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

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 (CA_i²⁺ → V_m ) 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.

Cardiac alternans is a precursor to life-threatening arrhythmias. Alternans can be caused by instability of the membrane voltage (V_m ), instability of the intracellular Ca²⁺ ( Ca i2+) cycling, or both. V_m 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 (I_Ks ) and the small conductance Ca²⁺ -activated potassium (SK) current (I_SK ). 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 V_m and Ca i2+ cycling dynamics ( Ca i2+→V_m 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 I_Ks and I_SK promote negative Ca i2+→V_m coupling at the cellular level. Specifically, when alternans is Ca²⁺ -driven, electromechanically (APD-Ca²⁺ ) concordant alternans becomes electromechanically discordant alternans as I_Ks or I_SK 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.