Calcium oscillations and membrane transport: The importance of two time scales

It has been observed experimentally that, in many cell types, calcium fluxes across the plasma membrane affect inositol trisphosphate (IP3)-induced calcium oscillations. This is somewhat puzzling; 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. We carry out a bifurcation analysis of the model in two time scales, treating the slow variable as a bifurcation parameter, thus simulating a closed-cell model, in which there is no Ca2+ transport to and from the external medium. The presence of a homoclinic bifurcation in the closed-cell model accounts for the existence of a critical value of the Ca2+ load which controls the existence of cytosolic Ca2+ oscillations. Our model predictions are confirmed by experimental results. Since similar behavior 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.