Abstract
Cell-to-cell heterogeneity is driven by stochasticity in intracellular reactions and the population dynamics. While these sources are usually studied separately, we develop an agent-based framework that accounts for both factors while tracking every single cell of a growing population. Apart from the common intrinsic variability, the framework also predicts extrinsic noise without the need to introduce fluctuating rate constants. Instead, extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age. We provide explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics in two-colour experiments. We find that these statistics differ significantly depending on the experimental setup used to observe the cells. We illustrate this fact using (i) averages over an isolated cell lineage tracked over many generations as observed in the mother machine, (ii) population snapshots with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots with unknown cell ages as measured from static images or flow cytometry. Applying the method to models of stochastic gene expression and feedback regulation elucidates that isolated lineages, as compared to snapshot data, can significantly overestimate the mean number of molecules, overestimate extrinsic noise but underestimate intrinsic noise and have qualitatively different sensitivities to cell cycle fluctuations.
Highlights
Cellular behaviour varies substantially from cell to cell and over time[1,2,3]
Cells divide at random times, so divisions occur asynchronously, which results in distributed cell ages and molecule numbers across the population
The approximation assumes Gaussian fluctuations and provides closed-form expressions for the mean molecule numbers EΠ[x|τ] and the covariance matrix CovΠ[x|τ] = EΠ[xxT| τ] − EΠ[x|τ]EΠ[xT|τ], which leads to the moment equations
Summary
Cellular behaviour varies substantially from cell to cell and over time[1,2,3]. Identifying the sources of these fluctuations can help reveal the function of gene circuits and signalling networks and understand how clonal cells diversify their responses. Extrinsic noise originates from factors affecting both circuits in the same way These can, for instance, be modelled by reaction rates that fluctuate between cells or over time due to shared resources, promoter architecture or upstream pathways. Generation times in Escherichia coli[18], budding yeast[19] and mammalian cells[20] vary about 30–50% These sources should prevail in growing cells, populations and tissues. Modelling approaches for understanding the cell cycle effects on gene expression noise are only recently being developed[21,22,23,24,25,26,27] These studies are often restricted to a single isolated cell observed over successive cell divisions and measuring variability over time, similar to a lineage in the mother machine[28]. We are lacking the means with which to understand, compare and integrate www.nature.com/scientificreports/
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