SIAM Journal on Applied Mathematics, Volume 80, Issue 3, Page 1336-1355, January 2020.
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.

中文翻译：

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零膨胀负二项式模型的单细胞RNA测序数据的动力学基础

2020年1月，SIAM应用数学杂志，第80卷，第3期，第1336-1355页。
单细胞RNA测序数据具有复杂的特征，例如丢失事件，过度分散和高幅离群值，从而导致了mRNA丰度的复杂概率分布，并通过零膨胀负二项式（ZINB）模型进行了统计表征。在这里，我们基于转录的生化反应动力学为广泛使用的ZINB模型提供了介观动力学基础。使用多尺度建模和简化技术，我们表明，mRNA丰度的ZINB分布和相关的转录爆发现象自然从三态随机转录模型中出现。我们进一步揭示了辍学事件与转录爆发之间非平凡的定量关系，它提供了有关突发大小和突发频率如何影响丢包率的新颖见解。在单细胞水平上也阐明了过度分散的两种不同的生物物理起源。