Statistical mechanics approach to the sample deconvolution problem

Parameterizing cell-to-cell regulatory heterogeneities via stochastic transcriptional profiles

Regulated changes in gene expression underlie many biological processes, but globally profiling cell-to-cell variations in transcriptional regulation is problematic when measuring single cells. Transcriptome-wide identification of regulatory heterogeneities can be robustly achieved by randomly collecting small numbers of cells followed by statistical analysis. However, this stochastic-profiling approach blurs out the expression states of the individual cells in each pooled sample. Here, we show that the underlying distribution of single-cell regulatory states can be deconvolved from stochastic-profiling data through maximum-likelihood inference. Guided by the mechanisms of transcriptional regulation, we formulated plausible mixture models for cell-to-cell regulatory heterogeneity and maximized the resulting likelihood functions to infer model parameters. Inferences were validated both computationally and experimentally for different mixture models, which included regulatory states for multicellular function that were occupied by as few as 1 in 40 cells of the population. Importantly, when the method was extended to programs of heterogeneously coexpressed transcripts, we found that population-level inferences were much more accurate with pooled samples than with one-cell samples when the extent of sampling was limited. Our deconvolution method provides a means to quantify the heterogeneous regulation of molecular states efficiently and gain a deeper understanding of the heterogeneous execution of cell decisions.