Dynamical effects of calcium-sensitive potassium currents on voltage and calcium alternans.

KEY POINTS: A mathematical model of a small conductance Ca2+ -activated potassium (SK) channel was developed and incorporated into a physiologically detailed ventricular myocyte model. Ca2+ -sensitive K+ currents promote negative intracellular Ca2+ to membrane voltage (CAi2+ → Vm ) coupling. Increase of Ca2+ -sensitive K+ currents can be responsible for electromechanically discordant alternans and quasiperiodic oscillations at the cellular level. At the tissue level, Turing-type instability can occur when Ca2+ -sensitive K+ currents are increased. ABSTRACT: Cardiac alternans is a precursor to life-threatening arrhythmias. Alternans can be caused by instability of the membrane voltage (Vm ), instability of the intracellular Ca2+ ( Ca i2+) cycling, or both. Vm dynamics and Ca i2+ dynamics are coupled via Ca2+ -sensitive currents. In cardiac myocytes, there are several Ca2+ -sensitive potassium (K+ ) currents such as the slowly activating delayed rectifier current (IKs ) and the small conductance Ca2+ -activated potassium (SK) current (ISK ). However, the role of these currents in the development of arrhythmias is not well understood. In this study, we investigated how these currents affect voltage and Ca2+ alternans using a physiologically detailed computational model of the ventricular myocyte and mathematical analysis. We define the coupling between Vm and Ca i2+ cycling dynamics ( Ca i2+→Vm coupling) as positive (negative) when a larger Ca2+ transient at a given beat prolongs (shortens) the action potential duration (APD) of that beat. While positive coupling predominates at baseline, increasing IKs and ISK promote negative Ca i2+→Vm coupling at the cellular level. Specifically, when alternans is Ca2+ -driven, electromechanically (APD-Ca2+ ) concordant alternans becomes electromechanically discordant alternans as IKs or ISK increase. These cellular level dynamics lead to different types of spatially discordant alternans in tissue. These findings help to shed light on the underlying mechanisms of cardiac alternans especially when the relative strength of these currents becomes larger under pathological conditions or drug administrations.