From channels to systems: Ca²⁺‐sensitive K⁺ currents, alternans and cardiac arrhythmia

Surface membrane ion channel function and its modification by intracellular, metabolic or Ca homeostatic, conditions underlies both stable and pro-arrhythmic cardiac electrophysiological activity. Biophysical studies provide much understanding of the properties of specific channel types. However, in vivo action potential (AP) activation, propagation, and recovery reflect complex interconnected voltage-dependent interactions between multiple channels. These require study at the systems level beyond cell and molecular level analysis, either experimentally employing genetic or pharmacological manipulation, or by mathematical modelling, of cardiomyocytes, tissue segments or intact isolated hearts. Either approach seeks to demonstrate arrhythmogenesis at the systems level and then to resolve underlying cellular mechanisms in the corresponding model system. An important computational study in this Journal of Physiology issue (Kennedy et al. 2017) investigated effects of the Ca2+-activated, slowly activating delayed rectifier and small conductance potassium (SK) channels, respectively carrying IKs and ISK, on pro-arrhythmic instabilities producing AP duration (APD) alternans. Such alternans can reflect membrane potential (Vm(t)) instabilities from steep dependences of APD restitution upon diastolic interval (DI) and are known clinically to presage major ventricular arrhythmias. Figure 1A points out that decreasing steady-state basic cycle lengths (BCL; Aa) reduces the DIs separating successive APs, since DI = (BCL − APD). This limits attainable heart rates as DI converges to the effective refractory period, ultimately causing 2:1 block (Ab and Ac: dashed lines). Alternatively, if APD varies with DI (Ab and Ac: continuous lines), attainment of unity slope in the resulting APD(DI) restitution curve (Ad: dashed tangent) predicts instability and APD alternans. Alternans can also accompany instabilities in intracellular calcium (Cai) cycling through steep dependences of sarcoplasmic reticular Ca2+ release upon Ca load/refractoriness (Groenendaal et al. 2014). Finally, interactions between Cai and K+ channels also affect AP recovery: increased Ca2+ transients in given beats prolonging or shortening APD may positively or negatively couple Vm and Cai cycling. The analysis integrated computational models for IKs and ISK and their [Ca2+] dependence into a physiologically detailed mathematical formulation of AP and Cai cycling in ventricular myocytes, extending the cellular representation into a mono-domain one-dimensional cable (Shiferaw et al. 2005). After first confirming that ISK shortens APD, it explored stability boundaries for a baseline system before and following introducing IKs or ISK. The latter caused a negative Cai→Vm coupling and negative ΔAPD vs. ΔCa slopes leading to predictions of a succession from Vm-driven electromechanically concordant alternans, through Cai-driven electromechanically discordant alternans, to quasiperiodic oscillations capable of generating tissue level Turing-type instabilities. This confirmed previous experimental voltage and Ca2+ recordings. The report thus clarifies contributions of Ca2+-sensitive K+ channels on temporal electrophysiological heterogeneities and their consequences for membrane stability as might be studied in recordings from single cells (Ae). In future, this systems analysis could be extended to the corresponding spatial heterogeneities thereby potentially informing the increasing interest in experimental mapping studies of cardiac electrophysiological activity in both normal and arrhythmic hearts (Martin et al. 2011). Transforms of Vm(t) (Aa), APD (Ab) and DI (Ac) mapped over time, t, giving APD(DI) restitution properties (Ad), could yield spatial representations over the tissue geometry, x, by introducing a conduction velocity term θ (Ba). The resulting V(x) over space, x, yields active, λ (Bb), and resting AP wavelengths λ0 (Bc) corresponding to wavefronts of electrophysiological AP excitation and recovery that together make up the respective basic cycle distances (Ba: BCD = λ + λ0). The unity slope instability criterion in the resulting λ(λ0) plot (Bd; dashed tangent) now encompasses AP propagation in addition to recovery characteristics (Matthews et al. 2013), and offers one of many possible developments of this elegant approach. None declared. C.L.-H.’s work is funded by the Medical Research Council (MR/M001288/1), Wellcome Trust (105727/Z/14/Z), British Heart Foundation (PG/08/116), the McVeigh Benefaction and SADS UK.