Fig. 3: SOTIP accurately quantifies spatial heterogeneity.

a Schematic diagram of a eukaryotic cell. b Summary of the SHN quantification performance on all 13 samples. The AUC is used to estimate the performance. Two-sided Wilcoxon rank-sum test. The detailed definition of box plot elements is described in Methods. The boxplots show n = 13 biologically independent cells. c Visualization of the ground truth (1st column) and SHN values computed by NUCC (2nd column), IGD (3rd column), and SOTIP (4th column) in cell 118. White arrows point out the same position of nuclear envelope. Orange arrow points out a computed potential intracellular membrane structure. d Similar with c but for cell 119. e Overlay of SOTIP computed SHN values with PCNA protein expression in cell 118. White arrow points out the same position with Fig. 3c. f Overlay of clipped SOTIP computed SHN values with p-RPS6 expression in cell 118. Orange arrow points to the same position as in Fig. 3c 4th column. g Histological image of the zebrafish data. Tumor region is annotated with black dashed line. Scale bar: 2 mm. h 10x Visium spots are paired with Fig. 3g, colored according to SOTIP computed SHN values. i The stability (y-axis) of SHN computed using different methods, with different clustering resolutions (x-axis). The stability is evaluated by computing the correlations between SHN values under resolution 1 and SHN values under different resolutions. j Schematic diagram of the cerebral cortex. k Region annotation of the osmFISH mouse cortex dataset. Each point is a cell colored by its layer. l 5 FOVs of seqFISH+ cortex data. The layer depth (Layer 2–6) increased with the FOV label (0–4). m Distribution of SHN values (y-axis) computed using SOTIP in each cortical layer of osmFISH dataset (x-axis). Each violin represents a distribution of SHN values (y-axis) of MECNs in one layer (x-axis), and each point in one violin represents a MECN’s SHN value. The violin-plot is colored by the layer label of the MECN. The x-axis is arranged in ascending order of the cortical depth. n Similar with (n) but with seqFISH+ dataset. The gradient pattern of SHN along the cortical layer depth. Violin-plots were colored according to (m). Source data are provided as a Source Data file. The experiment results in (g, h) were similar with three independent repeats.