DOI: 10.5281/zenodo.17336677
title: PhaseT3M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval

description: Supplementary Data and Codes

The data and source codes for the paper [J. Lee, S. W. Song, M. G. Cho, G. Varnavides, S. M. Ribet, C. Ophus, M. C. Scott, & M. L. Whittaker, PhaseT3M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval. Preprint at https://doi.org/10.48550/arXiv.2504.16332 (2025). (the cite information will be updated after publication)] are posted below. 

Overview

Electron cryo-tomography (cryo-ET) enables 3D imaging of complex, radiation-sensitive structures with molecular detail. However, image contrast from the interference of scattered electrons is nonlinear with atomic density and multiplescattering further complicates interpretation. These effects degrade resolution, particularly in conventional reconstruction algorithms, which assume linearity. Particle averaging can reduce such issues but is unsuitable for heterogeneous ordynamic samples ubiquitous in biology, chemistry, and materials sciences. Here, we develop a phase retrieval-based cryo-ET method, PhaseT3M. We experimentally demonstrate its application to an approximately 7 nm Co3O4 nanoparticle on an approximately 30 nm carbon substrate, achieving a maximum resolution of 1.6 Å, surpassing conventional limits using standard cryo-TEM equipment. PhaseT3M uses a multislice model for multiple scattering and Bayesian optimization for alignment and computational aberration correction, with a positivity constraint to recover ‘missing wedge’ information. Applied directly to biological particles, it enhances reconstruction quality and reduces artifacts, establishing a new standard for routine 3D imaging with phase contrast.

System Requirements

1. All software dependencies and operating systems (including version numbers)

Language: Python (3.11 and 3.9)

Operating systems: Linux (Ubuntu 20.04, 22.04)

 

2. Any required non-standard hardware

There is no non-standard hardware

 



Repository Contents


1. Raw tilt data

Folder: Raw_tilt_data

This folder includes experimental tilt series of a Co3O4 nanoparticle and HIV-1 particles. All tilt series were motion-corrected and tilt-aligned. The HIV-1 particle data were obtained from the open source EMPIAR-10164 dataset, which we further processed by performing motion correction and alignment.

Contents:





Co3O4/Co3O4_denoised_tilt_series.h5 - denoised tilt series data of the Co3O4 nanoparticle

HIV-1/HIV-1_tilt_series.h5 - tilt series data of the HIV-1 particles


 


2. Image preprocessing

Folder: Image_preprocessing

 

This folder contains Jupyter notebook files for image-preprocessing in tomography, including motion correction, defocus value estimation, focal/tilt series alignment, and microscope parameter refinement.

 

Contents:





SP1_motion_correction/Motion_correction.ipynb - motion correction code

SP1_motion_correction/Rough_alignment.ipynb - rough alignment code using isolated particle position

SP2_defocus_estimation/estimate_defocus_value.ipynb - defocus value estimation code using CTFFIND

SP3_focal_series_alignment/focal_series_alignment.ipynb - focal series alignment code

SP4_tilt_series_alignment/tilt_series_alignment.ipynb - tilt series alignment code

SP5_refinement/optimize_paras_BO.ipynb - Bayesian optimization code for refining microscope parameters

utils: utility Python codes



 

3. Reconstruction code

Folder: reconstruction_code

This folder includes Jupyter notebook files for PhaseT3M reconstruction codes

Contents:





Co3O4/PhaseT3M_Recon.ipynb - PhaseT3M reconstruction code for the Co3O4 nanoparticle

HIV-1/PhaseT3M_Recon.ipynb - PhaseT3M reconstruction code for the HIV-1 particles

HIV-1/conventional_tomography.ipynb - Conventional reconstruction code for the HIV-1 particles


 


4. Reconstruction data

Folder: reconstruction_data

This folder includes reconstruction data of the Co3O4 nanoparticle and HIV-1 particles.

