CryoEM map interpretation requires features that are spatially localized, consistent across samples, and informative across spatial scales. Most deep learning methods for map annotation extract features from fixed voxel grids. However, implicit neural representations (INRs) are able to model volumetric data as scale-agnostic, coordinate-conditioned functions. INRs are therefore attractive for cryoEM, but fitting a separate INR for each map is too expensive for large-scale feature extraction and produces representations that are not aligned across samples. We introduce Atelier, a self-supervised framework that amortizes INR fitting for reconstructed cryoEM maps. Pretrained on 5,439 Electron Microscopy Data Bank maps, Atelier is a transformer-based hypernetwork that generates high-fidelity reconstructions across a wide range of protein structures, including large multi-subunit assemblies. Beyond reconstruction, the INR generated by the pretrained transformer exposes a continuous, local feature field through its intermediate activations at any spatial query point, a property that voxel grid and patch-tokenizer architectures do not naturally provide. Used as auxiliary channels to a 3D nested U-Net annotation head trained from scratch, these coordinate-conditioned features improve performance on eight voxel-level property prediction tasks over a volume-only baseline. Our results demonstrate that amortized implicit neural representations are an effective primitive for geometry-aware analysis of cryoEM data.
Figures & tables
Figure 1: Overview. Atelier is a self-supervised framework for learning geometry-aware implicit neural representations of cryoEM density maps via hypernetworks. The generated representations expose local features at arbitrary spatial resolution, supporting downstream tasks on unseen protein structures.
Figure 2: Atelier architecture. (a) A cryoEM volume V occupies a (D,D,D) -shaped bounding box, split into non-overlapping patches of size (P,P,P) . Since the (D,D,D) volume is naturally sparse with most voxels being background (set to a value of 0 ), we collect the active patches containing non-background voxels into a batch and discard the rest. These patches are fed through a convolutional neural network that transforms each patch into a volume token. The volume tokens are passed into a transformer along with learnable weight tokens; 3D rotary positional embeddings inform the volume tokens of the patch that they came from. The contextualized weight tokens output by the transformer are then projected to the input volume-conditioned weight matrices θV of an INR decoder M , which can be queried at arbitrary spatial points in [0,1]3 to produce a reconstructed volume V . Density map of EMDB-0406 [ 37 ] visualized with ChimeraX. (b) The INR naturally exposes an interface for fine-grained, coordinate-conditioned feature extraction. At inference, the transformer Hφ produces weight matrices θV that parameterize the INR MθV . For any query coordinate x∈[0,1]3 , we extract the post-activation hidden states from each of the K INR layers (pink) and stack them into a query-conditioned feature fV,x∈RH×K . Because x is continuous, features can be queried at sub-voxel resolution and are spatially localized to the geometry around x without interpolation.
Figure 3: Atelier successfully generalizes to unseen volumes. Here we show ground truth (orange) and INR-rendered (blue) volumes for four representative samples in the test set, as well as the Fourier shell correlation curves between them. We also show close ups for the predicted densities overlaid over ground truth atomic models to demonstrate that Atelier is able to reconstruct near atomic-level detail. Note the biological diversity of structures; from left to right, the structures are a membrane-bound enzyme (EMDB-25368 [ 46 ] ), a nanobody bound to an HIV envelope glycoprotein (EMDB-23480 [ 47 ] ), a nucleosome–kinetochore complex (EMDB-7293 [ 48 ] ), and a fully assembled TCR/CD3/pMHC immune-recognition complex (EMDB-28571 [ 45 ] ).
Figure 4: Atelier generates meaningful local continuous features. (a) After pretraining, Atelier is able to generate local features invariant to global symmetries due to its geometrically-driven pretraining task in two structures from Figure 3 . Box denotes minimum, quartiles, and maximum. (b) PyMol visualization of the same two structures evaluated in part (a), with atoms colored by trilinearly interpolating voxel features projected and scaled to [0,1]3 via PCA. Observe in the nucleosome (EMDB-7293) that the histones (center, green) primarily occupy a different color space than the surrounding DNA (purple) and centromere protein (upper left, teal). In the TCR/CD3/pMHC complex (EMDB-28571), there is considerably less variation within chains than across chains. Note, for example, the consistent coloring of the transmembrane region (bottom, purple).
