Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Holehouse, James; Grima, Ramon

doi:10.1016/j.bpj.2019.08.021

Cited by 26 publications

(26 citation statements)

References 58 publications

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“…Potential extensions include (i) the impact of cell cycle effects such as binomial partitioning and variability in the cell cycle duration; (ii) introducing a detailed description of polymerase movement along the gene during elongation. The use of the recently developed linear mapping approximation [32] appears to be a promising means to extend the analytical solution of the present model to include feedback loops via DNA-protein interactions [33,34].…”

Section: Resultsmentioning

confidence: 99%

A stochastic model of gene expression with polymerase recruitment and pause release

Cao

Филатова

Oyarzún

et al. 2019

Preprint

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Transcriptional bursting is a major source of noise in gene expression. Motivated by recent experiments, we study a model including slow burst initiation and termination, and fast RNA polymerase recruitment and pause release. We show that the time-dependent distribution of mRNA numbers is accurately approximated by a telegraph model with a Michaelis-Menten like dependence of the e↵ective transcription rate on polymerase abundance. We also show that gene dosage compensation, a common feature of mammalian gene expression, is an emergent property of our stochastic model.

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Section: Resultsmentioning

confidence: 99%

A stochastic model of gene expression with polymerase recruitment and pause release

Cao

Филатова

Oyarzún

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…Potential extensions include 1) the impact of cell cycle effects such as binomial partitioning and variability in the cell cycle duration and 2) introducing a detailed description of polymerase movement along the gene during elongation. The use of the recently developed linear mapping approximation (32) appears to be a promising means to extend the analytical solution of this model to include feedback loops via DNAprotein interactions (33,34).…”

Section: Discussionmentioning

confidence: 99%

A Stochastic Model of Gene Expression with Polymerase Recruitment and Pause Release

Cao

Филатова

Oyarzún

et al. 2020

Biophysical Journal

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Transcriptional bursting is a major source of noise in gene expression. The telegraph model of gene expression, whereby transcription switches between on and off states, is the dominant model for bursting. Recently, it was shown that the telegraph model cannot explain a number of experimental observations from perturbation data. Here, we study an alternative model that is consistent with the data and which explicitly describes RNA polymerase recruitment and polymerase pause release, two steps necessary for messenger RNA (mRNA) production. We derive the exact steady-state distribution of mRNA numbers and an approximate steady-state distribution of protein numbers, which are given by generalized hypergeometric functions. The theory is used to calculate the relative sensitivity of the coefficient of variation of mRNA fluctuations for thousands of genes in mouse fibroblasts. This indicates that the size of fluctuations is mostly sensitive to the rate of burst initiation and the mRNA degradation rate. Furthermore, we show that 1) the time-dependent distribution of mRNA numbers is accurately approximated by a modified telegraph model with a Michaelis-Menten like dependence of the effective transcription rate on RNA polymerase abundance, and 2) the model predicts that if the polymerase recruitment rate is comparable or less than the pause release rate, then upon gene replication, the mean number of RNA per cell remains approximately constant. This gene dosage compensation property has been experimentally observed and cannot be explained by the telegraph model with constant rates.

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“…We next focus on the regime of fast gene switching, i.e., σ b , σu ≫ ρ b , ρu, d. While this is a common simplifying assumption in many theoretical studies, 25,26 it is also supported by recent singlecell data in bacteria. 27 In this case, the Markovian model illustrated in Fig.…”

Section: The Journal Of Chemical Physicsmentioning

confidence: 94%

Dynamical phase diagram of an auto-regulating gene in fast switching conditions

Chen

Grima

2020

The Journal of Chemical Physics

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While the steady-state behavior of stochastic gene expression with auto-regulation has been extensively studied, its time-dependent behavior has received much less attention. Here, under the assumption of fast promoter switching, we derive and solve a reduced chemical master equation for an auto-regulatory gene circuit with translational bursting and cooperative protein-gene interactions. The analytical expression for the time-dependent probability distribution of protein numbers enables a fast exploration of large swaths of the parameter space. For a unimodal initial distribution, we identify three distinct types of stochastic dynamics: (i) the protein distribution remains unimodal at all times; (ii) the protein distribution becomes bimodal at intermediate times and then reverts back to being unimodal at long times (transient bimodality); and (iii) the protein distribution switches to being bimodal at long times. For each of these, the deterministic model predicts either monostable or bistable behavior, and hence, there exist six dynamical phases in total. We investigate the relationship of the six phases to the transcription rates, the protein binding and unbinding rates, the mean protein burst size, the degree of cooperativity, the relaxation time to the steady state, the protein mean, and the type of feedback loop (positive or negative). We show that transient bimodality is a noiseinduced phenomenon that occurs when the protein expression is sufficiently bursty, and we use a theory to estimate the observation time window when it is manifested.

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Revisiting the Reduction of Stochastic Models of Genetic Feedback Loops with Fast Promoter Switching

Cited by 26 publications

References 58 publications

A stochastic model of gene expression with polymerase recruitment and pause release

A stochastic model of gene expression with polymerase recruitment and pause release

A Stochastic Model of Gene Expression with Polymerase Recruitment and Pause Release

Dynamical phase diagram of an auto-regulating gene in fast switching conditions

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