Accurate inference of stochastic gene expression from nascent transcript heterogeneity

Abstract

Transcriptional rates are often estimated by fitting the distribution of mature mRNA numbers measured using smFISH (single molecule fluorescence in situ hybridization) with the distribution predicted by the telegraph model of gene expression, which defines two promoter states of activity and inactivity. However, fluctuations in mature mRNA numbers are strongly affected by processes downstream of transcription. In addition, the telegraph model assumes one gene copy, but in experiments cells may have two gene copies as cells replicate their genome during the cell cycle. It is thus unclear how accurately the inferred parameters reflect transcription. To address these issues, here we measure both mature and nascent mRNA distributions of GAL10 in yeast cells using smFISH and classify each cell according to its cell cycle stage. We infer transcriptional parameters from mature and nascent mRNA distributions, with and without accounting for cell cycle stage and compare the results to live-cell transcription measurements of the same gene. We conclude that: (i) not accounting for cell cycle dynamics in nascent mRNA data overestimates the magnitude of promoter switching rates and the initiation rate, and underestimates the fraction of time spent in the active state and the burst size. (ii) use of mature mRNA data, instead of nascent data, significantly increases the errors in parameter estimation and can mistakenly classify a gene as non-bursting. Furthermore, we show how to correctly adjust for measurement noise in sm-FISH at low nascent transcript numbers. Simulations with parameters estimated from nascent smFISH data corrected for cell cycle phases and measurement noise leads to autocorrelation functions that agree with those obtained from live-cell imaging. Therefore, our novel data curation method yields a quantitatively accurate picture of gene expression.