Positive rate‐dependent action potential prolongation by modulating potassium ion channels

Figures

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  FIGURE 1. Features of the action potential. Top: Action potential calculated with the TNNP model. The figure shows the features of the action potential used in this study: Action potential amplitude (APA); action potential duration at 90% repolarization (APD90); duration of phase 1, phase 2, and phase 3; average ionic current during phase 2 (Iion, phase2) and during phase 3 (Iion, phase3). Bottom: Total ionic current during the repolarization of the action potential. The vertical dashed line shows the time when Iion changes from negative to positive indicating the end of phase 1 and the beginning of phase 2 repolarization.

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  FIGURE 2. Rate dependence of APD prolongation with the TNNP and ToR‐ORd models. Panel a (top): APD rate dependence during control (gray circles), and for four interventions that prolonged the control APD to 330 ms when BCL = 3000 ms, using the TNNP model. The vertical dashed lines indicate BCL = 400 and 3000 ms, respectively. Panel a (bottom): APD prolongation at the different BCLs compared with APD prolongation at BCL = 3000 ms for the four interventions in Panel a (top). Positive values indicate a positive rate dependence and a negative value indicates reverse rate dependence. Panel b (top): APD rate dependence during control (gray circles), and for three interventions that prolonged the control APD to 320 ms at BCL = 3000 ms, using the ToR‐ORd model. The vertical dashed lines indicate BCL = 400 and 3000 ms, respectively. Panel b (bottom): APD prolongation at the different BCLs compared with APD prolongation at BCL = 3000 ms for the three interventions in Panel a (top). Positive values indicate a positive rate dependence and a negative value indicates reverse rate dependence. See text for detailed description.

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  FIGURE 3. Panel a (top): Percentage APD shortening between BCL = 3000 ms and 400 ms, for different interventions prolonging APD to 320, 330, and 340 ms when BCL = 3000 ms (vertical dashed‐dot lines) by blocking a unique type of potassium channel (black circles), and by activation/block of several potassium channels identified by POS optimization (red circles), using the TNNP model. Panel a (bottom): Difference between the prolongation of APD with BCL = 400 ms and BCL = 3000 ms for the interventions in panel a (top). Negative values indicate reverse rate dependence and positive values indicates positive rate dependence. White bars with red edges labeled 1, 2, 3 indicate interventions that modulate several potassium channels and correspond to the red circles in panel a (top). Gray bars indicate interventions that block a unique potassium channel and correspond to the black circles in panel a (top). Panel b (top) percentage APD shortening between BCL = 3000 ms and 400 ms for interventions that prolong APD to 320, 330, and 340 ms when BCL = 3000 ms (vertical dashed‐dot lines), using the ToR‐ORd model. Black and red circles and labels have the same meaning as in Panel a (top). Panel b (bottom):…

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  FIGURE 4. Influence of the action potential shape on its rate dependence (TNNP model). Panel a: Action potentials for different interventions that prolong the action potential to 320 ms for BCL = 3000 ms (top) with the corresponding total ionic currents (bottom) (vertical dashed‐dot line through red circle labeled as 1 in Figure 3a, top). Panel b: Action potentials for BCL = 3000 (solid line) and 400 ms (dashed line) for the interventions in panel a. The action potential with a faster phase 2 repolarization and slower phase 3 repolarization (2(IKs) + 0.41(IKr) + 0.2(IK1)) results is a smaller APD shortening with increasing stimulation rate than the other two: 48 ms versus 88 ms for 0.5(IK1) and 102 ms for 0.8(IKs).

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  FIGURE 5. Influence of the action potential shape on its rate dependence (TNNP model). The figure shows action potentials and ionic currents resulting from interventions that prolong the action potential to 330 ms for BCL = 3000 ms (vertical dashed‐dot line through red circle labeled as 2 in Figure 3a, top). The figure uses the same format as Figure 4.

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  FIGURE 6. Influence of the action potential shape on its rate dependence (TNNP model). The figure shows action potentials and ionic currents resulting from interventions that prolong the action potential to 340 ms for BCL = 3000 ms (vertical dashed‐dot line through red circle labeled as 3 in Figure 3a, top). The figure uses the same format as Figure 4.

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  FIGURE 7. Features extracted from action potentials corresponding for the interventions in Figures 4 (APD = 320 ms), 5 (APD = 330 ms), and 6 (APD = 340 ms) for BCL = 3000 ms (TNNP model). White vertical bars represent interventions identified by the POS optimization algorithm, which involve the modulation of several potassium channels; gray vertical bars represent interventions involving modulation of one potassium channel. The features show the average ionic current during phase 2 (panel a), the average ionic current during phase 3 (panel b), the ratio of the average currents during phase 3 and phase 2 (panel c), and the area under the action potential (AUAP) normalized to APA and APD90 (panel d). The interventions identified by the POS algorithm result in a more triangularized action potential (smaller ratio in panel c and a smaller AUAP in panel d), with a positive rate dependence (Figure 3a, bottom).

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  FIGURE 8. Percentage prolongation of the APD when a constant depolarizing current of −0.1pA/pF is applied during the action potential for control (bar with the hatched pattern), and the different interventions that result in APDs of 320, 330, and 340 ms at a BCL = 3000 ms (TNNP model). A larger APD prolongation indicates a decreasing repolarization reserve. White bars indicate interventions with a robust positive rate dependence (see Figure 3a, bottom). Gray bars indicate interventions with reverse or moderate positive rate dependence (see Figure 3a, bottom).

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  FIGURE 9. Interventions (x‐axis) that result in a positive rate dependence response (gray bars, left y‐axis) for different minimum values of IK1 block (80%, 50%, 30%, and 0%) in the POS optimization algorithm that result in APDs of 320 (panel a), 330 (panel b), and 340 ms (panel c) at a BCL = 3000 ms (TNNP model). The right y‐axis (red) shows the percentage prolongation of the APD when a constant depolarizing current of −0.1pA/pF is applied during the action potential. A larger APD prolongation indicates a decreasing repolarization reserve. The red horizontal dashed line shows the repolarization reserve for a control action potential. See text for detailed description.