Kinetic Foundation of the Zero-Inflated Negative Binomial Model for Single-Cell RNA Sequencing Data

Single-cell RNA sequencing data have complex features such as dropout events, overdispersion, and high-magnitude outliers, resulting in complicated probability distributions of mRNA abundances that are statistically characterized in terms of a zero-inflated negative binomial (ZINB) model. Here we provide a mesoscopic kinetic foundation for the widely used ZINB model based on the biochemical reaction kinetics underlying transcription. Using multiscale modeling and simplification techniques, we show that the ZINB distribution of mRNA abundance and the related phenomenon of transcriptional bursting naturally emerge from a three-state stochastic transcription model. We further reveal a nontrivial quantitative relationship between dropout events and transcriptional bursting, which provides novel insights into how the burst size and burst frequency affect the dropout rate. Two different biophysical origins of overdispersion are also clarified at the single-cell level.