Extended Data Fig. 8: Statistical analysis of the variation in cell, nuclear and cellular structure sizes.
From: Integrated intracellular organization and its variations in human iPS cells
a. Heat map in four parts summarizing the results of a systematic, comparative analysis of the relationship between the volumes of the15 cellular structures validated for structural volume analysis and five cell and nuclear size metrics: the volume and surface area of the cell and the nucleus, and fifth, the cytoplasmic volume (the difference between cell and nuclear volumes), referred to as cell vol, cell area, nuc vol, nuc area, and cyto vol, respectively; Supplementary Methods). The number of cells in a–k are either all cells (n = 202,847) or per cellular structure (Extended Data Fig. 1d). The leftmost column (green heat map, scaling rate) indicates the percentage increase in structure volume given one doubling in cell volume over a well-represented volume range in the cell population (1160 to 2320 µm3). For example, the volume of mitochondria increased by an average 84% (from 108 to 199 µm3) for this doubling in cell volume (a doubling is an increase of 100%). The structures with the greatest relative scaling rates were the peroxisomes, followed closely by both nucleolar structures and then microtubules, all of which nearly doubled in structure volume with the doubling of cell volume. Simple linear regression was used to fit the data and to calculate the percent of the variation in cellular structure volumes that can be explained by each of the five cell and nuclear size metrics (next five columns in a, blue-red heat map, explained variance). The percent explained variance was substantially greater for some structures, such as mitochondria (54%) than for other structures, such as endosomes (2%). For nuclear structures like the nucleolar DFC, more of the variance in their volumes could be explained by nuclear volume than by cell volume (77% vs. 68%, respectively). A multivariate model was applied to calculate the total percentage of the variance explained for each of these structures by the combination of all four cell and nuclear size metrics (centre single column, all metrics). At the lowest end were the centrioles, which are discrete structures that double in number during the cell cycle, but with a negligible volume increase. Centrioles should not get continuously bigger as cells grow and were thus invariant with all size metrics. At the highest end were the nuclear envelope and the plasma membrane, which, as expected, correlated well with nuclear and cell surface areas, respectively. Notably, the volumes of all three nuclear body structures (nucleolar DFC, GC, and speckles) had high explained variances. Cell and nuclear metrics show a large degree of collinearity, which makes it non-trivial to isolate the effect of one particular cell or nuclear metric on structure volume. The multivariate model was used to calculate the unique contributions of both cell size metrics, both nuclear size metrics, and each of the four metrics individually (last six columns, orange heat map, unique explained variance). For all five nucleus-related structures, the variance in structure volume was better explained by nuclear size metrics than by cellular size metrics. For the nuclear envelope, more of the variance was uniquely attributable to the nuclear surface area than nuclear volume; this anticipated result confirmed the validity of this approach. b. Scatterplot of nuclear vs. cell volumes for all cells, coloured based on an empirical density estimate. The green line is a running average and the grey line is the linear regression model, also used to calculate the scaling rate (see a). c. Line plots showing the scaling rate for three cellular structures (yellow line and numbers in top left corners). The regions filled in grey are the interquartile range (IQR) measured across cells that were binned in 10 cell volume bins. The xy axes to the far left are used to indicate the values of the tick marks in each of the three plots. d–g. Scatterplots and statistical measures as in (b), for mitochondria (d), endosomes (e), and nucleoli (DFC, f and g). h. Scatterplot of the relative volume scaling rate vs. the total percent explained variance for the 15 cellular structures. Error bars are 5-95% confidence intervals calculated via bootstrap (n = 100). Structures along top and right side are rank ordered. The structures with the lowest relative volume scaling rates were also the structures identified as having the lowest explained variance (endosomes, centrioles). For most structures, however, relative scaling rates were at least 60%, consistent with the simple expectation that larger cells typically would also have larger organelles. Two structures whose volumes correlated most strongly with nuclear surface area (nuclear envelope, nuclear speckles) showed lower scaling rates. This was consistent with surface area generally scaling less quickly than volume. For example, doubling the size of a perfect sphere leads to only a 59% increase in its surface area. The peroxisomes stood out as exhibiting an unusual pattern of both a high relative volume scaling rate and great variability in peroxisome volume from cell to cell. i. Scatter plot of nuclear surface area vs. nuclear volume for all cells (blue points), cells with spherical nuclei (n = 19,927, brown points), perfect spheres (magenta dashed line) and linear and non-linear model fits on spherical cells or all cells (cyan and black as indicated; Supplementary Methods). The volume (V) and surface area (A) of a sphere don’t scale linearly, instead A ~ V2/3. However, on this dataset a linear model of nuclear volume explains as much variation in nuclear area as a model with the theoretically correct non-linear scaling factor. j. Scatterplot of explained variance for linear vs non-linear models for all cases in the heat map of explained variance in a (n = 190; Supplementary Methods). Median (across 100 bootstraps of the regression model; blue points) and 95% confidence interval (from 2.5% to 97.5% across the 100 bootstraps; red lines) are indicated. k. Heat map of percent explained variance between size-scaling metrics (rows) and shape modes (SM, columns). Correlations of structure volume to Shape Mode 5 likely occur due the moderate correlation between Shape Mode 5 (elongation) and cell surface area.