We generated binary masks for chromatin from the ChromSTEM tomograms based on automatic thresholding in Fiji (Otsu’s method) as reported previously (8). Unlike the ChromEMT study using TEM, our tomography data were obtained through STEM HAADF imaging mode, and we fine-tuned the imaging processing parameters. The set of parameters were optimized by comparing their performance with manually segmented chromatin mask on the same structure (fig. S8D). For all chromatin masks used in this work, the following procedure was performed. First, the local contrast of the tomograms was enhanced by CLAHE, with a block size of 120 pixels. Then, Ostu’s segmentation algorithm with automatic threshold was used. Last, we removed both dark and bright outliers using a threshold of 50 and a radius of 2 to refine the chromatin mask. All imaging processing was performed in FIJI (49).

On the binary chromatin masks, mass scaling analysis was performed to unveil the chromatin packing structure. The mass scaling relation M(r) is the mass of chromatin (M) contained within a sphere of radius r, and it dictates the relationship between the physical size and the genomic size of the chromatin. For a fractal structure, the mass scaling follows a power-law relation, and the scaling exponent is the packing scaling D. To calculate the mass scaling curve from ChromSTEM data, the total chromatin M(r) was calculated within concentric circles for each radius r. One hundred nonzero pixels were randomly chosen on each slice of the tomography data as the origin of the concentric circles. The average mass scaling curve was calculated from individual mass scaling curves to reduce noise.

In addition, average mass scalings within 3D moving windows were used to calculate the spatial distribution of packing scaling Ds for the entire field of view. The average 2D mass scaling curve was calculated over multiple individual mass scaling curves centered on nonzero pixels located in the center region (~15 nm3) in each window. To calculate D, we used linear regression on the average mass scaling curve in the log-log scale, fitting from ~10 to ~30 nm. We then assigned this value to the center pixel of the 3D window to map the spatial distribution of D.

A contrast enhancement (CLAHE plugin in FIJI) (49) and a flooding algorithm (MATLAB) were implemented to segment individual PDs with similar packing scaling. We defined the boundary of each PD as the spatial separation where the mass scaling curve deviates from a fractal behavior, and the distance from the center of the PD to the boundary is the PD radius Rf. One of the four criteria has to be met if the mass scaling curve deviates from a fractal behavior: (i) The linear fit of the power-law from 11.7 to 33.3 nm is 5% different from the mass scaling curve (multiple packing scalings); (ii) the slope of the mass scaling curve reaches 2 (not fractal); (iii) the curvature (second derivative) of the mass scaling curve reaches 2 (nonlinear); (iv) the radial CVC of the PD starts to increase (other PDs). If all criteria are satisfied, we chose the smallest value to be Rf. An example of such a process can be found in fig. S3. We calculated the average mass scaling from individual mass scaling centered on all the nonzero voxels in the middle region within one PD and quantified the D and Rf. Assuming that the highest intensity in the tomograms represents 100% unhydrated DNA (density = 2 g/cm3) and the average molecular weight for a nucleotide is 325 Da, we calculated the highest mass (m) per voxel (dr = 2 nm) to be ~15 bp. We further calculated the average genomic size of PDs to be 352.6 kbp by M=m(Rfdr)D, with Rf = 96.0 nm and D = 2.60.

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