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. 2022 Jan 31;11:e68048. doi: 10.7554/eLife.68048

Figure 2. Age-related change in gene expression variation among tissues estimated with coefficient of variation (CoV).

(a) Transcriptome-wide mean CoV trajectory with age. Each point represents the mean CoV value of all protein-coding genes (15,063) for each mouse (n = 15) except the one that lacks expression data in the cortex. (b) Age effect on CoV value of the Cd93 gene which has the highest rank for the divergence-convergence (DiCo) pattern in four tissues (Materials and methods). CoV increases during development and decreases during ageing, indicating expression levels show DiCo patterns among tissues. (c) Expression trajectories of the gene Cd93 in four tissues. (d) The number of significant CoV changes with age (false discovery rate [FDR]-corrected p-value<0.1) during development (left, nconverge = 772, ndiverge = 1809) and ageing (right, nconverge = 42, ndiverge = 20). Converge: genes showing a negative correlation (ρ) between CoV and age; diverge: genes showing a positive correlation between CoV and age. (e) Log2 ratio of convergent/divergent genes in development and in ageing. The graph represents only genes showing significant CoV changes (FDR-corrected p-value<0.1, given in panel d). Error bars represent the range of log2 ratios calculated from leave-one-out samples using the jackknife procedure (Materials and methods, values are given in Figure 2—source data 1).

Figure 2—source data 1. All the data related to divergence-convergence (DiCo) pattern: age-related coefficient of variation (CoV) change of genes, pairwise tissue expression correlations, analysis of independent datasets; GSE34378 (Jonker et al.), GSE132040 (Schaum et al.), and GTEx.

Figure 2.

Figure 2—figure supplement 1. Age-related change in coefficient of variation (CoV) summarised across genes using median CoV values.

Figure 2—figure supplement 1.

Each point represents the median CoV value (instead of the mean given in Figure 2a) of all protein-coding genes (15,063) for each mouse except the one that lacks expression data in the cortex (n = 15). x-axis is in log2 scale. The dashed grey line shows the start of the ageing period. The Spearman’s correlation coefficient and p-value for each period are indicated separately on the plot.
Figure 2—figure supplement 2. Clustering of divergence-convergence (DiCo) genes by expression variations (coefficient of variation [CoV]) among tissues.

Figure 2—figure supplement 2.

k-means clustering (k = 7) of DiCo genes (4802) using CoV values. Numbers in the parentheses show the number of genes in each cluster. CoV values were scaled across genes (mean = 1, sd = 0) before clustering. The optimal number of clusters was determined with gap statistics (Materials and methods). The list of genes belonging to each cluster and their age-related CoV change correlations are given in Figure 2—source data 1.
Figure 2—figure supplement 3. Clustering of divergence-convergence (DiCo) genes by expression levels in tissues.

Figure 2—figure supplement 3.

k-means clustering (k = 25) of DiCo genes (n = 4802) using gene expression levels. Numbers in the parentheses show the number of genes in each cluster. Expression levels of genes were scaled across tissues (mean = 1, sd = 0) before clustering. The optimal number of clusters was determined with gap statistics (Materials and methods). The list of genes belonging to each cluster and their age-related CoV change correlations are given in Figure 2—source data 1.
Figure 2—figure supplement 4. Number of genes with inter-tissue divergence and convergence tendencies in development and ageing.

Figure 2—figure supplement 4.

The number of coefficient of variation (CoV) changes with age (without a significance cutoff) during development and ageing. Converge: genes showing negative correlation (ρ < 0) between CoV and age; diverge: genes showing positive correlation (ρ > 0) between CoV and age (development: nconverge = 5939, ndiverge = 9058; ageing: nconverge = 7748, ndiverge = 7187).
Figure 2—figure supplement 5. Pairwise tissue expression correlations.

Figure 2—figure supplement 5.

