Bhattacharyya Bhaswati, Kalay Ziya
Institute for Integrated Cell-Material Sciences (WPI-iCeMS), Kyoto University, Yoshida Ushinomiya-cho, Sakyo-ku, 606-8501, Japan.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012715. doi: 10.1103/PhysRevE.89.012715. Epub 2014 Jan 21.
Observation of phenotypic diversity in a population of genetically identical cells is often linked to the stochastic nature of chemical reactions involved in gene regulatory networks. We investigate the distribution of population-averaged gene expression levels as a function of population, or sample, size for several stochastic gene expression models to find out to what extent population-averaged quantities reflect the underlying mechanism of gene expression. We consider three basic gene regulation networks corresponding to transcription with and without gene state switching and translation. Using analytical expressions for the probability generating function of observables and large deviation theory, we calculate the distribution and first two moments of the population-averaged mRNA and protein levels as a function of model parameters, population size, and number of measurements contained in a data set. We validate our results using stochastic simulations also report exact results on the asymptotic properties of population averages which show qualitative differences among different models.
在基因相同的细胞群体中观察表型多样性，通常与基因调控网络中化学反应的随机性有关。我们研究了几种随机基因表达模型中群体平均基因表达水平随群体或样本大小的分布情况，以确定群体平均量在多大程度上反映了基因表达的潜在机制。我们考虑了三种基本的基因调控网络，分别对应有和没有基因状态转换的转录以及翻译过程。利用可观测量的概率生成函数的解析表达式和大偏差理论，我们计算了群体平均mRNA和蛋白质水平的分布以及前两个矩，它们是模型参数、群体大小和数据集中测量次数的函数。我们通过随机模拟验证了结果，并报告了群体平均值渐近性质的精确结果，这些结果显示了不同模型之间的定性差异。
