  Single-cell RNA sequencing data have complex features such as dropout events,
over-dispersion, 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 of 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 phenomenon of transcriptional bursting naturally emerge
from a three-state stochastic transcription model. We further reveal a
nontrivial quantitative relation between dropout events and transcriptional
bursting, which provides novel insights into how and to what extent the burst
size and burst frequency could reduce the dropout rate. Three different
biophysical origins of over-dispersion are also clarified at the single-cell
level.
