MEGPNM as a multiscale edge-aware GAT network with hybrid pooling predicting permeability of non-peptidic macrocycles

Abstract

Non-peptidic macrocycles are attractive therapeutic candidates for targets that are difficult to drug, while still offering a path toward oral exposure. Predicting their membrane permeability, however, remains difficult because these molecules are conformationally flexible and can display molecular chameleon behavior. These properties make permeability prediction particularly challenging, so macrocycle-specific models are needed. In this work, we propose MEGPNM for permeability prediction. Our approach leverages multilayer edge-aware graph attention, incorporates Jumping Knowledge. We evaluate MEGPNM on PAMPA dataset from the Non-peptidic Macrocycle Membrane Permeability Database and benchmark it against fingerprint-based machine learning baselines and representative deep learning models, achieving the best performance. In addition, attention analyses highlight recurring structural motifs associated with permeability, providing practical clues for permeability-guided macrocycle optimization. We also release a web server for rapid permeability prediction and structure visualization to help early-stage screening.

Non-peptidic macrocycles present a promising avenue for drug development, yet their conformational flexibility complicates membrane permeability prediction. Here, the authors introduce MEGPNM, a model that utilizes multilayer edge-aware graph attention, outperforms existing methods in predicting effective permeability, and reveals structural motifs linked to permeability, with a web server facilitating early-stage drug screening.

Introduction

Drug discovery is a complex, lengthy, and costly process, typically requiring over a decade from candidate compound identification to market approval, with an average cost of billions of dollars^1,2. Among disease-related targets, a substantial fraction of disease-relevant targets are considered ‘undruggable’ or ‘difficult-to-drug’, which often feature flat, shallow, or groove-like binding sites^3,4 that are challenging to modulate effectively with traditional small molecule drugs adhering to Lipinski’s Rule of Five (Ro5)⁵. While biologics such as antibodies can target certain difficult-to-drug targets, their poor cell membrane permeability prevents effective access to intracellular targets, and they typically require injection administration, limiting their clinical application^6,7.

Macrocyclic compounds are typically defined as cyclic structures containing at least 12 atoms, and have attracted considerable attention in recent years as compounds with tremendous therapeutic potential⁸. Macrocyclization offers a strategic advantage by restricting conformation, allowing these molecules to bind “undruggable” targets with high affinity^9,10. Despite their large size often placing them in the “beyond Rule of 5” (bRo5) space, macrocycles frequently maintain oral bioavailability. In fact, roughly 30-40% of macrocyclic drugs manage to bridge the gap between small-molecule permeability and the target specificity of biologics¹¹. Some macrocyclic drugs have been approved by regulatory authorities, including the immunosuppressant cyclosporine¹² and the hepatitis C virus (HCV) NS3/4 A protease inhibitor simeprevir¹³, demonstrating the potential of macrocycles in drug development^11,14–17.

However, rational design of macrocycles faces numerous challenges^11,18. Membrane permeability is a critical determinant of whether a drug can reach intracellular targets and achieve oral administration^19,20. The membrane permeability test of Macrocyclic Compounds is time-consuming and costly, and it is difficult to carry out high throughput²¹. Notably, cyclic peptides and non-peptidic macrocycles exhibit significant differences in pharmaceutical properties. Cyclic peptides typically exhibit poor cell membrane permeability and metabolic stability due to polar amide bonds in the peptide backbone, which represent a major obstacle to oral administration. In contrast, non-peptidic macrocycles, unburdened by polar backbones, more frequently exhibit favorable oral bioavailability²². Nevertheless, accurate prediction of membrane permeability for non-peptidic macrocycles remains highly challenging. This kind of compound has great flexibility, and its conformation is affected by ring strain, intramolecular hydrogen bonds and transannular interactions. It may also have the characteristic of “molecular chameleon”-changing different conformation in different polar environments to shield polar groups^23,24.

Artificial intelligence has shown strong progress in predicting drug–drug interactions (DDI) and drug–target interactions (DTI)^15,25,26. Graph Neural Networks (GNNs) have become mainstream methods for property prediction^27,28. While early models focused on node features, subsequent studies like D-MPNN²⁹ demonstrated the importance of message passing along chemical bonds. Advanced architectures such as R-MAT³⁰ and MolCLR³¹ have further added self-attention and contrast learning to capture long-range dependencies and learn more robust representations. In the study of macrocycles, deep learning has recently shown promise for cyclic peptides. For example, Multi_CycGT³² and MultiCycPermea³³ have been developed to integrate multimodal features, including sequence motifs and graphs, to predict permeability. However, these advancements have not yet been effectively applied to non-peptide macrocycles. Unlike cyclic peptides, which often share defined backbone motifs, non-peptide macrocycles exhibit higher scaffold diversity and physicochemical profiles that lie bRo5^34,35. Standard GNNs trained on common small-molecule datasets often fail to generalize to this specific chemical space due to domain shift³⁶, while the complex interplay between macrocyclic rigidity and adaptive conformational behavior poses modeling challenges that general-purpose architectures have not addressed well^37,38. Zhang et al proposed Multi_DDPP³⁹  which integrates multisource data for cyclic peptides and macrocycles via knowledge distillation and Swing Range, but the framework is limited to qualitative classification and provides insufficient quantitative regression guidance for lead optimization.

Data resources have been crucial for computational studies of non-peptidic macrocycles. Feng et al²² recently constructed the Non-peptidic Macrocycle Membrane Permeability Database (NPMMPD) with 5638 permeability measurements across 4216 compounds, covering structures from fully non-peptidic to semi-peptidic. By comparison, CycPeptMPDB focuses on cyclic peptides, containing data for 7991 highly polar peptidic macrocycles. While several deep learning models have been built using CycPeptMPDB⁴⁰, NPMMPD now provides a resource specifically suited for non-peptidic macrocycles. The challenge is developing prediction models that can fully exploit this dataset and capture the distinct structural features of non-peptidic macrocycles.

