Modeling synthetic gene oscillators

O’Brien, Erin L.; Itallie, Elizabeth Van; Bennett, Matthew R.

doi:10.1016/j.mbs.2012.01.001

Cited by 61 publications

(65 citation statements)

References 106 publications

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“…In this case, the exponent (N H ) of the Hill function represents the number of monomers in the polymer, which is rarely large in biological systems [35,36,66,67]. Alternatively, repression based on multiple phosphorylations has been proposed as a more realistic mechanism that can be described by the Hill function with a large Hill exponent [36,68].…”

Section: Introductionmentioning

confidence: 99%

Protein sequestration versus Hill‐type repression in circadian clock models

Kim¹

2016

IET syst. biol.

107

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Circadian (~24hr) clocks are self-sustained endogenous oscillators with which organisms keep track of daily and seasonal time. Circadian clocks frequently rely on interlocked transcriptionaltranslational feedback loops to generate rhythms that are robust against intrinsic and extrinsic perturbations. To investigate the dynamics and mechanisms of the intracellular feedback loops in circadian clocks, a number of mathematical models have been developed. The majority of the models use Hill functions to describe transcriptional repression in a way that is similar to the Goodwin model. Recently, a new class of models with protein sequestration-based repression has been introduced. Here, we discuss how this new class of models differs dramatically from those based on Hill-type repression in several fundamental aspects: conditions for rhythm generation, robust network designs and the periods of coupled oscillators. Consistently, these fundamental properties of circadian clocks also differ among Neurospora, Drosophila, and mammals depending on their key transcriptional repression mechanisms (Hill-type repression or protein sequestration). Based on both theoretical and experimental studies, this review highlights the importance of careful modeling of transcriptional repression mechanisms in molecular circadian clocks.

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Section: Introductionmentioning

confidence: 99%

Protein sequestration versus Hill‐type repression in circadian clock models

Kim¹

2016

IET syst. biol.

107

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“…In the first case, a mathematical model under the assumption of a homogeneous mixture of both cell types follows from Michaelis-Menten enzyme kinetics equations [26] and can be written in dimensionless form as a system of partial differential equations:

\begin{matrix} center \partial_{t} x = \frac{1}{1 + {(l_{1} ∕ L)}^{m}} - x & center \partial_{t} y = \frac{1}{1 + {(l_{2} ∕ L)}^{m}} - y \\ center \frac{1}{γ_{2}} \partial_{t} l_{1} = l_{0} \frac{μ + r_{τ}}{1 + r_{τ}} - l_{1} & center \frac{1}{γ_{2}} \partial_{t} l_{2} = l_{0} \frac{μ + a_{τ}}{1 + a_{τ}} - l_{2} \\ center \partial_{t} a = b_{a} x - γ_{3} a + D Δ a & center \partial_{t} r = b_{r} y - γ_{3} r + D Δ r, \end{matrix}

where the dimensionless state variables are normalized concentrations: x and y — of LuxI1 and LuxI2 (proteins which mediate synthesis of AHL1,2), l 1 and l 2 — of LacI in cells of type A and type B, a and r – of AHL1 and AHL2. Parameter l 0 is the relative strength of lacI gene expression, b a and b r determine the synthesis rates of AHL1 and AHL2 per unit of volume of the medium (by implication, they are directly proportional to the corresponding cell strain concentrations).…”

Section: Mathematical Modelmentioning

confidence: 99%

Spatiotemporal dynamics of distributed synthetic genetic circuits

Kanakov

Laptyeva

Tsimring

et al. 2016

Physica D: Nonlinear Phenomena

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We propose and study models of two distributed synthetic gene circuits, toggle-switch and oscillator, each split between two cell strains and coupled via quorum-sensing signals. The distributed toggle switch relies on mutual repression of the two strains, and oscillator is comprised of two strains, one of which acts as an activator for another that in turn acts as a repressor. Distributed toggle switch can exhibit mobile fronts, switching the system from the weaker to the stronger spatially homogeneous state. The circuit can also act as a biosensor, with the switching front dynamics determined by the properties of an external signal. Distributed oscillator system displays another biosensor functionality: oscillations emerge once a small amount of one cell strain appears amid the other, present in abundance. Distribution of synthetic gene circuits among multiple strains allows one to reduce crosstalk among different parts of the overall system and also decrease the energetic burden of the synthetic circuit per cell, which may allow for enhanced functionality and viability of engineered cells.

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“…Later, Elowitz and Leibler (2000) proposed a repressilator model by extending the Goodwin oscillator model to a cycle of three genes, in which the oscillations are induced by repressing its successor genes in the cell cycle. In recent years, the robustness analysis of genetic oscillators has received considerable research attention (Amos 2014;O'Brien et al 2012). An example for a natural genetic oscillator includes a tumor suppressor protein p53 in relation to cancer (Lahav et al 2004).…”

Section: Introductionmentioning

confidence: 99%

Delay decomposition approach to $$\mathcal {H}_{\infty }$$ H ∞ filtering analysis of genetic oscillator networks with time-varying delays

Revathi

Balasubramaniam

2016

Cogn Neurodyn

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In this paper, the H 1 filtering problem is treated for N coupled genetic oscillator networks with timevarying delays and extrinsic molecular noises. Each individual genetic oscillator is a complex dynamical network that represents the genetic oscillations in terms of complicated biological functions with inner or outer couplings denote the biochemical interactions of mRNAs, proteins and other small molecules. Throughout the paper, first, by constructing appropriate delay decomposition dependent Lyapunov-Krasovskii functional combined with reciprocal convex approach, improved delay-dependent sufficient conditions are obtained to ensure the asymptotic stability of the filtering error system with a prescribed H 1 performance. Second, based on the above analysis, the existence of the designed H 1 filters are established in terms of linear matrix inequalities with Kronecker product. Finally, numerical examples including a coupled Goodwin oscillator model are inferred to illustrate the effectiveness and less conservatism of the proposed techniques.

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Modeling synthetic gene oscillators

Cited by 61 publications

References 106 publications

Protein sequestration versus Hill‐type repression in circadian clock models

Protein sequestration versus Hill‐type repression in circadian clock models

Spatiotemporal dynamics of distributed synthetic genetic circuits

Delay decomposition approach to $$\mathcal {H}_{\infty }$$ H ∞ filtering analysis of genetic oscillator networks with time-varying delays

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