Reconstruction of promoter activity statistics from reporter protein population snapshot data

A critical step in the analysis of the dynamics of gene expression and regulation from protein reporter data is the reconstruction of promoter activity. While devoted significant attention in a population-average setting, the problem has not been addressed in much detail for stochastic models and individual cell data. In this work we address the reconstruction of time profiles of promoter activity statistics, such as population mean and variance, from the corresponding statistics of reporter protein abundance in cell samples collected at subsequent times. Based on the so-called random telegraph model of gene expression, we address the problem both in terms of structural and practical identifiability of the model parameters and of the direct reconstruction of promoter activity mean and variance profiles via regularized deconvolution, providing analysis tools, theoretical results and application of our methods to the in silico analysis of a relevant example.