Effects of cell cycle variability on lineage and population measurements of mRNA abundance

<jats:title>Abstract</jats:title><jats:p>Many models of gene expression do not explicitly in-corporate a cell cycle description. Here we derive a theory describing how mRNA fluctuations for constitutive and bursty gene expression are influenced by the stochasticity in the duration of the cell cycle and DNA replication. By means of the analytical expressions for the moments, we show that the error introduced in the predicted mean number of mRNAs, when noise in the cell cycle duration isomitted, is a monotonic decreasing function of <jats:italic>η</jats:italic> which is proportional to the ratio of the mean cell cycle duration and the mRNA lifetime; contrastingly, the error in the variance of the mRNA distribution peaks for intermediate values of <jats:italic>η</jats:italic> 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%. Further-more we derive an accurate negative binomial mixture approximation to the mRNA distribution and show that under certain conditions, bimodality can result from the doubling of the transcription rate when DNA duplicates. Finally, we show that for real genomic data, dis-regarding cell cycle stochasticity can introduce errors in the inference of transcription rates larger than 10%, supporting the relevance of the analysis presented.</jats:p>