Electrical bursting and intracellular Ca²⁺ oscillations in excitable cell models

Abstract

In bursting excitable cells such as pancreaticβ-cells and molluscanAplysia 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 multi-peaked oscillations and chaos in certain ranges of the gating variables and the intracellular Ca²⁺ buffer concentration.