Chen Xi, Kang Yan-Mei, Fu Yu-Xuan
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China.
School of Mathematics and Statistics, Xi'an Jiaotong University, Xi'an, 710049, China.
J Theor Biol. 2017 Dec 21;435:134-144. doi: 10.1016/j.jtbi.2017.09.010. Epub 2017 Sep 12.
The non-Gaussian noise is multiplicatively introduced to model the universal fluctuation in the gene regulation of the bacteriophage λ. To investigate the key effect of non-Gaussian noise on the genetic on/off switch dynamics from the viewpoint of quantitative analysis, we employ the high-order perturbation expansion to deduce the stationary probability density of repressor concentration and the mean first passage time from low concentration to high concentration and vice versa. The occupation probability of different concentration states can be estimated from the height and shape of the peaks of the stationary probability density, which could be used to determine the overall expression level. A further concern is the mean first passage time, also referred to as the mean switching time, which can be adopted as an important measure to characterize the adaptability of gene expression to the environmental variation. Through our investigation, it is observed that the non-Gaussian heavy-tailed noise can better induce the switches between distinct genetic expression states and additionally, it accelerates the switching process more evidently compared to the Gaussian noise and the bounded noise.
引入乘性非高斯噪声来模拟噬菌体λ基因调控中的普遍涨落。为了从定量分析的角度研究非高斯噪声对遗传开关动力学的关键影响，我们采用高阶微扰展开来推导阻遏物浓度的稳态概率密度以及从低浓度到高浓度（反之亦然）的平均首次通过时间。不同浓度状态的占据概率可以从稳态概率密度峰值的高度和形状来估计，这可用于确定整体表达水平。另一个关注点是平均首次通过时间，也称为平均切换时间，它可以作为表征基因表达对环境变化适应性的重要指标。通过我们的研究发现，非高斯重尾噪声能够更好地诱导不同基因表达状态之间的切换，此外，与高斯噪声和有界噪声相比，它更明显地加速了切换过程。
