Population growth affects intrinsic and extrinsic noise in gene expression

Clonal cells of exponentially growing populations vary substantially from cell to cell. The main drivers of this heterogeneity are the population dynamics and stochasticity in the intracellular reactions, which are commonly studied separately. Here we develop an agent-based framework that allows tracking of the biochemical dynamics in every single cell of a growing population that accounts for both of these factors. Apart from the common intrinsic variability of the biochemical reactions, the framework also predicts extrinsic noise arising from fluctuations in the histories of cells without the need to introduce fluctuating rate constants. Instead, these extrinsic fluctuations are explained by cell cycle fluctuations and differences in cell age, which are ubiquitously observed in growing populations. We give explicit formulas to quantify mean molecule numbers, intrinsic and extrinsic noise statistics as measured in two-colour experiments. We find that these statistics may 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) snapshots of a growing population with known cell ages as recorded in time-lapse microscopy, and (iii) snapshots of unknown cell ages as measured from static images. Our integrated approach applies to arbitrary biochemical networks and generation time distributions. By employing models of stochastic gene expression and feedback regulation, we elucidate 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.