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Mixture of neural fields for heterogeneous reconstruction in cryo-EM
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Proposes Hydra, an ab initio cryo-EM heterogeneous reconstruction method that models compositional and conformational heterogeneity jointly using a mixture of K neural fields trained with a likelihood-based loss and autodecoding.
Problem
Cryo-EM reconstruction of datasets mixing multiple protein species with continuous conformational variability, requiring joint inference of pose, class, and conformation without upstream poses.
Approach
Represent the set of structures as arising from one of K neural fields (each a conformation manifold parameterized by a latent code), with a mixture-model negative log-likelihood over class scores, latent codes, and poses, optimized via autodecoding with hierarchical pose search followed by SGD.
Key results
- On tomotwin3 with K=3, Hydra achieves ARI 1.00 and best per-image FSC on 6id1 and 4cr2-level metrics versus DRGN-AI (ARI 0.59) and CryoDRGN2 (ARI 0.36).
- On the ribosplike dataset, Hydra (K=3) reaches ARI 0.997 and per-image FSC 0.414, versus CryoDRGN2 0.399 and CryoSPARC 0.344 and DRGN-AI 0.207.
- On the experimental RyR dataset, Hydra with K=4 separates three protein complexes (RyR, p97, CIII) plus a junk class, which DRGN-AI fails to do.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use a mixture of neural fields (K=3) instead of a single neural field | DRGN-AI-style ab initio reconstruction · tomotwin3 | ARI: 0.59 -> 1.00 | Helped |
| Use a mixture of neural fields (K=3) instead of a single neural field | DRGN-AI-style ab initio reconstruction · tomotwin3, PDB 6up6 | Per-image FSC: 0.0242 ± 0.003 -> 0.25 ± 0.03 | Helped |
| Use a mixture of neural fields (K=3) instead of a single neural field | DRGN-AI-style ab initio reconstruction · tomotwin3, PDB 6id1 | Per-image FSC: 0.040 ± 0.005 -> 0.394 ± 0.001 | Helped |
| Use a mixture of neural fields (K=3) instead of a single neural field | DRGN-AI-style ab initio reconstruction · tomotwin3, PDB 4cr2 | Per-image FSC: 0.042 ± 0.004 -> 0.367 ± 0.001 | Helped |
| Use K=5 rather than K=3 neural fields (ablation) | Hydra · tomotwin3 | ARI: 1.00 -> 1.00 | No clear effect |
| Use K=5 rather than K=3 neural fields (ablation) | Hydra · tomotwin3, PDB 6id1 | Per-image FSC: 0.394 ± 0.001 -> 0.396 ± 0.001 | No clear effect |
| Use K=5 rather than K=3 neural fields (ablation) | Hydra · tomotwin3, PDB 4cr2 | Per-image FSC: 0.367 ± 0.001 -> 0.367 ± 0.001 | No clear effect |
| Use K=5 rather than K=3 neural fields (ablation) | Hydra · tomotwin3, PDB 6up6 | Per-image FSC: 0.25 ± 0.03 -> 0.25 ± 0.03 | No clear effect |
| Use Hydra's mixture-of-fields reconstruction rather than single-field DRGN-AI | Ab initio reconstruction · ribosplike | Img-FSC: 0.207 -> 0.414 | Helped |
| Use Hydra's mixture-of-fields reconstruction rather than single-field DRGN-AI | Ab initio reconstruction · ribosplike | Pose Err.: 45.379 -> 1.070 | Helped |
| Use Hydra's mixture-of-fields reconstruction rather than CryoDRGN2 | Ab initio reconstruction · ribosplike | Img-FSC: 0.399 -> 0.414 | Helped |
| Use Hydra's mixture-of-fields reconstruction rather than CryoSPARC | Ab initio reconstruction · ribosplike | ARI: 0.972 -> 0.997 | Helped |
Surprising findings
- Over-parameterized K=5 on tomotwin3 leaves 2 of 5 classes empty at convergence while still achieving perfect classification.
- A consensus-then-fixed-pose DRGN-AI workflow fails to recover non-RyR densities, showing sequential strategies miss compositional heterogeneity.
Limitations
- Requires specifying the number of classes K in advance; over-parameterization leaves empty classes.
- Latent dimension d must be the same across all classes.
- Expensive hierarchical pose search and multi-GPU compute; evaluated mainly on synthetic data plus one experimental dataset.
Experimental setup
Datasets: tomotwin3 (synthetic, constructed from TomoTwin PDB entries 6up6, 6id1, 4cr2) ribosplike (synthetic, from spliceosome, 80S ribosome, SARS-CoV-2 spike) experimental red blood cell lysate ryanodine receptor dataset (EMPIAR CTF source EMPIAR-11247)
Benchmarks: tomotwin3 ribosplike experimental ryanodine receptor dataset
Metrics: adjusted Rand index per-image FSC rotation error translation error resolution at 0.5 FSC
Baselines: DRGN-AI CryoDRGN2 CryoSPARC RELION
Builds on: DRGN-AI cryoDRGN cryoSPARC HyperNeRF
Closest papers by meaning
- Reconstructing Heterogeneous Biomolecules via Hierarchical Gaussian Mixtures and Part Discovery (NeurIPS 2025 · similarity 0.92)
- cryoSPHERE: Single-Particle HEterogeneous REconstruction from cryo EM (ICLR 2025 · similarity 0.92)
- Multiscale guidance of protein structure prediction with heterogeneous cryo-EM data (NeurIPS 2025 · similarity 0.91)
- CryoBench: Diverse and challenging datasets for the heterogeneity problem in cryo-EM (NeurIPS 2024 · similarity 0.91)
- CryoFM: A Flow-based Foundation Model for Cryo-EM Densities (ICLR 2025 · similarity 0.90)
- CryoSPIN: Improving Ab-Initio Cryo-EM Reconstruction with Semi-Amortized Pose Inference (NeurIPS 2024 · similarity 0.89)
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