Protein Graph Neural Networks for Heterogeneous Cryo-EM Reconstruction

Jonathan Krook; Axel Janson; Joakim Andén; Melanie Weber; Ozan Öktem

cs.CVFeb 25, 2026

Protein Graph Neural Networks for Heterogeneous Cryo-EM Reconstruction

Authors: Jonathan Krook, Axel Janson, Joakim Andén, Melanie Weber, Ozan Öktem

Organizations: KTH Royal Institute of Technology · Harvard University Department of Mathematics School of Engineering and Applied Sciences

Abstract

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.

Figures & tables

Figure 1: Principal overview of our method. A data point in the form of an EM image is indexed by a low dimensional variable, and then mapped via a GNN to a reconstructed conformation. Blue indicates components that are only used during optimization, where the deformed template is posed and compared to data, and regularization is added.

Panel of Figure 2 — Figure 2: Top: Closed and open conformations of ADK. Bottom: Heterogeneous conformations of NSP.

Figure 3: Histogram of ground truth RMSD values for all 102k conformations in the ADK dataset, before and after optimizing the GNN autodecoder with

\mathcal{R}_{2}

-regularization and ESL.

Panel of Figure 4 — Figure 4: Representative reconstruction. (a): Ground truth conformation. (b): Simulated cryo-EM image with randomized orientation. (c): Template conformation generated by AlphaFold 3, with a ground truth RMSD of 6.93 Å. (d): Final prediction by GNN autodecoder, with a ground truth RMSD of 1.85 Å.

		With $\mathcal{R}_{2}$	Without $\mathcal{R}_{2}$
ADK (ESL)	GNN	1.92	2.21
ADK (ESL)	MLP	1.95	2.94
ADK (Known poses)	GNN	1.09	1.44
ADK (Known poses)	MLP	1.24	2.30
NSP (Known poses)	GNN	2.08	2.38
NSP (Known poses)	MLP	2.37	3.32

Table 1: Final RMSD averages (Å).

Appendix figures & tables1 asset

Supplementary material from the paper’s appendix.

Appendix

Dataset	GNN				MLP
Dataset	$K$	$C$	$N$	Weights	$H$	$D$	Weights
ADK	16	16	16	35k	8	32	30k
NSP	16	16	32	172k	8	64	148k

Appendix

Table 1: Model hyperparameters for experiments

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Fold'EM: Direct atomic structure inference from Cryo-EM particles

Advaith Maddipatla, Märt-Erik Mäeots, Marco Pegoraro, Nikolaus Dräger+4

Institute of Science and Technology Austria · University of Zurich · Frankfurt Institute for Advanced Studies+2

Cryo-Electron Microscopy

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Single-particle cryo-electron microscopy (cryo-EM) has become a widely adopted technique for biomolecular structure determination. The conventional cryo-EM computational pipeline first combines many particle images to reconstruct an electrostatic potential (ESP) map and then fits an atomic model to the recovered map. Density reconstruction has high sample complexity, requiring large numbers of particle images and making structure determination high-cost and low-throughput, particularly for heterogeneous samples. Downstream atomic model building, in turn, becomes increasingly difficult as the resolution of the reconstructed map deteriorates. Protein structure prediction models provide strong sequence-derived priors on atomic structure, and experiment-guided approaches can use these priors to recover structures consistent with experimental measurements. Yet, in cryo-EM, such priors are typically integrated only after density reconstruction during atomic model fitting. We introduce Fold'EM, an inference-time framework that combines priors from protein generative models directly with cryo-EM particle images to determine atomic models from a small number of single particle images, bypassing both intermediate density reconstruction and downstream model building against the reconstructed map. Across synthetic and experimental cryo-EM datasets, Fold'EM recovers accurate atomic structures both with known particle orientations and in an ab-initio setting where orientations are inferred jointly with structure. In heterogeneous datasets, Fold'EM further resolves distinct conformational states from mixed particle populations without separately reconstructing a density map and building an atomic model for each state. We believe these results open new avenues for structure determination in the low-sample regime and for characterizing low-population conformational states directly from cryo-EM particles.

Abstract

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