Division of Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing 100193, China.
School of Biological Sciences, University of Edinburgh, Edinburgh, United Kingdom.
J Chem Phys. 2020 Feb 28;152(8):084115. doi: 10.1063/1.5144578.
A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here, we derive an alternative model that takes into account these fluctuations and, hence, can be used to study low protein number effects. The exact steady-state protein number distribution is derived as a sum of Gaussian hypergeometric functions. We use the theory to study how promoter switching rates and the type of feedback influence the size of protein noise and noise-induced bistability. Furthermore, we show that our model predictions for the protein number distribution are significantly different from those of Kumar et al. when the protein mean is small, gene switching is fast, and protein binding to the gene is faster than the reverse unbinding reaction.
库马尔等人的关于自调节突发基因表达的随机模型[Phys. Rev. Lett. 113, 268105 (2014)]在稳态条件下被精确求解，隐含的假设是蛋白质数量足够大，以至于由于可逆的蛋白质-启动子结合而导致的蛋白质数量的波动可以忽略不计。在这里，我们推导出一个考虑到这些波动的替代模型，因此可以用于研究低蛋白质数量的影响。精确的稳态蛋白质数量分布被推导为高斯超几何函数的和。我们使用该理论来研究启动子切换率和反馈类型如何影响蛋白质噪声的大小和噪声诱导的双稳性。此外，我们表明，当蛋白质平均值较小时，基因切换速度较快，并且蛋白质与基因的结合速度快于反向解结合反应时，我们的模型对蛋白质数量分布的预测与库马尔等人的预测有显著差异。
