PhaseT3M: 3D Imaging at 1.6 Å Resolution via Electron Cryo-Tomography with Nonlinear Phase Retrieval

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