Electrical bursting and intracellular Ca2+ oscillations in excitable cell models

In bursting excitable cells such as pancreatic beta-cells and molluscan Aplysia neuron cells, intracellular Ca2+ ion plays a central role in various cellular functions. To understand the role of [Ca2+]i (the intracellular Ca2+ concentration) in electrical bursting, we formulate a mathematical model which contains a few functionally important ionic currents in the excitable cells. In this model, inactivation of Ca2+ current takes place by a mixture of voltage and intracellular Ca2+ ions. The model predicts that, although the electrical bursting patterns look the same, the shapes of [Ca2+]i oscillations could be very different depending on how fast [Ca2+]i changes in the cytosolic free space (i.e., how strong the cellular Ca2+ buffering capacity is). If [Ca2+]i changes fast, [Ca2+]i oscillates in bursts in parallel to electrical bursting such that it reaches a maximum at the onset of bursting and a minimum just after the termination of the plateau phase. If the change is slow, then [Ca2+]i oscillates out-of-phase with electrical bursting such that it peaks at a maximum near the termination of the plateau and a minimum just before the onset of the active phase. During the active phase [Ca2+]i gradually increases without spikes. In the intermediate ranges, [Ca2+]i oscillates in such a manner that the peak of [Ca2+]i oscillation lags behind the electrical activity. The model also predicts the existence of multipeaked oscillations and chaos in certain ranges of the gating variables and the intracellular Ca2+ buffer concentration.