Age-related changes in pairwise Spearman’s correlation coefficients for the expression levels (y-axis) between tissues of the same individual mouse in our dataset. The dashed grey line indicates the start of the ageing period. The Spearman’s correlation coefficients and p-values for each period are indicated separately on the plot.
Figure 2—figure supplement 6. Summary of pairwise expression correlations among tissues.

Figure 2—figure supplement 6.

Age-related change in the mean (left) or the median (right) pairwise expression correlations among tissues. Each point represents the mean (left) or the median (right) of pairwise expression correlations among tissues of the same mouse (mean/median values are calculated from Figure 2—figure supplement 5). (a) Absolute expression correlations were used to calculate the mean or the median. (b) Expression correlations were scaled within each tissue pair (mean = 1, sd = 0) before calculating the mean and median. The Spearman’s correlation coefficients and p-values for each period are indicated separately on the plot.
Figure 2—figure supplement 7. Coefficient of variation (CoV) and pairwise correlation analysis of Jonker dataset.

Figure 2—figure supplement 7.

(a, b) Principal components analysis (PCA) of expression values of 17,661 protein-coding genes across five tissues (brain [cortex], liver, lung, kidney, spleen) of 18 individuals in the Jonker dataset (contains samples only from the ageing period). Values in parentheses show the variance explained by each PC. (c) The change in mean pairwise Euclidean distance between the PC values for the tissues of the same individuals (y-axis) with age (x-axis). Transcriptome-wide (d) mean and (e) median CoV changes with age across five tissues. The x-axis shows age in days. Each point represents the mean or median CoV value of all protein-coding genes for each individual. (f) Associationbetween age (x-axis) and gene expression correlations of each individual in pairwise tissues (y-axis). Spearman’s correlation coefficient and p-values are indicated in each plot.
Figure 2—figure supplement 8. Principal components analysis (PCA) of GTEx dataset covering cortex, liver, lung, and muscle tissues.

Figure 2—figure supplement 8.

(a, b) PCA of expression values of 16,197 genes across four tissues (cortex, liver, lung, muscle) of 47 individuals in GTEx. Values in parentheses show the variance explained by each PC. (c) The change in mean pairwise Euclidean distance between the PC values for the tissues of the same individuals (y-axis) with age (x-axis). (d–g) Association between the first four PCs (y-axis) and age (x-axis). The tissue and age of the samples are indicated by the colour and size of the points, respectively. Spearman’s correlation test results are indicated in each plot.
Figure 2—figure supplement 9. Coefficient of variation (CoV) and pairwise correlation analysis of GTEx dataset covering cortex, liver, lung, and muscle tissues.

Figure 2—figure supplement 9.

(a, b) Transcriptome-wide mean (a) and median (b) CoV change with age across four tissues (cortex, liver, lung, muscle) in GTEx. Each point represents the mean or median CoV value of all protein-coding genes (16,197) for each individual (n = 47) in GTEx. Spearman’s correlation coefficients and p-values are also presented in the plot. (c) The change in pairwise Spearman’s correlation coefficient between gene expression values of the same individual across ages (y-axis) with age (x-axis). Spearman’s correlation coefficient and p-values between the pairwise tissue correlations and age are also presented in each plot.
Figure 2—figure supplement 10. Principal components analysis (PCA) of GTEx dataset with 10 tissues.

Figure 2—figure supplement 10.

(a, b) PCA of expression values of 16,290 genes across 10 tissues of 35 individuals in GTEx. Values in parentheses show the variance explained by each PC. (c) The change in mean pairwise Euclidean distance between the PC values for the tissues of the same individuals (y-axis) with age (x-axis). (d–g) Association between the first four PCs (y-axis) and age (x-axis). The tissue and age of the samples are indicated by the colour and size of the points, respectively.
Figure 2—figure supplement 11. Coefficient of variation (CoV) and pairwise correlation analysis of GTEx dataset with 10 tissues.

Figure 2—figure supplement 11.

