Gene expression is an inherently stochastic process with transcription of mRNAs often occurring in bursts: short periods of activity followed by typically longer periods of inactivity. While a simple model involving switching between two promoter states has been widely used to analyze transcription dynamics, recent experimental observations have provided evidence for more complex kinetic schemes underlying bursting. Specifically, experiments provide evidence for complexity in promoter dynamics during the switch from the transcriptionally inactive to the transcriptionally active state. An open question in the field is: what is the minimal complexity needed to model promoter dynamics and how can we determine this? Here, we show that measurements of mRNA fluctuations can be used to set fundamental bounds on the complexity of promoter dynamics. We study models wherein the switching time distribution from transcriptionally inactive to active states is described by a general waiting-time distribution. Using approaches from renewal theory and queueing theory, we derive analytical expressions which connect the Fano factor of mRNA distributions to the waiting-time distribution for promoter switching between inactive and active states. The results derived lead to bounds on the minimal number of promoter states and thus allow us to derive bounds on the minimal complexity of promoter dynamics based on single-cell measurements of mRNA levels.

中文翻译：

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使用基因表达的波动来限制启动子动力学的复杂性。

基因表达是一个内在的随机过程，其mRNA的转录通常会突然爆发：活动的时间很短，随后通常是较长的不活动时间。虽然一个简单的模型涉及两个启动子状态之间的切换已被广泛用于分析转录动力学，但最近的实验观察为爆裂背后更复杂的动力学方案提供了证据。具体而言，实验提供了从转录无活性到转录活性状态的转换过程中启动子动力学复杂性的证据。该领域的一个悬而未决的问题是：对启动子动力学进行建模所需的最小复杂度是多少？我们如何确定这一点？在这里，我们表明，mRNA波动的测量可用于设置启动子动力学复杂性的基本界限。我们研究模型，其中从转录非激活状态到激活状态的切换时间分布由一般的等待时间分布来描述。使用来自更新理论和排队论的方法，我们得出了解析表达式，这些表达式将mRNA分布的Fano因子与启动子在非活动状态和活动状态之间切换的等待时间分布联系起来。得出的结果导致最小数目的启动子状态的界限，因此使我们能够基于mRNA水平的单细胞测量来得出最小的启动子动力学复杂性的界限。我们得到分析表达式，其将mRNA分布的Fano因子与启动子在非活性状态和活性状态之间切换的等待时间分布联系起来。得出的结果导致最小数目的启动子状态的界限，因此使我们能够基于mRNA水平的单细胞测量来得出最小的启动子动力学复杂性的界限。我们得到分析表达式，其将mRNA分布的Fano因子与启动子在非活性状态和活性状态之间切换的等待时间分布联系起来。得出的结果导致最小数目的启动子状态的界限，因此使我们能够基于mRNA水平的单细胞测量来得出最小的启动子动力学复杂性的界限。