Recent advances in fluorescence microscopy have made it possible to measure the fluctuations of nascent (actively transcribed) RNA. These closely reflect transcription kinetics, as opposed to conventional measurements of mature (cellular) RNA, whose kinetics is affected by additional processes downstream of transcription. Here, we formulate a stochastic model which describes promoter switching, initiation, elongation, premature detachment, pausing, and termination while being analytically tractable. By computational binning of the gene into smaller segments, we derive exact closed-form expressions for the mean and variance of nascent RNA fluctuations in each of these segments, as well as for the total nascent RNA on a gene. We also derive exact expressions for the first two moments of mature RNA fluctuations, and approximate distributions for total numbers of nascent and mature RNA. Our results, which are verified by stochastic simulation, uncover the explicit dependence of the statistics of both types of RNA on transcriptional parameters and potentially provide a means to estimate parameter values from experimental data.

中文翻译：

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转录起始，延伸，暂停和终止的随机模型中新生RNA和成熟RNA波动的统计数据

荧光显微镜的最新进展使得测量新生（主动转录）RNA的波动成为可能。与成熟的（细胞）RNA的常规测量相反，它们紧密反映了转录动力学，而后者的动力学受转录下游附加过程的影响。在这里，我们制定了一个随机模型，该模型描述了启动子的切换，启动，延伸，过早脱离，暂停和终止，同时具有分析性。通过将基因分装成较小的片段，我们得出了每个片段中新生RNA波动的均值和方差以及基因上新生RNA的精确封闭形式表达。我们还可以得出成熟的RNA波动的前两个时刻的精确表达式，以及新生和成熟RNA总数的近似分布。我们的结果（通过随机模拟验证）揭示了两种RNA的统计数据对转录参数的明确依赖性，并可能提供一种从实验数据估算参数值的方法。