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Improving resolution and resolvability of single-particle cryoEM structures using Gaussian mixture models

Nature Methods volume 21, pages 37–40 (2024)Cite this article

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Abstract

Cryogenic electron microscopy is widely used in structural biology, but its resolution is often limited by the dynamics of the macromolecule. Here we developed a refinement protocol based on Gaussian mixture models that integrates particle orientation and conformation estimation and improves the alignment for flexible domains of protein structures. We demonstrated this protocol on multiple datasets, resulting in improved resolution and resolvability, locally and globally, by visual and quantitative measures.

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Fig. 1: Refinement of GPCR (EMPIAR-10786) and SARS-CoV-2 spike (EMPIAR-10492) datasets.
Fig. 2: Refinement of the ABC transporter (EMPIAR-10374).

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Data availability

The three datasets used in the paper are publicly available through EMPIAR: EMPIAR-10786 for the GPCR, EMPIAR-10492 for the SARS-CoV-2 spike, and EMPIAR-10374 for the ABC transporter. Structures produced in this paper are deposited in EMDatabank, and the corresponding refined models in the PDB: EMD-41840, 8U26 for the GPCR; EMD-41841, 8U28 for SARS-CoV-2 spike; and EMD-41845, 8U2C for the ABC transporter.

Code availability

All computational tools described here are implemented in EMAN2, a free and open source software for cryoEM/cryogenic electron tomography imaging processing. The code is available at github.com/cryoem/eman2, and a tutorial for these tools can be found through eman2.org/e2gmm_refine.

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Acknowledgements

This research has been supported by NIH grant R21MH125285 and R01GM150905 to M.C., and R01GM113195 and the Chan Zuckerberg Initiative fund from Silicon Valley Community Foundation (award no. 2021-234593) to W.C. Computational resources from SLAC Shared Scientific Data Facility (SDF) are used for the work. We thank G. Pintilie for helping with the final model refinement for PDB deposition.

Author information

Authors and Affiliations

  1. Division of CryoEM and Bioimaging, SSRL, SLAC National Accelerator Laboratory, Stanford University, Menlo Park, CA, USA

    Muyuan Chen, Michael F. Schmid & Wah Chiu

  2. Department of Bioengineering, and of Microbiology and Immunology, Stanford University, Stanford, CA, USA

    Wah Chiu

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  1. Muyuan Chen
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Contributions

M.C. designed the algorithm. M.C. implemented the software and performed the experiments. M.C., M.F.S. and W.C. contributed to data interpretation and manuscript preparation.

Corresponding author

Correspondence to Muyuan Chen.

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The authors declare no competing interests.

Peer review

Peer review information

Nature Methods thanks Ellen Zhong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. Primary Handling Editor: Arunima Singh, in collaboration with the Nature Methods team. Peer reviewer reports are available.

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Extended data

Extended Data Fig. 1 Workflow diagram for GMM-based particle orientation and conformation refinement.

Each block represents one step of processing, and the arrows indicate the sequence of the processes. The right side, DNN-based heterogeneity analysis is optional and is only recommended when large scale movement is present in the system. The result of the DNN-based refinement focusing on one region can be treated as one patch and merged into the patch-by-patch refinement results from the main workflow.

Extended Data Fig. 2 Detailed results of the GPCR dataset (EMPIAR-10786).

(a) ‘Gold-standard’ FSC curves of the reconstruction using initial orientation (gray), global GMM-based refinement (yellow) and patch-by-patch refinement (pink). (b) Q-score comparison of the three corresponding maps. (c-d) Overall structure of the three reconstructions, colored by local resolution, and comparison of local real space features. The cyan boxes in C highlight the location of features in the corresponding columns shown in D.

Extended Data Fig. 3 Detailed results of the SARS-COV2 dataset (EMPIAR-10492).

(a) ‘Gold-standard’ FSC curves of the reconstruction using initial orientation (gray), global GMM-based refinement (yellow) and patch-by-patch refinement (pink). (b) Q-score comparison of the three corresponding maps. (c-d) Overall structure of the three reconstructions, colored by local resolution, and comparison of local real space features. The cyan boxes in C highlight the location of features in the corresponding columns shown in D.

Extended Data Fig. 4 Detailed results of the ABC transporter dataset (EMPIAR-10374).

