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Harmony addresses a critical geometric mismatch in current diffusion-based molecular docking models by explicitly incorporating the periodic nature of torsional angles into its noise schedule. This approach leverages harmonic potentials on a torus to provide frequency-aware inductive biases, significantly improving pose accuracy and physical validity for flexible protein-ligand complexes. The work demonstrates that aligning score parameterization with the underlying geometry of the diffusion process is a highly effective strategy for advancing computational drug discovery.
Harmonic Torsional Diffusion for Protein-Ligand Flexible Docking
arXiv:2608.20366v1 Announce Type: cross Abstract: Molecular docking requires reasoning jointly about ligand pose and protein flexibility. Most diffusion-based docking models predict torsional updates with generic Euclidean heads that ignore the periodic geometry of angular variables. This mismatch is especially limiting in flexible docking, where ligand conformations and pocket side chains co-adapt to form the bound complex. Here, we introduce Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking. Harmony parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle, whose noise-level dependence is supplied analytically by the heat semigroup of variance-exploding diffusion on the torus. This construction makes periodicity explicit and gives the model a frequency-aware inductive bias over rotameric motion. On the PDBBind benchmark, Harmony improves ligand pose accuracy and pocket all-atom reconstruction over recent flexible docking methods. On PoseBusters, it improves the physical validity of generated complexes. Case studies on EBNA1 and KRAS G12D illustrate the method's behavior on a polar and a shallow binding site, respectively. Together, these results indicate that aligning the score parameterization with the geometry of the diffusion process is a simple and effective lever for improving flexible docking.
Abstract:Molecular docking requires reasoning jointly about ligand pose and protein flexibility. Most diffusion-based docking models predict torsional updates with generic Euclidean heads that ignore the periodic geometry of angular variables. This mismatch is especially limiting in flexible docking, where ligand conformations and pocket side chains co-adapt to form the bound complex. Here, we introduce Harmony, a harmonic torsional diffusion framework for flexible protein-ligand docking. Harmony parameterizes ligand and side-chain torsional score fields as derivatives of learned harmonic potentials on the circle, whose noise-level dependence is supplied analytically by the heat semigroup of variance-exploding diffusion on the torus. This construction makes periodicity explicit and gives the model a frequency-aware inductive bias over rotameric motion. On the PDBBind benchmark, Harmony improves ligand pose accuracy and pocket all-atom reconstruction over recent flexible docking methods. On PoseBusters, it improves the physical validity of generated complexes. Case studies on EBNA1 and KRAS G12D illustrate the method's behavior on a polar and a shallow binding site, respectively. Together, these results indicate that aligning the score parameterization with the geometry of the diffusion process is a simple and effective lever for improving flexible docking.
Biomolecules (q-bio.BM); Machine Learning (cs.LG)
arXiv:2608.20366 [q-bio.BM]
(or arXiv:2608.20366v1 [q-bio.BM] for this version)
https://doi.org/10.48550/arXiv.2608.20366 Focus to learn more arXiv-issued DOI via DataCite
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