layer
trained near/far ratio
untrained near/far ratio
layer 1
18.6 [13.7, 29.9]
1.01 [0.98, 1.02]
layer 2
25.1 [16.3, 38.3]
0.99 [0.93, 1.03]
layer 3
34.4 [23.6, 39.9]
0.99 [0.96, 1.03]
layer 4
29.3 [17.7, 38.4]
1.00 [0.98, 1.03]
Table 1: Per-layer median near/far average corruption effect (see Equation ( 3 )) over 16 holdout volumes (95% bootstrap confidence interval) for trained and untrained Atelier model. For the trained model, perturbations local to a point change intermediate activations significantly more than distant perturbations, while for the untrained model, local and distant perturbations have nearly identical effect. This indicates that Atelier activations capture local information, and that this locality is learned.
classification (balanced accuracy ↑ )
regression (relative error ↓ )
network input
sec. struc.
amino
mol. type
mol. class.
hydro.
abs. SASA
rel. SASA
B-fact.
volume alone
0.729
0.207
0.232
0.903
0.806
0.475
0.425
0.369
w/ coarse feats.
0.788
0.249
0.296
0.974
0.761
0.397
0.357
0.381
w/ rand. feats.
0.755
0.231
0.283
0.968
0.762
0.392
0.338
0.399
w/ fine feats.
0.797
0.235
0.300
0.976
0.752
0.386
0.331
0.363
Table 2: Comparison on property prediction performance on the test set for (a) vanilla EMNUSS that takes the single-channel volume alone as input, (b) EMNUSS with inputs augmented with coarse features as additional channels, and (c) EMNUSS with inputs augmented with fine features as extra channels. Metrics are averaged over all labeled voxels in the test set; a more detailed, per-volume statistical analysis is reported in § B.4 . Augmentation with fine features outperforms the volume-alone model in eight out of eight tasks, and outperforms the coarse model in seven out of eight tasks.
Figure 5: Illustration of the family of four complexes compared in Table 3 .
comparison
fine feature cosine similarity between volumes (mean ± std.)
base vs. same
0.949 ± 0.059
base vs. homolog
0.926 ± 0.095
base vs. different
0.774 ± 0.321
Table 3: Cosine similarities between Atelier fine features at corresponding coordinates between four different structures (mean ± std. over 80 sampled points). The results suggest that at corresponding locations, the activations for more similar structures are more similar than those of distantly related structures, even after spatial alignment. As negative controls, we also computed the cosine similarities between the 80 points in the base structure and the same 80 points in a completely unrelated decoy volume (EMDB-28571, a TCR/CD3 complex, cosine similarities 0.450 ± 0.417, as well as computing the cosine similarity between a base point and one mismatched point each from the same/homologous/different structures (0.021 ± 0.441).
Appendix figures & tables4 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 6: Illustration of the effect of our denoising method on four uncurated cryoEM volumes. By thresholding out the “dust” present in raw deposited maps, it becomes straightforward for the tokenizer component of Atelier to only tokenize patches containing real signal.
Figure 7: The transformer-only ablation architecture. (a) As an ablation, we train a transformer-only model that directly maps per-patch volume tokens to patch reconstructions through a learnable linear projection. (b) Coarse patch-level features can be extracted by returning the transformed volume token corresponding to the patch px containing a query point x . Note that all query points within the same patch will have the same coarse feature.
network input
sec. struc.
amino
mol. type
mol. class.
volume alone
0.607
0.186
0.223
0.756
w/ coarse feats.
0.681
0.227
0.293
0.940
w/ rand. feats
0.675
0.205
0.272
0.935
w/ fine feats.
0.705
0.217
0.294
0.950
Appendix
Table 4: Matthews correlation coefficient (MCC ↑ ) on the classification tasks from Table 2 . Metrics are averaged over all labeled voxels in the test set.
Task
Comparison
p (Wilcoxon)
p (Holm–Bonferroni)
Win rate
Hodges–Lehmann Effect (95% CI)
1
sec. struc.
fine > coarse
2.89×10−13 (****)
2.31×10−12 (****)
0.642
+0.0092 , [0.0069, 0.0115]
2
sec. struc.
fine > random
2.13×10−80 (****)
3.41×10−79 (****)
0.869
+0.0366 , [0.0343, 0.0389]
3
sec. struc.
