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Ordered-water prediction for protein structures by flow matching, adding the crystal symmetry mates that coordinate waters at lattice contacts.
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A water molecule sitting in a crystal contact is held there by atoms that are not in the file. The deposited coordinates describe one asymmetric unit; the neighboring copies that pack against it and donate half of that water's hydrogen bonds exist only implicitly, in the space group and unit cell. A model trained on the asymmetric unit alone therefore learns from coordination that is systematically incomplete, and has no way to resolve those sites.
WaterFlow closes that gap by expanding the crystal. Symmetry mates within 8 Å enter the input graph as ordinary protein nodes — whole residues, ligands, ions and cofactors, but never mate waters, which would leak the label. Over that graph a flow-matching generator learns a velocity field transporting waters sampled from a protein-anchored prior onto crystallographic positions, and a second network scores each candidate so a user keeps only the confident ones. That expansion is what separates it from the prior state of the art, SuperWater: it lifts recall for waters within hydrogen-bonding distance of a lattice neighbor from 0.29 to 0.60, while barely moving the rest.
The model comes from the Wankowicz lab at Vanderbilt University with the Radial division of the Astera Institute, which funded the work, and crystallographic collaborators at Lawrence Berkeley National Laboratory, UCSF, SLAC and Los Alamos National Laboratory. It was posted as a preprint in August 2026 and is not yet peer reviewed.
Both stages share a geometric vector perceptron backbone: three message-passing layers over a protein-water graph with an 8 Å radius cutoff, 256 scalar and 64 vector hidden channels, conditioned on 1536-dimensional ESM3 residue embeddings broadcast to individual atoms. Each released checkpoint is about 16 MB. The generator trains with a flow-matching loss for 110 epochs; the confidence model warm-starts from its encoder and trains with binary cross-entropy against a target near 1 within 0.5 Å of a deposited water, decaying to zero by 1.5 Å.
Training structures come from PDB-REDO in two curations trading quantity against quality: LARGE, 67,272 structures of 50–500 residues at ≤3.0 Å and R-free ≤0.20, and SMALL, 22,318 at ≤2.0 Å. Splits are clustered by sequence with MMseqs2 and by fold with Foldseek — 15,573 and 5,424 clusters — with SMALL nested inside LARGE so one 698-structure holdout serves both. At a 1.0 Å acceptance radius WaterFlow reaches maximum precision/recall of 0.92/0.83 against 0.80/0.59 for SuperWater retrained on the same splits; tightening to 0.5 Å the gap widens to 0.88/0.64 against 0.73/0.33. At parity — as many predicted waters as deposited ones — F1 at 1.0 Å is 0.63 against 0.41.
It is intended as a solvent module: hydrating structures before docking or free-energy work, seeding molecular dynamics, and placing waters during crystallographic refinement. On a matched apo/ATP pair of the quorum-sensing regulator LuxO it recovers the bridging waters between ligand and protein to within 0.1 Å and reproduces the displacement of one water by the adenine ring. Added to an unrefined DJ-1 model its waters raise R-free from 0.200 to 0.227, a gap that refining their B-factors narrows to 0.016 and full refinement to 0.012.
The paper's second contribution measures what any such model can achieve. Clustering waters across isomorphous structures of lysozyme, endothiapepsin and carbonic anhydrase shows that up to 30% of deposited waters are not reproduced in otherwise identical structures, putting the best attainable F1 between 0.78 and 0.94 — so models here are limited by the consistency and diversity of the training structures, not by capacity. Filtering low-quality waters out of training did not help; adding distinct high-quality structures did. The stated limits are concrete: accuracy drops on predicted structures, whose different bond geometry the confidence model was never calibrated for; training covered proteins only, leaving nucleic acids and cryo-EM untested; and no B-factors or hydrogens are predicted. Code and both checkpoints are on GitHub with no license file attached; the supplementary dataset tables are archived on Zenodo under CC BY 4.0.
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