Computational modelling of the pro‐ and antiarrhythmic effects of atrial high rate‐dependent trafficking of small‐conductance calcium‐activated potassium channels

Figure 1. Model components, voltage clamp protocols, and frequency‐dependent temporal dynamics of the Ca2+ sensor A, the SK‐channel trafficking model, adapted from the Kv11.1 trafficking model by Meier et al. (2023), consists of two states (M: membrane; S: submembrane) and four rates (ψ: production rate; α: forward trafficking rate; β: internalization rate; δ: degradation rate). Forward trafficking (α) is modulated by Ca2⁺ sensor activation, which depends on subsarcolemmal Ca2⁺ concentration ([Ca2⁺]sl). SK‐channel activity is influenced by both [Ca2⁺]sl and junctional Ca2⁺ concentration ([Ca2⁺]j). This trafficking framework was integrated into the human atrial cardiomyocyte model (HACM) developed by Grandi et al. (2011) and extended with an SK‐channel formulation developed by Heijman et al. (2023). B, two voltage clamp protocols, adapted from Heijman et al. (2023), were implemented using MyoKit (Clerx et al., 2016). The 5 Hz triangular protocol (left) simulates AP‐like stimulation, whereas the square pulse protocol (right) was used for I–V curve analysis. C, the Ca2⁺ sensor's frequency and temporal dynamics are illustrated under free (left) and buffered intracellular Ca2⁺ conditions…

Figure 2. Calibration of the SK‐channel model A, the SK current–voltage (I–V) relationship was calibrated using the square‐pulse voltage clamp protocol from Fig. 1B (right), under both buffered intracellular Ca2⁺ (fixed at 500 nm) and free Ca2⁺ conditions. Simulated results were compared to the experimental I–V curves (mean ± SD) from Heijman et al. (2023). Right: I SK traces following 10 min of stimulation with the triangular voltage clamp protocol at 0.1 Hz. B, the increase in I SK after 10 min of triangular stimulation at 5 Hz for both free and buffered intracellular Ca2⁺ conditions without (left) or with (right) 70% l‐type Ca2⁺ channel block (simulating the effects of 1 µmol L−1 nifedipine (Heijman et al., 2023; Shen et al., 2000)). C, Post 5 Hz stimulation I–V relationships for both free and buffered Ca2⁺ conditions (left) and overview of SK‐current amplitudes at +80 mV for baseline, post 5 Hz stimulation, and post 5 Hz stimulation with LTCC block (right). Experimental data and SDs are included for comparison (Heijman et al., 2023).

Figure 3. Sensitivity of SK channel behaviour to changes in the Ca2⁺ sensor activation rate (α) A, effect of scaling (3‐, 2‐, 1‐, 0.5‐ or 0.33‐fold) α on the number of SK channels in the membrane and their dynamics after 10 min of triangular voltage clamp stimulation at either 1 Hz (left) or 5 Hz (right). B, corresponding changes in the number of submembrane SK channels under identical conditions. C, activation and dynamic behaviour of the Ca2⁺ sensor at different α values, highlighting the rate‐dependent differences between 1 Hz (left) and 5 Hz (right) stimulations.

Figure 4. Sensitivity of SK channel behaviour to changes in the Ca2⁺ sensor de‐activation rate (β) A, effect of scaling (3‐, 2‐, 1‐, 0.5‐ or 0.33‐fold) β on the number of SK channels in the membrane and their dynamics after 10 min of triangular voltage clamp stimulation at either 1 Hz (left) or 5 Hz (right). B, Corresponding changes in the number of submembrane SK channels under identical conditions. C, activation and dynamic behaviour of the Ca2⁺ sensor at different β values, highlighting the rate‐dependent differences between 1 Hz (left) and 5 Hz (right) stimulations.

Figure 5. Sensitivity of SK channel behaviour to changes in the trafficking factor (χ) A, effect of scaling (3‐, 2‐, 1‐, 0.5‐ or 0.33‐fold) χ on the number of SK channels in the membrane and their dynamics after 10 min of triangular voltage clamp stimulation at either 1 Hz (left) or 5 Hz (right). B, Corresponding changes in the number of submembrane SK channels under identical conditions. C, Activation and dynamic behaviour of the Ca2⁺ sensor at different χ values, highlighting the rate‐dependent differences between 1 Hz (left) and 5 Hz (right) stimulations.

Figure 6. Population of models (PoM) analysis of SK trafficking and Ca2⁺ sensor parameters SK‐channel trafficking and Ca2⁺ sensor parameters were randomly varied using a normal distribution (σ = 0.1) to generate 100 distinct parameter sets. This protocol was repeated five times to evaluate the impact of each parameter on SK membrane channels (A) and APD (B) after 1 min at 1 Hz (black) followed by 10 min at 5 Hz pacing (shown in red), and to compute the mean ± SD of their influence under each condition.

