论文标题
生物细胞转录调节的随机模型
Stochastic Models of Regulation of Transcription in Biological Cells
论文作者
论文摘要
在本文中，我们使用特定的宏观分子6s RNA研究了生物细胞转录的重要全球调节机制。 6S RNA的功能特性是在细胞的环境不利时阻止RNA的转录。我们通过对随机模型的缩放分析研究了这种机制的效率。我们模型的演化方程是由质量作用定律驱动的，聚合酶的总数用作缩放参数。分析了两个制度：当细胞的环境有利于其增长的环境以及资源稀缺时的固定阶段时，指数阶段。在这两个制度中，通过定义模型的正确职业度量，我们证明了相关的多维马尔可夫流程在方便的时间表上的平均原理，以及系统快速变量的收敛结果。特别是获得了固定相聚合酶的渐近分数的分析表达。讨论了这些结果的后果。
In this paper we study an important global regulation mechanism of transcription of biological cells using specific macro-molecules, 6S RNAs. The functional property of 6S RNAs is of blocking the transcription of RNAs when the environment of the cell is not favorable. We investigate the efficiency of this mechanism with a scaling analysis of a stochastic model. The evolution equations of our model are driven by the law of mass action and the total number of polymerases is used as a scaling parameter. Two regimes are analyzed: exponential phase when the environment of the cell is favorable to its growth, and the stationary phase when resources are scarce. In both regimes, by defining properly occupation measures of the model, we prove an averaging principle for the associated multi-dimensional Markov process on a convenient timescale, as well as convergence results for fast variables of the system. An analytical expression of the asymptotic fraction of sequestrated polymerases in stationary phase is in particular obtained. The consequences of these results are discussed.
