Inferring RNA production rates and rate-limiting steps in transcription from single-cell, single-RNA microscopy images at two time moments

A technique was recently proposed to dissect the in vivo kinetics of transcription initiation from single-cell microscopy data. It requires tracking cells and their fluorescently tagged RNAs by cell segmentation at many time moments, which is laborious and time consuming. We propose a novel method, based on differential equations and statistical techniques, to infer the mean of RNA production intervals from microscopy images taken at two time moments.
For this, we first extract the distribution of MS2-GFP RNA spot intensities from a cell population at the two time moments and quantify the corresponding single-cell RNA numbers, by fitting a Gaussian mixture model. Then, from the RNA distribution in these two moments, the RNA production intervals are estimated by solving the chemical master equation. This is performed by applying maximum likelihood fit on the distribution of single-cell RNA numbers in the two moments, in order to infer the best fitted model, its rate liming steps, and the associated intervals.
Afterwards, from inferred intervals from cells differing in intracellular RNA polymerase concentration but similar growth rates, the two main rate-limiting steps of transcription initiation are dissected. In the end, we show that our method provides a similarly accurate result to the method that requires tracking cells for many consecutive time moments.