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. Author SummaryIt has been suggested that genes randomly transit between inactive and active states, with mRNA produced only when a gene is active. The gene activation process has been modeled as a framework of multiple rate-limiting steps listed sequentially, parallel, or in combination. The system step numbers and parameters can be predicted by computationally fitting sophisticated single-cell transcription data. However, current algorithms require a prior hypothetical framework of gene activation. We found that the prior estimation of the framework can be achieved using the traditional dynamical data of mRNA average level M (t) which present easily discriminated dynamical features. The theory regarding M (t) profiles allows us to confidently rule out other frameworks and to determine optimal frameworks by fitting M (t) data. We successfully applied this procedure to a large number of mouse fibroblast genes and confirmed that M (t) is capable of providing a reliable estimation of gene activation frameworks and system parameters.