Blending experimental electron density information to protein-ligand interaction

Seonghyun Park; Shuan Chen; Jun Jin Choong; Noboru Kuno; Gyubok Lee; Kaushalya Madhawa; Keisuke Ozawa; Hikaru Shindo

cs.LGOct 10, 2026

Blending experimental electron density information to protein-ligand interaction

Authors: Seonghyun Park, Shuan Chen, Jun Jin Choong, Noboru Kuno, Gyubok Lee, Kaushalya Madhawa, Keisuke Ozawa, Hikaru Shindo, +1 more

Organizations: KAIST · SB Intuitions

Abstract

Machine learning models for protein-ligand interactions commonly rely on atomic coordinates, which are constructed by fitting molecular models to experimental electron-density maps. However, most models represent each complex as a single fitted structure, which can omit information about conformational heterogeneity, positional uncertainty, and local density support for individual atoms at binding interfaces. To fill this gap, we present CoDE, a Coordinate and Density Encoder, pre-trained on experimental density maps. We represent each binding site on a shared three-dimensional voxel grid combining atomic occupancy, experimental electron density, and its gradient magnitude. Using approximately 100K curated complexes, we pre-train a channel-wise vision transformer to jointly reconstruct masked atomic and density channels, learning a representation that integrates structural and experimental information. We evaluate the frozen encoder on two downstream tasks: (i) binding-affinity regression under leakage-controlled splits and (ii) pocket-conditioned ligand generation. Across these settings, CoDE improves over an identically pre-trained coordinate-only encoder and remains competitive with task-specific baselines, showing that density complements fitted atomic coordinates for protein-ligand interaction modeling and that the density-blended representation is useful for structure-based ligand generation.

Figures & tables

Figure 1: Overview of pre-training and downstream transfers. Each protein–ligand complex is voxelized into 13 channels: seven ligand and four pocket heavy-atom occupancy channels, plus experimental density and its gradient magnitude. A Channel-ViT is trained to reconstruct masked regions. For downstream transfer, the frozen encoder is used with a regressor for binding-affinity regression, or fused with a generator for pocket-conditioned ligand generation.

			Test (N=1320)			CL3 filtered Test (N=733)
Input	Method	Pre.	Pearson r $\uparrow$	Spearman $\rho$ $\uparrow$	RMSE $\downarrow$	Pearson r $\uparrow$	Spearman $\rho$ $\uparrow$	RMSE $\downarrow$
Seq.	DeepDTA	✗	0.535 $\,{\scriptstyle\pm\,0.022}$	0.500 $\,{\scriptstyle\pm\,0.023}$	1.510 $\,{\scriptstyle\pm\,0.026}$	0.513 $\,{\scriptstyle\pm\,0.026}$	0.481 $\,{\scriptstyle\pm\,0.022}$	1.505 $\,{\scriptstyle\pm\,0.028}$
	MolTrans	✗	0.494 $\,{\scriptstyle\pm\,0.030}$	0.461 $\,{\scriptstyle\pm\,0.026}$	1.567 $\,{\scriptstyle\pm\,0.056}$	0.415 $\,{\scriptstyle\pm\,0.131}$	0.404 $\,{\scriptstyle\pm\,0.116}$	1.585 $\,{\scriptstyle\pm\,0.076}$
	HonestAffinity	✓	0.472 $\,{\scriptstyle\pm\,0.040}$	0.459 $\,{\scriptstyle\pm\,0.046}$	1.582 $\,{\scriptstyle\pm\,0.034}$	0.466 $\,{\scriptstyle\pm\,0.030}$	0.436 $\,{\scriptstyle\pm\,0.030}$	1.563 $\,{\scriptstyle\pm\,0.034}$
	Nesso-1 †	✓	0.670	0.663	1.410	0.673	0.659	1.367
Struc.	HBGSA	✗	0.567 $\,{\scriptstyle\pm\,0.016}$	0.542 $\,{\scriptstyle\pm\,0.022}$	1.703 $\,{\scriptstyle\pm\,0.191}$	0.568 $\,{\scriptstyle\pm\,0.015}$	0.548 $\,{\scriptstyle\pm\,0.011}$	1.586 $\,{\scriptstyle\pm\,0.201}$

Table 1: Binding-affinity prediction on LP-PDBBind test and CL3-filtered test sets. Seq. and Struc. denote sequence and structure inputs; structural inputs include coordinates and their chemical features. Results are averaged over five seeds. Affinity-leaked cases are marked with

\dagger

, included for context only. Bold and underlining indicate the best and second-best results; overlapping intervals are marked together. N/A denotes unavailable metrics, and Pre. denotes pre-training.

