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%.

中文翻译：

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细胞周期变异性对信使 RNA 丰度的谱系和种群测量的影响

许多基因表达模型并未明确包含细胞周期描述。在这里，我们推导出了一个理论，描述了组成型和突发基因表达的信使 RNA (mRNA) 波动如何受到细胞周期持续时间和 DNA 复制时间的随机性的影响。矩的分析表达式表明，省略细胞周期持续时间会在 mRNA 的预测平均数中引入误差，这是 η 的单调递减函数，它与平均细胞周期持续时间和 mRNA 寿命的比率成正比。相比之下，对于与许多生物体的全基因组测量一致的 η 中间值，mRNA 分布方差的误差最高。使用真核细胞数据，我们估计均值和方差的误差最多为 3% 和 25%，分别。此外，我们推导出了 mRNA 分布的准确负二项式混合近似。这表明细胞周期中的随机性会导致 mRNA 数量的波动，这类似于突发转录的影响。最后，我们表明，对于真实的实验数据，忽略细胞周期随机性可能会在转录率的推断中引入大于 10% 的错误。