Here we present MEGPNM, a macrocycle-enhanced graph neural network tailored for membrane permeability prediction in non-peptidic macrocycles, as shown in Fig. 1. The model couples an edge-aware, multiscale attention encoder with Jumping Knowledge fusion to combine signals from different depths and uses a gated hybrid pooling head to integrate graph-level features across layers and scales. To make the predictions more interpretable, MEGPNM retains attention weights and links them to systematic fragmentation analyses. We evaluate the model on the effective-permeability subset of NPMMPD²² under both random and activity cliff splits, and compare it with descriptor-based machine-learning baselines and widely used deep-learning molecular models. Experiments show that MEGPNM outperforms descriptor-based and deep learning baselines across multiple data-splitting scenarios, and its attention weights help identify macrocyclic fragments relevant to permeability. These results indicate that reliable permeability prediction for non-peptidic macrocycles requires architectures tailored to macrocyclic chemistry.

Fig. 1. Overall architecture of MEGPNM for macrocycle membrane permeability prediction.

A Molecular feature encoding. B Multilayer edge-aware GAT layers. C JK fusion and pooling. D MultiScale hybrid fusion and gating aggregation. E Prediction head.

Results and discussion

Performance comparison of MEGPNM and baseline methods

MEGPNM was evaluated against 17 baseline models under three splitting strategies: random split, activity cliff split, and scaffold split. As shown in Table 1, MEGPNM achieved the best performance on the random split across all five metrics, obtaining the lowest RMSE of 0.463. The closest baselines were MolCLR and Multi_DDPP, with RMSEs of 0.487 and 0.496, respectively. Geometry-aware models such as SchNet and DimeNet outperformed most sequence-based and traditional baselines but did not match the top-ranked methods. Table 2 reports results on the activity cliff split, which is more challenging because it requires distinguishing structurally similar molecules that exhibit markedly different permeability. MEGPNM again obtained the lowest RMSE of 0.561, followed by KnoMol at 0.594 and Multi_DDPP at 0.618, and remained the best performer on the remaining metrics. Several graph- and pretraining-based baselines showed substantial degradation in this setting; for instance, GCN rose to an RMSE of 0.798, performing worse than the SVM baseline of 0.741, suggesting that conventional message-passing networks struggle to capture the subtle structural differences underlying activity cliffs. For the scaffold split shown in Table 3, MEGPNM again ranked first with an RMSE of 0.519, followed by Multi_DDPP at 0.529 and KnoMol at 0.552. DimeNet and SchNet outperformed most traditional and sequence-based baselines. MEGPNM also led in the remaining metrics across all three splits, indicating more robust generalization than the other methods under varying distributional conditions.

Table 1.

Model performance on random split dataset

method	RMSE(↓)	R²(↑)	CI(↑)	PCC(↑)	SCC(↑)
SVM	0.544	0.559	0.774	0.750	0.751
RandomForest	0.532	0.577	0.782	0.764	0.759
XGBoost	0.525	0.589	0.783	0.768	0.762
TextCNN	0.563	0.526	0.768	0.735	0.734
BiLSTM	0.542	0.562	0.781	0.759	0.753
Bert	0.586	0.487	0.755	0.702	0.700
GCN	0.543	0.559	0.776	0.750	0.746
GAT	0.513	0.607	0.800	0.781	0.793
GIN	0.540	0.564	0.780	0.760	0.759
ChemBerta	0.787	0.094	0.642	0.384	0.427
Unimol	0.681	0.308	0.717	0.608	0.615
MolCLR	0.487	0.646	0.806	0.810	0.813
R-MAT	0.550	0.549	0.780	0.753	0.762
KnoMol	0.528	0.582	0.804	0.792	0.798
Multi_DDPP	0.496	0.633	0.805	0.798	0.797
SchNet	0.523	0.591	0.788	0.776	0.778
DimeNet	0.516	0.602	0.789	0.777	0.784
MEGPNM	0.463	0.680	0.824	0.830	0.837

The best result is highlighted in bold.

Table 2.

Model Performance on Activity Cliff Split Dataset

method	RMSE(↓)	R²(↑)	CI(↑)	PCC(↑)	SCC(↑)
SVM	0.741	0.322	0.703	0.574	0.589
RandomForest	0.668	0.450	0.745	0.677	0.688
XGBoost	0.669	0.448	0.742	0.670	0.683
TextCNN	0.740	0.324	0.700	0.572	0.585
BiLSTM	0.665	0.454	0.736	0.675	0.669
Bert	0.762	0.283	0.700	0.561	0.563
GCN	0.798	0.214	0.677	0.497	0.512
GAT	0.690	0.413	0.731	0.633	0.659
GIN	0.712	0.375	0.715	0.613	0.611
ChemBerta	0.840	0.129	0.641	0.447	0.420
Unimol	0.780	0.250	0.697	0.548	0.562
MolCLR	0.652	0.477	0.759	0.701	0.714
R-MAT	0.702	0.392	0.718	0.632	0.628
KnoMol	0.594	0.564	0.790	0.761	0.777
Multi_DDPP	0.618	0.529	0.775	0.735	0.715
SchNet	0.651	0.478	0.757	0.693	0.712
DimeNet	0.685	0.421	0.737	0.657	0.674
MEGPNM	0.561	0.611	0.797	0.789	0.792

The best result is highlighted in bold.

Table 3.

