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Multi-stable dynamics of the non-adiabatic repressilator

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Multi-stable dynamics of the non-adiabatic repressilator. / Potapov, Ilya; Zhurov, Boris; Volkov, Evgeny.

In: Journal of the Royal Society. Interface, Vol. 12, No. 104, 20141315, 06.03.2015.

Research output: Contribution to journalArticleScientificpeer-review

Harvard

Potapov, I, Zhurov, B & Volkov, E 2015, 'Multi-stable dynamics of the non-adiabatic repressilator', Journal of the Royal Society. Interface, vol. 12, no. 104, 20141315. https://doi.org/10.1098/rsif.2014.1315

APA

Potapov, I., Zhurov, B., & Volkov, E. (2015). Multi-stable dynamics of the non-adiabatic repressilator. Journal of the Royal Society. Interface, 12(104), [20141315]. https://doi.org/10.1098/rsif.2014.1315

Vancouver

Potapov I, Zhurov B, Volkov E. Multi-stable dynamics of the non-adiabatic repressilator. Journal of the Royal Society. Interface. 2015 Mar 6;12(104). 20141315. https://doi.org/10.1098/rsif.2014.1315

Author

Potapov, Ilya ; Zhurov, Boris ; Volkov, Evgeny. / Multi-stable dynamics of the non-adiabatic repressilator. In: Journal of the Royal Society. Interface. 2015 ; Vol. 12, No. 104.

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@article{28dfca1dfa914fb8b9523d0f3300a1c8,
title = "Multi-stable dynamics of the non-adiabatic repressilator",
abstract = "The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.",
keywords = "Adiabatic, Bimodality, Genetic oscillator, Hysteresis, Multi-stability",
author = "Ilya Potapov and Boris Zhurov and Evgeny Volkov",
year = "2015",
month = "3",
day = "6",
doi = "10.1098/rsif.2014.1315",
language = "English",
volume = "12",
journal = "Journal of the Royal Society. Interface",
issn = "1742-5689",
publisher = "Royal Society, The",
number = "104",

}

RIS (suitable for import to EndNote) - Download

TY - JOUR

T1 - Multi-stable dynamics of the non-adiabatic repressilator

AU - Potapov, Ilya

AU - Zhurov, Boris

AU - Volkov, Evgeny

PY - 2015/3/6

Y1 - 2015/3/6

N2 - The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.

AB - The assumption of the fast binding of transcription factors (TFs) to promoters is a typical point in studies of synthetic genetic circuits functioning in bacteria. Although the assumption is effective for simplifying the models, it becomes questionable in the light of in vivo measurements of the times TF spends searching for its cognate DNA sites. We investigated the dynamics of the full idealized model of the paradigmatic genetic oscillator, the repressilator, using deterministic mathematical modelling and stochastic simulations. We found (using experimentally approved parameter values) that decreases in the TF binding rate changes the type of transition between steady state and oscillation. As a result, this gives rise to the hysteresis region in the parameter space, where both the steady state and the oscillation coexist. We further show that the hysteresis is persistent over a considerable range of the parameter values, but the presence of the oscillations is limited by the low rate of TF dimer degradation. Finally, the stochastic simulation of the model confirms the hysteresis with switching between the two attractors, resulting in highly skewed period distributions. Moreover, intrinsic noise stipulates trains of large-amplitude modulations around the stable steady state outside the hysteresis region, which makes the period distributions bimodal.

KW - Adiabatic

KW - Bimodality

KW - Genetic oscillator

KW - Hysteresis

KW - Multi-stability

UR - http://www.scopus.com/inward/record.url?scp=84923240824&partnerID=8YFLogxK

U2 - 10.1098/rsif.2014.1315

DO - 10.1098/rsif.2014.1315

M3 - Article

VL - 12

JO - Journal of the Royal Society. Interface

JF - Journal of the Royal Society. Interface

SN - 1742-5689

IS - 104

M1 - 20141315

ER -