Figure 1.

Calcium and voltage oscillations in the modeled cell. (A) In a nonexcitable cell, the dynamics of calcium concentrations has an unstable fixed point. A small perturbation in the cytosolic calcium concentration (an increase by 10⁻³ μM), denoted by an arrow, drives the cell away from the fixed point into stable oscillations of both the cytosolic (A1) and the stores (A2) calcium concentrations. The constant calcium current U (see Eq. 1 and the Appendix) is taken to be U = −184 nAmp/cm². (B) In an excitable cell (see Eq. 2 and the Appendix), the membrane stabilizes the fixed point. A much larger perturbation (an increase of the cytosolic calcium concentration by 0.1 μM), denoted by an arrow, generates one spike in calcium concentration but the system converges back to the stable fixed point. An increase in the shunt conductance (an extra conductance of 2⋅10⁴ μS/cm²) destabilizes the fixed point such that even a small perturbation (same as in A), denoted by an arrow, leads to cytosolic calcium oscillations (C1) and consequently to membrane potential oscillations (C2). I_Ca at the fixed point is equal to U (−184 nAmp/cm²). The unstable fixed points in A and C are not realizable experimentally but serve to demonstrate the dynamical principle.