Model Performance on Scaffold Split Dataset

method	RMSE(↓)	R²(↑)	CI(↑)	PCC(↑)	SCC(↑)
SVM	0.641	0.396	0.728	0.631	0.643
RandomForest	0.608	0.456	0.744	0.688	0.685
XGBoost	0.597	0.474	0.748	0.694	0.694
TextCNN	0.638	0.400	0.723	0.634	0.638
BiLSTM	0.601	0.468	0.751	0.696	0.691
Bert	0.658	0.362	0.713	0.620	0.608
GCN	0.652	0.374	0.727	0.625	0.645
GAT	0.605	0.460	0.753	0.690	0.707
GIN	0.583	0.499	0.759	0.713	0.718
ChemBerta	0.651	0.376	0.714	0.616	0.608
Unimol	0.658	0.362	0.725	0.612	0.638
MolCLR	0.604	0.463	0.748	0.683	0.687
R-MAT	0.681	0.316	0.700	0.578	0.588
KnoMol	0.552	0.551	0.775	0.752	0.750
Multi_DDPP	0.529	0.589	0.790	0.772	0.775
SchNet	0.597	0.474	0.753	0.694	0.699
DimeNet	0.585	0.496	0.762	0.708	0.724
MEGPNM	0.519	0.604	0.792	0.783	0.780

The best result is highlighted in bold.

To further evaluate the prediction accuracy and generalization ability of the model, we used a scatter plot and compared the predicted penetration rate value in the three cases of random, cliff and scaffold split with the experimental real value. Figure 2 shows the scatter plot of predicting the permeability value and the experimental real value in the three cases. The predicted value  approximately matches the experimental measurement value, and the data points are distributed along the diagonal reference line. The discrete patterns of the three split strategies are similar, and there is no obvious difference in the distribution. The visual results show that the predicted value is concentrated in the range of the penetration rate value, and there is no obvious systematic overvaluation or undervaluation in all three cases.

Fig. 2. Predicted versus experimental permeability values.

Scatter plots for the random split (left), activity cliff split (middle) and scaffold split (right) test sets; each point is one compound and the dashed line is y = x.

Ablation study

We performed ablation studies with five repeated experiments under the random, activity cliff aware, and scaffold split scenarios. Starting from the full MEGPNM model, we removed the multiscale hybrid module, edge features, gate control unit, and JK connections, respectively. We also replaced the proposed pooling strategy with average pooling, max pooling, sum pooling, and global attention pooling, as shown in Fig. 3.

Fig. 3. Ablation study of the MEGPNM components.

Results under the random split (top), activity cliff split (middle) and scaffold split (bottom); bars show the mean and error bars the standard deviation of n = 5 independent experiments.

Under the random split, among the component ablations, removing the multiscale hybrid module caused the largest decline, indicating its important role in molecular representation learning. Removing edge features, JK connections, or the gate control unit led to smaller decreases. For the pooling variants, average pooling caused the largest degradation in RMSE and R², while sum pooling was closest to the full model. Max pooling and global attention pooling also performed below MEGPNM, suggesting that the complete pooling design provides a more balanced molecular-level representation.

Under the activity-cliff-aware split, MEGPNM again performed best overall. Removing the gate control unit produced the largest decline R² among the component ablations. This suggests that adaptive feature gating may be useful when small structural changes are associated with large permeability shifts. Removing the multiscale hybrid module、edge features, and JK connections had a moderate effect. Among the pooling variants, average pooling and global attention pooling showed larger drops, whereas sum pooling remained the strongest single pooling choice but still underperformed the complete model.

Under the scaffold split, removing JK led to the most evident degradation among the component ablations, suggesting that edge features help improve generalization to unseen scaffolds. For pooling, global attention pooling showed the weakest overall performance, while max pooling was again the most competitive single pooling choice. Overall, these results indicate that MEGPNM's performance is supported by the combination of its message-passing components and its pooling design.

Ranking performance analysis

To assess the model’s ability to prioritize compounds by permeability, we ranked molecules by both the ground-truth and predicted permeability values, then grouped them into five quintiles. We used Sankey diagrams and confusion matrices to compare the rankings under the random split, the activity cliff split, and the scaffold split (Fig. 4).

Fig. 4. Ranking performance analysis.

Sankey diagrams illustrate the flow between true and predicted permeability quintiles under the random, activity cliff and scaffold splits, and heatmaps show the distribution of quintile assignments.

Under the random split, the confusion matrix showed strong diagonal dominance: 75 of 103 molecules were correctly assigned to the top quintile and 61 of 103 to the bottom, with the middle bins less accurate (44 of 102 in 40–60% and 55 of 102 in 60–80%). The Sankey diagram confirmed that errors occurred mainly between adjacent quintiles, while jumps across multiple intervals were rare. Under the activity cliff split, the diagonal pattern was retained but became weaker in the middle and upper ranges. Top quintile accuracy dropped to 64 of 103, and the 40–60% and 60–80% bins fell to 40 of 102 and 44 of 102. The bottom quintile remained relatively stable, with 66 of 103 molecules assigned correctly. The Sankey diagram showed a wider spread from the intermediate bins, but severe inversions between the two extremes remained very rare. Under the scaffold split, the diagonal pattern was preserved but further weakened in the middle bins. The top and bottom quintile accuracies were 61 of 103 and 62 of 103; the middle bins showed the weakest agreement, at 35 of 102 (40–60%) and 42 of 102 (60–80%); the 20–40% bin held at 40 of 102. As before, errors clustered in neighboring quintiles and cross-extreme misassignments were rare. Overall, MEGPNM preserved useful ranking information across the permeability range. Compounds at the two extremes were identified most reliably, while intermediate compounds were harder to rank, with degradation more evident under the activity cliff and scaffold splits, suggesting that structural discontinuity and scaffold-level generalization make prioritization more challenging.

