Anisotropy

All other image processing operations were performed in the XMIPP package.¹⁸ (link) Prior to refinement, all data sets were normalized using previously described procedures.⁵ (link) MAP refinements and projection matching refinements in XMIPP were performed with similar settings where possible. Although the implementation of the MAP approach readily handles anisotropic CTF models, all refinements were performed with isotropic CTFs (without envelope functions) for the sake of comparison with XMIPP. All orientational searches, or integrations in the statistical approach, were performed over the full five dimensions, that is, three Euler angles and two translations. For both the thermosome and the GroEL refinements, the first 10 iterations were performed with an angular sampling of 7.5°, and subsequent iterations were performed with an angular sampling interval of 3.75°. Thermosome refinements were stopped after 15 iterations, and GroEL refinements, after 20. Translational searches were limited to ± 10 pixels in both directions in the first 10 iterations and to ± 6 pixels in the subsequent iterations. Although it is common practice in XMIPP to reduce computational costs by breaking up the orientational search into separate rotational and translational searches and to limit rotational searches to local searches around previously determined orientations, this was not done in the refinements presented here for the sake of comparison with the MAP approach. Refinements with angular sampling intervals as fine as 1° where such tricks were employed did not result in better reconstructions (results not shown).
The true resolution of the GroEL reconstructions was assessed by FSC with a published crystal structure (Protein Data Bank ID: 1XCK). This structure contains 14 unique monomers in its asymmetric unit. Each of these monomers was fitted separately into the reconstructions using UCSF Chimera,⁴¹ (link) and for each monomer, the equatorial, intermediate, and apical domains were allowed to move independently as rigid bodies. The resulting coordinates were converted to an electron density map that was symmetrized according to D7 symmetry. Optimization of the relative magnification between this map and the cryo-EM reconstructions revealed that the effective pixel size of the cryo-EM images was 2.19 Å, differing by 3% from the nominal value, and this value was used to generate all plots in Fig. 3.
Ribosome refinements were performed for 25 iterations with an angular sampling of 7.5° and translational searches of ± 10 pixels. To generate K = 4 unsupervised initial starting models from a single  80-Å low-pass filtered initial ribosome structure, during the first iteration, we divided the data set into four random subsets in a way similar to that described before.²¹ (link)

A StarDist-3D model with a U-Net backbone (Çicek et al., 2016 (link)) was trained to detect and segment individual B. napus seeds in 3D µCT sub-volumes from the labelled ‘training’ dataset using the pipeline described by Weigert et al. (2020) . Model training was performed using a Google Colab runtime with 25.46 GB and a single GPU (Bisong, 2019 (link)). The StarDist-3D model was configured to use 96 Fibonacci rays in shape reconstruction, and to take into account the mean empirical anisotropy, of all labelled seeds in the dataset along each axis as calculated using the method described by Weigert et al., 2020 (X-axis = 1.103448275862069, Y-axis anisotropy = 1.032258064516129, Z-axis anisotropy = 1.0). The training patch size, referring to the size of the tiled portion of the 3D sub-volumes in the ‘training’ within view of the neural network at any one time, was set to Z = 24, X= 96, and Y = 96 and training batch size set to 2. Training ran for 400 epochs with 100 steps per epoch and took 1.36 hours to complete (123ms/step).
Model validation was then performed by using the fine-tuned StarDist-3D algorithm to predict seed labels for all 3D µCT sub-volumes from the ‘validation’ dataset, which were then compared to the number and shape of seeds manually counted and labelled during annotation. Accuracy of seed detection and segmentation was then quantified for various levels of threshold τ, defined as the IoU between the predicted label and ground-truth label for each seed. The value of τ ranged between 0, where even a very slight overlap between predicted seeds and actual seeds counted as correctly predicted, and 1, where only predicted seed labels with pixel-perfect overlap with ground-truth labels counted as correctly predicted (Weigert et al., 2020 ).
Object detection accuracy was measured using the number of true positive results (TP), or number manually counted and labelled seeds that were correctly detected seeds, the number of false negative results (FN), or the number of manually counted and labelled seeds that were missed, the number of false positive results (FP), or number of objects other than seeds than were detected, recall, precision and F1-score. Recall related to the fraction of relevant objects that were successfully detected and was defined as:
Precision related to the fraction of all detected objects that were relevant and was defined as:
F1-score related to the harmonic mean of precision and recall, with the impact of precision and recall being given equal weight. F1-score was defined as:
The accuracy of seed segmentation, or the accuracy of seed size and shape prediction, for the validation dataset was determined based on the mean matched score, defined as the mean IoU between the predicted and actual shape of true positive results, the mean true score, defined as the mean IoU between the predicted and actual shape of true positive results normalised by the total number of ground-truth labelled seeds, and panoptic quality, as defined in Eq.1 of Kirillov et al., 2019 .
StarDist-3D models allow for specification of two values, the τ-threshold and the nms-threshold to optimize model output (Schmidt et al., 2018 ; Weigert et al., 2020 ). The τ-threshold refers to the minimum intersection-over-union between pairs of predicted and ground-truthed seeds required for detections to be classified as true positives, and can be set at 0.1 interval levels between 0.1 and 1 with 0.1 indicating a 10% overlap in the pixels within the predicted shape of a seed and the ground-truthed label and 1 respreseting a 100% overlap (Schmidt et al., 2018 ; Weigert et al., 2020 ). The nms-threshold, refers to the level of non-maximum suppression applied to the results of object detection and instance segmentation to prune the number of predicted star-convex polyhedra in ideally retain a single predicted shape for each true object, in this case each seed, within an image. The nms-threshold can be set at 0.1 interval levels between 0 and 1 with higher levels indicating more aggressive pruning of predicted shapes which therefore leads to fewer detections in the final model output. Therefore a higher nms-threshold is valuable in cases where the number of false positives expected in unfiltered model predictions is high. Both the τ-threshold and the nms-threshold for the fine-tuned StarDist-3D algorithm were set to optimal values based on the ‘validation’ dataset using the ‘optimize_thresholds’ function of StarDist (Schmidt et al., 2018 ).

For fMRI data, the pre-processing was performed using SPM12 (Wellcome Department of Imaging Neurosciences, University College London, UK, http://www.fil.ion.ucl.ac.uk/spm), and the statistical analyses of imaging data were performed using GRETNA (GRETNA v2.0) in Matlab R2021b. First, the first 10-time point-scanned images were removed owing to the instability of the magnetic field at the beginning of the scan. Second, all functional images were realigned to the first image to correct head movement. All participants met the criteria of < 2 mm translation and < 2° rotation in any direction. Otherwise, their data were excluded. Third, the functional images were normalized to the MNI space using DARTEL and resampled to a 3 × 3 × 3 mm³ voxel size^{62 (link)}. Fourth, we used an anisotropic 6-mm full-width half-maximum Gaussian kernel⁶³ for spatial smoothing of the obtained images. Fifth, we detrended and removed linear trends. Sixth, we removed covariates, excluding white matter, grey matter, and cerebrospinal fluid influences. Seventh, 0.01‒0.08 Hz bandpass filtering was used to remove high and low-frequency signals. Eighth, we removed the FD_Threshold > 0.5 mm time points by “scrubbing” 1-time point before and 2-time points after. In summary, the pre-processing procedures included slice timing correction, realignment, normalization, smoothing, detrending, filtering, and scrubbing.