转录速率动力学与RNA拷贝数噪声：一般关系与数据驱动的预测
Transcription rate dynamics and RNA copy number noise: General relations and data-driven predictions
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中文总结 AI 辅助
本研究提出双重随机框架，推导RNA Fano因子与转录速率自协方差的关系，并验证数据驱动估计器及多种速率模型的解析结果。
中文摘要 AI 辅助
基因表达的随机模型通常从转录的微观模型出发，并将其统计特性传播到RNA分布。在此，我们开发了一个双重随机框架，其中RNA的产生在给定随时间变化的转录速率$\lambda(t)$的条件下服从泊松过程。对于从任意有限均值分布中独立抽取的RNA寿命，我们根据寿命生存函数和$\lambda(t)$的自协方差推导出RNA的Fano因子。对于速率为$\mu$的泊松降解过程，生存核提供了一个指数时间滤波器，结果仅取决于$\lambda(t)$的均值、方差和归一化自相关。这些量可以从显式速率模型计算，或在遍历性和充分采样的条件下，从足够长的速率轨迹中估计。我们使用模拟的转录速率轨迹验证了数据驱动的估计器，而未向估计器提供已知的自相关。我们还获得了由离散M/M/1过程以及具有反射、周期或首达重置边界的漂移-扩散过程建模的转录速率动力学的精确解析结果，并通过耦合转录速率和RNA拷贝数过程的直接模拟验证了每个结果。
英文摘要
Stochastic models of gene expression typically begin with a microscopic model of transcription and propagate its statistics to the RNA distribution. Here we develop a doubly stochastic framework in which RNA production is Poisson conditional on a time-varying transcription rate $λ(t)$. For RNA lifetimes drawn independently from an arbitrary finite-mean distribution, we derive the RNA Fano factor in terms of the lifetime survival function and the autocovariance of $λ(t)$. For a Poisson degradation process with rate $μ$, the survival kernel provides an exponential temporal filter, and the result depends only on the mean, variance, and normalized autocorrelation of $λ(t)$. These quantities may be calculated from an explicit rate model or, under ergodicity and adequate sampling, estimated from a sufficiently long rate trajectory. We validate the data-driven estimator using simulated transcription-rate trajectories, without supplying the known autocorrelation to the estimator. We also obtain exact analytical results for transcription-rate dynamics modeled by a discrete M/M/1 process and by drift-diffusion with reflecting, periodic, or first-passage-reset boundaries, and verify each result by direct simulation of the coupled transcription-rate and RNA copy-number processes.
发表机构
- New York University（纽约大学）
- University of Illinois at Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校）
- Tel Aviv University（特拉维夫大学）
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