Learned representation analysis

To assess whether the learned representation reflects the structure related to permeability, we use t-SNE⁴¹ to map molecules in three cases: random segmentation, active cliff segmentation, and scaffold split based on original input features and learned embedded vectors, as is shown in Fig. 5. Each point represents a molecule and is colored according to its permeability after logarithmic transformation. The lighter the color, the higher the permeability. In the original feature space (top row), the point distribution is scattered, and the color mixing is serious, indicating that the initial descriptor is not clear enough for the permeable organization. In the learned embeddings (bottow row) space becomes noticeably more organized. Molecules cluster more clearly according to permeability, and the colors transition more gradually with less mixing. Across all three splitting strategies, these results suggest that MEGPNM captures latent chemical representations that underlie permeability differences.

Fig. 5. t-SNE visualization of molecular representations.

Initial representations and final learned representations, before and after model training, under the random split, activity cliff split and scaffold split scenarios.

Performance of MEGPNM under cross-validation and external validation

To complement the regression analyses above, we further evaluated MEGPNM under 10-fold cross-validation and an external validation set (Fig. 6). For the cross-validation analysis, predictions were binarised at label = −6.0 and assessed using Accuracy (Acc), F1 score, Recall, Precision, and the area under the ROC curve (AUC). As summarized in Fig. 6, MEGPNM achieved the best performance across all five classification metrics, with an Accuracy of 0.871, F1 of 0.872, Recall of 0.883, Precision of 0.861, and AUC of 0.939. The closest baselines were KnoMol and Multi_DDPP, both reaching an Accuracy of 0.850 and an AUC of 0.925 and 0.929, respectively, followed by MolCLR (Acc 0.842, AUC 0.921). Transformer-based  models such as Bert performed the worst on most metrics, while traditional and graph-based baselines clustered in the 0.80–0.84 Accuracy range. The relatively small standard deviations further suggest that MEGPNM maintained stable performance across different folds.

Fig. 6. Performance of MEGPNM under cross-validation and external validation.

a–e Classification metrics from 10-fold cross-validation. For each model, the shaded area represents the kernel density of the 10 fold-level values, dots indicate individual folds, and the horizontal bar shows the mean ± s.d, with the central tick indicating the mean. f–j Regression metrics on the external validation set.

We then evaluated all models on an independent external validation set using the same five regression metrics. The training data consisted of more than 3000 molecules from Feng et al., while the external validation set contained 187 molecules from 10 independent literature sources, all of which were available from the swemacrocycledb database. As shown in Fig. 6, MEGPNM ranked first on all five metrics on the external validation set, achieving an RMSE of 0.750, an R² of 0.536, a CI of 0.787, a PCC of 0.756, and an SCC of 0.767. The closest competitor differed by metric. SchNet was the strongest baseline in terms of error and explained variance, yet its RMSE of 0.840 and R² of 0.418 still fell well short of MEGPNM. GCN led the baselines on the ranking and correlation metrics, reaching a CI of 0.761, a PCC of 0.725, and an SCC of 0.739, roughly 0.03 below MEGPNM in each case. Several other molecular representation models, including UniMol, Multi_DDPP, DimeNet, and GAT, were competitive on individual metrics, but none was best across the full set. The traditional machine-learning baselines lagged further behind: SVM, RandomForest, and XGBoost gave RMSEs of 1.015, 0.984, and 0.952, with corresponding R² values of only 0.151, 0.201, and 0.252. Overall, these results are consistent with the cross-validation findings regarding the generalization behavior of MEGPNM.

Molecular fragment and attention analysis

To interpret attention at the substructure level, we annotated each molecule in the random testset using BRICS, Bemis–Murcko scaffolds, and a macrocycle ring rule³⁸. Briefly, BRICS cuts each bond whose two end-atom environments match an allowed pair drawn from a predefined set of 16 environment labels (ring bonds are by design not cut); the standard (non-generic) Bemis–Murcko scaffold is obtained by retaining all ring systems and the linker atoms/bonds connecting them while removing peripheral substituents, with the original atom and bond types preserved; and the macrocycle rule additionally treats each ring with ≥10 atoms as a single fragment, providing an explicit ring-only feature. The fragment distribution, permeability ranges, and attention weights are summarized in Fig. 7. Due to the finer granularity of the fragmentation scheme, BRICS yielded the highest number of fragments, whereas the macrocycle rule and Bemis–Murcko scaffolds accounted for a significantly smaller proportion as illustrated in Fig. 7A. When fragments were categorized by their importance in Fig. 7B, we observed that Bemis–Murcko scaffolds were rarely prioritized by the model and were typically grouped into the others. In contrast, macrocycle fragments were more frequently identified among the top-ranked features. The BRICS fragments were numerous, so many were relegated to the “others” group. Despite these distributional differences, Fig. 7C demonstrates that all three schemes covered a broadly comparable range of permeability values. Fragments spanned the full log-permeability range from about −8.5 to −4.2, with the highest density concentrated in the mid-range.

Fig. 7. Model interpretation through structural fragmentation and attention analysis.

All panels derive from the random-split test set. A Distribution of fragmentation methods. B Fragment composition by attention-rank category. C Permeability distribution across fragment types. D The 15 fragments most often ranked in the model’s top 3, with associated permeability and attention. For each fragment, n is the number of independent compounds in which it was top ranked, printed beside the bar (n = 126, 121, 89, 74, 63, 39, 38, 37, 34, 31, 29, 27, 26, 24 and 21). Dots are means and error bars ± s.d. of the measured permeability across those compounds. E Attention-weighted visualization of four representative macrocyclic compounds with high-attention structural regions highlighted.