Panel of Figure 2 — Figure 2: Structural uncertainty in representations and affinity prediction. 2(a) Decoding structure uncertainty. B-factors at complex, residue, and atom levels are decoded from the frozen representation of the CL3 test complexes. DeepDTA and Nesso-1 appear only at the complex level, since their representations are not tied to residue and atom levels. 2(b) Binding-affinity improvement. We split the test complexes into three complex contact B-factor bins ( $<20$ , $[20,30)$ , $\geq 30$ Å 2 ), and show the CoDE $-$ CoE Spearman gain. Results are averaged over five seeds, and points are placed at bin medians. The gray curve is the cumulative distribution of the complex contact B-factor.

Design choices	Pearson r $\uparrow$	Spearman $\rho$ $\uparrow$	RMSE $\downarrow$
CoDE (Ours)	0.667 $\,{\scriptstyle\pm\,0.005}$	0.638 $\,{\scriptstyle\pm\,0.006}$	1.314 $\,{\scriptstyle\pm\,0.017}$
- w.o. D , G ( CoE )	0.620 $\,{\scriptstyle\pm\,0.010}$	0.572 $\,{\scriptstyle\pm\,0.011}$	1.401 $\,{\scriptstyle\pm\,0.030}$
- CoE + D recon.	0.597 $\,{\scriptstyle\pm\,0.021}$	0.562 $\,{\scriptstyle\pm\,0.015}$	1.421 $\,{\scriptstyle\pm\,0.048}$
- w.o. D channel	0.652 $\,{\scriptstyle\pm\,0.005}$	0.621 $\,{\scriptstyle\pm\,0.005}$	1.326 $\,{\scriptstyle\pm\,0.010}$
- w.o. G channel	0.644 $\,{\scriptstyle\pm\,0.008}$	0.605 $\,{\scriptstyle\pm\,0.006}$	1.347 $\,{\scriptstyle\pm\,0.016}$
- w. noisy D,G	0.627 $\,{\scriptstyle\pm\,0.008}$	0.586 $\,{\scriptstyle\pm\,0.010}$	1.380 $\,{\scriptstyle\pm\,0.035}$

Table 2: Design choice results . Bold marks best, D and G denote density and gradmag.

		Vina evaluation								Sample quality
		Score $\downarrow$		Min $\downarrow$		Dock $\downarrow$		High aff. % $\uparrow$		QED $\uparrow$		SA $\uparrow$		Div. $\uparrow$		# atoms / mol
Method	$n$	Avg.	Med.	Avg.	Med.	Avg.	Med.	Avg.	Med.	Avg.	Med.	Avg.	Med.	Avg.	Med.	Avg.	Med.
Reference	79	-6.21	-6.10	-6.66	-6.15	-7.32	-6.99	-	-	0.46	0.46	0.72	0.75	-	-	22.8	21.0
AR	7,655	-5.76	-5.58	-6.16	-5.85	-6.73	-6.54	41.8	37.0	0.50	0.50	0.63	0.62	0.71	0.71	17.2	16.0
Pocket2Mol	7,772	-5.06	-4.78	-6.47	-5.90	-7.27	-6.79	51.2	51.0	0.57	0.57	0.74	0.75	0.72	0.78	18.5	16.0
DiffSBDD	7,720	-2.70	-4.62	-4.89	-5.41	-6.71	-6.78	41.3	36.4	0.49	0.50	0.63	0.62	0.80	0.80	20.2	20.0

Table 3: Pocket-conditioned ligand generation results on the CrossDocked2020 benchmark for 79 test pockets with experimental density maps. Vina evaluation metrics are taken over all of the generated molecules as in prior works. High aff. denotes the per-pocket percentage of the generated molecules with a better Vina docking score than the reference, aggregated over pockets, and

n

denotes the number of valid molecules, counted as distinct per pocket for VoxBind variants.

