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Abstract：
Stochastic gene expression dynamics can be modelled either discretely or continuously. Previous studies have shown that the mRNA or protein number distributions of some simple discrete and continuous gene expression models are related by Gardiner\'s Poisson representation. Here, we systematically investigate the Poisson representation in complex stochastic gene regulatory networks. We show that when the gene of interest is unregulated, the discrete and continuous descriptions of stochastic gene expression are always related by the Poisson representation, no matter how complex the model is. This generalizes the results obtained in Dattani & Barahona (Dattani & Barahona 2017 J. R. Soc. Interface 14, 20160833 (doi:10.1098/rsif.2016.0833)). In addition, using a simple counter-example, we find that the Poisson representation in general fails to link the two descriptions when the gene is regulated. However, for a general stochastic gene regulatory network, we demonstrate that the discrete and continuous models are approximately related by the Poisson representation in the limit of large protein numbers. These theoretical results are further applied to analytically solve many complex gene expression models whose exact distributions are previously unknown.
摘要：
随机基因表达动力学可以离散地或连续地建模。先前的研究表明，一些简单的离散和连续基因表达模型的mRNA或蛋白质数量分布与Gardiner的泊松表示有关。这里,我们系统地研究了复杂随机基因调控网络中的泊松表示。我们发现当感兴趣的基因不受调节时，随机基因表达的离散和连续描述总是与泊松表示相关，不管模型有多复杂。这概括了Dattani&Barahona(Dattani&Barahona2017J.R.Soc.界面14,20160833(doi:10.1098/rsif.2016.0833))。此外,使用一个简单的反例，我们发现，当基因受到调节时，泊松表示通常无法将这两个描述联系起来。然而,对于一般的随机基因调控网络，我们证明了离散和连续模型在大蛋白质数量的限制下通过泊松表示近似相关。这些理论结果进一步应用于分析解决许多复杂的基因表达模型，这些模型的确切分布是以前未知的。
