Abstract
Gene expression is made up of inherently stochastic processes within single cells and can be modeled through stochastic reaction networks (SRNs). In particular, SRNs capture the features of intrinsic variability arising from intracellular biochemical processes. We extend current models for gene expression to allow the transcriptional process within an SRN to follow a random step or switch function which may be estimated using reversible jump Markov chain Monte Carlo (MCMC). This stochastic switch model provides a generic framework to capture many different dynamic features observed in single cell gene expression. Inference for such SRNs is challenging due to the intractability of the transition densities. We derive a model-specific birth–death approximation and study its use for inference in comparison with the linear noise approximation where both approximations are considered within the unifying framework of state-space models. The methodology is applied to synthetic as well as experimental single cell imaging data measuring expression of the human prolactin gene in pituitary cells.
Highlights
In single cells, gene expression is made up of fundamentally stochastic processes (Raj and Van Oudenaarden, 2008) due to intrinsic and extrinsic variation
We investigate the performance of the linear noise approximation (LNA) and BDA for approximating the posterior f (θ | y) of the underlying stochastic reaction networks (SRNs)
One could choose several candidates and perform model selection a posteriori, we found two components sufficient to capture the variability in the data, which is supported by the biological hypothesis that transcription will typically occur at either a high or low rate
Summary
Gene expression is made up of fundamentally stochastic processes (Raj and Van Oudenaarden, 2008) due to intrinsic and extrinsic variation. An important statistical problem arising from the use of reporter constructs, such as fluorescent and luminescent proteins, is to infer the unobserved transcriptional activity of the reporter, which can be related to the activity of the native gene (Finkenstadt and others, 2008). This activity is highly variable, occurring in stochastic pulses for many genes, including prolactin (Harper and others, 2011; Suter and others, 2011). We introduce a general stochastic switch model (SSM), to study pulsatile gene expression dynamics within single cells
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