We examined the 15 fragments most frequently ranked among the model’s top-3 attributed substructures and summarized their structures, number of substructure, associated permeability levels, and attention weights (Fig. 7D). The two most frequently observed substructures occurred across the largest number of compounds but received comparatively low attention. A substantial subset of the top-ranked fragments originated from macrocycle-focused fragmentation rules, and these motifs exhibited in different permeability and attention patterns than the BRICS-derived fragments. Among these fragments, a short linear alkyl chain drew the closest attention despite occurring at only mid-range frequency. One possible reading is that the model places weight on aliphatic linker regions, which may influence local lipophilicity and conformational flexibility. That said, attention weights are model-specific and carry no causal interpretation. Nevertheless, attention weight was uncorrelated with prevalence across these fragments, indicating that the model may attend to chemically meaningful motifs rather than simply tracking fragment frequency^42–44.

To illustrate model interpretability, four macrocyclic compounds were visualized using attention-based fragment highlighting in Fig. 7E. For each molecule, the three highest attention fragments were highlighted in yellow, where darker shades indicate higher attention. Across these examples, attention is often focused on the macrocyclic scaffold and selected peripheral groups, including aromatic and aliphatic substituents, which may be related to polarity, conformational behavior, and local lipophilicity. These maps offer a qualitative view of the substructures that the model repeatedly emphasizes and provide practical hypotheses for macrocycle optimization.

Web server implementation

To facilitate practical application of MEGPNM in drug discovery, a user-friendly web server was developed and deployed at http://112.124.26.17:7014/MEGPNM (Fig. 8). To our knowledge, this represents the first publicly accessible platform specifically designed for membrane permeability prediction of non-peptidic macrocyclic compounds. The server accepts molecular input in SMILES format and supports both single-molecule queries and batch predictions for up to 100 molecules simultaneously. In addition to predicting membrane permeability, the web server provides 2D molecular structures, physicochemical properties and more.

Fig. 8. MEGPNM web server interface.

The platform predicts the membrane permeability of non-peptidic macrocycles and is accessible at http://112.124.26.17:7014/MEGPNM. The input panel (left) supports SMILES input along with worked examples and usage instructions, while the output panel (right) displays the predicted permeability, corresponding 2D chemical structures.

Conclusions

We presented MEGPNM to predict the membrane permeability of non-peptidic macrocycles. The model combines edge-aware attention with a Multiscale Jumping Knowledge fusion strategy. Across random, activity-cliff-aware, and scaffold-based splits, MEGPNM showed consistently strong performance compared with traditional machine learning models, sequence-based neural networks, GNNs, and pretrained molecular models, etc. An additional 10-fold cross-validation and external validation further supported the robustness of the proposed framework. The ablation results indicate that the multiscale representation module, readout strategy, edge features, gate control unit, and Jumping Knowledge connections make complementary contributions to model performance. The model also excels at ranking compounds; it effectively separates high-permeability molecules from low ones with few errors. Attention analysis highlights features such as aromatic substituents, linkers, and the macrocyclic scaffold, consistent with their effects on permeability. To assist in drug discovery, we deployed the model on a public web server. This tool provides quantitative predictions and structural visualizations to help researchers prioritize candidates.

However, this study has several limitations. We used permeability data from parallel artificial membrane assays, which provide a limited view of membrane permeability. In addition, although the current model incorporates chemically informative graph features, its primary representation remains based on SMILES-derived molecular topology and does not fully capture three-dimensional conformational information. The current graph feature representation may also benefit from further refinement. Moving forward, we plan to incorporate higher-quality conformational ensembles, solvent-aware descriptors, and more diverse macrocycle permeability datasets, and to further explore hybrid 2D/3D graph learning architectures. We anticipate that these improvements will better support permeability optimization efforts and ultimately aid in the design of orally bioavailable cyclic therapeutics.

Methods

Datasets

We obtained the dataset from the Non-peptide Macrocycle Membrane Permeability Database²², focusing on effective permeability ($\log P_{eff}$) as the target variable. This category was selected not only because it represents the largest available sample set of 3546 entries (accessed June 2025) but also due to its critical role in assessing the oral bioavailability of macrocycles. To ensure the reliability of the training data, we performed quality control on duplicate SMILES entries. Among the 3546 log${\mathrm{P}}_{\mathrm{eff}}$ records, 134 unique SMILES had duplicate measurements. For each duplicated SMILES group, the repeated measurements originated from the same source and assay protocol within NPMMPD. These duplicates showed good consistency, with a median standard deviation of 0.18 log units and 98.5% of duplicated groups falling within a 1.0-log-unit range. We therefore averaged the duplicate measurements, resulting in a final dataset of 3412 unique macrocyclic structures and preventing molecules with repeated records from being overrepresented during model training. To rigorously evaluate model performance, we employed three complementary data splitting strategies. The dataset was partitioned into training, validation, and test sets using three distinct strategies. The data was divided into training, validation, and test sets in a 7:1.5:1.5 ratio. First, a random split was used to assess performance under standard conditions, with samples assigned without structural constraints. Second, an activity cliff-based split was applied to evaluate the model’s sensitivity to molecular activity cliffs. Morgan fingerprints and Tanimoto coefficients were computed to quantify pairwise structural similarity, identifying pairs with high similarity yet substantial property deviations as cliff edges. These paired molecules were prioritized for distribution across the training and test sets to challenge the model. To strictly maintain the defined ratio, the remaining capacity in each subset was filled with unassigned molecules randomly selected after the initial allocation of cliff compounds. Third, a scaffold-based split was used to assess structural generalization by keeping molecules with the same Bemis–Murcko⁴⁵ scaffold within a single subset.

