  We consider a general model for intracellular calcium dynamics. This model
has solutions that evolve on multiple timescales, but cannot be written in the
so-called standard form for geometric singular perturbation theory (GSPT). We
propose a biologically motivated process-based approach for the identification
of timescales and small parameters in the model. Using a coordinate-independent
formulation of GSPT in combination with the blow-up method, we then prove the
existence of relaxation oscillations with three distinct timescales in a
certain parameter regime. Finally, we identify both singular and regular
Andronov-Hopf bifurcations occurring as a possible mechanism for the onset of
the relaxation oscillations under variations of important model parameters.