Figure 3: Mean (left) and median (right) Vina docking scores for generated molecules over 79 test pockets with experimental density maps, sorted by the CoDE Vina docking score. CoDE achieves better mean and median Vina docking scores than VoxBind for 66% and 63% of the pockets.

Panel of Figure 4 — Figure 4: 4(a) Qualitative examples of the generated ligands . For pocket 5LIU , the best Vina-scoring ligand from each method is shown, with its docking score at the bottom right. 4(b) Median Vina docking score by the number of heavy atoms , with the distribution of generated ligand sizes at the bottom right. Docking scores do not simply become better proportionally to the molecule size, yet VoxBind + CoDE lowers them across atom counts. 4(c) Novelty against the reference ligands , measured by molecule-level and scaffold-level novelty and nearest-neighbor similarity.

Panel of Figure 5 — Figure 5: PoseCheck evaluation of generated molecule poses. Method colors are consistent across panels, with reference ligands shown in gray. 5(a) Strain energy distributions shown by the empirical cumulative distribution function. 5(b) Median strain energy as a function of the number of heavy atoms. 5(c) Number of steric clashes. Boxes denote the interquartile range, center lines denote the medians, whiskers extend to 1.5 times the interquartile range, and outliers are shown as individual points. 5(d) Median re-docking RMSD. Labels above the bars indicate the percentage of poses with RMSD within 2 Å, and the gray horizontal line marks the reference median of 2.69 Å. 5(e) Jensen-Shannon distance (JSD) to reference ligands for atom types, heavy-atom pair distances, bond lengths, ring sizes, and ring counts.

Figure 6: Rigid fragment consistency results. Median rigid-fragment RMSD between generated and force-field-relaxed pose after fragment-wise alignment, grouped by the number of heavy atoms. Boxes indicate the interquartile range, horizontal lines denote medians, and whiskers extend to 1.5 times the interquartile range. Lower RMSD indicates local geometry closer to a relaxed pose.

Figure 7: Chemical validity by PoseBusters , split by category (colors) with all-passed rate labeled; axis starts at 50%.

Appendix figures & tables29 assets

Supplementary material from the paper’s appendix.

Appendix

Dataset	Source size	Used after preprocessing	Role
PLINDER	449,383 systems (1,357,906 instances)	112,000 / 100 / -	Encoder pre-training
PDBBind v2020	19,443 complexes	12,674 voxelized complexes	Source of affinity-labelled complexes
LP-PDBBind	18,795 split-assigned complexes	3,850 / 817 / 1,320	Affinity regression
CASF-2016	285 complexes	- / - / 92	Clean held-out affinity evaluation
CrossDocked2020	22.5M poses (processed into 99,881 / / 100)	78,512 / 100 / 79	Pocket-conditioned ligand generation

Appendix

Table 4: Datasets used in this work. Split counts are reported as train/validation/test.

PLINDER
All annotated ligand instances	1357906
X-ray diffraction	1046290
Proper ligand; excluding ions, artifacts, and cofactors	300276
Valid and RDKit-loadable	289986
6–50 ligand heavy atoms	259509
Non-covalent	197369

Appendix

Table 5: Dataset preprocessing. Counts are cumulative. PLINDER counts refer to ligand instances, whereas PDBBind counts refer to complexes.

Encoder
Patch size	$8^{3}$ voxels (2 Å), 512 patches per group
Tokens	1536 (3 groups $\times$ 512)
Width / depth / heads	640 / 18 / 10
MLP ratio / activation	4 / GELU
Dropout	0.1
Positional embedding	learnable, shared across groups, plus a learnable group embedding

Appendix

Table 6: CoDE hyperparameters. Pre-training and affinity-probing settings of the encoder behind the main affinity results.

Figure 8: Similarity to the test reference ligand. Each generated molecule is compared with the crystal ligand of its pocket. The per-pocket mean (left) and median (middle) of the ECFP4 Tanimoto similarity are averaged over pockets. On the right is the percentage of molecules whose Bemis–Murcko scaffold equals the reference’s. The dashed line marks 0.093, the mean similarity of the 79 crystal ligands to one another, which is the level of two unrelated ligands on this fingerprint.

