论文标题
基因表达的随机动力学中泊松分布的起源
The origin of the Poisson distribution in stochastic dynamics of gene expression
论文作者
论文摘要
泊松分布是给定时间段内独立事件数量的概率分布。尽管泊松分布在基因表达的各种随机动力学中普遍存在，但无论是时间依赖性分布还是固定分布，引起这种分布的独立事件的基本事件尚不清楚，尤其是在基因产物降解的情况下，这不是Poisson过程。我表明，实际上，遵循泊松分布的变量是创建生物分子的独立事件的数量，这些事件注定要生存，直到给定时间持续时间结束为止。这种新的观点使我们能够得出时间相关的泊松分布，作为通用类蛋白质生产和降解动态类的主方程的解决方案，包括具有时间依赖性速率的模型和具有延迟降解的非马克维亚模型。然后，我通过将泊松分布与二项式或多项式分布相结合，从而得出了一般时间依赖性概率分布的分析形式。
The Poisson distribution is the probability distribution of the number of independent events in a given period of time. Although the Poisson distribution appears ubiquitously in various stochastic dynamics of gene expression, both as time-dependent distributions and the stationary distributions, underlying independent events that give rise to such distributions have not been clear, especially in the presence of the degradation of gene products, which is not a Poisson process. I show that, in fact, the variable that follows the Poisson distribution is the number of independent events where biomolecules are created, which are destined to survive until the end of a given time duration. This new viewpoint allows us to derive time-dependent Poisson distributions as solutions of master equations for general class of protein production and degradation dynamics, including models with time-dependent rates and a non-Markovian model with delayed degradation. I then derive analytic forms of general time-dependent probability distributions by combining the Poisson distribution with the binomial or the multinomial distributions.
