Learning from Hetero Density for Cryo-EM Protein Reconstruction

Xu Han; Chaozhuo Li; Xiaowei Yuan; Yuancheng Sun; Kang Liu; Qiwei Ye

cs.LGOct 8, 2026

Learning from Hetero Density for Cryo-EM Protein Reconstruction

Authors: Xu Han, Chaozhuo Li, Xiaowei Yuan, Yuancheng Sun, Kang Liu, Qiwei Ye

Organizations: University of Chinese Academy of Sciences, Beijing, China · Key Laboratory of Complex Systems Cognition and Decision, Institute of Automation, Chinese Academy of Sciences, Beijing, China · Beijing Academy of Artificial Intelligence, Beijing, China · Beijing University of Posts and Telecommunications, Beijing, China · Ant Group, China

Abstract

Reconstructing protein structures from cryo-electron microscopy (cryo-EM) maps is essential for understanding macromolecular assemblies. Although learning-based methods have improved protein reconstruction, information from hetero components remains underused. Our analysis finds both false predictions and reference protein sites near hetero components; filtering nearby candidates can improve or impair chain construction. We introduce CryoCue, a framework that uses hetero information to guide protein reconstruction. An anchor-supervised detector learns hetero representations across five component classes. Multiscale hetero features guide backbone localization, while predicted hetero candidates condition structure refinement through their class, confidence, and frame-relative geometry. Experiments show that CryoCue improves backbone localization near hetero components and achieves more accurate protein structure reconstruction.

Figures & tables

Figure 1: Hetero context in cryo-EM maps. A, Density assigned to protein and hetero using reference coordinates. B, Local contacts between protein and hetero components in reference structures; gray meshes show experimental density. C, Hetero prevalence and voxel counts across the sample dataset. M denotes million voxels.

Figure 2: Analysis of protein candidates near hetero components. a, Patterns of false protein candidates and protein support near hetero components. b, Effects of candidate filtering on chain construction, shown as improved, degraded, or unchanged.

Figure 3: Overview of CryoCue . a, Hetero-guided protein reconstruction. b, Anchor-supervised detection produces multiscale features and class predictions. c, Coarse attention and fine-scale gating condition backbone localization. d, Predicted hetero candidates condition refinement through their class, confidence, and geometry relative to evolving residue frames.

	Structure reconstruction				Density support	Connectivity
Method	TM-score $\uparrow$	lDDT $\uparrow$	Coverage (%) $\uparrow$	RMSD (Å) $\downarrow$	Q-score $\uparrow$	Break rate (%) $\downarrow$
EMProt	0.805	0.740	81.07	0.576	0.604	1.20
E3-CryoFold	0.711	0.512	67.05	1.085	0.369	8.72
ModelAngelo	0.728	0.658	73.22	0.592	0.613	2.61
EModelX	0.805	0.687	82.43	0.842	0.447	6.96
CryoCue (ours)	0.846	0.789	85.02	0.571	0.593	0.69

Table 1: Protein reconstruction performance. Results on the test set. Values are map-level means; bold indicates the best mean.

	Overall backbone		Hetero neighborhood		Protein–hetero contacts
Method	CA precision $\uparrow$	CA recall $\uparrow$	CA precision $\uparrow$	CA recall $\uparrow$	Precision $\uparrow$	Recall $\uparrow$
EMProt	96.534	82.675	93.035	86.181	85.646	73.993
E3-CryoFold	86.013	79.818	71.638	76.606	67.762	59.699
ModelAngelo	93.688	81.225	97.511	84.937	87.765	73.145
EModelX	92.946	83.557	75.846	86.832	71.419	64.636
CryoCue (ours)	96.897	85.693	96.271	89.883	86.396	77.877

Table 2: Backbone localization and protein–hetero contact. All scores are percentages; higher is better. Bold indicates the best mean among the compared methods.

