The reduction of gene expression variability from single cells to populations follows simple statistical laws

Recent studies on single cells and population transcriptomics have revealed striking differences in global gene expression distributions. Single cells display highly variable expressions between cells, while cell populations present deterministic global patterns. The mechanisms governing the reduction of transcriptome-wide variability over cell ensemble size, however, remain largely unknown. To investigate transcriptome-wide variability of single cells to different sizes of cell populations, we examined RNA-Seq datasets of 6 mammalian cell types. Our statistical analyses show, for each cell type, increasing cell ensemble size reduces scatter in transcriptome-wide expressions and noise (variance over square mean) values, with corresponding increases in Pearson and Spearman correlations. Next, accounting for technical variability by the removal of lowly expressed transcripts, we demonstrate that transcriptome-wide variability reduces, approximating the law of large numbers. Subsequent analyses reveal that the entire gene expressions of cell populations and only the highly expressed portion of single cells are Gaussian distributed, following the central limit theorem.