Minimal model for Ca(2+)-dependent oscillations in excitable cells

A minimal model for calcium controlled oscillations is presented. The model considers only an exchange of potassium and calcium ions over the plasma membrane. Calcium ions leak into the cell through a potential dependent channel and is extruded by a pump. Potassium leaks out through a calcium dependent, but voltage independent, channel. The cytosolic calcium concentration is buffered, so a fixed fraction is free. Inactivation, membrane capacity, and time delays for the conductance changes are not included, so the time dependence is solely introduced through the temporal changes of the intracellular Ca(2+)-concentration. With continuous parameter changes the model can switch between five states: (1) a non-excitable, stable state; (2) single-spike excitability; (3) slow, spontaneous oscillations; (4) reverse-spike excitability; and (5) another non-excitable, stable state. One of the key parameters for this switching behavior is the rate constant for the calcium pump.