	Structure reconstruction				Density	Connectivity
Method	TM-score $\uparrow$	lDDT $\uparrow$	Coverage (%) $\uparrow$	RMSD (Å) $\downarrow$	Q-score $\uparrow$	Break rate (%) $\downarrow$
Protein-only	0.780	0.711	77.44	0.609	0.602	1.54
Backbone fusion only	0.819	0.760	82.53	0.588	0.622	1.06
Full w/o anchor supervision	0.747	0.692	75.80	0.715	0.545	1.78
Full w/ fixed hetero geometry	0.840	0.782	84.54	0.573	0.596	0.75
Full model	0.846	0.789	85.02	0.571	0.593	0.69

Table 3: Ablation of hetero representation and conditioning. Variants isolate hetero fusion during backbone localization, anchor-based supervision, and dynamic frame-relative conditioning.

Figure 4: Hyperparameter sensitivity and inference efficiency. Left: TM-score under different candidate caps

K

and neighborhood radii

r

, with the other hyperparameter fixed. Right: end-to-end inference time across methods.

Figure 5: Case study of global reconstruction and recovery near a hetero component. a, Global reconstruction of 8IH5 (EMD-35440) by EMProt, ModelAngelo, and CryoCue; the highlighted region is enlarged below. b, Reconstruction near the corresponding hetero component. Magenta markers indicate unrecovered reference protein sites.

Appendix figures & tables13 assets

Supplementary material from the paper’s appendix.

Appendix

Step	Criteria
Database search	Single-particle cryo-EM maps in EMDB and electron-microscopy structures in RCSB, with reported resolution $\leq 4$ Å.
Pair eligibility	A released primary map, an official fitted EMD–PDB association, available map and coordinate files, and at least one protein chain.
Structure validation	Parseable required mmCIF fields and reliable component classification using the Chemical Component Dictionary (CCD) ( Westbrook et al., 2015 ) and entity/polymer metadata. Pairs with unresolved classification conflicts are excluded.
Raw-map quality	Complete downloads; MRC dimensions and voxel spacing consistent with official metadata.

Appendix

Table 4: Data collection and quality control. These checks determine pair eligibility; local label validity is handled separately in Appendix B.4 .

Split or test subset	Pairs	Grid crops
Training	17,820	185,373,427
Validation	300	3,543,489
Test	300	2,029,806

Appendix

Table 5: Dataset split sizes and complete stride-16 crop-grid counts. Grid counts include empty-density regions and boundary crops; they are not counts of independently sampled training examples.

Step	Operation
Coordinate alignment	Use MRC axis order, header origin, and grid starts to express voxels and fitted coordinates in the same physical frame.
Resampling	Resample to isotropic 1 Å spacing using cubic convolution ( $a=-0.5$ ), preserving map–coordinate alignment.
Normalization	Apply full-map quantile clipping and scaling, as defined below.
Input crops	Extract $48^{3}$ crops at stride 16. Zero-pad positions outside the map and exclude them from supervision.

Appendix

Table 6: Map preprocessing for the detector and backbone network.

Class	Definition	Anchor
Polymeric nucleic acid	Nucleotides assigned to nucleic acid polymers	C4 ′ per nucleotide residue
Glycan	Sugar residues, including NAG, MAN, and FUC	C1 per sugar residue
Nucleotide/cofactor	Free nucleotides and nucleotide-derived cofactors, including NAD/NADH, FAD/FMN, and SAM/SAH	C4 ′
Other ligand	Other reliably classified non-polymer ligands	Representative heavy atom
Lipid/detergent	Classified lipid and detergent components	Representative heavy atom

Appendix

Table 7: Hetero class definitions and supervision anchors. Named anchors must be uniquely present in the corresponding residue or component.

Split or test subset	Polymeric nucleic acid	Glycan	Nucleotide/cofactor	Other ligand	Lipid/detergent
Training	4,040	3,983	3,859	8,161	1,743
Validation	104	31	68	99	17
Test	110	32	53	98	21

Appendix

Table 8: Pair-level presence of the five hetero classes. A pair is counted once for each class present in its structural labels, so counts across classes are not additive.

Support class	Voxels	Share
Background	474,145,598,844	97.8487%
Protein backbone	3,256,567,203	0.6721%
Protein side chain	5,496,114,368	1.1342%
Polymeric nucleic acid	1,472,613,528	0.3039%
Glycan	50,586,134	0.01044%
Nucleotide/cofactor	9,619,500	0.00199%

Appendix

Table 9: Class composition of the masked structural-support census in the training split, before anchor-target restriction.

