Communications in Information and Systems
Volume 18 (2018)
Dynamics of gene expression based on epigenetic modifications
Pages: 125 – 148
Gene expression is a basic process in life activities. Precise description of gene expression is essential for understanding many biological systems quantitatively. Here, we propose an analytical method to accurately calculate the mRNA distribution in equilibrium and non-equilibrium state based on a three-stage model. First, we consider a three-stage model of gene expression and obtain the mRNA distribution in equilibrium state under the absence of epigenetic modifications. Next, applying the characteristic line method of two-element PDE, we obtain accurate distribution function of non-equilibrium state which describes the evolution dynamics of the gene expression process. Moreover, based on the three-stage model, we construct a mathematical framework to illustrate the ergodic principle by which the time average is equivalent to the space average or ensemble average in a time-continuous dynamical system. We further consider the influence of DNA methylation in the transcription process. By considering methylation allocation during cell division and the influence for transition rate, we obtain analytic expression and make Gillespie random simulation for mRNA number in a cell population. The results reveal five types of diversified and novel mRNA distributions, which are highly consistent with single-cell sequence data. These results provide useful insights for our understanding of the gene expression process.
gene expression, mRNA distribution, three-stage model, ergodic principle, epigenetic modification