\n\nAs discussed in Eq. 5 of the main text, we aggregate multiple pocket–ligand pose embeddings to improve the accuracy of bioactivity prediction. In our current experiments, all models use mean aggregation unless otherwise specified. The only exception is DTIGN, which by default employs its own attention-based aggregation strategy.\n\nTo analyze the effect of different aggregation strategies, we conducted controlled comparisons where both the baseline DTIGN and our enhanced DTIGN were equipped with the same aggregation function—either mean, sum, or attention. As in our other experiments, this comparison ensures that the observed improvements stem from our method rather than differences in aggregation. The results on three datasets (I1, I2, E1) show that our method consistently improves performance across all aggregation strategies, though the extent of improvement varies. In all settings, our enhanced DTIGN outperforms the original DTIGN with the same aggregation function:\n\n- With mean aggregation, our method achieves an average RMSE reduction of 9.62%, along with improvements of 26.43% in Pearson’s $r$ and 25.42% in Kendall’s $\\tau$ .\n- With sum aggregation, improvements are more pronounced: 14.26% reduction in RMSE, and increases of 32.44% in $r$ and 46.54% in $\\tau$.\n- With attention-based aggregation, the enhanced model achieves the best results—12.16% lower RMSE, and substantial gains in correlation metrics: 41.54% in $r$ and 52.46% in $\\tau$.\n\nThese results demonstrate that our method is robust to different aggregation choices, enhancing the baseline model regardless of the specific strategy used.\n\n|Dataset/Aggfunction|Method|RMSE(↓)|Pearson(↑)|Tau(↑)|\n|:-----|:----|:-----|:--------|:----|\n|DTIGNI1 / Mean|DTIGN|1.1971|0.4431|0.3307|\n||DTIGN Enhanced|**1.0183**|**0.6352**|**0.4356**|\n|DTIGNI2 / Mean|DTIGN|0.7863|0.6760|0.4340|\n||DTIGN Enhanced|**0.6781**|**0.7786**|**0.5453**|\n|DTIGNE1 / Mean|DTIGN|0.8817|0.4121|0.3166|\n||DTIGN Enhanced|**0.8803**|**0.4976**|**0.3764**|\n|Overall / Mean|Avg. imp(%)|9.62%|26.43%|25.43%|\n|DTIGNI1 / Sum|DTIGN|1.1441|0.4708|0.2947|\n||DTIGN Enhanced|**0.9781**|**0.6744**|**0.4872**|\n|DTIGNI2 / Sum|DTIGN|0.7466|0.7186|0.5044|\n||DTIGN Enhanced|**0.6170**|**0.8164**|**0.5932**|\n|DTIGNE1 / Sum|DTIGN|0.9313|0.3782|0.2620|\n||DTIGN Enhanced|**0.8298**|**0.5312**|**0.4105**|\n|Overall / Sum|Avg. imp(%)|14.26%|32.44%|46.54%|\n|DTIGNI1 / Attn|DTIGN|1.1977|0.3547|0.2445|\n||DTIGN Enhanced|**1.0364**|**0.5895**|**0.4239**|\n|DTIGNI2 / Attn|DTIGN|0.7952|0.7128|0.4922|\n||DTIGN Enhanced|**0.6507**|**0.7888**|**0.5454**|\n|DTIGNE1 / Attn|DTIGN|0.9086|0.3363|0.2139|\n||DTIGN Enhanced|**0.8645**|**0.4969**|**0.3705**|\n|Overall / Attn|Avg. imp(%)|12.16%|41.54%|52.46%|\n\n\n### **In response to Weakness 2**\n\nAs shown in Figure 2c (Page 4) of [1], the SIU dataset contains a total of 249,631 pocket-ligand pairs across 9,544 protein pockets, indicating an average of approximately 26 ligands per pocket.\n\nAlthough the SIU paper [1] states in the \"Pocket definition\" section (Page 19) that \"For each PDB ID, a single pocket was extracted, defined as the region centered on the co-crystal ligand within a 15 Å radius\", the datasets they released via their Hugging Face repository (linked from their GitHub page, which is referenced in the paper's abstract) contain only local pockets surrounding the individual ligand poses. In other words, the single pocket they used for docking was not fully utilized when constructing the pocket–ligand graphs in their released dataset.\nIn our implementation, for each protein conformation, we use the predefined global pocket—docked by all its associated ligands—as the Union-Pocket. By combining this with GeoREC and our pairwise contrastive loss, our method was able to leverage richer spatial and geometric context. As a result, it performed well on the SIU dataset also.\n\n\n### **In response to Weakness 3**\n\nLigand binding affinity is typically quantified by the dissociation constant (Kd), which is included in the SIU dataset. To evaluate our method’s performance on this task, we analyzed the Kd and Ki prediction results across both SIU0.9 and SIU0.6 subsets.\nFrom the results summarized below, we observe that out of the 48 performance metrics reported across all models and datasets, only 5 metrics do not show improvement with our method. All five are correlation coefficients (Pearson and Spearman) on the SIU0.6 / Kd dataset, which corresponds to the LBA task where the training and test proteins share less than 60% sequence identity.\nThis suggests that while our method is tailored to improve bioactivity prediction, it may be less effective at enhancing correlation-based metrics for ligand binding affinity on highly dissimilar proteins. Nevertheless, our method consistently improves RMSE and MAE on these more challenging cases, and achieves clear improvements across all four LBA metrics (RMSE, MAE, Pearson, Spearman) on the SIU0.9 datasets, where proteins in the training and test sets are more similar.