Reconstructing Statistics of Promoter Switching from Reporter Protein Population Snapshot Data

The use of fluorescent reporter proteins is an established experimental approach for dynamic quantification of gene expression over time. Yet, the observed fluorescence levels are only indirect measurements of the relevant promoter activity. At the level of population averages, reconstruction of mean activity profiles from mean fluorescence profiles has been addressed with satisfactory results. At the single cell level, however, promoter activity is generally different from cell to cell. Making sense of this variability is at the core of single-cell modelling, but complicates the reconstruction task. Here we discuss reconstruction of promoter activity statistics from time-lapse population snapshots of fluorescent reporter statistics, as obtained e.g. by flow-cytometric measurements of a dynamical gene expression experiment. After discussing the problem in the framework of stochastic modelling, we provide an estimation method based on convex optimization. We then instantiate it in the fundamental case of a single promoter switch, reflecting a typical random promoter activation or deactivation, and discuss estimation results from in silico experiments.