Dattani Justine, Barahona Mauricio
Department of Mathematics, Imperial College London, London SW7 2AZ, UK.
Department of Mathematics, Imperial College London, London SW7 2AZ, UK
J R Soc Interface. 2017 Jan;14(126). doi: 10.1098/rsif.2016.0833.
Gene transcription is a highly stochastic and dynamic process. As a result, the mRNA copy number of a given gene is heterogeneous both between cells and across time. We present a framework to model gene transcription in populations of cells with time-varying (stochastic or deterministic) transcription and degradation rates. Such rates can be understood as upstream cellular drives representing the effect of different aspects of the cellular environment. We show that the full solution of the master equation contains two components: a model-specific, upstream effective drive, which encapsulates the effect of cellular drives (e.g. entrainment, periodicity or promoter randomness) and a downstream transcriptional Poissonian part, which is common to all models. Our analytical framework treats cell-to-cell and dynamic variability consistently, unifying several approaches in the literature. We apply the obtained solution to characterize different models of experimental relevance, and to explain the influence on gene transcription of synchrony, stationarity, ergodicity, as well as the effect of time scales and other dynamic characteristics of drives. We also show how the solution can be applied to the analysis of noise sources in single-cell data, and to reduce the computational cost of stochastic simulations.
基因转录是一个高度随机且动态的过程。因此，给定基因的mRNA拷贝数在细胞之间以及随时间都是异质的。我们提出了一个框架，用于对具有随时间变化（随机或确定性）转录和降解速率的细胞群体中的基因转录进行建模。这些速率可以理解为代表细胞环境不同方面影响的上游细胞驱动因素。我们表明，主方程的完整解包含两个部分：一个特定于模型的上游有效驱动因素，它封装了细胞驱动因素的影响（例如夹带、周期性或启动子随机性），以及一个下游转录泊松部分，这是所有模型共有的。我们的分析框架一致地处理细胞间和动态变异性，统一了文献中的几种方法。我们应用得到的解来表征具有实验相关性的不同模型，并解释同步性、平稳性、遍历性对基因转录的影响，以及时间尺度和驱动因素的其他动态特征的影响。我们还展示了该解如何应用于单细胞数据中噪声源的分析，并降低随机模拟的计算成本。