			CL1 filtered (N=1166)			CL2 filtered (N=1149)
Input	Method	Pre.	Pearson r	Spearman $\rho$	RMSE $\downarrow$	Pearson r	Spearman $\rho$	RMSE $\downarrow$
Seq.	DeepDTA	✗	0.554 $\,{\scriptstyle\pm\,0.008}$	0.508 $\,{\scriptstyle\pm\,0.009}$	1.493 $\,{\scriptstyle\pm\,0.008}$	0.541 $\,{\scriptstyle\pm\,0.013}$	0.495 $\,{\scriptstyle\pm\,0.006}$	1.491 $\,{\scriptstyle\pm\,0.018}$
	MolTrans	✗	0.499 $\,{\scriptstyle\pm\,0.036}$	0.467 $\,{\scriptstyle\pm\,0.034}$	1.564 $\,{\scriptstyle\pm\,0.051}$	0.513 $\,{\scriptstyle\pm\,0.027}$	0.478 $\,{\scriptstyle\pm\,0.026}$	1.528 $\,{\scriptstyle\pm\,0.040}$
	HonestAffinity	✓	0.477 $\,{\scriptstyle\pm\,0.025}$	0.453 $\,{\scriptstyle\pm\,0.025}$	1.598 $\,{\scriptstyle\pm\,0.020}$	0.483 $\,{\scriptstyle\pm\,0.033}$	0.450 $\,{\scriptstyle\pm\,0.034}$	1.580 $\,{\scriptstyle\pm\,0.032}$
	Nesso-1 †	✓	0.703	0.694	1.367	0.707	0.698	1.354
Struc.	HBGSA	✗	0.554 $\,{\scriptstyle\pm\,0.029}$	0.537 $\,{\scriptstyle\pm\,0.017}$	1.628 $\,{\scriptstyle\pm\,0.169}$	0.567 $\,{\scriptstyle\pm\,0.021}$	0.541 $\,{\scriptstyle\pm\,0.015}$	1.953 $\,{\scriptstyle\pm\,0.653}$

Appendix

Table 7: LP-PDBBind binding-affinity prediction on the CL1-filtered and CL2-filtered test sets. Results are averaged over five seeds, with zero-shot scorers reported with a single prediction

			CASF-2016 clean held-out (N = 92)
Input	Method	Pre.	Pearson r	90% CI	Spearman $\rho$	90% CI	RMSE $\downarrow$	90% CI
Seq.	DeepDTA	✗	0.520 $\,{\scriptstyle\pm\,0.054}$	$[0.39,\,0.63]$	0.488 $\,{\scriptstyle\pm\,0.037}$	$[0.35,\,0.61]$	1.735 $\,{\scriptstyle\pm\,0.058}$	$[1.57,\,1.93]$
	MolTrans	✗	0.529 $\,{\scriptstyle\pm\,0.026}$	$[0.41,\,0.63]$	0.500 $\,{\scriptstyle\pm\,0.035}$	$[0.37,\,0.61]$	1.732 $\,{\scriptstyle\pm\,0.034}$	$[1.57,\,1.93]$
	HonestAffinity	✓	0.477 $\,{\scriptstyle\pm\,0.071}$	$[0.36,\,0.58]$	0.432 $\,{\scriptstyle\pm\,0.074}$	$[0.30,\,0.55]$	1.777 $\,{\scriptstyle\pm\,0.085}$	$[1.63,\,1.95]$
	Nesso-1 †	✓	0.621	$[0.47,\,0.73]$	0.631	$[0.49,\,0.74]$	1.721	$[1.50,\,2.04]$
Struc.	HBGSA	✗	0.598 $\,{\scriptstyle\pm\,0.021}$	$[0.48,\,0.68]$	0.586 $\,{\scriptstyle\pm\,0.023}$	$[0.45,\,0.69]$	1.800 $\,{\scriptstyle\pm\,0.189}$	$[1.63,\,2.01]$

Appendix

Table 8: CASF-2016 held-out binding-affinity prediction. 90% confidence intervals (CI) using BCa are reported.

Figure 9: Mean and median Vina docking scores per pocket. of all generated molecules, with 79 test pockets having experimental density maps, sorted by the CoDE Vina docking score.

Figure 10: Median Vina docking scores per number of heavy atoms. of all generated molecules, with 79 test pockets having experimental density maps, sorted by the CoDE Vina docking score.

