Hopf Bifurcation Analysis in an Intracellular Calcium Oscillation Model

Abstract

Besides the mechanism of the calcium-induced calcium release (CICR), the Kummer-Olsen Calcium oscillation model focuses on the effect of the feedback inhibition on the initial agonist receptor complex by calcium and activated phospholipase C, as well as receptor type-dependent self-enhanced behavior of the activated Gα subunit. The nonlinear dynamics of this model are investigated based on the theory of center manifold, bifurcations and stability of the equilibrium. Computations show that both appearance and disappearance of calcium oscillations of this system are related to supercritical Hopf bifurcation of the equilibrium. Numerical simulations including bifurcation diagram, temporal evolution and phase portraits, are performed to confirm the theoretical analysis. These results may be instructive for understanding the mechanism of other similar calcium oscillation models. © Springer-Verlag Berlin Heidelberg 2013.