(a, b) Transcriptome-wide mean (a) and median (b) CoV change with age across 10 tissues in GTEx. Each point represents the mean or median CoV value of all protein-coding genes (16,290) for each individual (n = 35) in GTEx. Spearman’s correlation coefficients and p-values are also presented in the plot. (c) Age-related changes in pairwise Spearman’s correlation coefficient between gene expression values of the same individual. The colour of points shows the correlations between age and pairwise correlations, where darker red colour indicates an increased correlation with age and darker blue indicates a decreased correlation. The size of points shows the mean similarity (correlation) between tissues using all ages. None of the correlations is significant after multiple testing correction (using Benjamini–Hochberg [BH]).
Figure 2—figure supplement 12. Permutation test result for the proportion of divergence-convergence (DiCo) genes.

Figure 2—figure supplement 12.

DiCo genes (n = 4802) were tested with a permutation-based test explained in Materials and methods. We kept the divergent genes (n = 9058) in development constant and permuted age labels of individuals in the ageing period. Then, we calculated the DiCo proportion among those genes in permutations. ‘Obs‘: observed DiCo proportion (Obs = 4802/9058, i.e. DiCo/(DiCo + Di–); Di~: divergence across lifetime). Estimated false-positive proportion (eFPP) was calculated as the median expected proportion divided by the observed value. The p-value was calculated as the proportion of permutations that are higher than or equal to the observed value.
Figure 2—figure supplement 13. Clustering of tissues by the presence of samples from the same individuals.

Figure 2—figure supplement 13.

Heatmap showing whether individuals (columns) have samples (light blue colour) in tissues (y-axis).
Figure 2—figure supplement 14. Reproducing Figure 2 results with variance stabilising transformation (VST) normalisation.

Figure 2—figure supplement 14.

(a) Transcriptome-wide mean coefficient of variation (CoV) trajectory with age. Each point represents the mean CoV value of all protein-coding genes (14,973) for each mouse (n = 15) except the one that lacks expression data in the cortex. (b) Age effect on CoV value of the Cd93 gene which has the highest rank for the divergence-convergence (DiCo) pattern in four tissues (Materials and methods). CoV increases during development and decreases during ageing, indicating expression levels show DiCo patterns among tissues. (c) Expression trajectories of the gene Cd93 in four tissues. (d) The number of significant CoV changes with age (false discovery rate [FDR]-corrected p-value<0.1) during development (left, nconverge = 398, ndiverge = 3,078) and ageing (right, nconverge = 13, ndiverge = 6). Converge: genes showing a negative correlation (ρ) between CoV and age; diverge: genes showing a positive correlation between CoV and age. (e) Log2 ratio of convergent/divergent genes in development and in ageing. The graph represents only genes showing significant CoV changes (at FDR-corrected p-value<0.1, given in panel d). Error bars represent the range of log2 ratios calculated from leave-one-out samples in jackknife procedure.
Figure 2—figure supplement 15. Effect of heteroscedasticity to divergence-convergence (DiCo) pattern.

Figure 2—figure supplement 15.

Two different heteroscedasticity tests were performed to compare DiCo (n = 4802) vs. divergent-divergent (DiDi) (n = 4182, divergent throughout the lifetime) genes to test whether the convergence pattern is a result of the regression towards the mean. (a) Density plots of Spearman’s correlation coefficients (x-axis) between heterogeneity and age for DiCo and DiDi genes in each tissue. Heterogeneity was calculated as the absolute residuals of the linear regression between age (log2 scale) and expression (see Materials and methods). Only in muscle tissue the two-sided Kolmogorov–Smirnov (KS) test result was marginally significant in the direction of higher heterogeneity change for DiDi genes (p=0.0496). (b) Density plots of chi-square test statistics (x-axis) from Breusch–Pagan test (from ‘car’ package in R) between expression level and age (log2 scale) for DiCo and DiDi genes in each tissue. Only in muscle tissue the two-sided KS test result was significant in the direction of higher heterogeneity change for DiDi genes (p=0.0423). p-Values of KS test results between DiCo and DiDi genes are given within each plot.
Figure 2—figure supplement 16. Sex effect on coefficient of variation (CoV) analysis using GTEx.

