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

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

    Research output: Contribution to journalArticle

    47 Citations (Scopus)

    Abstract

    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.

    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. (C) 2010 Elsevier Ltd. All rights reserved.

    Original languageEnglish
    Pages (from-to)15-31
    Number of pages17
    JournalJournal of Theoretical Biology
    Volume273
    Issue number1
    DOIs
    Publication statusPublished - 21 Mar 2011

    Keywords

    • Intracellular signalling
    • Negative feedback
    • Hes1
    • P53
    • Cancer
    • GENETIC-CONTROL
    • FEEDBACK LOOP
    • DNA-DAMAGE
    • OSCILLATORY EXPRESSION
    • EMBRYONIC LETHALITY
    • MDM2-DEFICIENT MICE
    • TIME DELAYS
    • P53 PULSES
    • DYNAMICS
    • DIFFUSION

    Cite this

    Sturrock, M., Terry, A. J., Xirodimas, D. P., Thompson, A. M., & Chaplain, M. A. J. (2011). Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. Journal of Theoretical Biology, 273(1), 15-31. https://doi.org/10.1016/j.jtbi.2010.12.016
    Sturrock, Marc ; Terry, Alan J. ; Xirodimas, Dimitris P. ; Thompson, Alastair M. ; Chaplain, Mark A. J. / Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. In: Journal of Theoretical Biology. 2011 ; Vol. 273, No. 1. pp. 15-31.
    @article{79423dfe0286420eb7af56bd5a37d55a,
    title = "Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways",
    abstract = "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.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. (C) 2010 Elsevier Ltd. All rights reserved.",
    keywords = "Intracellular signalling, Negative feedback, Hes1, P53, Cancer, GENETIC-CONTROL, FEEDBACK LOOP, DNA-DAMAGE, OSCILLATORY EXPRESSION, EMBRYONIC LETHALITY, MDM2-DEFICIENT MICE, TIME DELAYS, P53 PULSES, DYNAMICS, DIFFUSION",
    author = "Marc Sturrock and Terry, {Alan J.} and Xirodimas, {Dimitris P.} and Thompson, {Alastair M.} and Chaplain, {Mark A. J.}",
    year = "2011",
    month = "3",
    day = "21",
    doi = "10.1016/j.jtbi.2010.12.016",
    language = "English",
    volume = "273",
    pages = "15--31",
    journal = "Journal of Theoretical Biology",
    issn = "0022-5193",
    publisher = "Elsevier",
    number = "1",

    }

    Sturrock, M, Terry, AJ, Xirodimas, DP, Thompson, AM & Chaplain, MAJ 2011, 'Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways', Journal of Theoretical Biology, vol. 273, no. 1, pp. 15-31. https://doi.org/10.1016/j.jtbi.2010.12.016

    Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways. / Sturrock, Marc; Terry, Alan J.; Xirodimas, Dimitris P.; Thompson, Alastair M.; Chaplain, Mark A. J.

    In: Journal of Theoretical Biology, Vol. 273, No. 1, 21.03.2011, p. 15-31.

    Research output: Contribution to journalArticle

    TY - JOUR

    T1 - Spatio-temporal modelling of the Hes1 and p53-Mdm2 intracellular signalling pathways

    AU - Sturrock, Marc

    AU - Terry, Alan J.

    AU - Xirodimas, Dimitris P.

    AU - Thompson, Alastair M.

    AU - Chaplain, Mark A. J.

    PY - 2011/3/21

    Y1 - 2011/3/21

    N2 - 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.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. (C) 2010 Elsevier Ltd. All rights reserved.

    AB - 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.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. (C) 2010 Elsevier Ltd. All rights reserved.

    KW - Intracellular signalling

    KW - Negative feedback

    KW - Hes1

    KW - P53

    KW - Cancer

    KW - GENETIC-CONTROL

    KW - FEEDBACK LOOP

    KW - DNA-DAMAGE

    KW - OSCILLATORY EXPRESSION

    KW - EMBRYONIC LETHALITY

    KW - MDM2-DEFICIENT MICE

    KW - TIME DELAYS

    KW - P53 PULSES

    KW - DYNAMICS

    KW - DIFFUSION

    U2 - 10.1016/j.jtbi.2010.12.016

    DO - 10.1016/j.jtbi.2010.12.016

    M3 - Article

    VL - 273

    SP - 15

    EP - 31

    JO - Journal of Theoretical Biology

    JF - Journal of Theoretical Biology

    SN - 0022-5193

    IS - 1

    ER -