Figure 11: Mean and median Vina docking scores per pocket compared against each baseline with 79 test pockets having experimental density maps, sorted by the CoDE Vina docking score.

Panel of Figure 12 — Figure 12: Qualitative examples of the generated ligands. The lowest Vina docking-score ligand generated is shown, with its docking score at the bottom right. Pockets 5TJN , 1RS9 , 4KCQ , and 1COY are shown from left to right, from top to bottom.

Panel of Figure 13 — Figure 13: Generated macrocycles by maximum ring size. 13(a) Distribution of the largest SymmSSSR ring size per method. 13(b) Median Vina Dock score, UFF strain energy (logarithmic axis), steric clash count, and PoseBusters pass rate at each exact ring size, without binning or smoothing. Shading shows the 25th–75th percentiles and error bars 95% Wilson intervals. Sizes with fewer than five evaluations for a method and metric are omitted, breaking the lines.

Panel of Figure 14 — Figure 14: Strain energy of rotatable bonds. Strain energy is shown on a log scale, with the median value shown as a horizontal line and the box colored. The box represents the 25th-75th percentile, with outliers additionally plotted.

Figure 15: Protein–ligand interaction. Left side of each method represents metrics measured from the generated pose, while the right side of each method with slashes is measured from relaxed poses.

Panel of Figure 16 — Figure 16: Qualitative examples of the re-docked ligands. Pockets 5LIU , 1H0I , 1E8H , and 4U5S are shown from left to right, from top to bottom. Carbon atoms are colored with the method color. Re-docking RMSD and docked Vina score are each visualized in the bottom left and bottom right.

Figure 17: Heavy-atom element shares. Percentage of a set’s heavy atoms at each element, split across three linearly scaled panels so that rare elements are not flattened against carbon: C, then N and O, then F, P, S, and Cl.

Figure 18: Interatomic distance distributions. All heavy-atom pairs within a molecule closer than 12Å is shown above, and carbon–carbon pairs closer than 2Å below. Distances are computed from coordinates and elements alone, without bond perception. The dashed gray outline is the reference ligand, the number in the corner shows the JSD, and the vertical scale is shared.

Figure 19: Bond-length Jensen–Shannon distance per bond type (top) and detailed distribution (bottom) , for the eight bond types, the lower the value, the closer to the reference distribution. The dashed gray outline is the reference distribution, and the number in the corner is that panel’s JSD. Distances are scored in 0.005Å bins and drawn four bins at a time, and the vertical scale is shared.

Figure 20: Ring statistics, one column per method. Ring sizes, rings per molecule, and the aromatic fraction of a molecule’s atoms and of its rings, with the reference ligands repeated in gray.

Figure 21: Ring-size distribution. The three panels are scaled independently: six-membered rings, then three-, five-, and seven-membered rings, then four-, eight-, and nine-membered rings.

Figure 22: Rings per molecule. Percentage of a set’s molecules containing each number of rings, with the final bar pooling molecules with eight or more rings.

Figure 23: Aromatic content. Top: the fraction of a molecule’s heavy atoms that are aromatic. Bottom: the fraction of a molecule’s aromatic rings, meaning every bond of the ring is aromatic, computed over molecules with at least one ring. Both panels show the percentage of a set’s molecules in each fraction bin, with the reference ligands drawn alongside the methods.

Figure 24: Rigid fragment consistency expanded to more number of fragment size.

Figure 25: Rigid fragment size distribution from generated molecules.

Figure 26: PoseBusters validity per category.

Figure 27: PoseBusters validity upset plot. Relation between PoseBusters categories.

Figure 28: Diagnostic categories of PoseBusters ring non-flatness failures. Each bar splits the molecules of one method that fail non-aromatic_ring_non-flatness into the four categories, as a percentage of its failing molecules; segments narrower than about

5\%

of the axis are left unlabeled. The horizontal axis is stretched below

25\%

and compressed above it (dashed line), each part linear, so that the small causes remain legible. On the right are the number of failing molecules and the failure rate over all generated molecules; the AR bar rests on only four molecules.

