Dual effects of the small-conductance Ca ²⁺ -activated K ⁺ current on human atrial electrophysiology and Ca ²⁺ -driven arrhythmogenesis: an in silico study

Figures

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  Figure 1.. Increasing SK channel conductance shortens human atrial myocyte action potential duration (APD) and effective refractory period (ERP) in normal sinus rhythm (nSR) and chronic atrial fibrillation (cAF). A: time course of membrane potential (Em), cytosolic Ca2+ concentration ([Ca2+]i), and SK current (ISK) in nSR and cAF myocytes during 1-Hz pacing for different values of SK channel maximal conductance (GSK). B: effects of GSK modulation on frequency dependence of APD at 90% repolarization (APD90), resting membrane potential (RMP), Ca2+ transient amplitude (CaTamp), and ERP in nSR and cAF myocytes. Note that, when the cAF model develops alternans (i.e., at pacing rates of ≥3 Hz), values obtained at two subsequent alternating beats are reported.

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  Figure 2.. Sensitivity analysis reveals that SK channel conductance has a prominent role in modulating atrial myocyte action potential duration (APD) and effective refractory period (ERP). Top panels report histograms showing the distribution of APD90 (A), CaTamp (B), and ERP (C) assessed at 1-Hz pacing in nSR and cAF populations of 1,000 models. Bottom panels report the results of linear regression analysis performed to quantify the sensitivity of APD90, CaTamp, and ERP (assessed at 1-Hz pacing) to changes in the listed individual parameters in the nSR and cAF models. Simulated data were obtained in nSR and cAF populations built upon baseline models with nominal SK channel maximal conductance (i.e., 100% GSK). Model variants exhibiting AP irregularities (1 in nSR, 4 in cAF) were excluded from linear regression analysis. APD90, APD at 90% repolarization; cAF, chronic atrial fibrillation; CaTamp, Ca2+ transient amplitude; nSR, normal sinus rhythm.

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  Figure 3.. Increasing SK channel conductance modestly favors development of alternans in nSR and cAF myocytes. A: effect of GSK modulation on the maximal basic cycle length (BCL) inducing voltage (solid lines)- and Ca2+ (dotted lines)-driven alternans in the baseline nSR and cAF models. B: time course of membrane potential and cytosolic Ca2+ concentration obtained at steady state in the baseline nSR and cAF models during 5-Hz pacing with variable SK channel maximal conductance. C: results of linear regression analysis performed to quantify the sensitivity of maximal BCL for voltage-driven alternans development (BCL alternans) to changes in the listed model parameters in nSR and cAF. Simulated data were obtained in populations of 1,000 nSR and cAF models built upon baseline models with nominal SK channel maximal conductance (i.e., 100% GSK). Model variants exhibiting alternans at 1-Hz pacing rate (1 in nSR, 4 in cAF) and model variants that never exhibited alternans (14 in nSR) were excluded from the linear regression analysis, which was performed analyzing the remaining 985 nSR and 996 cAF models. cAF, chronic atrial fibrillation; nSR, normal sinus rhythm.

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  Figure 4.. Increasing SK channel conductance protects against delayed afterdepolarization (DAD) development in nSR and cAF myocytes. A: effect of GSK modulation on the maximal basic cycle length (BCL) inducing DADs in the baseline nSR and cAF models. B: time course of membrane potential and cytosolic Ca2+ concentration elicited in the baseline nSR and cAF models after pausing the electrical stimulation after 10 s of 2-Hz pacing in the presence of Isoproterenol (1 µM) with variable GSK. Only the last two paced beats are reported in the figure. C: results of linear regression analysis quantifying the sensitivity of maximal BCL for DAD development (BCL-DAD) to changes in the listed model parameters in nSR and cAF. D: results of logistic regression analysis quantifying the impact of the listed model parameters on the probability of DAD development in nSR and cAF at 2-Hz pacing (i.e., BCL = 500 ms). Intercept terms b0 (determining the probability of DAD development in the absence of parameter perturbations) are −19.1 for nSR and +12.7 for cAF. Inset: number of model variants showing DADs during 2-Hz pacing within the nSR and cAF populations. Simulated data analyzed in C and D were obtained in…

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  Figure 5.. Increasing SK channel conductance protects against DADs by enhancing the repolarizing force that counteracts the Ca2+-dependent depolarization. A: effect of changes in GSK on the maximal basic cycle length (BCL) inducing DADs and spontaneous Ca2+ release events (SCRs) in a human atrial myocyte model with 3-D Ca2+ diffusion. Thresholds for DADs and SCRs were set to 10 mV and 300 nM, respectively. The simulations were repeated for 10 randomly generated tubular structures. B, top: representative transverse line scans of local cytosolic Ca2+ concentration obtained pausing the electrical stimulation after a train of impulses at 3-Hz pacing for different GSK values. The last three paced beats are reported in the figure. B, bottom: time course of corresponding global cytosolic Ca2+ concentration and membrane potential. C: summary data resulting from simulating the protocol described in B in the 10 different tubular structures. Top panels show amplitude of Em and [Ca2+]i oscillations (ΔEm and ΔCa), and the ΔEm/ΔCa ratio in function of different GSK values. Statistical analysis was performed by one-way ANOVA with Bonferroni correction (***P < 0.001; **P < 0.01; *P < 0.05; ns: not…

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  Figure 6.. Dual effects of SK channel activation in human atrial myocytes. Our simulations indicate that increased SK current promotes 1) APD and ERP shortening, 2) slight increase in propensity for alternans, 3) depressed Ca2+ cycling, 4) decrease in ΔEm/ΔCa ratio (i.e., enhanced repolarizing force), and 5) reduced propensity for DADs. Although effects 1 and 2 promote the development of an arrhythmogenic reentrant substrate, effects 3, 4, and 5 counteract triggered activity. APD, action potential duration; DAD, delayed afterdepolarization; ERP, effective refractory period.