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# Informed protein–ligand docking via geodesic guidance in translational, rotational and torsional spaces | Nature Machine Intelligence

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Published: 15 August 2025
Informed protein–ligand docking via geodesic guidance in translational, rotational and torsional spaces
Raúl Miñán, Javier Gallardo, Álvaro Ciudad & Alexis Molina

Nature Machine Intelligence 
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1555–1560 (2025)Cite this article

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A preprint version of the article is available at arXiv.

Abstract

Molecular docking plays a crucial role in structure-based drug discovery, enabling the prediction of how small molecules interact with protein targets. Traditional docking methods rely on scoring functions and search heuristics, whereas recent generative approaches, such as DiffDock, leverage deep learning for pose prediction. However, blind-diffusion-based docking often struggles with binding site localization and pose accuracy, particularly in complex protein–ligand systems. This work introduces GeoDirDock (GDD), a guided diffusion approach to molecular docking that enhances the accuracy and physical plausibility of ligand docking predictions. GDD guides the denoising process of a diffusion model along geodesic paths within multiple spaces representing translational, rotational and torsional degrees of freedom. Our method leverages expert knowledge to direct the generative modelling process, specifically targeting desired protein–ligand interaction regions. We demonstrate that GDD outperforms existing blind docking methods in terms of root mean squared distance accuracy and physicochemical pose realism. Our results indicate that incorporating domain expertise into the diffusion process leads to more biologically relevant docking predictions. Additionally, we explore the potential of GDD as a template-based modelling tool for lead optimization in drug discovery through angle transfer in maximum common substructure docking, showcasing its capability to accurately predict ligand orientations for chemically similar compounds. Future applications in real-world drug discovery campaigns will naturally continue to refine and extend the utility of prior-informed diffusion docking methods.

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Main

In drug discovery, molecular docking is pivotal for probing interactions between molecules and specific protein cavities, also known as binding pockets1. These regions on protein surfaces are targets for docking algorithms, aiming to establish the most stable configurations of ligands, or ligand poses, for assessing potential drug–receptor interactions. Docking traditionally relies on empirical data from in vitro experiments, such as crystal structures and molecular dynamics simulations, to locate these cavities for molecular binding assessment. Renowned methods like Glide, Vina and rDock leverage physics-based scoring and a rich database of molecular interactions to navigate this process2,3,4.

Although traditional methods have long been a cornerstone in computational chemistry, the field experienced a paradigm shift with DiffDock5. This seminal contribution postulated molecular docking as a generative task, marking a substantially shift through the development of a diffusion method that operates, without a prior over the binding site location, across the various degrees of freedom inherent in molecular docking. However, limitations appear during prospective applications, due to its blind docking strategy. Directed docking, which uses expert knowledge or pocket prediction to identify binding regions, has demonstrated superior performance compared with blind docking6. Additionally, the use of ligand root mean squared distance (RMSD) as the sole performance metric has been contested for not fully capturing the ligand position accuracy, raising questions about the effectiveness of recent deep learning innovations in this field7,8.

In this work, we introduce GeoDirDock (GDD), a diffusion method that integrates expert knowledge into the diffusion process over translations, rotations and torsions, to direct the diffusion process towards a desired region of the protein structure. Our results show that this directed docking approach notably improves on blind docking methods, achieving close-to-ground-truth RMSD conformations in self-docking scenarios and demonstrating enhanced performance in both RMSD accuracy and physicochemical pose plausibility. Moreover, we validate the robustness of our approach through a maximum common substructure (MCS) docking test, highlighting its effective generalization across diverse and previously unseen ligand chemistries and showcasing practical applications in drug discovery and lead optimization.

Related work

Traditional prior-informed docking methods: traditional docking evaluates how likely molecules are to bind to specific areas of proteins, mainly focusing on binding pockets. These methods capitalize on data from crystal structures, literature and molecular dynamics simulations to set pose search parameters and find the most suitable docking positions, using physics-based scoring methods to measure molecular interactions1,9,10. However, the effectiveness of these methods largely relies on having access to high-quality data, which can be a limitation in cases where such data are scarce.

