title: Influence of the nuclear membrane, active transport, and cell shape on the Hes1 and p53-Mdm2 pathways: insights from spatio-temporal modelling.
abstract: There are many intracellular signalling pathways where the spatial distribution of the molecular species cannot be neglected. These pathways often contain negative feedback loops and can exhibit oscillatory dynamics in space and time. Two such pathways are those involving Hes1 and p53-Mdm2, both of which are implicated in cancer. In this paper we further develop the partial differential equation (PDE) models of Sturrock et al. (J. Theor. Biol., 273:15-31, 2011) which were used to study these dynamics. We extend these PDE models by including a nuclear membrane and active transport, assuming that proteins are convected in the cytoplasm towards the nucleus in order to model transport along microtubules. We also account for Mdm2 inhibition of p53 transcriptional activity. Through numerical simulations we find ranges of values for the model parameters such that sustained oscillatory dynamics occur, consistent with available experimental measurements. We also find that our model extensions act to broaden the parameter ranges that yield oscillations. Hence oscillatory behaviour is made more robust by the inclusion of both the nuclear membrane and active transport. In order to bridge the gap between in vivo and in silico experiments, we investigate more realistic cell geometries by using an imported image of a real cell as our computational domain. For the extended p53-Mdm2 model, we consider the effect of microtubule-disrupting drugs and proteasome inhibitor drugs, obtaining results that are in agreement with experimental studies.
authors.affiliation: Division of Mathematics, University of Dundee, Dundee, DD1 4HN, UK. msturrock@maths.dundee.ac.uk
authors.forename: Marc
authors.initials: M
authors.lastname: Sturrock
authors.forename: Alan J
authors.initials: AJ
authors.lastname: Terry
authors.forename: Dimitris P
authors.initials: DP
authors.lastname: Xirodimas
authors.forename: Alastair M
authors.initials: AM
authors.lastname: Thompson
authors.forename: Mark A J
authors.initials: MA
authors.lastname: Chaplain
mesh_terms: D021581:Active Transport, Cell Nucleus; D000818:Animals; D051792:Basic Helix-Loop-Helix Proteins / Q000378:metabolism*; D048430:Cell Shape; D002478:Cells, Cultured; D003198:Computer Simulation; D004791:Enzyme Inhibitors / Q000494:pharmacology; D018398:Homeodomain Proteins / Q000378:metabolism*; D051379:Mice; D008870:Microtubules / Q000187:drug effects / Q000378:metabolism; D008954:Models, Biological; D009685:Nuclear Envelope / Q000378:metabolism*; D046988:Proteasome Endopeptidase Complex / Q000378:metabolism; D061988:Proteasome Inhibitors; D051736:Proto-Oncogene Proteins c-mdm2 / Q000378:metabolism*; D015398:Signal Transduction / Q000502:physiology*; D000072056:Transcription Factor HES-1; D016159:Tumor Suppressor Protein p53 / Q000378:metabolism*
chemical_list: D051792:Basic Helix-Loop-Helix Proteins; D004791:Enzyme Inhibitors; D018398:Homeodomain Proteins; D046988:Proteasome Endopeptidase Complex; D061988:Proteasome Inhibitors; D051736:Proto-Oncogene Proteins c-mdm2; D000072056:Transcription Factor HES-1; D016159:Tumor Suppressor Protein p53; C489734:Hes1 protein, mouse; C497207:Mdm2 protein, mouse