Abstract
Two-state models (telegraph-like models) have a successful history of predicting distributions of cellular and nascent mRNA numbers that can well fit experimental data. These models exclude key rate limiting steps, and hence it is unclear why they are able to accurately predict the number distributions. To answer this question, here we compare these models to a novel stochastic mechanistic model of transcription in mammalian cells that presents a unified description of transcriptional factor, polymerase and mature mRNA dynamics. We show that there is a large region of parameter space where the first, second and third moments of the distributions of the waiting times between two consecutively produced transcripts (nascent or mature) of two-state and mechanistic models exactly match. In this region: (i) one can uniquely express the two-state model parameters in terms of those of the mechanistic model, (ii) the models are practically indistinguishable by comparison of their transcript numbers distributions, and (iii) they are distinguishable from the shape of their waiting time distributions. Our results clarify the relationship between different gene expression models and identify a means to select between them from experimental data.
Highlights
One of the most popular models of gene expression is the telegraph model, a twostate model where genes are assumed to be either on or off, being able to produce mature messenger RNA in the on state and having no mature mRNA production in the off state [1,2,3]
We have investigated to what extent can twostate models predict the active polymerase II (Pol II) and mature mRNA dynamics of a more realistic mechanistic model that incorporates transcriptional factor binding and unbinding, Pol II dynamics and mature mRNA dynamics
We found that there is a region of parameter space where there exists a choice of parameters of two-state models in terms of the mechanistic model such that the first three moments of their waiting time distributions exactly match
Summary
One of the most popular models of gene expression is the telegraph model, a twostate model where genes are assumed to be either on or off , being able to produce mature messenger RNA (mRNA) in the on state and having no mature mRNA production in the off state [1,2,3]. Because each actively transcribing Pol II has attached to it an incomplete nascent mRNA, one can use the delay telegraph model to numerically calculate the steadystate distribution of nascent mRNA numbers which can be fitted to distributions obtained using single-molecule fluorescence in situ hybridization (smFISH) [20] Despite their success in predicting distributions of transcript numbers that match those calculated from experimental data, it is important to remember that both the telegraph model and the delayed telegraph model do not include a description of all the key rate limiting steps. Two other recent studies [27,28] explore similar models albeit in the context of transcription reinitiation [29] It is currently not so clear why the telegraph model is so successful in fitting experimental mature mRNA distributions, even though it misses important reaction steps 2 which are key control points for gene expression.
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