Bayesian inference on stochastic gene transcription from flow cytometry data

Motivation Transcription in single cells is an inherently stochastic process as mRNA levels vary greatly between cells, even for genetically identical cells under the same experimental and environmental conditions. We present a stochastic two-state switch model for the population of mRNA molecules in single cells where genes stochastically alternate between a more active ON state and a less active OFF state. We derive the stationary solution of such a model and prove that it can be written as a mixture of a Poisson and a Poisson-beta probability distribution. This finding facilitates inference for single cell data, observed at a single time point, from flow cytometry experiments such as FACS or FISH as it allows one to sample directly from the equilibrium distribution of the mRNA population. We hence propose a Bayesian inferential methodology using a pseudo-marginal approach and a recent approximation to integrate over unobserved states associated with measurement error. Results We provide a general inferential framework which can be widely used to study transcription in single cells from the kind of data arising in flow cytometry experiments. The approach allows us to separate between the intrinsic stochasticity of the molecular dynamics and the measurement noise. The methodology is tested in simulation studies and results are obtained for experimental multiple single cell data from in situ hybridization (FISH) flow cytometry experiment