Using steady-state formula to estimate time-dependent parameters of stochastic gene transcription models

Abstract

When studying stochastic gene transcription, it is important to understand how system parameters are temporally modulated in response to varying environments. Experimentally, the dynamic distribution data of RNA copy numbers measured at multiple time points are often fitted to stochastic transcription models to estimate time-dependent parameters. However, current methods require determining which parameters are time-dependent, as well as their analytical formulas, before the optimal fit. In this study, we developed a method to estimate time-dependent parameters in a classical two-state model without prior assumptions regarding the system parameters. At each measured time point, the method fitted the dynamic distribution data using a steady-state distribution formula, in which the estimated constant parameters were approximated as time-dependent parameter values at the measured time point. The accuracy of this method can be guaranteed for RNA molecules with relatively high degradation rates and genes with relatively slow responses to induction. Furthermore, we implemented this method on two sets of dynamic distribution data from prokaryotic and eukaryotic cells, and revealed the temporal modulation of transcription burst size in response to environmental changes.

What can we learn when fitting a simple telegraph model to a complex gene expression model?

“…Once ρ0 is determined, the initial values of the other two parameters, λ0 and γ0 , can be determined by matching the mean and variance of gene product fluctuations [16,18]. By fitting gene expression data to the telegraph model, one can understand how all parameters change in response to varying experimental conditions [12,15,37]. Previous studies have revealed rich gene regulation mechanisms under different induction conditions or promoter architectures.…”

“…Previous studies have revealed rich gene regulation mechanisms under different induction conditions or promoter architectures. For instance, the up-regulation of gene expression levels can be achieved by increasing the gene activation rate λ for zinc-induced yeast ZRT1 gene [6], decreasing the gene inactivation rate γ for over 20 Escherichia coli (E. coli) promoters under different growth conditions [7,13], increasing e f the synthesis rate ρ for serum-induced mammalian ctgf gene [38], or a combined effect of both the burst frequency λ and burst size ρ/γ in prokaryotic and eukaryotic cells [29,37,39]. However, the conventional telegraph model is limited in its predictive power because it lacks a description of some important biological mechanisms such as feedback regulation, non-exponential gene inactivation durations, and multiple gene activation pathways (Fig.…”