A dynamic P53-MDM2 model with time delay

Mihalas, G. I.; Neamţu, Mihaela; Opris, Dumitru; Horhat, Raul Florin

doi:10.1016/j.chaos.2005.08.206

Cited by 19 publications

(19 citation statements)

References 6 publications

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“…These mod-els were the first to make the important distinction between nuclear and cytoplasmic concentrations. Some models have taken stochastic effects into account (Puszyński et al 2008;Proctor and Gray 2008;Ouattara et al 2010) while others have used time delays (Mihalas et al 2006;Ma et al 2005;Batchelor et al 2008), in a manner similar to that discussed for the Hes1 system previously. An attempt was made to model the spatial aspect of the system by Gordon (Gordon et al 2009), but this model also relied on time delays to produce oscillations.…”

Section: The P53-mdm2 Systemmentioning

confidence: 99%

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

Sturrock

Terry

Xirodimas

et al. 2011

Journal of Theoretical Biology

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The correct localisation of transcription factors is vitally important for the proper functioning of many intracellular signalling pathways. Experimental data has shown that many pathways exhibit oscillations in concentrations of the substances involved, both temporally and spatially. Negative feedback loops are important components of these oscillations, providing fine regulation for the factors involved. In this paper we consider mathematical models of two such pathways -Hes1 and p53-Mdm2.Building on previous mathematical modelling approaches, we derive systems of partial differential equations to capture the evolution in space and time of the variables in the Hes1 and p53-Mdm2 systems. Through computational simulations we show that our reaction-diffusion models are able to produce sustained oscillations both spatially and temporally, accurately reflecting experimental evidence and advancing previous models. The simulations of our models also allow us to calculate a diffusion coefficient range for the variables in each mRNA and protein system, as well as ranges for other key parameters of the models, where sustained oscillations are observed. Finally, by exploiting the explicitly spatial nature of the partial differential equations, we are also able to manipulate mathematically the spatial location of the ribosomes, thus controlling where the proteins are synthesized within the cytoplasm. The results of these simulations predict an optimal distance outside the nucleus where protein synthesis should take place in order to generate sustained oscillations. Preprint submitted to Journal of Theoretical BiologyDecember 8, 2010 Using partial differential equation models, new information can be gained about the precise spatio-temporal dynamics of mRNA and proteins. The ability to determine spatial localisation of proteins within the cell is likely to yield fresh insight into a range of cellular diseases such as diabetes and cancer.

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Section: The P53-mdm2 Systemmentioning

confidence: 99%

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

Sturrock

Terry

Xirodimas

et al. 2011

Journal of Theoretical Biology

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“…In (2) with τ 1 = τ, τ 2 = 0, d 12 = 0 we obtain the model from [14] and it was studied in [13] which suggests that there is an oscillatory behavior based on observations obtained using only numerical simulations.…”

Section: Introductionmentioning

confidence: 96%

A dynamic p53-mdm2 model with distributed delay

Horhat¹,

Horhat²

2014

AIP Conference Proceedings

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Specific activator and repressor transcription factors which bind to specific regulator DNA sequences, play an important role in gene activity control. Interactions between genes coding such transcripion factors should explain the different stable or sometimes oscillatory gene activities characteristic for different tissues. In this paper, the dynamic P53-Mdm2 interaction model with distributed delays is investigated. Both weak and Dirac kernels are taken into consideration. For Dirac case, the Hopf bifurcation is investigated. Some numerical examples are finally given for justifying the theoretical results.

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“…The dynamical consequences of the p53-Mdm2 negative feedback loop have been explored in numerous mathematical models. Such models have assumed a variety of forms, including ordinary differential equations (ODEs) [10,45], delay differential equations (DDEs) [3,19,23,24], and partial differential equations (PDEs) [12,39,40]. There have also been models containing a stochastic component [28,29,31].…”

Section: Introductionmentioning

confidence: 99%

Oscillations and DNA Repair in a Spatio-Temporal Model of the p53 Signalling Pathway

Terry

2014

Math. Model. Nat. Phenom.

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In mammalian cells, the p53 pathway regulates the response to a variety of stresses, including oncogene activation, heat and cold shock, and DNA damage. Here we explore a mathematical model of this pathway, composed of a system of partial differential equations. In our model, the p53 pathway is activated by a DNA-compromising event of short duration. As is typical for mathematical models of the p53 pathway, our model contains a negative feedback loop representing interactions between the p53 and Mdm2 proteins. A novel feature of our model is that we combine a spatio-temporal approach with the appearance and repair of DNA damage. We investigate the behaviour of our model through numerical simulations. By ignoring the possibility of DNA repair, we first explore the scenario in which the cell has a very inefficient DNA repair mechanism. We find that spatio-temporal oscillations in p53 and Mdm2 may occur, consistent with experimental data. We then allow p53 to be directly involved in repairing DNA damage, since experimental evidence suggests this can happen. We find that oscillations in p53 and Mdm2 can still occur, but their amplitude damps down quickly as the DNA damage is repaired. Finally, we find that a minor change to the location of the DNA damage can notably change the spatial distribution of p53 within the nucleus. We discuss the biological implications of our results.

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A dynamic P53-MDM2 model with time delay

Cited by 19 publications

References 6 publications

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

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

A dynamic p53-mdm2 model with distributed delay

Oscillations and DNA Repair in a Spatio-Temporal Model of the p53 Signalling Pathway

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