Diffusion-based molecular modelling: recent advancements in diffusion models have relied on the concept of blind docking, which does not rely on pre-existing receptor–ligand binding information. DiffDock, for example, replaces traditional methods with a denoising process that manipulates translations, rotations and torsion angles in a ${{\mathbb{T}}}^{3}\times {\rm{SO}}(3)\times {\rm{SO}}{(2)}^{m}$ diffusion space, evaluated using a confidence-scoring network. Ref. 11 approached the diffusion problem in R3, incorporating equivariant constraints across the entire space and using an equivariant graph neural network for scoring. Ref. 12 introduced contact prediction modules to direct the molecular diffusion process through the R3 manifold, assessing sample plausibility with invariant point attention.

Informed diffusion for directed docking. Most existing diffusion-based methods, including the ones discussed above, do not explicitly consider the precise location of the binding cavity. Despite the technical advancements in blind diffusion docking, these methods have not yet achieved the same level of effectiveness as traditional approaches. This gap has opened opportunities for developing methods that incorporate elements of traditional docking. To the best of our knowledge, the only method integrating the ${{\mathbb{T}}}^{3}\times {\rm{SO}}(3)\times {\rm{SO}}{(2)}^{m}$ diffusion process with targeted guidance to specific protein surface points is DiffDock-Pocket13 (hereafter referred to as DD-Pocket). This method not only adopts a more traditional approach to docking but also extends it by allowing flexibility in side chains.

Experiments

To assess our approach, we use the testing set from PDBBind proposed in ref. 14, applying a twofold evaluation strategy. First, we analyse the docking pose RMSD, focusing on the top-1 and top-5 poses by confidence for both apo and holo structures, and introduce mean squared error (MSE) as an additional metric to evaluate errors in rotation states and torsion angles (Supplementary Section C).

Second, we examine the physical plausibility of these docking poses using the PoseBusters suite7, providing insights into the realism of the predicted conformations. Furthermore, we explore the possibility of coupling GDD to a pocket prediction method to assess the performance of our method on a completely blind docking scenario.

Finally, we perform an additional evaluation to assess the capabilities of our method in real-world drug discovery scenarios and tasks such as virtual screening and structure-based drug design. To this end, we conduct two experiments using GDD as a template-based modelling tool.

Evaluation of docking poses

We evaluated GDD against DiffDock across various setups by comparing the RMSD of the generated poses with crystal structures and examining the convergence based on the number of denoising steps taken.

Initially, we tested GDD with translation guidance only (GDD-TR), mimicking conventional docking’s focus on specific geometric volumes. Results showed GDD-TR surpassing DiffDock across all metrics, achieving lower RMSD values in fewer steps and maintaining performance across both apo and holo receptor configurations, suggesting that targeted guidance enhances docking accuracy and efficiency (Table 1).

Table 1 RMSD performance comparison for holo and apo settings across docking methods, showing top-1 and top-5 prediction accuracies
Full size table

On extending guidance to include torsions and rotations, imposing a more substantial prior than translation alone, we anticipated improvements in the reconstruction of crystallographic structures. GDD-Full, informed across all three spaces, markedly outperformed both GDD-TR and DiffDock, recovering approximately 68% of poses within 2 Å of the reference, notably higher than with translation-only guidance. This comprehensive approach not only improved the pose accuracy but also maintained the trend of achieving optimal results in fewer steps with only a slight computational overhead, highlighting the efficacy of our method in enhancing docking precision and computational efficiency. Supplementary Section B provides more details regarding the runtime and memory requirements and Supplementary Sections C and G provides detailed MSE analyses for the torsion and rotation case and the visualized case, respectively.

Physical plausibility of informed diffusion poses

The PoseBusters evaluation (Table 2) reveals that GDD-Full outperforms GDD-TR and DiffDock in holo structures, demonstrating its superior accuracy in docking and re-docking tasks. This success highlights GDD-Full’s ability to align with the physical aspects of molecular docking, attributed to its comprehensive guidance across multiple spaces.