fine > volume alone
1.78×10−102 (****)
3.56×10−101 (****)
0.938
+0.0612 , [0.0575, 0.0651]
4
amino
fine > coarse
3.78×10−56 (****)
4.54×10−55 (****)
0.212
−0.0123 , [ − 0.0138, − 0.0109]
5
amino
fine > random
5.73×10−05 (****)
1.72×10−04 (***)
0.527
+0.0026 , [0.0013, 0.0040]
6
amino
fine > volume alone
1.31×10−100 (****)
2.50×10−99 (****)
0.954
+0.0267 , [0.0255, 0.0279]
Appendix
Table 5: Per-volume comparison on fine Atelier features against baselines. We see that for amino acid prediction, coarse significantly outperforms fine (row 4, note the negative effect size), while for B-factor, fine does not significantly outperform volume-alone (row 24). For all other comparisons, the improvement is modest but significant, supporting the efficacy of Atelier-derived features.
Despite the growing availability of cryo-electron microscopy (cryo-EM) density maps, effectively leveraging them for protein representation remains challenging. First, current methods lack a general-purpose protein pretraining framework tailored for cryo-EM density maps, designed for protein-related property prediction. Second, existing approaches typically partition density maps into local box regions and model them independently, overlooking interactions across boxes which are essential for capturing global structural context in cryo-EM density map. To address these challenges, we propose CryoProt, a protein pretraining framework designed for cryo-EM density maps. CryoProt introduces a Map Encoder based on multi-head latent attention (MLA), where box-level representations interact through a shared latent space, enabling explicit modeling of cross-box dependencies within the density map. Furthermore, we adopt a multi-task pretraining strategy to learn generalizable representations that can be effectively transferred to diverse downstream tasks, such as protein flexibility prediction, where cryo-EM density maps are not required and can be inferred implicitly by the pretrained model. Experimental results demonstrate that CryoProt consistently outperforms existing state-of-the-art methods across multiple benchmarks, achieving up to 12% improvement over the best-performing baselines, highlighting the importance of modeling cross-box interactions in cryo-EM data. The source code is publicly available at https://anonymous.4open.science/r/CryoProt.
Dan Luo, Xuan Lin, Peng Zhou +4
College of Computer Science and Electronic Engineering, Hunan University · School of Computer Science, Xiangtan University
Understanding biomolecular function requires characterizing three-dimensional structure and conformational variability, for which cryogenic electron microscopy (cryo-EM) is a powerful tool. Cryo-EM produces noisy two-dimensional particle images in which molecular structure, particle pose, and imaging conditions are jointly encoded. Recovering biological information from these observations spans inverse problems including pose estimation, heterogeneity analysis, and reconstruction. These tasks are usually addressed independently despite shared protein structure and image formation, motivating a common representation across inverse problems. Since biologically meaningful differences may be spatially localized, we study self-distillation with complementary global and masked patch objectives. Because experimental dataset discrimination can reflect acquisition-specific cues, we develop controlled synthetic and experimental evaluations and find that structural discrimination benefits from dense spatial features. We introduce the EMber family of vision transformers, pre-trained on >50 million experimental particle images from 214 EMPIAR datasets together with simulated projections from 268,000 molecular assemblies. EMber improves upon existing methods at conformational and compositional discrimination by 14.85 and 14.26 percentage points, estimates conformational populations to within 1.59pp error with a linear probe, and produces particle assignments yielding reference-quality reconstructions in fewer epochs. We demonstrate how to learn representations that capture biological information for use across multiple cryo-EM inverse problems.
Nithin Chalapathi, Theo Sternlieb, Ethan Han +4
University of California, Berkeley · Flatiron Institute · University of Maryland, College Park
We present a geometry-aware method for heterogeneous single-particle cryogenic electron microscopy (cryo-EM) reconstruction that predicts atomic backbone conformations. To incorporate protein-structure priors, we represent the backbone as a graph and use a graph neural network (GNN) autodecoder that maps per-image latent variables to 3D displacements of a template conformation. The objective combines a data-discrepancy term based on a differentiable cryo-EM forward model with geometric regularization, and it supports unknown orientations via ellipsoidal support lifting (ESL) pose estimation. On synthetic datasets derived from molecular dynamics trajectories, the proposed GNN achieves higher accuracy compared to a multilayer perceptron (MLP) of comparable size, highlighting the benefits of a geometry-informed inductive bias.
Jonathan Krook, Axel Janson, Joakim Andén +2
KTH Royal Institute of Technology · Harvard University Department of Mathematics School of Engineering and Applied Sciences