Minimal model for calcium alternans due to SR release refractoriness

In the heart, rapid pacing rates may induce alternations in the strength of cardiac contraction, termed pulsus alternans. Often, this is due to an instability in the dynamics of the intracellular calcium concentration, whose transients become larger and smaller at consecutive beats. This alternation has been linked experimentally and theoretically to two different mechanisms: an instability due to (1) a strong dependence of calcium release on sarcoplasmic reticulum (SR) load, together with a slow calcium reuptake into the SR or (2) to SR release refractoriness, due to a slow recovery of the ryanodine receptors (RyR2) from inactivation. The relationship between calcium alternans and refractoriness of the RyR2 has been more elusive than the corresponding SR Ca load mechanism. To study the former, we reduce a general calcium model, which mimics the deterministic evolution of a calcium release unit, to its most basic elements. We show that calcium alternans can be understood using a simple nonlinear equation ...