Table 2 Assessment of PoseBusters scores for holo and apo scenarios, comparing docking structure and re-docking accuracies across DiffDock and GDD methods
Full size table

By contrast, GDD-TR suffers a performance degradation in both holo and apo structures. This aligns with our hypothesis of full guidance being needed to reproduce physically plausible poses, as the main objective of translational guidance is the correct selection of the binding pocket, not the increment of physical plausibility of poses.

Compared with DiffDock-Pocket, all methods fall behind when considering apo structures. This gap in performance is due to DiffDock and GDD being rigid docking methods, which do not take into account the changes that can occur in the protein and that can play a crucial role in modelling binding processes13.

Coupling GDD to binding pocket prediction methods

To assess the performance of GDD in a completely blind setting, we couple GDD-TR with P2Rank15 and fpocket16, guiding the diffusion process towards the top predicted pocket for each method, and compare the results using the ground-truth one.

As shown in Fig. 1, using pocket detection tools also leads to fewer multimodal distributions for certain complexes, avoiding pockets that might not be of interest. However, when considering the entire PDBBind test set, we find that DiffDock obtains better performance, indicating that it might act as a better pocket predictor for the given data. Nevertheless, this opens an interesting venue for future work by using pocket prediction tools that are biased towards less probable pockets that might be of interest, such as cryptic sites that DiffDock or other pocket prediction methods might fail to explore.

Fig. 1: RMSD distributions and cumulative success rates of docking methods for Complex 6QR3.

Left: RMSD distribution of all generated poses for 6QR3 (N = 40). Statistics (min, Q1, median, Q3, max): DiffDock (1.49, 2.82, 13.20, 24.01, 28.38), fpocket (0.79, 1.82, 2.36, 2.89, 7.14), P2Rank (1.02, 1.72, 2.38, 5.04, 6.91) and transferred (1.22, 1.95, 2.55, 4.67, 7.34). For each box plot, boxes span from quartile 1 (Q1) to quartile 3 (Q3) and the fences span ±1.5× the interquartile range (Q3–Q1). Median and mean are displayed with continuous and dashed lines, respectively. Right: fraction of top hits with RMSD below given thresholds for the PDBBind test set (N = 373).

Full size image
GDD as a potential tool for template-based modelling

In the lead optimization phase of drug discovery, template-based modelling is crucial for assessing binding affinity changes among chemically similar compounds17. This approach involves using a single as a reference template to consistently maintain a shared topology and optimize the distinct molecular features. By leveraging structural information from known complexes, template-based modelling can improve the docking accuracy and guide ligand optimization (Fig. 2).

Fig. 2: RMSD and torsion-angle error distributions for top-1 BACE08 poses.

Top-1 predictions for BACE08 (protein choosen as docking system (PDB ID 6QR3) from the D3R Grand Challenge 4) for DiffDock (grey) and GDD-Tor (blue) compared with transferred ground truth (red).

Full size image

A key aspect of template-based modelling is the ability to transfer both binding site and binding mode information from the template molecules. To achieve the latter, we use MCS search between the template and target molecules, transferring the torsion angles associated with heavy atoms and leaving the rest uninformed.

First, we evaluate the ability of our method to generalize across structurally related compounds. For this, we conduct an experiment using a congeneric series derived from PDB ID 6QR3. Following a subset of the structures released in ref. 18, we select one protein–ligand complex as a template and use it to guide the docking of related ligands within the series, transferring both binding site and mode information by applying guidance to translation and torsion (GDD-TrTor).

As shown in Supplementary Fig. 4 and Table 3, GDD-TrTor demonstrates improved performance in both RMSD and torsion angles MSE over the uninformed process.

Table 3 Comparison of docking performance, showing RMSD and MSE metrics for top-1 and top-5 predictions between DiffDock and GDD-TrTor methods
Full size table
Angle transfer as a method for MCS docking

To isolate the effect of angle transfer, we perform another experiment in which we only apply torsion guidance (GDD-Tor). For this, we selected crystallized BACE structures from the D3R Grand Challenge 4 (ref. 19) and followed the same procedure, using previously identified templates for angle transfer.