\n\nThese results demonstrate that our approach effectively enhances bioactivity modeling and LBA prediction on proteins with moderate to high similarity, and still offers tangible benefits—particularly in reducing absolute error—even on dissimilar protein targets.\n\n\n|Dataset/label|Method|RMSE(↓)|MAE(↓)|Pearson(↑)|Spearman(↑)|\n|:-|:-|:-|:-|:-|:-|\n|SIU0.9 / Kd|Unimol|1.364|1.141|-0.033|-0.082|\n||DTIGN|1.839|1.490|-0.001|-0.042|\n||DTIGN enhanced|**1.304**|**1.060**|**0.321**|**0.326**|\n||GIGN|1.708|1.367|0.070|0.038|\n||GIGN enhanced|**1.455**|**1.139**|**0.296**|**0.261**|\n||GAT|1.545|1.240|0.092|0.082|\n||GAT enhanced|**1.473**|**1.166**|**0.261**|**0.254**|\n|SIU0.9 / Ki|Unimol|1.235|1.017|0.485|0.452|\n||DTIGN|1.607|1.276|0.360|0.329|\n||DTIGN enhanced|**1.296**|**1.054**|**0.485**|**0.441**|\n||GIGN|1.597|1.337|0.223|0.167|\n||GIGN enhanced|**1.487**|**1.240**|**0.371**|**0.338**|\n||GAT|1.706|1.386|0.301|0.262|\n||GAT enhanced|**1.625**|**1.339**|**0.316**|**0.294**|\n|SIU0.6 / Kd|Unimol|1.389|1.192|-0.149|-0.206|\n||GIGN|1.371|1.115|0.265|**0.281**|\n||GIGN enhanced|**1.326**|**1.078**|**0.280**|0.227|\n||DTIGN|1.349|1.079|**0.329**|**0.329**|\n||DTIGN enhanced|**1.332**|**1.069**|0.327|0.248|\n||GAT|1.521|1.285|0.233|0.157|\n||GAT enhanced|**1.424**|**1.182**|0.107|0.133|\n|SIU0.6 / Ki|Unimol|1.255|1.034|0.472|0.452|\n||GIGN|1.789|1.503|0.225|0.230|\n||GIGN enhanced|**1.404**|**1.165**|**0.498**|**0.463**|\n||DTIGN|1.993|1.653|0.123|0.091|\n||DTIGN enhanced|**1.321**|**1.079**|**0.472**|**0.452**|\n||GAT|1.976|1.690|-0.060|-0.096|\n||GAT enhanced|**1.694**|**1.381**|**0.303**|**0.263**|\n\n\n### **In response to Weakness 4**\n\nIn our current implementation, multiple complex conformations are explicitly modeled by processing each conformation independently through the graph neural network to obtain individual graph-level embeddings. These embeddings are then aggregated—using either mean or attention-based pooling—before being passed to the bioactivity prediction network (typically a multi-layer perceptron). In this way, our method does support multiple complex conformations as input while leveraging shared network weights to process each conformation consistently.\n\n\n### **In response to Limitations**\n\nWe fully acknowledge that inaccurate complex conformations generated by docking methods can negatively affect model performance. To clarify this limitation, we will add the following note to the appendix:\n\n> **Limitations of Docking-Based Structures:**  \n> Docking methods can generate inaccurate complex conformations, which may impair the performance of models trained on docked structures. Users should be aware of this potential issue and are encouraged to use biologically plausible docking poses obtained from well-established software tools. In the DTIGN dataset, ligand poses were generated using AutoDock Vina [2], and the top-ranked poses were selected for model training (as stated in the “Docking method” section on Page 2 and the footnote of Table 1 in [3]). In the SIU dataset, docking was performed using AutoDock Vina [2], Glide [4], and GOLD [5], with a voting strategy applied to select representative poses (as described in the “Structural data construction via multi-software docking” section on Page 5 of [1]).\n\n\n### **References**  \n[1] Redefining the task of Bioactivity Prediction, ICLR, 2025\n\n[2] AutoDock Vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading, Journal of Computational Chemistry, 2010\n\n[3] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024\n\n[4] Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy, Journal of Medicinal Chemistry, 2004\n\n[5] Improved protein–ligand docking using GOLD, Proteins: Structure, Function, and Bioinformatics, 2003"}]

Author rebuttal:

Meta-review: This paper presents a method for structure-based bioactivity prediction that integrates spatial details extending beyond conventional binding interactions. The authors develop GeoREC, a technique that represents the unoccupied space surrounding atoms in a protein-ligand complex, along with Union-Pocket, a strategy for merging multiple pockets from a single protein to ensure uniform structural context across different ligands. A hybrid loss function is employed to better maintain bioactivity rankings. The approach yields enhanced results compared to certain baseline models on the DTIGN and SIU datasets, and an ablation study verifies that every element contributes to the overall improvement.

The authors' compelling rebuttal successfully addressed the reviewers' most concerns. Please include reviewers' comments into the final version.
Decision: Accept (poster)