Stochastic gene expression out-of-steady-state in the cyanobacterial circadian clock

Recent advances in measuring gene expression at the single- cell level have highlighted the stochastic nature of messenger RNA and protein synthesis(1-3). Stochastic gene expression creates a source of variability in the abundance of cellular components, even among isogenic cells exposed to an identical environment. Recent integrated experimental and modelling studies(4-13) have shed light on the molecular sources of this variability. However, many of these studies focus on systems that have reached a steady state and therefore do not address a large class of dynamic phenomena including oscillatory gene expression. Here we develop a general protocol for analysing and predicting stochastic gene expression in systems that never reach steady states. We use this framework to analyse experimentally stochastic expression of genes driven by the Synechococcus elongatus circadian clock. We find that, although the average expression at two points in the circadian cycle separated by 12 hours is identical, the variability at these two time points can be different. We show that this is a general feature of out- of- steady- state systems. We demonstrate how intrinsic noise sources, owing to random births and deaths of mRNAs and proteins, or extrinsic noise sources, which introduce fluctuations in rate constants, affect the cell- to- cell variability. To distinguish experimentally between these sources, we measured how the correlation between expression fluctuations of two identical genes is modulated during the circadian cycle. This quantitative framework is generally applicable to any out- of steady state system and will be necessary for understanding the fidelity of dynamic cellular systems.