As shown by the results in Table 4, this angle transfer already marks an improvement in both RMSD and torsion MSE. These preliminary results outline great potential for our method and we look to further develop this application and the corresponding benchmarks.

Table 4 Comparison of MCS docking performance, showing RMSD and MSE metrics for top-1 and top-5 predictions between DiffDock and GDD-Tor methods
Full size table
Conclusions and future work

In this study, we introduce GDD, a framework that enhances generative docking models through geodesic guidance. GDD notably improves the docking precision and boosts the physical plausibility of results compared with traditional blind docking methods like DiffDock. By incorporating guidance across translation, torsion and rotation dimensions, GDD outperforms both DiffDock and its translation-only variant, achieving precise docking poses with fewer computational steps. These results pose guided docking as a promising avenue for artificial-intelligence-enabled molecular docking, ensuring both efficiency and accuracy in molecular docking.

Future work would focus on improving in generalizability to completely unseen ligand and protein chemistries, thereby postulating GDD as a valuable tool for prospective docking campaigns. Similar to ligands, backbone and side chains can be modelled through angles in a similar hypertoroidal space. Therefore, we are keen on extending this algorithm towards the inclusion of protein flexibility in the docking procedure, aiming for a more realistic setting of the docking protocol. The incorporation of more realistic priors, in both backbone and side-chain angles, would also solve possible steric clashes between ligands and proteins, performing implicit induced-fit docking. Although more efforts are still required in proving that GDD is fully applicable in real-world scenarios, it provides a solid framework to guide diffusion-based docking methods, potentially enhancing performance and usability.

Methods

Our approach builds on the concept prevalent in traditional docking strategies, where specific geometric shapes like spheres or boxes demarcate potential binding areas, excluding the remainder of the protein structure. We refine this concept in DiffDock by directing incremental updates during the denoising procedure towards a targeted binding region and conformation.

We utilize a guided diffusion strategy, drawing inspiration from ref. 20, by introducing a guiding vector Vguide in place of a conventional trained classifier. This vector integrates domain expertise into the diffusion process by altering the update mechanism. The intensity of these alterations is controlled by the hyperparameter γ, allowing for dynamic adjustments based on the proximity and direct route to the target regions. This method ensures that the direction and magnitude of Vguide are precisely aligned with the distance and shortest path to the designated areas, optimizing the diffusion trajectory towards the desired binding site.

$${V}_{\rm{update}}=(1-\gamma ){V}_{\rm{DiffDock}}+\gamma {V}_{\rm{guide}},$$
(1)

where

$${V}_{\rm{guide}}=\alpha {v}_{\rm{dir}},$$
(2)

vdir is the vector tangent to the shortest path and α is the distance towards the selected centre or boundary region. Supplementary Section E provides a detailed analysis of the range of possible γ values.

Although implementing this method in R3 would be straightforward, DiffDock operates in a more complex space, $P={{\mathbb{T}}}^{3}\times{\rm{SO}}(3)$$\times {\rm{SO}}{(2)}^{m}$, to accurately reflect the degrees of freedom involved in molecular docking. Consequently, we calculate the shortest paths and distances within each component of this product space, effectively tailoring the diffusion process to this task.

Boundaries and geodesics

Shortest paths in ${{\mathbb{T}}}^{3}$ can easily be determined by leveraging straight lines and the geometry of a hypothetical sphere to effectively integrate binding pocket information. This approach helps mitigate the risk of selecting incorrect docking pockets, a prevalent issue in blind docking strategies that often leads to out-of-distribution errors6. The incorporation of this spherical model is instrumental in refining the selection process, enhancing the algorithm’s ability to direct the denoising process to given docking sites.