Network structure

We present MEGPNM, an enhanced graph neural network framework for predicting molecular properties. As illustrated in Fig. 1, the architecture comprises five distinct modules: (1) Molecular Feature Encoding; (2) Multiscale Edge-Aware GAT layer that processes local chemical environments; (3) Jumping Knowledge (JK) module for cross-layer feature aggregation; (4) JK-MultiScale Hybrid Pooling module that adaptively fuses structural features; and (5) Final prediction head.

Molecular feature encoding

SMILES strings were parsed with RDKit⁴⁶ and converted into input features, where atoms are treated as nodes and chemical bonds as edges. We encoded each node with a 110-dimensional atom feature vector and each edge with a 9-dimensional bond feature vector to capture basic chemical identity and connectivity patterns relevant to permeability prediction. The complete feature definitions and encoding details are provided in Table 4.

Table 4.

Atomic and bond features used for molecular graph construction

Type	Feature	Size	Description
atomic	Atom type	44	One-hot encoding for 44 atom types (e.g., C, N, O… Unknown)
atomic	Atom degree	11	Number of bonded neighbors
atomic	Hydrogens	11	Number of bonded hydrogens
atomic	Atom valence	11	Atom’s valence
atomic	Aromaticity	1	Whether the atom is aromatic
atomic	Formal charge	7	Formal charge (−3 to 3)
atomic	Hybridization	6	Hybridization type (e.g., SP, SP2, SP3)
atomic	Is in ring	1	Whether the atom is in a ring
atomic	Ring size Info	8	Ring sizes the atom belongs to (3–10 membered rings)
atomic	Chiral Info	4	Chiral tag (UNSPECIFIED, CW, CCW, OTHER)
atomic	Atomic number	1	Normalized atomic number
atomic	Atomic mass	1	Normalized atomic mass
atomic	Implicit valence	1	Normalized implicit valence
atomic	Is heteroatom	1	Whether it is a heteroatom (not C or H)
atomic	Estimated lone pair	1	Normalized estimate of lone pairs
atomic	H-inclusive atomic degree	1	Normalized total connections (degree + H count)
Bond	Bond type	4	Bond type (SINGLE, DOUBLE, TRIPLE, AROMATIC)
Bond	Conjugation	1	Whether the bond is conjugated
Bond	Is in ring	1	Whether the bond is in a ring
Bond	Stereochemistry	3	Bond stereochemistry (STEREONONE, STEREOZ, STEREOE)

Multilayer edge-aware graph attention

Unlike standard GAT⁴⁷, which usually overlooks bond information, our dual-pathway architecture explicitly integrates node and edge features. Formally, given a molecular graph $G=\left(V,E\right)$, where $V$ denotes the set of atom nodes and $E$ denotes the set of chemical bond edges, the node features ${\mathrm{h}}_i\in {\mathbb{R}}^{d_{in}}$ are updated through a multihead attention mechanism:

$${\mathrm{h}}_i^{\left(l+1\right)}={\parallel }_{k=1}^K\sigma \left({\sum }_j\in \mathcal{N}\left(i\right){\alpha }_{ij}^k{\mathrm{W}}^k{\mathrm{h}}_j^{\left(l\right)}\right)$$

where $K$ represents the number of attention heads, ${\alpha }_{ij}^k$ denotes the attention weight of the $k$-th head, ${\mathrm{W}}^k$ is a learnable parameter matrix, and $\sigma$ is the ELU activation function.

To extract features at multiple scales, edge features ${\mathrm{e}}_{ij}\in {\mathbb{R}}^{d_e}$ are processed through two parallel one-dimensional convolutional layers:

$$e_{ij}^{\left(s_1\right)}={\mathrm{Conv}1D}_{{\mathrm{s}}_1}\left({\mathrm{e}}_{ij}\right),{\mathrm{e}}_{ij}^{\left(s_2\right)}={\mathrm{Conv}1D}_{{\mathrm{s}}_2}\left({\mathrm{e}}_{ij}\right)$$

The edge features at both scales are integrated through concatenation and a fusion layer:

$$e_{ij}^{\mathrm{multi}}=\mathrm{ELU}\left(W_f\left[e_{ij}^{\left(s_1\right)}\mid \mid e_{ij}^{\left(s_2\right)}\right]\right)$$

These multiscale edge features are then aggregated to target nodes through a message-passing mechanism:

$${\mathrm{h}}_i^{\mathrm{edge}}=\frac{1}{\mid \mathcal{N}\left(i\right)\mid }{\sum }_{j\in \mathcal{N}\left(i\right)}{\mathrm{e}}_{ij}^{\mathrm{multi}}$$

The final node representation is obtained by concatenating node and edge-aggregated features, followed by MLP fusion:

$${\mathrm{h}}_i^{\mathrm{final}}=\mathrm{MLP}\left(\left[h_i^{\left(l+1\right)}\parallel h_i^{\mathrm{edge}}\right]\right)$$

This fusion module incorporates linear transformation, layer normalization, ELU activation, and dropout regularization.

Jumping knowledge cross-layer fusion and pooling

We use a Jumping Knowledge (JK) module to combine node representations from different GAT depths. Let ${\mathrm{H}}^{\left(l\right)}\in {\mathbb{R}}^{N\times d}$ denote all nodes’ feature matrix at layer $l$, where $N$ is the number of nodes and $d$ is the hidden size. We adopt the concatenation variant of JK and project the concatenated features back to d dimensions:

$${\mathrm{H}}^{JK}={\mathrm{W}}_{\mathrm{proj}}\left[{\mathrm{H}}^{\left(1\right)}∥\begin{array}{c}\hfill {\mathrm{H}}^{\left(2\right)}\hfill \end{array}∥\cdots \parallel {\mathrm{H}}^{\left(L\right)}\right]$$

where $\parallel$ denotes concatenation along the feature dimension and ${\mathrm{W}}_{\mathrm{proj}}$ is a learnable projection.

