Supplementary Figure 7: The defocus refinement at different resolution range.

a) 3D reconstruction of the Thermoplasma acidophilum 20S proteasome calculated by THUDNER, and b) corresponding FSC curves before and after the defocus refinement. c, d and e) the histogram of the defocus statistics before and after the defocus refinement for the proteasome CCD dataset, CNG dataset and the high-resolution proteasome dataset from EMPIAR, respectively. To test the performance of the defocus refinement of THUNDER on low-quality and low-resolution dataset, we collected a dataset of proteasome on a Tecnai F20 200kV microscope with Gatan US4000 CCD camera. This dataset contains 42 untilted micrographs and 44 tilted micrographs (20^o tilted). The initial defocus was measured by CTFFind3 for untilted micrographs and CTFTilt for tilted micrographs (the per-particle defocus was estimated according to the measured tilting angle and tilting axis from CTFTilt). Because the per-particle defocus values measured directly from the entire micrograph might be very coarse, it was expected to see more significant improvement after defocus refinement. The final reconstruction at 8.1 Å resolution were calculated from 21404 particles. Comparing the FSC curves before and after defocus refinement, there is just a small improvement after defocus refinement. A further test was then designed by adding ~ 500 Å defocus shift to the refined defocus of each particle and then examining whether the defocus refinement by THUNDER could recover them. c) The histograms of defocus distribution. The black curve is the distribution of the initial defocus, and blue curve is that after a shift of ~ 500 Å, and the red curve is that after the defocus refinement. The vertical dashed lines indicate the mean of defocus distributions. It can be seen that the defocus is partially recovered after defocus refinement. We also did the same tests for d) the CNG and e) the high-resolution proteasome dataset from EMPIAR. It is seen that the defocus can be recovered nearly perfectly. These results indicate that the defocus refinement by THUNDER can also work for the data collected by a CCD camera. But the performance of defocus refinement is limited by the low sensitivity of 3D reconstruction to the defocus errors at ~ 9 Å resolution level.