Oscillations in the Expression of a Self-Repressed Gene Induced by a Slow Transcriptional Dynamics

Morant, Pierre-Emmanuel; Thommen, Quentin; Lemaire, François; Vandermoëre, Constant; Parent, Benjamin; Lefranc, Marc

doi:10.1103/physrevlett.102.068104

Cited by 26 publications

(31 citation statements)

References 28 publications

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“…This finding makes us realize that the transcription equation which contains the MM mRNA synthesis term is the fundamental part of a basic autoregulation model, while other intermediate steps (with non-MM synthesis) play the role of introducing slow dynamics for certain intermediate variables, as described in [8]. The above suggests that one may expect to compact any Goodwin model to a single equation for gene transcription like Eq.…”

Section: Methodsmentioning

confidence: 93%

“…In such way, sufficient time delay is considered to be one of the general requirements for sustained oscillations [7]. Another method is inserting an additional equation for lagging fast change in protein level, which plays a dynamical role similar to explicit time delays or to transport equations [8]. The two methods above display certain sorts of memory effects in gene transcription [7], [8].…”

Section: Introductionmentioning

confidence: 99%

“…Another method is inserting an additional equation for lagging fast change in protein level, which plays a dynamical role similar to explicit time delays or to transport equations [8]. The two methods above display certain sorts of memory effects in gene transcription [7], [8]. These optimizations in timescale are designed merely for a specific intermediate product (e.g.…”

Section: Introductionmentioning

confidence: 99%

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Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

et al. 2012

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In dynamical systems theory, a system which can be described by differential equations is called a continuous dynamical system. In studies on genetic oscillation, most deterministic models at early stage are usually built on ordinary differential equations (ODE). Therefore, gene transcription which is a vital part in genetic oscillation is presupposed to be a continuous dynamical system by default. However, recent studies argued that discontinuous transcription might be more common than continuous transcription. In this paper, by appending the inserted silent interval lying between two neighboring transcriptional events to the end of the preceding event, we established that the running time for an intact transcriptional event increases and gene transcription thus shows slow dynamics. By globally replacing the original time increment for each state increment by a larger one, we introduced fractional differential equations (FDE) to describe such globally slow transcription. The impact of fractionization on genetic oscillation was then studied in two early stage models – the Goodwin oscillator and the Rössler oscillator. By constructing a “dual memory” oscillator – the fractional delay Goodwin oscillator, we suggested that four general requirements for generating genetic oscillation should be revised to be negative feedback, sufficient nonlinearity, sufficient memory and proper balancing of timescale. The numerical study of the fractional Rössler oscillator implied that the globally slow transcription tends to lower the chance of a coupled or more complex nonlinear genetic oscillatory system behaving chaotically.

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Section: Methodsmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

et al. 2012

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“…A number of mechanisms can be used by organisms to give a reasonably coherent oscillation, including three-gene repressilator systems [1][2][3], self-repressors with maturation times or other explicit, deterministic time delays (as opposed to intermediate steps which would result from a full treatment of chemical intermediates) [4][5][6][7], more complex negative feedback loops tied to population dynamics [8] combined repression and activation loops [9], highly non-linear protein degradation [10], very large numbers (hundreds) of intermediate steps [11], and self-repressors whose production and gene repression involve diffusion through the nuclear membrane [12,13]. A number of mechanisms can be used by organisms to give a reasonably coherent oscillation, including three-gene repressilator systems [1][2][3], self-repressors with maturation times or other explicit, deterministic time delays (as opposed to intermediate steps which would result from a full treatment of chemical intermediates) [4][5][6][7], more complex negative feedback loops tied to population dynamics [8] combined repression and activation loops [9], highly non-linear protein degradation [10], very large numbers (hundreds) of intermediate steps [11], and self-repressors whose production and gene repression involve diffusion through the nuclear membrane [12,13].…”

Section: Introductionmentioning

confidence: 99%

Oscillation, cooperativity, and intermediates in the self-repressing gene

Lepzelter

Feng

Wang

2010

Chemical Physics Letters

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a b s t r a c tBiological oscillators are vital to living organisms, which use them as clocks for time-sensitive processes. However, much is unknown about mechanisms which can give rise to coherent oscillatory behavior, with few exceptions (e.g., explicitly delayed self-repressors and simple models of specific organisms' circadian clocks). We present what may be the simplest possible reliable gene network oscillator, a self-repressing gene. We show that binding cooperativity, which has not been considered in detail in this context, can combine with small numbers of intermediate steps to create coherent oscillation. We also note that noise blurs the line between oscillatory and non-oscillatory behavior.

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“…when the gene is permanently protein-bound and repressed (resp., unbound and active) [4,17]. Such an average activity appears naturally in rate equations derived from a moment expansion of the chemical master equation [18].…”

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confidence: 99%

Heterodimer Autorepression Loop: A Robust and Flexible Pulse-Generating Genetic Module

2016

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We investigate the dynamics of the heterodimer autorepression loop (HAL), a small genetic module in which a protein A acts as an auto-repressor and binds to a second protein B to form a AB dimer. For suitable values of the rate constants the HAL produces pulses of A alternating with pulses of B. By means of analytical and numerical calculations, we show that the duration of A-pulses is extremely robust against variation of the rate constants while the duration of the B-pulses can be flexibly adjusted. The HAL is thus a minimal genetic module generating robust pulses with tunable duration an interesting property for cellular signalling.

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Oscillations in the Expression of a Self-Repressed Gene Induced by a Slow Transcriptional Dynamics

Cited by 26 publications

References 28 publications

Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

Fractional Dynamics of Globally Slow Transcription and Its Impact on Deterministic Genetic Oscillation

Oscillation, cooperativity, and intermediates in the self-repressing gene

Heterodimer Autorepression Loop: A Robust and Flexible Pulse-Generating Genetic Module

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