Quantity	Value
Analyzed map–structure pairs	1,868
Pairs with nonzero hetero-labeled voxels	1,458 (78.05%)
Protein-associated voxels / full grid	0.709909%
Hetero-associated voxels / full grid	0.116131%
Background voxels / full grid	99.173960%
Hetero / protein-plus-hetero voxels	14.06%

Appendix

Table 10: Full-map statistics for the 1,868-pair preliminary-analysis subset. Voxel fractions are pooled over complete map grids. The final three rows summarize residue-level proximity for 176,963 non-water, non-protein residues retained by the historical parser and are not five-class prevalence estimates.

Class	Pairs	Residues	FP only	FP + protein support	Protein support only	Neither	FP occurrences	TP occurrences
Nucleic acid	264	105,890	78.4%	1.5%	0.1%	19.9%	501,865	1,326
Glycan	396	14,330	72.9%	6.6%	0.6%	20.0%	68,320	910
Nucleotide/cofactor	273	1,172	21.2%	71.2%	6.9%	0.6%	6,881	1,143
Other ligand	751	7,114	50.2%	44.0%	2.6%	3.2%	42,118	4,021
Lipid/detergent	207	6,007	77.3%	20.0%	0.4%	2.3%	40,676	1,246

Appendix

Table 11: Protein candidate patterns near hetero components in the 1,362 audited cases. Percentages are pooled over residue neighborhoods within each analysis group. Protein support includes either a TP candidate or a reference protein site. FP and TP occurrences allow the same candidate to appear in overlapping neighborhoods. Rounding may cause small departures from 100%.

Class	Paired $n$	Win/loss	Net $\Delta$ TP	Removed states/map
Nucleic acid	102	84/17	+4,620	961
Glycan	172	96/70	+687	104
Nucleotide/cofactor	84	40/41	+200	34
Other ligand	357	185/158	+389	45
Lipid/detergent	111	65/44	+523	78

Appendix

Table 12: Effects of candidate filtering on chain construction for the hetero groups defined above. Win/loss reports the numbers of paired cases with increased or decreased C

\alpha

F 1 at 3 Å; paired

n

includes unchanged cases. Net

\Delta

TP is the total change in matched protein sites, and removed states/map is the mean number of filtered candidate states in each paired subset.

Stage	Feature shape	Operation
Input	$1\times 48^{3}$	Normalized density
Scale 1	$32\times 48^{3}$	Stem and local blocks
Scale 2	$64\times 24^{3}$	Downsampling and local blocks
Scale 4	$128\times 12^{3}$	Downsampling and local blocks
Scale 8	$256\times 6^{3}$	Bottleneck
Global context	$384\times 6^{3}$	10 Transformer blocks

Appendix

Table 13: Architecture of the hetero detector. Spatial scales are downsampling factors relative to the input crop.

Scale $s$	Protein $F_{s}^{p}$	Hetero $F_{s}^{h}$	Fusion
8	$256\times 6^{3}$	$256\times 6^{3}$	Global cross-attention
4	$128\times 12^{3}$	$128\times 12^{3}$	Window cross-attention
2	$64\times 24^{3}$	$64\times 24^{3}$	Gated convolution
1	$32\times 48^{3}$	$64\times 48^{3}$	Gated convolution

Appendix

Table 14: Multiscale hetero fusion in the backbone predictor. Shapes give channels and spatial dimensions for a

48^{3}

input crop.

Setting	Hetero detector	Backbone predictor	Amino acid predictor
GPUs	8	32	32
Per-device batch	32	16	16
Global batch size	256	512	512
Optimizer updates	225,170	95,231	95,231
Learning rate	$10^{-4}$	$10^{-4}$	$10^{-4}$
Warmup updates	1,000	500	500

Appendix

Table 15: Optimization settings for the voxel-stage models. Learning rates are peak values and training duration is measured in optimizer updates.

Class	Precision (%)	Recall (%)	F 1 (%)
Nucleic acid	95.71	63.08	76.04
Glycan	45.33	15.20	22.77
Nucleotide/cofactor	80.76	16.10	26.85
Other ligand	51.52	46.90	49.10
Lipid/detergent	15.15	13.13	14.07

Appendix

Table 16: Class-wise hetero detection performance. Precision, recall, and F 1 are reported for the five hetero classes.

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