Bayesian inference of transcription dynamics from population snapshots of single-molecule RNA FISH in single cells

Single-molecule RNA fluorescence in situ hybridization (smFISH) provides unparalleled resolution on the abundance and localization of nascent and mature transcripts in single cells. Gene expression dynamics are typically inferred by measuring mRNA abundance in small numbers of fixed cells sampled from a population at multiple time-points after induction. The sparse data that arise from the small number of cells obtained using smFISH present a challenge for inferring transcription dynamics. Here, we developed a computational pipeline (BayFish) to infer kinetic parameters of gene expression from smFISH data at multiple time points after induction. Given an underlying model of gene expression, BayFish uses a Monte Carlo method to estimate the Bayesian posterior probability of the model parameters and quantify the parameter uncertainty given the observed smFISH data. We tested BayFish on smFISH measurements of the neuronal activity inducible gene Npas4 in primary neurons. We showed that a 2-state promoter model can recapitulate Npas4 dynamics after induction and we inferred that the transition rate from the promoter OFF state to the ON state is increased by the stimulus.\n\nAuthor SummaryGene expression can exhibit cell-to-cell variability due to the stochastic nature of biochemical reactions. Single cell assays (e.g. smFISH) directly quantify stochastic gene expression by measuring the number of active promoters and transcripts per cell in a population of cells. The data are distributions and their shape and time-evolution contain critical information on the underlying process of gene expression. Recent work has combined models of stochastic gene expression with maximum likelihood methods to infer kinetic parameters from smFISH distributions. However, these approaches do not provide a probability distribution or likelihood of model parameters inferred from the smFISH data. This information is useful because it indicates which parameters are loosely constrained by the data and suggests follow up experiments. We developed a suite of MATLAB programs (BayFish) that estimate the Bayesian posterior probability of model parameters from smFISH data. The user specifies an underlying model of stochastic gene expression with unknown parameters ({theta}) and provides smFISH data (Y). BayFish uses a Monte Carlo algorithm to estimate the Bayesian posterior probability P({theta}|Y) of model parameters. BayFish is easily modified and can be applied to other models of stochastic gene expression and smFISH data sets.