An information-theoretic view of sc-Seq data. Transcripts, or more generally counts, of a given gene (shown here as horizontal bars) are assigned to cells after sequencing. If the cell population is homogeneous with respect to the expression of g , then the heterogeneity I ( g ) will be zero (top left population, I(g)=0 ). In practice, the transcript assignment process is stochastic, and so there will always be some deviation from this ideal (bottom left population, I ( g ) small). (Note that the technical effects of this stochasticity on the information obtained may be reduced by using a shrinkage estimator to determine the distribution of transcripts (see “ Methods ” Section)). If the population is heterogeneous, then transcripts may be preferentially expressed in a subset of cells and the information obtained from the experiment, as measured by I ( g ) will be larger (top right population, I ( g ) large), reaching a maximum at log (N) , where N is the number of cells sequenced, when only one cell expresses the gene (bottom right population, I(g) = ln (5) ≈ 1.61 largest).Note that the population heterogeneity I ( g ) is independent of any decomposition of the cell populations into subpopulations (shown here as yellow and purple cells, for illustration). However, given any grouping of the cells into subpopulations, I ( g ) can be formally decomposed as the sum of the heterogeneity explained by within and in-between subpopulations (see “ Results ” Section and Fig. 3 ). This decomposition, but not the overall value of I ( g ), does depend on the chosen assignment of cells to subpopulations
