Framework estimation of stochastic gene activation using transcription average level
Gene activation is usually a non-Markovian process that has been modeled as various frameworks that consist of multiple rate-limiting steps. Understanding the exact activation framework for a gene of interest is a central problem for single-cell studies. In this paper, we focus on the dynamical data of the average transcription level M(t), which is typically neglected when deciphering gene activation. Firstly, the smooth trend lines of M(t) data present rich, visually dynamic features. Secondly, tractable analysis of M(t) allows the establishment of bijections between M(t) dynamics and system parameter regions. Because of these two clear advantages, we can rule out frameworks that fail to capture M(t) features and we can further test potential competent frameworks by fitting M(t) data. We implemented this procedure to determine an exact activation framework for a large number of mouse fibroblast genes under tumor necrosis factor induction; the cross-talk between the signaling and basal pathways is crucial to trigger the first peak of M(t), while the following damped gentle M(t) oscillation is regulated by the multi-step basal pathway. Moreover, the fitted parameters for the mouse genes tested revealed two distinct regulation scenarios for transcription dynamics. Taken together, we were able to develop an efficient procedure for using traditional M(t) data to estimate the gene activation frameworks and system parameters. This procedure, together with sophisticated single-cell transcription data, may facilitate a more accurate understanding of stochastic gene activation.