Bursting, chaos and birhythmicity originating from self-modulation of the inositol 1,4,5-trisphosphate signal in a model for intracellular Ca2+ oscillations

We investigate the various types of complex Ca2+ oscillations which can ari se in a model based on the mechanism of Ca2+-induced Ca2+ release (CICR), t hat takes into account the Ca2+-stimulated degradation of inositol 1,4,5-tr isphosphate (InsP(3)) by a 3-kinase. This model was previously proposed in the course of an investigation of plausible mechanisms capable of generatin g complex Ca2+ oscillations (Borghans et al., 1997). Besides simple periodi c behavior, this model for cytosolic Ca2+ oscillations in nonexcitable cell s shows complex oscillatory phenomena like bursting or chaos. We show that the model also admits a coexistence between two stable regimes of sustained oscillations (birhythmicity). The occurrence of these various modes of osc illatory behavior is analysed by means of bifurcation diagrams. Complex osc illations are characterized by means of Poincare sections, power spectra an d Lyapounov exponents. The results point to the role of self-modulation of the InsP(3) signal by 3-kinase as a possible source for complex temporal pa tterns in Ca2+ signaling. (C) 1999 Society for Mathematical Biology.