Fig 1.
Simulations of single-cell data reveal relative sensitivity of dispersion metrics across various data distributions.
(A) Examples of probability density functions of the Poisson, negative binomial, beta-Poisson, and uniform distributions with varying levels of dispersion, which were used to generate simulated single-cell counts. (B) Schematic of simulations of single-cell data. The Gini index, VMR, variance, entropy, CV, and CV2 were applied to the simulated data to assess their sensitivity to variability in the underlying distribution. The results were visualized in heatmaps. (C) Schematic for normalization of dispersion metrics.
Fig 2.
VMR is most sensitive to changes in dispersion.
(A) Heatmaps of each metric applied to simulated counts drawn from instances of the negative binomial distribution. The dispersion in the sampling distributions increases across the y-axis, as determined by the size parameter r for the negative binomial. The size of the simulated data increases across the x-axis, as determined by the number of cells in each counts matrix. (B) Heatmaps of relative change in each metric applied to counts from (A). (C) Histograms of deviation of relative change from mean relative change for each metric as calculated from the distributions described in (A). (D - F) Same as above for counts simulated from the beta-Poisson distribution. The theoretical variance increases as determined by a scaling factor on the β parameter.
Fig 3.
Examining the paradoxical behavior of the Gini index.
(A) The probability density functions of negative binomials with r = 1 and r = 10, both with p = 0.5. (B) Lorenz curve (blue) of data sampled from a negative binomial with r = 1 and r = 10, both with p = 0.5. The line of equality is shown in red.
Fig 4.
Absolute change in transcriptional variability is not correlated with transcription level, gene length, promoter GC content, and evolutionary gene age.
(A) Absolute change in transcriptional variability at E9.5 and at E11.5 is extremely weakly correlated with transcript levels as measured by average normalized counts. (B) The correlation coefficient of absolute change in transcriptional variability with transcript level varies with the threshold for removing lowly expressed genes at E9.5. Absolute change in transcriptional variability is also extremely weakly correlated with gene length (C), promoter GC content (D), and gene phylostrata (E).
Fig 5.
Transcriptional variability confirms known pathways involved in maternal hyperglycemia and suggests new targets.
(A) Venn diagram of the 100 most significant DEGs and the 100 genes with largest absolute change in VMR at E9.5 and at E11.5. There were 760 CMs in the control E9.5 conditions, 827 CMs in the matHG E9.5 condition, 752 CMs in the control E11.5 condition, and 1163 CMs in the matHG E11.5 condition. The significance of a DEG is measured by its adjusted p-value from differential gene expression testing using the Wilcoxon rank sum test. (B) GSEA using KEGG pathways on the 1000 most significant DEGs, ranked by log-fold change, and on the 1000 genes with largest absolute change in VMR, ranked by change in VMR at E9.5. (C) TF motif enrichment was performed on the 100 most significant DEGs and on the 100 genes with largest absolute change in VMR, and the top 5 enriched motifs from each are shown [37]. (D) Change in VMR versus average log-fold change in expression for genes in the KEGG Hippo signaling pathway. DEGs at E9.5 are shown in pink. (E) Dendrogram of TFs enriched among the 100 genes with largest absolute change in VMR at E9.5 and their target genes. Opacity of edge weights is determined by the change in VMR of the genes. DEGs are shown in gray.
Fig 6.
Change in VMR has a negative correlation with mean and fraction of expressing cells and varies between platforms.
In a Drop-seq neuron dataset, change in VMR inversely correlates with (A) the fraction of expressing cells and (B) change in mean expression. (C) Neurod6, a DEG, is the gene in this dataset with the largest absolute change in VMR between E11.5 and E17.5, whereas Stmn2, a non-DEG, also had a large absolute change in VMR between timepoints. In the 10x Genomics cardiomyocyte dataset comparing control and matHG conditions at E9.5, associations between VMR and UMI counts across cells behave similarly (D, E). Panel (F) shows Hbb-bt, a DEG with the largest absolute change in VMR at E9.5 between control and matHG. Igfbp5 had the 10th largest absolute change in VMR between conditions, and is not a DEG. A negative correlation between VMR changes and UMI distribution is again evident in the 10x Genomics dataset comparing WT and T21 cardiomyocytes (G, H). Panel (I) shows Thbs1, a gene with the largest absolute change in VMR between WT and T21 conditions. Col2a1 had the 10th largest absolute change in VMR between conditions, and had the largest fraction of expressing cells among the top 10 genes with largest change in VMR. Neither Thbs1 nor Col2a1 are DEGs.