Mitochondria not only govern energy production, but are also involved in crucial cellular signalling processes. They are one of the most important organelles determining the Ca(2+) regulatory pathway in the cell. Several mathematical models explaining these mechanisms were constructed, but only few of them describe interplay between calcium concentrations in endoplasmic reticulum (ER), cytoplasm and mitochondria. Experiments measuring calcium concentrations in mitochondria and ER suggested the existence of cytosolic microdomains with locally elevated calcium concentration in the nearest vicinity of the outer mitochondrial membrane. These intermediate physical connections between ER and mitochondria are called MAM (mitochondria-associated ER membrane) complexes. We propose a model with a direct calcium flow from ER to mitochondria, which may be justified by the existence of MAMs, and perform detailed numerical analysis of the effect of this flow on the type and shape of calcium oscillations. The model is partially based on the Marhl et al model. We have numerically found that the stable oscillations exist for a considerable set of parameter values. However, for some parameter sets the oscillations disappear and the trajectories of the model tend to a steady state with very high calcium level in mitochondria. This can be interpreted as an early step in an apoptotic pathway.

Abstract. Mitochondria are one of the most important organelles determining Ca 2+ regulatory pathway in the cell. Recent experiments suggested the existence of cytosolic microdomains with locally elevated calcium concentration (CMDs) in the nearest vicinity of the outer mitochondrial membrane (OMM). These intermediate physical connections between endoplasmic reticulum (ER) and mitochodria are called MAM (mitochondria-associated ER membrane) complexes.The aim of this paper is to take into account the direct calcium flow from ER to mitochondria implied by the existence of MAMs and perform detailed numerical analysis of the influence of this flow on the type and shape of calcium oscillations. Depending on the permeability of MAMs interface and ER channels, different patterns of oscillations appear (simple, bursting and chaotic). For some parameters the oscillatory pattern disappear and the system tends to a steady state with extremely high calcium level in mitochondria, which can be interpreted as a crucial point at the beginning of an apoptotic pathway.