Birhythmicity, trirhythmicity and chaos in bursting calcium oscillations.

We have analyzed various types of complex calcium oscillations. The oscillations are explained with a model based on calcium-induced calcium release (CICR). In addition to the endoplasmic reticulum as the main intracellular Ca2+ store, mitochondrial and cytosolic Ca2+ binding proteins are also taken into account. This model was previously proposed for the study of the physiological role of mitochondria and the cytosolic proteins in gene rating complex Ca2+ oscillations [1]. Here, we investigated the occurrence of different types of Ca2+ oscillations obtained by the model, i.e. simple oscillations, bursting, and chaos. In a bifurcation diagram, we have shown that all these various modes of oscillatory behavior are obtained by a change of only one model parameter, which corresponds to the physiological variability of an agonist. Bursting oscillations were studied in more detail because they express birhythmicity, trirhythmicity and chaotic behavior. Two different routes to chaos are observed in the model: in addition to the usual period doubling cascade, we also show intermittency. For the characterization of the chaotic behavior, we made use of return maps and Lyapunov exponents. The potential biological role of chaos in intracellular signaling is discussed.