Contents:





Co3O4/PhaseT3M_multislice_positivity/PhaseT3M_gs_align_new_denoise_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint

Co3O4/PhaseT3M_multislice_nonpositivity/PhaseT3M_gs_align_new_denoise_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_nopos.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction without a positivity constraint

Co3O4/PhaseT3M_single-slice_positivity/PhaseT3M_gs_align_new_denoise_gain_cor_real_vs600_ns1_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos.h5 - Co3O4 nanparticle PhaseT3M single-slice reconstruction with a positivity constraint

Co3O4/SIRT/Conventional_Tomo_new_denoise_iter200_include_Fourier_center.h5 - Co3O4 nanparticle SIRT reconstruction

Co3O4/PhaseT3M_dose_fractional_test/PhaseT3M_gs_align_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos_lowdoseNsub12.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint at electron dose level of 4,230 e/Å^2 (using 12 frames)

Co3O4/PhaseT3M_dose_fractional_test/PhaseT3M_gs_align_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos_lowdoseNsub12.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint at electron dose level of 4,230 e/Å^2 (using 12 frames)

Co3O4/PhaseT3M_dose_fractional_test/PhaseT3M_gs_align_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos_lowdoseNsub2.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint at electron dose level of 705 e/Å^2 (using 2 frames)

Co3O4/PhaseT3M_dose_fractional_test/PhaseT3M_gs_align_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos_lowdoseNsub1.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint at electron dose level of 353 e/Å^2 (using one frame)

Co3O4/PhaseT3M_dose_fractional_test/PhaseT3M_gs_align_gain_cor_real_vs600_ns600_gsf180_iter100_refine_focal_tilt_it1_pixel_BO_defocus_v1_C3_ss00005_as100_is001_FS_lp08_pos_lowdoseNsub1_df1.h5 - Co3O4 nanparticle PhaseT3M multislice reconstruction with a positivity constraint at an electron dose level of 118 e/Å^2 (using only one defocus image and one frame)




HIV-1/PhaseT3M_multilslice/PhaseT3M_ps12_vs360_iter100_ns360_ss0.00_css0.10_nopos.h5 - PhaseT3M multislice reconstruction of the HIV-1 particles

HIV-1/PhaseT3M_singleslice/PhaseT3M_ps12_vs360_iter100_ns1_ss0.10_css0.10_nopos.h5 - PhaseT3M single-slice reconstruction of the HIV-1 particles

HIV-1/SIRT/SIRT_ps12_vs360_iter500_nopos.h5 - SIRT reconstruction of the HIV-1 particles

HIV-1/RESIRE/RESIRE_ps12_nopos_rec_v360.mrc - RESIRE reconstruction of the HIV-1 particles

HIV-1/FBP/FBP_ps12_vs360.h5 - FBP reconstruction of the HIV-1 particles

HIV-1/WBP/WBP_ps12_vs360.h5 - WBP reconstruction of the HIV-1 particles

HIV-1/SART/SART_ps12_vs360_iter500_nopos.h5 - SART reconstruction of the HIV-1 particles

HIV-1/ART/ART_ps12_vs360_iter20_nopos.h5 - ART reconstruction of the HIV-1 particles


 


5. Analysis code

Folder: Analysis_code

This folder contains analysis codes, including plotting the power spectrum of a 3D volume, the leave-one-out method, and R-factor calculation.



power_spectrum/plot_power_spectrum.ipynb - Plotting power spectrum Python code

leave-one-out_method/Calculate_leave-one-out.ipynb - Leave-one-out calculation Python code

leave-one-out_method/leave_one_out/* - reconstruction files for calculating Leave-one-out validation

R_factor/Calculate_Rfactor.ipynb - R-factor Python code

R_factor/projections/* - ctf-corrected projection files for calculating R-factors


 





Additional Notes


If you use any of the above data or source codes in your publications or presentations, please cite the following paper: J. Lee, S. W. Song, M. G. Cho, G. Varnavides, S. M. Ribet, C. Ophus, M. C. Scott, & M. L. Whittaker, PhaseT3M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval. Preprint at https://doi.org/10.48550/arXiv.2504.16332 (2025).

 

For any questions regarding the data or source codes, please contact Juhyeok Lee, EGD/NCEM, Lawrence Berkeley National Laboratory. Email: jhlee0667@lbl.gov

 



The code is distributed under the terms of the GNU General Public License v3.0 (GPL-3.0).