Figure 6: Signalling entropy predicts regulated expression heterogeneity of single-cell populations.

(a) Definition of the measure of regulated expression heterogeneity (MRH). The MRH is a z-statistic, obtained by measuring the deviation of the signalling entropy (SR) of the bulk expression profile from the mean of single-cell entropies, taking into account the variability of single-cell entropies in the population. (b) Barplots of MRH for each cell-type population from Chu et al., representing the degree to which the signalling entropy of the cell population is higher than that of single cells. P values are from a one-tailed normal-deviation test. Dashed line indicates the line P=0.05. AvgBulkS compares the signalling entropy of the average expression over all bulk samples to that of the individual bulk samples, indicating that although the RHM is positive (signalling entropy increases), that it is not significantly higher than that of the individual bulk samples. (c) Scatterplot of the signalling entropy of bulk samples (y-axis), representing six cell-types (hESCs, NPCs, DEPs, TBs, HFFs, ECs) against the corresponding signalling entropies of these cell populations obtained by first averaging the expression profiles of single cells (‘Simulated Bulk’, x-axis). R² value and P value are given with green dashed line representing the fitted regression. Observe how the signalling entropy of bulk samples is always higher than that obtained from first averaging expression of single cells, in line with the fact that the assayed single cells are a subpopulation of the full bulk sample. (d) Left panel: comparison of the signalling entropy of an acute myeloid leukemia (AML) bulk sample (red line and point) to the signalling entropies of 96 single-AML cells (blue) from that bulk sample. P value is from a one-tailed normal deviation test. Right panel: comparison of the MRH value for the matched 96 single cells and bulk AML sample (SCs) to the MRH values obtained by comparing the signalling entropy of the average expression over 19 AML bulk samples to the signalling entropies of each individual AML bulk sample. The 19 AML bulk samples come in pairs, obtained at diagnosis (dgn) and relapse (rel), which are shown separately. P values are from a one-tailed normality deviation test.