However, the challenge of ensuring the physical realism of docking poses—highlighted by concerns over steric clashes and distorted bond angles7—necessitates further refinement of our model. To address these issues, our method extends to the SO(3) and SO(2)m spaces, where we use geodesics to define the shortest paths. This approach is critical for accurately guiding our diffusion updates with Vguide vectors, ensuring that the docking poses are not only theoretically viable but also physically plausible. Supplementary Section A provides an in-depth explanation of how Vguide vectors are defined and integrated into the diffusion process.

Soft constraints

To balance the precision and flexibility of DiffDock, we implement measures to modulate the influence of guidance vectors, recognizing their potential to alter the model’s learned dynamics and impact performance within designated spatial regions. We introduce a dynamic adjustment of the guidance vector’s influence through a decreasing sigmoid schedule for the γ parameter, progressively diminishing its impact through the diffusion process. This ensures the initial guidance by expert knowledge gradually cedes to the model’s intrinsic optimization capabilities.

Moreover, we enable the consideration of multiple potential regions within the SO(3) and SO(2)m spaces, guiding updates towards the nearest boundary. Once within a targeted region, DiffDock is allowed autonomy in refining the rotation and torsion angles, unencumbered by external guidance. This dual-phase optimization strategy—global optimization guided by expert knowledge in early steps, followed by local, autonomous refinement by DiffDock—ensures a balance between adherence to biologically plausible paths and the discovery of optimal docking configurations.

Evaluation

To facilitate high-throughput evaluation without direct expert input for each sample, we use a fuzzing strategy, adjusting true labels to simulate expert knowledge. This involves creating guidance spheres for translation with a 7-Å radius around the ligand’s actual centre, directing vectors toward these spheres’ peripheries, and ceasing guidance on entrance. For rotation and torsion, we define regions around true angles, adjusted by a fuzzing factor η of 0.15, guiding vectors towards these adjusted regions and turning off guidance when they enter. This fuzzing approach, robust across radius and η settings, allows for an effective approximation of expert-directed docking (Supplementary Section D). Moreover, we perform an ablation test of different initial γ values (Supplementary Section E) and test the generalization capabilities of our algorithm (Supplementary Section F).

Data availability

The datasets used for this work are available as follows: PDBBind (http://pdbbind.org.cn/), PoseBusters (https://github.com/maabuu/posebusters), DockGen (https://github.com/gcorso/DiffDock) and D3R Grand Challenge 4 (www.drugdesigndata.org).

Code availability

All source code as well as instructions on how to run the code are available via GitHub at https://github.com/NBDsoftware/GDD and via Zenodo at https://doi.org/10.5281/zenodo.15755564 (ref. 21).

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Acknowledgements

We thank all members of Nostrum Biodiscovery for the help provided and insightful discussions.

Author information
Authors and Affiliations

Department of Artificial Intelligence, Nostrum Biodiscovery, Barcelona, Spain

Raúl Miñán, Álvaro Ciudad & Alexis Molina

Delft University of Technology, Delft, Netherlands

Javier Gallardo

KTH Institute of Technology, Stockholm, Sweden

Javier Gallardo

Contributions

J.G. and R.M. developed the model architecture and conducted the experiments. R.M. contributed to the dataset curation and preprocessing. R.M. implemented the evaluation framework and conducted benchmarking. J.G., R.M., Á.C. and A.M. conceived the project. Á.C. and A.M. supervised the research. R.M. and Á.C. wrote the manuscript. A.M. revised the final draft and provided corrections. All authors reviewed and approved the final manuscript.

Corresponding authors

Correspondence to Álvaro Ciudad or Alexis Molina.

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Competing interests

R.M., Á.C. and A.M. are employees at Nostrum Biodiscovery. J.G. performed this work during an internship at Nostrum Biodiscovery.

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Nature Machine Intelligence thanks Alex Morehead, Shigenori Tanaka and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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Supplementary information
Supplementary information

Supplementary Sections A–G, Figs. 1–13, Methods, Discussion and Results.

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Miñán, R., Gallardo, J., Ciudad, Á. et al. Informed protein–ligand docking via geodesic guidance in translational, rotational and torsional spaces. Nat Mach Intell 7, 1555–1560 (2025). https://doi.org/10.1038/s42256-025-01091-x

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