Lin Genghong, Jiao Feng, Sun Qiwen, Tang Moxun, Yu Jianshe, Zhou Zhan
Center for Applied Mathematics, Guangzhou University, Guangzhou, 510006, People's Republic of China.
Department of Mathematics, Michigan State University, East Lansing, MI 48824, USA.
R Soc Open Sci. 2019 Mar 27;6(3):190286. doi: 10.1098/rsos.190286. eCollection 2019 Mar.
The transcription of inducible genes involves signalling pathways that induce DNA binding of the downstream transcription factors to form functional promoter states. How the transcription dynamics is linked to the temporal variations of activation signals is far from being fully understood. In this work, we develop a mathematical model with multiple promoter states to address this question. Each promoter state has its own activation and inactivation rates and is selected randomly with a probability that may change in time. Under the activation of constant signals, our analysis shows that if only the activation rates differ among the promoter states, then the mean transcription level () displays only a monotone or monophasic growth pattern. In a sharp contrast, if the inactivation rates change with the promoter states, then () may display multiphasic growth patterns. Upon the activation of signals that oscillate periodically, () also oscillates later, almost periodically at the same frequency, but the magnitude decreases with frequency and is almost completely attenuated at high frequencies. This gives a surprising indication that multiple promoter states could filter out the signal oscillation and the noise in the random promoter state selection, as observed in the transcription of a gene activated by p53 in breast carcinoma cells. Our approach may help develop a theoretical framework to integrate coherently the genetic circuit with the promoter states to elucidate the linkage from the activation signal to the temporal profile of transcription outputs.
可诱导基因的转录涉及信号通路，这些信号通路诱导下游转录因子与DNA结合，从而形成功能性启动子状态。转录动力学如何与激活信号的时间变化相关联，目前还远未完全清楚。在这项工作中，我们开发了一个具有多个启动子状态的数学模型来解决这个问题。每个启动子状态都有其自身的激活和失活速率，并以可能随时间变化的概率随机选择。在恒定信号的激活下，我们的分析表明，如果只有启动子状态之间的激活速率不同，那么平均转录水平（）仅显示单调或单相增长模式。与之形成鲜明对比的是，如果失活速率随启动子状态变化，那么（）可能显示多相增长模式。在周期性振荡信号的激活下，（）随后也会振荡，几乎以相同频率周期性振荡，但幅度随频率降低，在高频时几乎完全衰减。这给出了一个惊人的迹象，即多个启动子状态可以滤除信号振荡以及随机启动子状态选择中的噪声，正如在乳腺癌细胞中由p53激活的基因转录中所观察到的那样。我们的方法可能有助于建立一个理论框架，将遗传回路与启动子状态连贯地整合起来，以阐明从激活信号到转录输出时间分布的联系。
