Enhancing Bioactivity Prediction via Spatial Emptiness Representation of Protein-ligand Complex and Union of Multiple Pockets

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.

In response to Weakness 1

As 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.

To 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:

• 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 $\tau$ .
• With sum aggregation, improvements are more pronounced: 14.26% reduction in RMSE, and increases of 32.44% in $r$ and 46.54% in $\tau$.
• 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 $\tau$.

These results demonstrate that our method is robust to different aggregation choices, enhancing the baseline model regardless of the specific strategy used.

In response to Weakness 2

As 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.

Although 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. In 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.

In response to Weakness 3

Ligand 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. From 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. This 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.

These 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.

In response to Weakness 4

In 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.

In response to Limitations

We 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:

Limitations of Docking-Based Structures:
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]).

References

[1] Redefining the task of Bioactivity Prediction, ICLR, 2025

[2] AutoDock Vina: improving the speed and accuracy of docking with a new scoring function, efficient optimization, and multithreading, Journal of Computational Chemistry, 2010

[3] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024

[4] Glide: a new approach for rapid, accurate docking and scoring. 1. Method and assessment of docking accuracy, Journal of Medicinal Chemistry, 2004

[5] Improved protein–ligand docking using GOLD, Proteins: Structure, Function, and Bioinformatics, 2003

Thank you for your kind recognition of our work and for providing valuable suggestions. Our responses are as follows.

In response to Weakness 1

We 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.

In response to Weakness 2

GeoREC 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.

Consider:

• A surrounding sphere of radius $r$ is partitioned into $K$ cones.
• Volume per cone: $$V_{\text{cone}} = \frac{4}{3} \pi \frac{r^3}{K}$$
• If the nearest atom in a cone lies at distance $s$, the empty volume in that direction is at least: $$V_{\text{empty}} \ge \frac{4}{3} \pi \frac{s^3}{K}$$

Thus, 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.

In response to Question 1

Our 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.

In response to Question 2

In 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.

We 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.

As 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.

In response to Question 3

GeoREC 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.

In 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.

Additionally, 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.

Taken 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.

References

[1] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024

[2] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021

[3] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, BIB, 2024

Thank you to the authors for the thoughtful and thorough rebuttal. I appreciate the substantial effort put into addressing the feedback, particularly in conducting new experiments with stronger baselines such as EHIGN, SIGN, and MBP. These additions considerably strengthen the empirical evaluation and improve the completeness of the benchmarking.

Strengths of the Rebuttal: The inclusion of EHIGN, SIGN, and MBP in the evaluation is much appreciated. These results demonstrate the competitiveness and generalizability of the proposed method across a wider range of models and datasets. Also, as for ABFEP and MM-PB/GBSA, I just mean that you should add them as baselines but not apply your method to these baselines.

Clarification of Spatial Emptiness Modeling: The geometric construction approach using directional cones provides an interesting and compact proxy for spatial emptiness. The explanation of how this setup captures unoccupied volume is helpful and aligns well with the paper’s motivation.

Remaining Concerns: While I appreciate the attempt to encode directionality via edge lengths and intra/inter-molecular connectivity, the explanation remains somewhat ambiguous. Specifically, the claim that angular information is implicitly recoverable through edge-based triangle formations deserves a justification. It is mathematically possible, but hard to achieve by networks without any supervision signaling.

Conclusion: Overall, the rebuttal strengthens the paper. The added experiments are particularly valuable. However, I still find the explanation of directional encoding and its relation to performance somewhat not convincing, and therefore not entirely resolved. I will be maintaining my current score.

Thank you for your interest in our work and your insightful suggestions. Below are our responses to your questions.

In response to Weakness 1

We 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.

While 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.

In response to Weakness 2

GeoREC 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.

Consider:

• A surrounding sphere of radius $r$ is partitioned into $K$ cones.
• Volume per cone: $$V_{\text{cone}} = \frac{4}{3} \pi \frac{r^3}{K}$$
• If the nearest atom in a cone lies at distance $s$, the empty volume in that direction is at least: $$V_{\text{empty}} \ge \frac{4}{3} \pi \frac{s^3}{K}$$

Thus, 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.

In response to Weakness 3

The 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.

In response to Weakness 4

We 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.

In response to Question 1

The 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.

In response to Question 2

We have added more powerful baselines include SIGN, MBP and EHIGN. See tables above.

In response to Question 3

Here are more details about the difference between ours and other 2 works.

[1] In 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:

[2] In 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. In our work, the pairwise loss is a supplementary term in a hybrid loss for a regression task. Here is a table for the summary:

In response to Question 4

Predicting 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.

References

[1] A bioactivity foundation model using pairwise meta-learning, Nature Machine Intelligence, 2024

[2] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, Briefings in Bioinformatics, 2024

[3] Gradient Aligned Regression via Pairwise Losses, arXiv preprint, 2024

[4] Pairwise difference regression: a machine learning meta-algorithm for improved prediction and uncertainty quantification in chemical search, JCIM, 2021

[5] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024

[6] Redefining the task of Bioactivity Prediction, ICLR, 2025

[7] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024

[8] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021

[9] Generalist Equivariant Transformer Towards 3D Molecular Interaction Learning, ICML, 2024

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.

In response to Weakness 1

We 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.

In response to Weakness 2

We 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.

Together 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.

In response to Weakness 3

We 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.

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.)

In response to Weakness 4

Due 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.

In response to Weakness 5

We 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 $r$.

In response to Question 1

The 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.

In response to Question 2

Individual 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.

The 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.

In response to Question 3

The 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.

References

[1] Redefining the task of Bioactivity Prediction, ICLR, 2025

[2] Interaction-based inductive bias in graph neural networks: enhancing protein-ligand binding affinity predictions from 3D structures, TPAMI, 2024

[3] Structure-aware Interactive Graph Neural Networks for the Prediction of Protein-Ligand Binding Affinity, KDD, 2021

[4] Multi-task bioassay pre-training for protein-ligand binding affinity prediction, BIB, 2024

[5] Geometric interaction graph neural network for predicting protein–ligand binding affinities from 3d structures (GIGN), Journal of physical chemistry letters, 2023

[6] Advancing bioactivity prediction through molecular docking and self-attention, JBHI, 2024

[7] SiteFerret: beyond simple pocket identification in proteins, JCTC, 2023