A graph-level representation is then obtained via Global Attention Pooling:

$${\alpha }_i={softmax}_i\left({MLP}_{\mathrm{gate}}\left({\mathrm{h}}_i^{JK}\right)\right),{\mathrm{g}}^{JK}={\sum }_{i=1}^N{\alpha }_i{\mathrm{h}}_i^{JK}$$

where ${\mathrm{h}}_i^{JK}$ is the $i$ -th node embedding and ${softmax}_i$ is taken over nodes.

To capture complementary signals across depths, we also apply Mean, Max, and Sum pooling to each layer output ${\mathrm{H}}^{\left(l\right)}$ :

$${\mathrm{g}}_{\mathrm{mean}}^{\left(l\right)}=\frac{1}{N}{\sum }_{i=1}^N{\mathrm{h}}_i^{\left(l\right)},{\mathrm{g}}_{\max }^{\left(l\right)}={\max }_{i=1,\dots ,N}{\mathrm{h}}_i^{\left(l\right)},{\mathrm{g}}_{\mathrm{sum}}^{\left(l\right)}={\sum }_{i=1}^N{\mathrm{h}}_i^{\left(l\right)}$$

For an $L$ -layer network, this yields $3L$ graph-level vectors, stacked as:

$$\mathrm{p}={\left\{{\mathrm{g}}_{\mathrm{mean}}^{\left(l\right)},{\mathrm{g}}_{\max }^{\left(l\right)},{\mathrm{g}}_{\mathrm{sum}}^{\left(l\right)}\right\}}_{l=1}^L\in {\mathbb{R}}^{3L\times d}$$

MultiScale hybrid fusion strategy

Generating a strong graph-level representation is key for molecular property prediction. We therefore fuse the Jumping Knowledge (JK) information with the set of multiscale pooled features using a simple gating mechanism. Let ${\mathrm{g}}^{JK}$ be the JK graph representation and let ${\mathrm{p}}_s\in {\mathbb{R}}^d$ denote the pooled feature vectors collected from all layers and pooling operators, with $s=1,\dots ,3L$. We compute a gate for each ${\mathrm{p}}_s$ by conditioning on ${\mathrm{g}}^{JK}$ :

$${\beta }_s=\sigma \left({MLP}_{\mathrm{gate}}\left(\left[{\mathrm{g}}^{JK}\parallel {\mathrm{p}}_s\right]\right)\right),s=1,\dots ,3L,$$

where $\sigma \left(\cdot \right)$ is the sigmoid function. The gated multiscale feature is then aggregated as

$${\mathrm{g}}^{\mathrm{fused}}={\mathrm{W}}_{\mathrm{out}}\left({\sum }_{s=1}^{3L}{\beta }_s\cdot {\mathrm{W}}_v{\mathrm{p}}_s\right),$$

with ${\mathrm{W}}_v$ and ${\mathrm{W}}_{\mathrm{out}}$ as learnable projections. Finally, we concatenate the JK representation and the fused feature to form the final graph representation:

$${\mathrm{g}}^{\mathrm{final}}=\left[{\mathrm{g}}^{JK}\parallel {\mathrm{g}}^{\mathrm{fused}}\right].$$

This fusion lets the model weigh layer-wise and pooling-specific signals differently for each molecule, rather than treating all scales as equally informative.

Final prediction head

The final graph representation ${\mathbf{g}}^{\mathrm{final}}\in {\mathbb{R}}^{2d}$ is passed to multilayer perceptron classifier for prediction:

$${\mathrm{h}}_1=\text{ELU}\left(\mathrm{Dropout}\left({\mathrm{W}}_1{\mathrm{g}}^{\mathrm{final}}\right)\right)$$

$${\mathrm{h}}_2=\text{ELU}\left(\mathrm{Dropout}\left({\mathrm{W}}_2{\mathrm{h}}_1\right)\right)$$

$$\widehat{y}={\mathrm{W}}_3{\mathrm{h}}_2$$

Evaluation metrics

To evaluate MEGPNM, we used five commonly used metrics⁴⁸: Root Mean Square Error, Coefficient of Determination, Concordance Index, Pearson Correlation Coefficient, and Spearman’s Rank Correlation Coefficient.

Root Mean Square Error (RMSE): RMSE measures the differences between true or predicted values.

$$\mathrm{RMSE}=\sqrt{\frac{1}{N}{\sum }_{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2}$$

where $N$ is the number of samples, $y_i$ is the experimental value, and ${\widehat{y}}_i$ is the predicted value.

Coefficient of Determination ($R^2$): $R^2$ represents the proportion of variance in the dependent variable that is predictable from the independent variables, indicating the goodness of fit.

$$R^2=1-\frac{{\sum }_{i=1}^N{\left(y_i-{\widehat{y}}_i\right)}^2}{{\sum }_{i=1}^N{\left(y_i-ȳ\right)}^2}$$

where $ȳ$ is the mean of the experimental values.

Concordance Index (CI): the CI measures the probability that the predicted order of two randomly selected compounds matches their actual order, serving as a robust metric for global ranking performance.

$$CI=\frac{1}{z}{\sum }_{y_i>y_j}h\left({\widehat{y}}_i-{\widehat{y}}_j\right)$$

where $h\left(x\right)$ is a step function (1 if $x>0$, 0.5 if $x=0$, else 0) and $Z$ is the total number of comparable pairs $\left(i,j\right)$ such that $y_i>y_j$.

