Zeron E S, Santillán M
Centro de Investigación y de Estudios Avanzados del IPN, Departamento de Matemáticas, Av. Instituto Politécnico Nacional 2508, México DF, México.
Methods Enzymol. 2011;487:147-69. doi: 10.1016/B978-0-12-381270-4.00006-8.
In this work, we introduce a couple of algorithms to compute the stationary probability distribution for the chemical master equation (CME) of arbitrary chemical networks. We further find the conditions guaranteeing the algorithms' convergence and the unity and stability of the stationary distribution. Next, we employ these algorithms to study the mRNA and protein probability distributions in a gene regulatory network subject to negative feedback regulation. In particular, we analyze the influence of the promoter activation/deactivation speed on the shape of such distributions. We find that a reduction of the promoter activation/deactivation speed modifies the shape of those distributions in a way consistent with the phenomenon known as mRNA (or transcription) bursting.
在这项工作中，我们引入了几种算法来计算任意化学网络的化学主方程（CME）的稳态概率分布。我们进一步找到了保证算法收敛以及稳态分布的归一性和稳定性的条件。接下来，我们使用这些算法来研究受负反馈调节的基因调控网络中的mRNA和蛋白质概率分布。特别地，我们分析了启动子激活/失活速度对这些分布形状的影响。我们发现，启动子激活/失活速度的降低会以一种与称为mRNA（或转录）爆发的现象相一致的方式改变这些分布的形状。
