Abstract
Many models of gene expression do not explicitly incorporate a cell cycle description. Here, we derive a theory describing how messenger RNA (mRNA) fluctuations for constitutive and bursty gene expression are influenced by stochasticity in the duration of the cell cycle and the timing of DNA replication. Analytical expressions for the moments show that omitting cell cycle duration introduces an error in the predicted mean number of mRNAs that is a monotonically decreasing function of η, which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime. By contrast, the error in the variance of the mRNA distribution is highest for intermediate values of η consistent with genome-wide measurements in many organisms. Using eukaryotic cell data, we estimate the errors in the mean and variance to be at most 3% and 25%, respectively. Furthermore, we derive an accurate negative binomial mixture approximation to the mRNA distribution. This indicates that stochasticity in the cell cycle can introduce fluctuations in mRNA numbers that are similar to the effect of bursty transcription. Finally, we show that for real experimental data, disregarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%.
Highlights
Intrinsic noise in gene expression induces variability in the transcript number across a population of cells
In order to make this inference possible, it is necessary to have an accurate stochastic dynamical model that is able to relate the details of the messenger RNA number distribution to the different transcriptional and posttranscriptional molecular mechanisms involved in mRNA processing
We study the distribution of mRNA transcripts in single cells where expression can be bursty or non-bursty, with a cell cycle progression described as a number of stages having a stochastic duration
Summary
Intrinsic noise in gene expression induces variability in the transcript number across a population of cells. In order to make this inference possible, it is necessary to have an accurate stochastic dynamical model that is able to relate the details of the messenger RNA (mRNA) number distribution to the different transcriptional and posttranscriptional molecular mechanisms involved in mRNA processing This has been extensively done by describing the dynamics of the system by means of the Master Equation, a Markovian description whose solution gives the probability of observing a certain number of mRNAs in a cell at a certain time [4]. Similar discrepancies arise when mRNA distributions measured from snapshots of a growing cell population are compared with the temporal tracking of the expression levels of a single cell over time, apparently contradicting ergodicity between single cells and the population While this effect has been formalized mathematically [11], its relevance to the distributions of mRNA, or to the inference of different kinetic parameters, remains a conundrum.
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