Fig 1.
Defining a quantitative phenotype for invasion.
The method used to define a quantitative phenotype for invasion is outlined for an organoid that is highly invasive (panels A, B, C), moderately invasive (panels D,E,F), and weakly invasive (panels G,H,I). These three organoids were selected from the 43 organoids generated from tumor 10, illustrating heterogeneity within a single tumor sample. Differential interference contrast (DIC) microscopy was used for image acquisition, with a scale of approximately 0.5 μm per pixel and a field of view of approximately 530×710 μm (panels A,D,G). Boundaries were segmented manually from DIC images and interpolated to 256 equally spaced points, sufficiently dense to track even the most invasive boundaries (panels B,E,H). A discrete Fourier transform was then applied separately to the x and y components of the discrete points, and the magnitudes of the corresponding Fourier amplitudes were squared and added to obtain the raw spectral power. Fourier mode 0, which represents the centroid of the boundary, was set to 0. The remaining modes were normalized by the power of Fourier mode 1 to provide scale invariance. Filters were applied to smooth effects from discrete pixel size and to emphasize the contributions of higher frequency modes, yielding a smoothed and weighted power spectrum for each organoid (panels C,F,I). The sum of the area under the spectrum, termed the spectral power, provides a single quantitative measure of invasiveness.
Fig 2.
(A) Distribution of the number of manual segmentation boundary points per organoid. (B) Distribution of organoid effective diameter, defined as .
Fig 3.
Invasiveness is heterogeneous between and within tumors.
Organoid boundaries are shown for 823 organoids generated from 52 breast tumors and imaged after six days of growth in 3D culture. Each column corresponds to organoids from a single tumor, denoted by an identifier underneath the column. Organoid boundaries were converted to a quantitative spectral power phenotype, represented by a false color map from blue (non-invasive) to red (highly invasive). For each tumor, organoids are stacked from less invasive to more invasive as characterized by the spectral power. Tumors are then arranged from left to right based on the median organoid invasiveness. Differences in numbers of organoids per tumor are from constraints on experimental capacity rather than biological differences between tumors. Heterogeneity is observed on both the horizontal axis (between-tumor variation) and the vertical axis (within-tumor variation).
Fig 4.
Distribution of quantitative invasion phenotypes.
Each boxplot represents the distribution of invasion scores for organoids generated from a single tumor, with tumors ordered from left to right by median organoid invasiveness. The boxplot for each tumor indicates the median value (red bar), lower and upper quartile values (box extent), and outliers as individual points. (A) Distributions generated using invasion on an arithmetic scale are asymmetric, with the median closer to the first quartile and a larger upper tail. The interquartile range increases substantially with the median invasiveness. (B) Distributions generated using invasion on a logarithmic scale are more symmetric, with the median approximately halfway between the first and third quartile. The interquartile range increases less with the median.
Fig 5.
Bootstrapped Bayesian model selection.
(A) Bootstrap replicates were used to increase robustness to limited number of tumors and organoids per tumor. Bootstraps were conducted for all 52 tumors and then, with increasing stringency, for tumors generating at least 2 through 10 organoids, with 30 tumors meeting the final requirement (solid line). The average number of organoids per tumor increased from 15.8 to 22.9 for these replicates (dashed line). (B) Three generative models were considered for between-tumor and within-tumor variation in logarithmic-scale organoid invasiveness: Model 0 assumes a single mean and variance shared by all tumors; Model 1 assumes a shared variance, but assigns each tumor its own mean; Model 2 assigns each tumor its own mean and variance. Converged estimates were obtained from 10,000 bootstrap replicates for thresholds of 1 organoid per tumor up to 10 organoids per tumor. For these thresholds, the posterior probability is 55-65% for Model 1 (green bars), with the remaining probability assigned to Model 2 (blue bars). Model 0 (red bars) had vanishing probability, not visible on this scale.
Table 1.
Variance components of invasion.
Fig 6.
Power of a pooling-based design.
The critical effect size defined as variance explained, R2, is shown for (A) between-tumor tests and (B) within-tumor tests. Calculations assume 20,000 two-tailed gene-based tests with genome-wide significance level 2.5 × 10−6 and 80% power. For between-tumor tests, the ratio of within-tumor to between-tumor variance is set to the observed value of 2.6. For within-tumor tests, pooling is assumed to reduce efficiency to 80%. Color bars indicate contour levels; between-tumor tests are limited to much larger effects and use only the upper region of the scale.
Fig 7.
Defining a quantitative phenotype for invasion.
The DIC images (panels A,C,E) were paired with K14 epifluorescence images obtained at identical resolution (panels B,D,F). Dots indicate boundaries from the DIC images interpolated to 256 equally spaced points and superimposed on both the DIC and K14 images.
Fig 8.
(A) Histogram of total Keratin 14 (K14) expression per organoid, calculated as the sum of the K14 intensity on a [0, 1] scale for pixels within the organoid divided by the total number of image pixels. (B) Histogram of mean K14 expression, calculated as the sum of the K14 intensity divided by the area of the organoid in pixels. The organoid size is less than the image size, and therefore the mean K14 is greater than the total K14. Both the total and mean were rank-normalized to generate uniform distributions for robust statistical analysis.
Fig 9.
Association of invasiveness with total Keratin 14 protein expression.
(A) Between-tumor tests of tumor means (points) do not yield significance for a linear model (dashed line). (B) The within-tumor test shows a highly significant association (p = 2.3 × 10−45) for a linear model (dashed line) between invasiveness and total Keratin 14 protein expression for individual organoids corrected for their tumor-specific baselines. Organoids in the extreme tails are shown for symmetric tails of 10% through 50%, with organoids in the 10% tail also belonging to larger tails and so on. The dashed regression line uses all the observations (50% tails). (C) Tests performed using organoids restricted to extreme tails are also highly significant (solid line). Pooled tests of mean values for organoids in the upper vs. lower tail, performed as a paired-sample t-test for each tumor, retain sufficient power for a gene-based test at 0.05 family-wise error rate, p < 2.5 × 10−6 when correcting for 20,000 genes or proteins tested, compatible for use with RNA-Seq (dashed line).
Fig 10.
Association of invasiveness with mean organoid Keratin 14 protein expression.
(A) Between-tumor tests of tumor means (points) do not yield significance for a linear model (dashed line). (B) The within-tumor test shows a highly significant association (1.0 × 10−13) for a linear model (dashed line) between invasiveness and mean Keratin 14 protein expression for individual organoids corrected for their tumor-specific baselines. Organoids in the extreme tails are shown for symmetric tails of 10% through 50%, with organoids in the 10% tail also belonging to larger tails and so on. The dashed regression line uses all the observations (50% tails). (C) Tests performed using organoids restricted to extreme tails are also highly significant (solid line). Pooled tests of mean values for organoids in the upper vs. lower tail, performed as a paired-sample t-test for each tumor, retain sufficient power for validation of individual findings (p < 0.05) but would not have sufficient power if corrected for multiple testing with gene-based (RNA-Seq) or proteome-wide tests.
Fig 11.
Association of invasiveness with organoid area.
(A) Between-tumor tests between organoid size and invasiveness remain significant. (p = 0.008). (B) The within-tumor test shows a highly significant association (9.8 × 10−52) for a linear model (dashed blue line) between invasiveness and rank-transformed organoid area. Organoids are colored according to extreme tail membership. (C) Tests performed using organoids restricted to extreme tails are also highly significant (solid line), as are pooled tests for association of area with invasiveness.