Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

Sturrock, Marc; Terry, Alan J.; Xirodimas, Dimitris P.; Thompson, Alastair; Chaplain, M. A. J.

doi:10.1016/j.jtbi.2010.12.016

Cited by 66 publications

(90 citation statements)

References 42 publications

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“…The effect of low molecule numbers in Monk's DDE model of the Hes1 GRN was explored in Barrio et al (2006). A spatio-temporal model of the Hes1 GRN, using a partial differential equation (PDE) approach, was presented in Sturrock et al (2011) and extensions of this model were considered in Sturrock et al (2012). A spatial stochastic model of the Hes1 GRN in embryonic stem cells was studied in Sturrock et al (2013) -this model was derived using mass action kinetics and its mean behaviour was studied in Sturrock et al (2014b).…”

Section: Introductionmentioning

confidence: 99%

The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression

Sturrock

Shahrezaei

2017

Journal of Theoretical Biology

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Gene expression is an inherently noisy process. This noise is generally thought to be deleterious as precise internal regulation of biochemical reactions is essential for cell growth and survival. Selfrepression of gene expression, which is the simplest form of a negative feedback loop, is commonly believed to be employed by cellular systems to decrease the stochastic fluctuations in gene expression. When there is some delay in autoregulation, it is also believed that this system can generate oscillations. In eukaryotic cells, mRNAs that are synthesised in the nucleus must be exported to the cytoplasm to function in protein synthesis, whereas proteins must be transported into the nucleus from the cytoplasm to regulate the expression levels of genes. Nuclear transport thus plays a critical role in eukaryotic gene expression and regulation. Some recent studies have suggested that nuclear retention of mRNAs can control noise in mRNA expression. However, the effect of nuclear transport on protein noise and its interplay with negative feedback regulation is not completely understood. In this paper, we systematically compare four different simple models of gene expression. By using simulations and applying the linear noise approximation to the corresponding chemical master equations, we investigate the influence of nuclear import and export on noise in gene expression in a negative autoregulatory feedback loop. We first present results consistent with the literature, i.e., that negative feedback can effectively buffer the variability in protein levels, and nuclear retention can decrease mRNA noise levels. Interestingly we find that when negative feedback is combined with nuclear retention, an amplification in gene expression noise can be observed and is dependant on nuclear translocation rates. Finally, we investigate the effect of nuclear compartmentalisation on the ability of self-repressing genes to exhibit stochastic oscillatory dynamics.

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Section: Introductionmentioning

confidence: 99%

The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression

Sturrock

Shahrezaei

2017

Journal of Theoretical Biology

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“…In (see [28,13]) models without spatial localization of reactions were considered. Spatial dependence of intracellular transport was introduced in [20,19,26,29,11,10,31,32,8]. Recent developments have been obtained by Cangiani et al [3] and Dimitrio et al [9].…”

Section: Need Of Numerical Modelsmentioning

confidence: 99%

Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation

Leguèbe¹,

Notarangelo²,

Twarogowska³

et al. 2017

Mathematical Biosciences

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. Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation. Mathematical Biosciences, Elsevier, 2017, 285, pp.1-13. 10.1016/j.mbs.2016 Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation AbstractWe propose a mathematical model for the transport of DNA plasmids from the extracellular matrix up to the cell nucleus. The model couples two phenomena: the electroporation process, describing the cell membrane permeabilization to plasmids and the intracellular transport enhanced by the presence of microtubules. Numerical simulations of cells with arbitrary geometry, in 2D and 3D, and a network of microtubules show numerically the importance of the microtubules and the electroporation on the effectiveness of the DNA transfection, as observed by previous biological data. The paper proposes efficient numerical tools for forthcoming optimized procedures of cell transfection.

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“…Experimental data have shown that many regulatory networks exhibit temporal oscillations of concentrations of the substances involved [70,83]. Intracellular negative feedback loops are important components of these oscillations, providing fine regulation of the factors involved.…”

Section: Introductionmentioning

confidence: 99%

“…Intracellular negative feedback loops are important components of these oscillations, providing fine regulation of the factors involved. Two examples of such pathways, Hes1 and p53, which involve oscillations, are particularly studied in the literature [70,83]. These proteins act by binding to specific DNA sequences in the nucleus, either promoting or inhibiting the binding of RNA polymerase to DNA and are of fundamental importance for cellular normal homeostasis.…”

Section: Introductionmentioning

confidence: 99%

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Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling

Adimy

Crauste

2012

Math. Model. Nat. Phenom.

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Abstract. We illustrate the appearance of oscillating solutions in delay differential equations modeling hematopoietic stem cell dynamics. We focus on autonomous oscillations, arising as consequences of a destabilization of the system, for instance through a Hopf bifurcation. Models of hematopoietic stem cell dynamics are considered for their abilities to describe periodic hematological diseases, such as chronic myelogenous leukemia and cyclical neutropenia. After a review of delay models exhibiting oscillations, we focus on three examples, describing different delays: a discrete delay, a continuous distributed delay, and a state-dependent delay. In each case, we show how the system can have oscillating solutions, and we characterize these solutions in terms of periods and amplitudes.

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Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

Cited by 66 publications

References 42 publications

The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression

The influence of nuclear compartmentalisation on stochastic dynamics of self-repressing gene expression

Mathematical model for transport of DNA plasmids from the external medium up to the nucleus by electroporation

Delay Differential Equations and Autonomous Oscillations in Hematopoietic Stem Cell Dynamics Modeling

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