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

Holehouse, James; Grima, Ramon

doi:10.1101/657718

Cited by 7 publications

(11 citation statements)

References 56 publications

(48 reference statements)

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“…It is important to here emphasize that fast switching leads to effective transcription and degradation rates whereas it is customary to write reduced master equations in this parameter regime which only have effective transcription rates; this explains the discrepancies between conventional and exact master equation reduction reported in [39]. According to averaging theory [33,38], the effective transition rate from group n to group n + k is given by p qss (0,n)q (0,n),(0,n+k) + p qss (1,n−1)q (1,n−1),(1,n−1+k) = c n p k q and the effective transition rate from group n to group n − 1 is given by…”

Section: Regime Of Fast Gene Switchingmentioning

confidence: 99%

Small protein number effects in stochastic models of autoregulated bursty gene expression

Chen

Grima

2020

The Journal of Chemical Physics

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A stochastic model of autoregulated bursty gene expression by Kumar et al. [Phys. Rev. Lett. 113, 268105 (2014)] has been exactly solved in steady-state conditions under the implicit assumption that protein numbers are sufficiently large such that fluctuations in protein numbers due to reversible protein-promoter binding can be ignored. Here we derive an alternative model that takes into account these fluctuations and hence can be used to study low protein number effects. The exact steady-state protein number distributions is derived as a sum of Gaussian hypergeometric functions. We use the theory to study how promoter switching rates and the type of feedback influence the size of protein noise and noise-induced bistability. Furthermore we show that our model predictions for the protein number distribution are significantly different from those of Kumar et al. when the protein mean is small, gene switching is fast, and protein binding is faster than unbinding.

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Section: Regime Of Fast Gene Switchingmentioning

confidence: 99%

Small protein number effects in stochastic models of autoregulated bursty gene expression

Chen

Grima

2020

The Journal of Chemical Physics

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“…However, Kim et al [81] show that the accuracy of such stochastic QSSA is determined by timescale separation and by the sensitivity of the QSSA solution at the same time. Furthermore, by using both theory and simulations, James and Roman show that Hill functions in describing transcriptional regulation are only valid in a fast promoter switching condition [82]. Stochastic (tQSSA) is more accurate than the stochastic QSSA.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

Kirunda

Yang

Liu

et al. 2021

IET Systems Biology

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The bistable Rb-E2F gene regulatory network plays a central role in regulating cellular proliferation-quiescence transition. Based on Gillespie's chemical Langevin method, the stochastic bistable Rb-E2F gene's regulatory network with time delays is proposed. It is found that under the moderate intensity of internal noise, delay in the Cyclin E synthesis rate can greatly increase the average concentration value of E2F. When the delay is considered in both E2F-related positive feedback loops, within a specific range of delay (3-13)hr, the average expression of E2F is significantly increased. Also, this range is in the scope with that experimentally given by Dong et al. [65]. By analysing the quasi-potential curves at different delay times, simulation results show that delay regulates the dynamic behaviour of the system in the following way: small delay stabilises the bistable system; the medium delay is conducive to a high steady-state, making the system fluctuate near the high steady-state; large delay induces approximately periodic transitions between high and low steady-state. Therefore, by regulating noise and time delay, the cell itself can control the expression level of E2F to respond to different situations. These findings may provide an explanation of some experimental result intricacies related to the cell cycle.This is an open access article under the terms of the Creative Commons Attribution-NonCommercial License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited and is not used for commercial purposes.

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“…We next focus on the regime of fast gene switching, i.e. σ b , σ u ρ b , ρ u , d. While this is a common simplifying assumption in many theoretical studies [21,22], it is also supported by recent single-cell data in bacteria [23]. In this case, the Markovian model illustrated in Fig.…”

Section: Deriving a Reduced Model Of Auto-regulated Bursty Gene Exprementioning

confidence: 92%

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

Chen

Grima

2020

Preprint

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AbstractWhile 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 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 behaviour 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 noise-induced phenomenon that occurs when protein expression is sufficiently bursty and we use theory to estimate the observation time window when it is manifest.

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

Cited by 7 publications

References 56 publications

Small protein number effects in stochastic models of autoregulated bursty gene expression

Small protein number effects in stochastic models of autoregulated bursty gene expression

Effects of noise and time delay on E2F's expression level in a bistable Rb‐E2F gene’s regulatory network

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

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