Figure 2—figure supplement 16.

(a, b) Transcriptome-wide mean (a) and median (b) CoV change with age across four tissues (cortex, liver, lung, muscle) in GTEx for female (n = 11) and male (n = 36) individuals separately. Each point represents the mean or median CoV value of all protein-coding genes (16,197) for each individual. Spearman’s correlation coefficients and p-values are also presented in the plots. (c, d) The change in pairwise Spearman’s correlation coefficient between gene expression values of the same individual (y-axis) for (c) females (n = 11) and (d) males (n = 36), across ages (x-axis). Spearman’s correlation coefficient and p-values between the pairwise tissue correlations and age are also presented in each plot.
Figure 2—figure supplement 17. Principal components analysis (PCA) of Schaum dataset covering cortex, liver, lung, and muscle tissues.

Figure 2—figure supplement 17.

(a, b) PCA of expression values of 16,806 genes across four tissues (cortex, liver, lung, muscle) of 37 individuals in the Schaum dataset. Values in parentheses show the variance explained by each PC. (c) The change in mean pairwise Euclidean distance between the PC values for the tissues of the same individuals (y-axis) with age (x-axis, in months). (d–g) Association between the first four PCs (y-axis) and age (x-axis, in months). The tissue and age of the samples are indicated by the colour and size of the points, respectively. Spearman’s correlation test results are indicated in each plot.
Figure 2—figure supplement 18. Coefficient of variation (CoV) and pairwise correlation analysis of Schaum dataset covering cortex, liver, lung, and muscle tissues.

Figure 2—figure supplement 18.

(a, b) Transcriptome-wide mean (a) and median (b) CoV change with age (in months) across four tissues (cortex, liver, lung, muscle) in Schaum dataset. Each point represents the mean or median CoV value of all protein-coding genes (16,806) for each individual (n = 37). Spearman’s correlation coefficients and p-values are also presented in the plot. (c) The change in pairwise Spearman’s correlation coefficient between gene expression values of the same individual (y-axis) with age (x-axis, in months). Spearman’s correlation coefficient and p-values between the pairwise tissue correlations and age are also presented in each plot.
Figure 2—figure supplement 19. Principal components analysis (PCA) of Schaum dataset with eight tissues.

Figure 2—figure supplement 19.

(a, b) PCA of expression values of 17,619 genes across eight tissues of 26 individuals in the Schaum dataset. Values in parentheses show the variance explained by each PC. (c) The change in mean pairwise Euclidean distance between the PC values for the tissues of the same individuals (y-axis) with age (x-axis, in months). (d–g) Association between the first four PCs (y-axis) and age (x-axis, in months). The tissue and age of the samples are indicated by the colour and size of the points, respectively.
Figure 2—figure supplement 20. Coefficient of variation (CoV) and pairwise correlation analysis of Schaum dataset with eight tissues.

Figure 2—figure supplement 20.

(a, b) Transcriptome-wide mean (a) and median (b) CoV change with age (in months) across eight tissues (brain [cortex], heart, kidney, liver, lung, muscle, spleen, subcutaneous fat) in Schaum dataset. Each point represents the mean or median CoV value of all protein-coding genes (17,619) for each individual (n = 26). Spearman’s correlation coefficients and p-values are also presented in the plot. (c) Age-related changes in pairwise Spearman’s correlation coefficient between gene expression values of the same individual. The colour of points shows the correlations between age and pairwise correlations, where darker red colour indicates an increased correlation with age and darker blue indicates a decreased correlation. The size of points shows the mean similarity (correlation) between tissues using all ages. Significant correlations are indicated with circles around the points after multiple testing correction using ‘Benjamini–Hochberg (BH) (5/7 of significant correlations were positive).