Mark Chaplain abstract
Mark Chaplain, Division of Mathematics, University of Dundee
Title: Mathematical modelling of intracellular negative feedback systems
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 talk we present the results from recent mathematical models which have been used to study the spatio-temporal dynamics of such intracellular molecular systems. The models are systems of coupled nonlinear PDEs, including transport terms and reaction kinetics. The transport is assumed to be both random (diffusion) and active - proteins are convected in the cytoplasm toward the nucleus, modelling transport along microtubules. Internal structures such as ribosomes and the nuclear membrane are also modelled explicitly. Through numerical simulations we find ranges of values for the model parameters such that sustained oscillatory dynamics occur, consistent with available experimental measurements. 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. Applications to other important intracellular systems such as NFkB are also discussed.