(a) ‘Gold-standard’ FSC curves of the reconstruction using initial orientation (gray), global GMM-based refinement (yellow) and patch-by-patch refinement (pink). (b) Q-score comparison of the three corresponding maps. (c-d) Overall structure of the three reconstructions, colored by local resolution, and comparison of local real space features. The cyan boxes in C highlight the location of features in the corresponding columns shown in D.

Extended Data Fig. 5 Visualization of GMMs.

(a) Reconstruction of the GPCR using the voxel map representation, determined at 3.3 Å resolution. 6 × 106 floating point values are required to represent the structure. (b) GMM representation of the A, shown in isosurface view. 5 × 104 floating point values are used to represent the structure. (c) FSC curve between A and B. The two structures are virtually identical up to 3.3 Å. (d) Visualization of the GMM from B using 3D scatter plot. Each point is colored by the amplitude of the Gaussian function and the size of the points correspond to the width of Gaussian functions. (e) Overlay of the coordinates of Gaussian functions in the corresponding density map.

Extended Data Fig. 6 Diagram for the patch-by-patch refinement.

(a) Input density maps and GMMs from the global orientation refinement. (b) Scatter plot of Gaussian coordinates, colored by clustering result. (c) Soft masks for each cluster. Each mask is a sphere covering all Gaussian coordinates of the corresponding cluster, with a soft falloff. (d) Focused refinement results using the soft masks, colored by local resolution. Note that the same refinement process is done independently for the even/odd subsets of particles using the corresponding half map/GMM as reference. (e) Masked out density from the individual focused refinement result. (f) Final composite map generated by weighted averaging.

Extended Data Fig. 7 Orientation and translation change before and after GMM-based refinement.

(a) Histogram of particle orientation assignment change after the GMM-based global refinement. Mean = 2.34, std = 1.37 degrees. (b) Histogram of particle translation change after the GMM-based global refinement. Mean = 0.66, std = 0.46 pixels. (c) Histogram of particle orientation assignment change after the GMM-based focused refinement. Mean = 3.74, std = 1.76 degrees. (d) Histogram of particle translation change after the GMM-based global refinement. Mean = 0.89, std = 0.62 pixels.

Extended Data Fig. 8 Performance of GMM-based refinement in datasets at lower resolution.

(a–c) Refinement of a small subset of the GPCR dataset. (d–f) Refinement of a small subset of the SARS-COV2 dataset. (a, d) ‘Gold-standard’ FSC curves of the reconstruction using voxel-based refinement (gray), global GMM-based refinement (yellow) and patch-by-patch refinement (pink). (b, f) Overall structure of the initial reconstruction and the final patch-by-patch refinement result, colored by local resolution. (c, f) Comparison of local features from the voxel-based, global GMM-based and patch-by-patch refinement.

Extended Data Fig. 9 Impact of flexible domains on the global FSC curve.

(a) Simulated density map of β-galactosidase, with two rigid subunits at 2.5 Å and two flexible ones resolved at 15 Å. (b) Same simulated map as A, with the two flexible subunits resolved at 7 Å. (c) Comparison of ‘gold-standard’ FSC curves of the two structures. Blue - A, red - B.

Supplementary information

Reporting Summary

Peer Review File

Supplementary Video 1

Structure comparison of the GPCR dataset (EMPIAR-10786). Gray: reconstruction using initial orientation. Pink: reconstruction after GMM-based patch-by-patch refinement.

Supplementary Video 2

Structure comparison of the SARS-CoV-2 dataset (EMPIAR-10492). Gray: reconstruction using initial orientation. Pink: reconstruction after GMM-based patch-by-patch refinement.

Supplementary Video 3

Structure comparison of the ABC transporter dataset (EMPIAR-10374). Gray: reconstruction using initial orientation. Pink: reconstruction after GMM-based patch-by-patch refinement.

Supplementary Video 4

Converting structural heterogeneity to particle orientation focusing on the Fab of the ABC transporter (EMPIAR-10374).

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Chen, M., Schmid, M.F. & Chiu, W. Improving resolution and resolvability of single-particle cryoEM structures using Gaussian mixture models. Nat Methods 21, 37–40 (2024). https://doi.org/10.1038/s41592-023-02082-9

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