Identifying sub-populations of cells in single cell transcriptomic data – a Bayesian mixture modelling approach to zero-inflation of counts

In the study of single cell RNA-seq data, a key component of the analysis is to identify sub-populations of cells in the data. A variety of approaches to this have been considered, and although many machine learning based methods have been developed, these rarely give an estimate of uncertainty in the cluster assignment. To allow for this probabilistic models have been developed, but single cell RNA-seq data exhibit a phenomenon known as dropout, whereby a large proportion of the observed read counts are zero. This poses challenges in developing probabilistic models that appropriately model the data. We develop a novel Dirichlet process mixture model which employs both a mixture at the cell level to model multiple populations of cells, and a zero-inflated negative binomial mixture of counts at the transcript level. By taking a Bayesian approach we are able to model the expression of genes within clusters, and to quantify uncertainty in cluster assignments. It is shown that this approach out-performs previous approaches that applied multinomial distributions to model single cell RNA-seq counts and negative binomial models that do not take into account zero-inflation. Applied to a publicly available data set of single cell RNA-seq counts of multiple cell types from the mouse cortex and hippocampus, we demonstrate how our approach can be used to distinguish sub-populations of cells as clusters in the data, and to identify gene sets that are indicative of membership of a sub-population. The methodology is implemented as an open source Snakemake pipeline available from https://github.com/tt104/scmixture .