Emergent Statistical Laws in Single-Cell Transcriptomic Data

Large scale data on single-cell gene expression have the potential to unravel the specific transcriptional programs of different cell types. The structure of these expression datasets suggests a similarity with several other complex systems that can be analogously described through the statistics of their basic building blocks. Transcriptomes of single cells are collections of messenger RNA abundances transcribed from a common set of genes just as books are different collections of words from a shared vocabulary, genomes of different species are specific compositions of genes belonging to evolutionary families, and ecological niches can be described by their species abundances. Following this analogy, we identify several emergent statistical laws in single-cell transcriptomic data closely similar to regularities found in linguistics, ecology or genomics. A simple mathematical framework can be used to analyze the relations between different laws and the possible mechanisms behind their ubiquity. Importantly, treatable statistical models can be useful tools in transcriptomics to disentangle the actual biological variability from general statistical effects present in most component systems and from the consequences of the sampling process inherent to the experimental technique. Author summaryGene expression profiles represent how different cells use their genetic information. Similarly, books are specific collections of words chosen from a shared vocabulary, and many complex systems can be ultimately described by the statistics of their basic components. Leveraging on this analogy, we identified several emergent statistical laws in single-cell transcriptomic data that are universally found in complex component systems. A simple mathematical description sets these laws in a treatable quantitative framework and represents a useful tool for dissecting the different sources of gene expression variability.