Abstract:
In this thesis we study theoretically the dynamics of the free cytosolic Ca2+ concentration. We construct a mathematical model of the Ca2+ dynamics in pancreatic acinar cells. Although this model refers to a particular cell type, it also allows us to study some aspects of Ca2+ signalling in general. We begin by analysing the dependence of the Ca2+ oscillations on the plasma membrane transport. Further we study the propagation of intercellular Ca2+ waves in a pancreatic acinus.
It has been observed experimentally that, in many cell types, calcium fluxes across the plasma membrane affect inositol trisphosphate IP3-induced calcium oscillations. Since IP3-induced calcium oscillations involve the cycling of calcium to and from the endoplasmic reticulum, it is not well understood how they can be so strongly affected by membrane fluxes. We use a mathematical model to answer this question; a model that relies on the introduction of a slow variable, the Ca2+ load of the cell. Our model predictions are confirmed by experimental results. Since similar behaviour is observed in two other models of IP3-induced Ca2+ oscillations, it is possible that this bifurcation structure is a generic feature of Ca2+ oscillation models.
The effect of intercellular coupling on the oscillatory dynamics is investigated theoretically. It is demonstrated that junctional calcium diffusion can account for the co-ordination and synchronisation of cytosolic calcium oscillations in a coupled triplet of cells under the assumption of constant IP3 concentration in each individual cell. Furthermore a two dimensional version of that model, where Ca2+ and IP3 are assumed to diffuse within as well as between the cells, has been studied numerically. Compared to the results from the analysis of the ODE model, the results from the analysis of the PDE model (in two spatial dimensions) reveal some interesting spatial effects of the diffusion, and of the geometry of the cells on the collective oscillatory behaviour of the systen. Based on this combined approach, a suggestion about the specific role of both Ca2+ and IP3 in the intercellular Ca2+ signalling has been made.