Mathematical Modeling of Genetic Regulatory Networks: Stress Responses in<i>Escherichia coli</i>

Ropers, Delphine; Jong, Hidde de; Geiselmann, Johannes

doi:10.1002/9780470437988.ch7

Cited by 5 publications

(11 citation statements)

References 162 publications

(184 reference statements)

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“…Following [Shoval et al, 2011, Skataric & Sontag, 2012 let us introduce the main properties under consideration in this note.…”

Section: Scalability and Scale Invariancementioning

confidence: 99%

“…they are capable of maintaining the levels of essential variables in the admissible bounds in the presence of wide deviations of the range of inputs [Alon, 2006]. In some cases they even demonstrate a stronger property called (approximate) fold change detection, when the output of the system becomes (almost) the same after the input scaling [Shoval et al, 2011, Skataric & Sontag, 2012, Hamadeh et al, 2013. In general, a system admits the scale invariance property if a change of stimulus from a background level u 0 to a new level u, or from λu 0 to λu for some scalar λ > 0, results in a time response of the system that is entirely scaled by a function of λ.…”

Section: Introductionmentioning

confidence: 99%

“…Hence, constructive conditions to check the presence of scale invariance are demanded in systems biology for analysis and design. The conditions of scale invariance obtained in [Shoval et al, 2011, Skataric & Sontag, 2012, Hamadeh et al, 2013 are based on some kind of symmetry verification and linearization. It is shown that if a system is symmetric, then under some additional minor restrictions it has the scale invariance property.…”

Section: Introductionmentioning

confidence: 99%

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Scale invariance analysis for genetic networks applying homogeneity

2015

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Scalability is a property describing the change of the trajectory of a dynamical system under a scaling of the input stimulus and of the initial conditions. Particular cases of scalability include the scale invariance and fold change detection (when the scaling of the input does not influence the system output). In the present paper it is shown that homogeneous systems have this scalability property while locally homogeneous systems approximately possess this property. These facts are used for detecting scale invariance or approximate scalability (far from a steady state) in several biological systems. The results are illustrated by various regulatory networks.

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“…Following [Shoval et al, 2011, Skataric & Sontag, 2012 let us introduce the main properties under consideration in this note.…”

Section: Scalability and Scale Invariancementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Scale invariance analysis for genetic networks applying homogeneity

2015

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“…Example 5. Following Ropers et al [2009], consider a model of genetic regulatory network with a positive feedback: Fig. 2.…”

Section: Application Of Local Homogeneity For Pas Analysismentioning

confidence: 99%

Analysis of scale invariance property applying homogeneity

Bernuau

Efimov

Perruquetti

2014

IFAC Proceedings Volumes

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The problem of scalability of trajectories in homogeneous and locally homogeneous systems is considered. It is shown that the homogeneous systems have scalability property, and locally homogeneous systems possess this property approximately. The issue of closeness of trajectories for the system and its local homogeneous approximation is investigated. The notions of scale invariance and fold change detection are also studied. The results are illustrated by a cascade system analysis.

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“…The state variables may be concentrations of proteins, hormones, mRNA, and intracellular ions [10]. The framework has been applied to model real world networks: the initiation of sporulation in B. subtilis [11], and the response to nutritional stress and carbon starvation in E. coli [12,13], using Heaviside response functions. We assume the sigmoid functions are very steep Hill functions, viz.…”

Section: A Modeling Framework For the Study Of Grn Dynamicsmentioning

confidence: 99%

An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions

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Abstract. A specific class of ODEs has been shown to be adequate to describe the essential features of the complex dynamics of Gene-Regulatory Networks (GRN). But, the effective exploitation of such models to predict the dynamics of specific GRNs by classical numerical schemes is greatly hampered by the current lack of precise and quantitative information on regulation mechanisms and kinetic parameters. Due to the size and complexity of large GRNs, classical qualitative analysis could be very hard, or even impracticable, to be carried out by hand, and conventional qualitative simulation approaches rapidly lead to an exponential growth of the generated behavior tree that, besides all possible sound behaviors, may also contain spurious ones. This paper discusses the work-in-progress of a research effort aiming at the design and implementation of a computational framework for qualitative simulation of the dynamics of a class of ODE models of GRNs. The algorithm we propose results from a set of symbolic computation algorithms that carry out the integration of qualitative reasoning techniques with singular perturbation analysis methods. The former techniques allow us to cope with uncertain and incomplete knowledge whereas the latter ones lay the mathematical groundwork for a sound and complete algorithm capable to deal with regulation processes that occur at different time scales.

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Mathematical Modeling of Genetic Regulatory Networks: Stress Responses inEscherichia coli

Cited by 5 publications

References 162 publications

Scale invariance analysis for genetic networks applying homogeneity

Scale invariance analysis for genetic networks applying homogeneity

Analysis of scale invariance property applying homogeneity

An Algorithm for Qualitative Simulation of Gene Regulatory Networks with Steep Sigmoidal Response Functions

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