Method	Before	After	All rings	(%)	QED	SA	logP	Diversity
	Ring fail (%)			Changed
AR	0.1	0.1	0.0	0.0	0.504 $\to$ 0.504	0.629 $\to$ 0.629	0.37 $\to$ 0.37	0.709 $\to$ 0.709
Pocket2Mol	1.1	1.0	0.5	0.1	0.566 $\to$ 0.566	0.743 $\to$ 0.743	1.64 $\to$ 1.64	0.724 $\to$ 0.724
DiffSBDD	1.4	1.4	0.2	0.0	0.495 $\to$ 0.495	0.628 $\to$ 0.628	1.07 $\to$ 1.07	0.796 $\to$ 0.796
DecompDiff	1.9	1.8	0.5	0.2	0.494 $\to$ 0.494	0.666 $\to$ 0.666	1.12 $\to$ 1.12	0.711 $\to$ 0.711
TargetDiff	9.5	3.7	0.7	5.9	0.493 $\to$ 0.497	0.608 $\to$ 0.615	1.36 $\to$ 1.36	0.747 $\to$ 0.748

Appendix

Table 9: Evaluation metrics before and after alternative aromatic reassignment. A failing six-membered ring with benzene-like geometry is reassigned as aromatic by modifying the ring bond orders and the attached hydrogen counts, while preserving the heavy-atom connectivity and coordinates. Rings bearing an exocyclic double bond are left unchanged in the procedure. Ring fail is the share of molecules failing non-aromatic_ring_non-flatness , re-derived ring by ring (rings whose outcome depends on the sign of the plane normal count as failing). All rings is the rate if rings with an exocyclic double bond are re-assigned as well. QED, SA, and logP are means over all molecules; diversity is averaged over pockets.

Fix	$n$	$\Delta$ Score	$\Delta$ Min	$\Delta$ Dock	Same pose	Gen. $\to$ dock (Å)
Ring bond-order / H assignment (used)	49	$+0.008$ ( $+0.000$ )	$-0.068$ ( $+0.000$ )	$-0.007$ ( $+0.000$ )	40/49	3.37 $\to$ 3.41
Including exocyclic bond-order changes	49	$+0.187$ ( $+0.241$ )	$+0.242$ ( $+0.252$ )	$+0.188$ ( $+0.231$ )	10/49	2.27 $\to$ 2.42

Appendix

Table 10: Vina before and after the re-assignment : We randomly selected 50 molecules for each of two reassignment procedures: one that preserves exocyclic bond orders and one that also modifies them. Each molecule was docked before and after reassignment.

\Delta

is after minus before in kcal/mol, mean (median); positive is worse. Same pose : the two docked poses lie within

0.5

Å RMSD. Gen.

\to

dock : median RMSD between the generated and the docked pose, before

\to

after.

Panel of Figure 29 — Figure 29: Alternative molecular reconstruction of the same generated heavy atom geometry. A molecule generated by CoDE for CDK6 . The yellow square is the best-fit plane of the failing ring, with each ring atom’s signed distance to it in Å; orange marks the hydrogens on the two ring carbons that were CH 2 . The faint sticks are the Vina-docked pose, $0.70$ Å RMSD from the generated pose and identical for both assignments. The two reconstructions differ in ring bond orders and hydrogen counts, while their heavy-atom coordinates are identical. For this example, the Vina-docked poses and the reported Vina scores are unchanged.

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Protein-ligand modeling underpins computational drug discovery and molecular design. Existing protein-ligand benchmarks typically evaluate whether a protein and ligand interact and how strongly they bind, through tasks such as binary binding prediction and affinity regression. However, these evaluations provide limited evidence of whether models can localize binding sites or identify the non-covalent interactions underlying molecular recognition. To address this gap, we introduce InteractBind, a large-scale protein-ligand dataset comprising approximately 100k protein-ligand pairs, together with a benchmark for fine-grained evaluation. The core fine-grained task is that of binding-site localization, which uses protein-residue and ligand-atom interaction maps spanning six major types of non-covalent interactions to assess whether model-derived interaction maps localize binding sites. InteractBind further includes binding affinity and protein similarity-controlled splits to support realistic generalization assessment. Using InteractBind, we evaluate eight existing sequence-based and interaction-aware models, assessing binary binding prediction and binding-site localization. Results reveal limited binding-site localization despite strong binary binding prediction, with marked variation across non-covalent interaction types. Overall, InteractBind establishes a benchmark paradigm that encourages the development of more interpretable and physically grounded protein-ligand models.

Abstract

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