Pearson Correlation Coefficient (PCC): PCC measures the linear correlation between predicted and observed values, ranging from -1 to 1. It reflects the model’s ability to capture linear dependencies.

$$\mathrm{PCC}=\frac{{\sum }_{i=1}^N\left(y_i-\overline{y}\right)\left({\widehat{y}}_i-\overline{\widehat{y}}\right)}{\sqrt{{\sum }_{i=1}^{\mathrm{N}}{\left(y_i-\overline{y}\right)}^2}\sqrt{{\sum }_{i=1}^N{\left({\widehat{y}}_i-\overline{\widehat{y}}\right)}^2}}$$

Spearman’s Rank Correlation Coefficient (SCC): SCC assesses the monotonic relationship based on the rank order of values. It is less sensitive to outliers and provides insight into the model’s ranking capability. The following closed-form expression holds when there are no tied ranks:

$$\mathrm{SCC}=1-\frac{6{\sum }_{i=1}^N{d}_i^2}{N\left(N^2-1\right)}$$

where $d_i=\text{rank}\left(y_i\right)-\text{rank}\left({\widehat{y}}_i\right)$ represents the difference between the ranks of the experimental and predicted values for the $i$-th sample. In practice, SCC is often computed as the Pearson correlation coefficient between the ranked variables to handle potential ties.

Implementation details

MEGPNM was implemented in Python 3.11 using PyTorch 2.4.0 and DGL 2.4.0 with CUDA 12.1. Molecular structures were processed with RDKit 2025.09.1, and NumPy 2.2.6, pandas 2.3.3, SciPy 1.16.0 and scikit-learn 1.7.2 were used for data handling and evaluation. All models were trained on NVIDIA GeForce RTX 4090 hardware. The training configuration and the complete environment specification are provided in the code repository.

Baselines

To comprehensively evaluate the performance of MEGPNM, 17 baseline methods were selected, spanning traditional machine learning, deep learning, graph neural networks, and pre-trained molecular models.

Traditional machine learning methods. Three classical algorithms were implemented using molecular fingerprints as input features: Support Vector Machine^49,50, Random Forest, and XGBoost^48,51. Morgan fingerprints with radius 2 and 2048 bits were generated using RDKit for feature representation.

Sequence-based deep learning methods⁵². Three neural network architectures processing SMILES strings were evaluated. TextCNN employs convolutional filters to extract local patterns from character-level SMILES representations. BiLSTM captures bidirectional sequential dependencies in SMILES through long short-term memory units. BERT (Bidirectional Encoder Representations from Transformers) utilizes self-attention mechanisms to learn contextualized molecular representations from SMILES sequences⁵³.

Graph neural networks⁵⁴. Three canonical GNN architectures operating on molecular graphs were compared. Graph Convolutional Network aggregates information from neighboring nodes through spectral graph convolutions. Graph Attention Network introduces attention mechanisms to weight neighbor contributions dynamically. Graph Isomorphism Network employs injective aggregation functions to distinguish different graph structures. In addition, two 3D GNN architectures' coordinates were considered: SchNet⁵⁵ uses continuous-filter convolutional layers to model local molecular correlations, while DimeNet further incorporates bond angles via directional message passing with spherical Bessel and spherical harmonic basis functions. DimeNet⁵⁶ introduces directional message passing to capture spatial directional information with spherical Bessel and spherical harmonic basis functions.

Pre-trained molecular models⁵⁷. Two models leveraging large-scale pre-training were included. ChemBERTa adapts the RoBERTa architecture for molecular SMILES, pre-trained on millions of compounds from PubChem and ZINC databases. Uni-Mol incorporates three-dimensional conformational information through pre-training on molecular geometries and atomic coordinates.

Recent advanced methods. Apart from Multi_DDPP introduced above, three state-of-the-art approaches proposed in recent years were evaluated. MolCLR employs contrastive learning with graph-level and motif-level augmentations to learn invariant molecular representations without requiring labeled data. R-MAT introduces relative position encoding and molecule-specific attention mechanisms to capture long-range dependencies in molecular graphs. KnoMol⁵⁸ integrates external chemical knowledge graphs with graph neural networks, incorporating expert knowledge about functional groups, reactions, and molecular properties to enhance prediction performance.

To ensure a fair comparison, all baseline models were evaluated using the same training, validation, and test partitions as MEGPNM. For the fingerprint-based machine learning baselines, including SVM, Random Forest, and XGBoost, the main model parameters were optimized on the validation set rather than using simple default settings. For neural network, graph-based, pretrained, and recent advanced baselines, we followed the recommended settings of the original methods or public implementations where available, with validation-based model selection or early stopping applied when appropriate. When default settings led to non-convergence or unstable performance, key training parameters were adjusted to obtain stable and reasonable baseline performance.

Author contributions

S.H. performed the experiments and drafted the manuscript. L.W. collected and curated the datasets. W.Y. reviewed and edited the manuscript. Q.Z. and F.Z. provided theoretical guidance for the study. All authors participated in the revision of the manuscript and approved the final version.

Peer review

Peer review information

Communications Chemistry thanks Vasanthanathan Poongavanam and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Funding

This work was supported by the National Natural Science Foundation of China (No. 62303355, 32400544).

Data availability

The dataset supporting this study is the Non-peptidic Macrocycle Membrane Permeability Database (NPMMPD) described in Feng et al.²², which is available at https://swemacrocycledb.com/ and https://doi.org/10.6084/m9.figshare.26964259. The primary source data underlying Figs. 2–7 are provided in supplementary data (source_data.xlsx).

Code availability

The source code and dataset of MEGPNM are available at https://github.com/heshida01/MEGPNM and permanently archived on Zenodo at https://doi.org/10.5281/zenodo.21730542⁵⁹. A public web server for predicting the membrane permeability of non-peptidic macrocyclic compounds is deployed at http://112.124.26.17:7014/MEGPNM.

Competing interests

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s42004-026-02194-1.