Soltani Mohammad, Singh Abhyudai
Department of Electrical and Computer Engineering , University of Delaware, Newark , DE, USA.
Department of Electrical and Computer Engineering, University of Delaware, Newark, DE, USA; Department of Mathematical Sciences, University of Delaware, Newark, DE, USA; Department of Biomedical Engineering, University of Delaware, Newark, DE, USA.
R Soc Open Sci. 2016 Dec 7;3(12):160578. doi: 10.1098/rsos.160578. eCollection 2016 Dec.
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.
随着细胞在不同细胞周期阶段的转变，许多基因的表达会发生变化。随机表达与细胞周期之间的耦合如何影响蛋白质水平的细胞间变异性（噪声），目前还不太清楚。我们分析了一个模型，其中一种稳定的蛋白质以随机脉冲的形式合成，并且脉冲发生的频率在细胞周期内有所不同。推导了量化蛋白质拷贝数波动程度的公式，并将其分解为细胞周期和随机过程产生的成分。后一种随机成分代表了爆发式表达的贡献以及分子在子细胞间分配过程中产生的误差。这些公式揭示了一个有趣的权衡：放大爆发式表达噪声贡献的细胞周期依赖性也会减弱分配误差的贡献。我们研究了将表达与细胞周期耦合以最小化随机成分的最优策略的存在性。有趣的是，结果表明，在整个细胞周期中生产率为零，仅在细胞分裂前才进行表达，对于固定的平均蛋白质水平，可使爆发式表达产生的噪声最小化。相比之下，在存在分配误差的情况下，最优策略是在细胞分裂后合成蛋白质。我们提供了仅在细胞周期末期才表达的调节蛋白的例子，并认为这些策略增强了细胞周期决策对基因表达内在随机性的稳健性。
