Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Toner, David Lawrence Kinnersley; Grima, Ramon

doi:10.1038/srep02438

Cited by 12 publications

(7 citation statements)

References 36 publications

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“…It has been rigorously shown that when mRNA degrades much quicker than proteins (a common situation for bacteria and yeast cells), then the mRNA does not need to be explicitly described but rather implicitly manifests through protein bursts (50). Studies have elucidated the implications of taking into account protein bursting on downstream pathways and shown its importance (51). Hence, we now consider a feedback loop with an implicit mRNA description that has the effective reaction scheme…”

Section: Model Reduction For Bursty Feedback Loopsmentioning

confidence: 99%

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

Holehouse

Grima

2019

Biophysical Journal

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Propensity functions of the Hill type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation, and decay, we prove that in the limit of fast promoter switching, the distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore, we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.

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Section: Model Reduction For Bursty Feedback Loopsmentioning

confidence: 99%

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

Holehouse

Grima

2019

Biophysical Journal

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“…It has been rigorously shown that when mRNA degrades much quicker than proteins (a common situation for bacteria and yeast cells) then the mRNA does not need to be explicitly described but rather implicitly manifests through protein bursts [41]. Studies have elucidated the implications of taking into account protein bursting on downstream pathways and shown its importance [42]. Hence we now consider a feedback loop with an implicit mRNA description which has the effective reaction scheme:…”

Section: Model Reduction For Bursty Feedback Loopsmentioning

confidence: 99%

Revisiting the reduction of stochastic models of genetic feedback loops with fast promoter switching

Holehouse

Grima

2019

Preprint

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Propensity functions of the Hill-type are commonly used to model transcriptional regulation in stochastic models of gene expression. This leads to an effective reduced master equation for the mRNA and protein dynamics only. Based on deterministic considerations, it is often stated or tacitly assumed that such models are valid in the limit of rapid promoter switching. Here, starting from the chemical master equation describing promoter-protein interactions, mRNA transcription, protein translation and decay, we prove that in the limit of fast promoter switching, the probability distribution of protein numbers is different than that given by standard stochastic models with Hill-type propensities. We show that the differences are pronounced whenever the protein-DNA binding rate is much larger than the unbinding rate, a special case of fast promoter switching. Furthermore we show using both theory and simulations that use of the standard stochastic models leads to drastically incorrect predictions for the switching properties of positive feedback loops and that these differences decrease with increasing mean protein burst size. Our results confirm that commonly used stochastic models of gene regulatory networks are only accurate in a subset of the parameter space consistent with rapid promoter switching.

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“…It is a quite common feature that the concentrations of molecules that are genetically expressed change in time in an abrupt manner: The concentration can be almost constant for a long period of time, although the cell growth causes some gradual change. Occasionally the concentration jumps by a significant amount due to a translational (and/or transcriptional) burst or cell division [18][19][20][21][22][23][24]. This behavior contrasts the slow concentration drifts and only small fluctuations around the mean when there is a large number of molecules present in a reaction volume such as a biological the cell.…”

Section: Variance-corrected Michaelis-menten Equationmentioning

confidence: 99%

Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

Pulkkinen

Metzler

2015

Sci Rep

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Many chemical reactions in biological cells occur at very low concentrations of constituent molecules. Thus, transcriptional gene-regulation is often controlled by poorly expressed transcription-factors, such as E.coli lac repressor with few tens of copies. Here we study the effects of inherent concentration fluctuations of substrate-molecules on the seminal Michaelis-Menten scheme of biochemical reactions. We present a universal correction to the Michaelis-Menten equation for the reaction-rates. The relevance and validity of this correction for enzymatic reactions and intracellular gene-regulation is demonstrated. Our analytical theory and simulation results confirm that the proposed variance-corrected Michaelis-Menten equation predicts the rate of reactions with remarkable accuracy even in the presence of large non-equilibrium concentration fluctuations. The major advantage of our approach is that it involves only the mean and variance of the substrate-molecule concentration. Our theory is therefore accessible to experiments and not specific to the exact source of the concentration fluctuations.

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Effects of bursty protein production on the noisy oscillatory properties of downstream pathways

Cited by 12 publications

References 36 publications

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

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

Revisiting the reduction of stochastic models of genetic feedback loops with fast promoter switching

Variance-corrected Michaelis-Menten equation predicts transient rates of single-enzyme reactions and response times in bacterial gene-regulation

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