Abstract
Expression of many genes varies as a cell transitions through different cell-cycle stages. How coupling between stochastic expression and cell cycle impacts cell-to-cell variability (noise) in the level of protein is not well understood. We analyse a model where a stable protein is synthesized in random bursts, and the frequency with which bursts occur varies within the cell cycle. Formulae quantifying the extent of fluctuations in the protein copy number are derived and decomposed into components arising from the cell cycle and stochastic processes. The latter stochastic component represents contributions from bursty expression and errors incurred during partitioning of molecules between daughter cells. These formulae reveal an interesting trade-off: cell-cycle dependencies that amplify the noise contribution from bursty expression also attenuate the contribution from partitioning errors. We investigate the existence of optimum strategies for coupling expression to the cell cycle that minimize the stochastic component. Intriguingly, results show that a zero production rate throughout the cell cycle, with expression only occurring just before cell division, minimizes noise from bursty expression for a fixed mean protein level. By contrast, the optimal strategy in the case of partitioning errors is to make the protein just after cell division. We provide examples of regulatory proteins that are expressed only towards the end of the cell cycle, and argue that such strategies enhance robustness of cell-cycle decisions to the intrinsic stochasticity of gene expression.
Highlights
Advances in experimental technologies over the last decade have provided important insights into gene expression at a single-molecule and single-cell resolution
We illustrate an approach based on closing moment dynamics for deriving an exact analytical formula for the mean protein level
The first step is to obtain differential equations describing the time evolution of the statistical moments for x(t) and ci(t). These equations can be derived using the chemical master equation (CME) corresponding to the stochastic model presented in the previous section
Summary
Advances in experimental technologies over the last decade have provided important insights into gene expression at a single-molecule and single-cell resolution. Mathematical models have played a key role in predicting the impact of bursty expression on noise in the level of a given protein These studies have primarily relied on models where synthesis rates are assumed to be constant and invariant of cell-cycle processes. While such an assumption is clearly violated for cell-cycle-regulated genes [30], replication-associate changes in gene dosage can alter expression parameters genome wide [31–34]. In addition to stochastic expression in bursts, the model incorporates other physiological noise sources, such as variability in the duration of cell-cycle times and random partitioning of molecules between daughter cells at the time of division [38–46]. We discuss intuitive reasoning behind these optimal strategies, and provide examples of proteins that are expressed in this manner to enhance fidelity of cell-cycle decisions
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