The nonlinear dynamics and fluctuations of mRNA levels in cell cycle coupled transcription

by Qiwen Sun, Feng Jiao, Genghong Lin, Jianshe Yu, Moxun Tang

Gene transcription is a noisy process, and cell division cycle is an important source of gene transcription noise. In this work, we develop a mathematical approach by coupling transcription kinetics with cell division cycles to delineate how they are combined to regulate transcription output and noise. In view of gene dosage, a cell cycle is divided into an early stage S 1 and a late stage S 2. The analytical forms for the mean and the noise of mRNA numbers are given in each stage. The analysis based on these formulas predicts precisely the fold change r* of mRNA numbers from S 1 to S 2 measured in a mouse embryonic stem cell line. When transcription follows similar kinetics in both stages, r* buffers against DNA dosage variation and r* ∈ (1, 2). Numerical simulations suggest that increasing cell cycle durations up-regulates transcription with less noise, whereas rapid stage transitions induce highly noisy transcription. A minimization of the transcription noise is observed when transcription homeostasis is attained by varying a single kinetic rate. When the transcription level scales with cellular volume, either by reducing the transcription burst frequency or by increasing the burst size in S 2, the noise shows only a minor variation over a wide range of cell cycle stage durations. The reduction level in the burst frequency is nearly a constant, whereas the increase in the burst size is conceivably sensitive, when responding to a large random variation of the cell cycle durations and the gene duplication time.