GaussianEM: Model compositional and conformational heterogeneity using 3D Gaussians

TL;DR

GaussianEM introduces a scalable, Gaussian-based framework for cryo-EM heterogeneity analysis that jointly handles compositional and conformational variability. It represents macromolecules as thousands of 3D Gaussians and uses a two-encoder-one-decoder network to map images to per-Gaussian deformations, enabling real-space rendering and direct mapping to atomic coordinates. The method demonstrates superior ability to capture both discrete states and continuous motions across simulated and six public datasets, preserving local structural coherence and producing interpretable conformational landscapes. This approach bridges density-based heterogeneity analysis with pseudo-atomic interpretation, facilitating deeper insights into dynamic structural behavior and functional mechanisms.

Abstract

Understanding protein flexibility and its dynamic interactions with other molecules is essential for protein function study. Cryogenic electron microscopy (cryo-EM) provides an opportunity to directly observe macromolecular dynamics. However, analyzing datasets that contain both continuous motions and discrete states remains highly challenging. Here we present GaussianEM, a Gaussian pseudo-atomic framework that simultaneously models compositional and conformational heterogeneity from experimental cryo-EM images. GaussianEM employs a two-encoder-one-decoder architecture to map an image to its individual Gaussian components, and represent structural variability through changes in Gaussian parameters. This approach provides an intuitive and interpretable description of conformational changes, preserves local structural consistency along the transition trajectories, and naturally bridges the gap between density-based models and corresponding atomic models. We demonstrate the effectiveness of GaussianEM on both simulated and experimental datasets.

Figures (6)

• Figure 1: Architecture of GaussianEM. The GaussianEM method represents macromolecular structures using 3D Gaussians, and its heterogeneity analysis network consists of two encoders and one decoder. Each particle image is encoded into a continuous latent space, while each Gaussian is independently encoded to obtain a unique identifier (embedding). Then, the decoder combines the latent variable and each Gaussian embedding to estimate the parameter variations for Gaussians. The resulting deformed 3D Gaussians directly illustrate the structural changes of the protein, capturing both the compositional and conformational heterogeneity.
• Figure 2: GaussianEM captures large-scale motion in the simulated dataset.a The consensus map and atomic model from the simulation dataset, along with the initial 3D Gaussians used in GaussianEM. b The two-dimensional latent conformation space after dimensionality reduction, exhibiting a circular distribution that corresponds to the continuous 3D structural motion. c The estimated Gaussian displacements are directly mapped onto atomic coordinates (red) in real space, generating the deformed atomic model (purple). The deformed model is superimposed on the provided ground-truth structure (blue), yielding an RMSD of 2.26 Å, which demonstrates the accuracy of GaussianEM in capturing large-scale conformational motion. d Visualization of reconstructed atomic models. The left panel displays representative reconstructed atomic models. On the right, two RMSD distribution plots are shown: one for all estimated models and another categorized by rotation angles.
• Figure 3: Heterogeneity analysis of Ribosome assembly.a Visualization of the latent space encoded by GaussianEM, where dark blue dots denote the cluster centers corresponding to distinct conformational classes. b Ten representative density maps generated by GaussianEM from the cluster centers, each labeled with its class index. Regions showing major conformational differences are highlighted in red boxes. c Examples of ribosomal protein L16, L25 that are present, partially present and fully missing. d Visualization of the motion of the dynamic central protuberance domain alongside the corresponding changes in the atomic models and reconstructed map by CryoSPARC. A dotted envelope is fixed to better illustrate structural motion. e The distribution of learned Gaussian embeddings. Four distinct clusters are identified and reconstructed. On the right, the corresponding volumes are shown, with each volume illustrating the effect of removing one component.
• Figure 4: Heterogeneity analysis of precatalytic spliceosome.a Visualization of the latent space encoded by GaussianEM b Six representative density maps generated by GaussianEM from the cluster centers, each labeled with its class index. Major conformational differences are highlighted in red boxes. c Reconstructed maps by CryoSPARC using clustered projection from GaussianEM. d Visualization of segmented Gaussians. Different colored components roughly respond to different biological domains. e UMAP visualization of principal components 1, 2 and 3. The reconstructed volumes and their corresponding atomic models are shown on the right.
• Figure 5: Heterogeneity analysis of BtpeA-BtaeB-VgrG complex.a Generation of the initial Gaussians. Valid points were extracted from two density maps (EMD-61469 and EMD-61458) and combined to form the initial model. b Three reconstructed volumes along the first principal component. A region not present in publicly available data is highlighted by a red box. c Reconstructed maps by CryoSPARC using clustered projection from GaussianEM. d UMAP visualization of principal components 2 and 3. The reconstructed volumes and their corresponding atomic models are shown on the right.