Figure 7. Simulated SK channel and electrophysiological responses during and after an episode of rapid activation A and B, SK‐channel membrane levels (A) and corresponding SK current (I SK) (B) during 10 min of simulated sinus rhythm simulation (1 Hz activation by triangular voltage clamp pulses), followed by 10 min at 5 Hz (mimicking AF), and a return to 1 Hz for 10 min. Right: zoomed‐in view of the transitions between frequency changes to highlight acute changes. C and D, membrane potential changes (C) and corresponding action potential duration (APD90) (D) during pacing in current clamp mode for the same durations as in (A). The blue cross highlights instances with incomplete repolarization, precluding calculation of APD90. D, right: time‐dependent changes in APD90 at 1, 2, 3, 4 and 5 Hz pacing rates.

Figure 8. Simulated SK channel and electrophysiological responses during and after an episode of rapid activation while blocking SK‐channel trafficking A and B, SK‐channel membrane levels (A) and corresponding SK current (ISK) (B) during 10 min of simulated sinus rhythm simulation (1 Hz activation by triangular voltage clamp pulses), followed by 10 min at 5 Hz (mimicking AF), and a return to 1 Hz for 10 min in the absence of changes in SK‐channel trafficking. The right panel provides a zoomed‐in view of the transitions between frequency changes to highlight acute changes. C and D, membrane potential changes (C) and corresponding action potential duration (APD90) (D) during pacing in current clamp mode for the same durations as in (A). The blue cross highlights instances with incomplete repolarization, precluding calculation of APD90. D, right: time‐dependent variation in APD90 at 1, 2, 3, 4 and 5 Hz pacing rates.

Figure 9. Action potentials under different drug block conditions and pacing frequencies A, Action potentials and corresponding action potential duration (APD90, shown in the legend) of the last beat during 10 min of pacing at 1 Hz under control conditions, I SK block, I Kur block, I Kr block, I K2P block or I SK + I K2P block. B, Similar to (A) for the last second of 5 Hz pacing for 10 min, after 10 min of initial pacing at 1 Hz, for all drug conditions.

Figure 10. Re‐entry dynamics and arrhythmogenic risk during AF and recovery Re‐entry dynamics were assessed using 2‐D atrial‐tissue simulations (6 × 6 cm) initialized with the conditions from different durations of cellular pacing at 1 or 5 Hz in current clamp mode. A, representative snapshots of electrical activity for an S1S2 interval of 14 ms. Top row: based on conditions after 9 min of 1 Hz pacing, where S2 was blocked because of prior S1 activation. Second and third row: based on conditions after 3 or 9 min of 5 Hz pacing, where re‐entry was inducible, and re‐entry duration and wave break complexity increased after 9 min. Bottom row: based on conditions 3 min after resumption of 1 Hz pacing following 10 min of 5 Hz pacing; re‐entry remained inducible, but duration declined significantly compared to 9 min of 5 Hz pacing. B, quantification of the re‐entry durations for all S1S2 intervals for each condition. C, sum (Σ) of re‐entry durations for all S1S2 intervals in the four conditions, revealing a ∼4‐fold increase in total arrhythmogenic risk compared to shorter AF durations or 1 Hz pacing after 9 min of rapid activation. D, Number of subthreshold (*) or suprathreshold (**) DADs…

Figure 11. Effects of SK‐channel block on arrhythmogenic risk and re‐entry dynamics Re‐entry dynamics were assessed using 2‐D atrial‐tissue simulations (6 × 6 cm) initialized with the conditions from different durations of cellular pacing at 1 or 5 Hz in the presence of 80% SK‐channel block, in current clamp mode. A, representative snapshots of electrical activity for an S1S2 interval of 140 ms in the presence of 80% SK‐channel block. Top row: based on conditions after 9 min of 1 Hz pacing, where S2 was blocked because of prior S1 activation. Second and third row: based on conditions after 3 or 9 min of 5 Hz pacing; with short‐lasting re‐entry only inducible after 9 min of 5 Hz stimulation, followed by suprathreshold DADs after 0.6 and 1.1 s. Bottom row: based on conditions 3 min after resumption of 1 Hz pacing following 10 min of 5 Hz pacing; re‐entry was not inducible. B, quantification of the re‐entry durations for all S1S2 intervals for each condition. C, sum (Σ) of re‐entry durations for all S1S2 intervals in the four conditions. The total re‐entry duration was reduced by >90% to 1930 ms after 9 min of 5 Hz activity under SK‐channel block, compared to Fig. 8C . D, number of…