In silico analysis of ventricular action potential with a current–voltage‐time representation: Thresholds, membrane resistance, repolarization reserve

Figures

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  FIGURE 1. Experimental protocol for measuring quasi‐instantaneous IV curves. (a) During the repolarization phase of an ORd‐AP, at selected times (T = 210 ms in figure) the membrane potential is clamped for a time t vc, at values between −100 up to +50 mV (step 25 mV in figure, and step 2 mV in the rest of simulations of the study). (b) The I ion current flowing before and during t vc is reported. (c–e) IVtvc curves for total I ion (black) and for I Kr (red), I K1 (magenta), and I CaL are reported as measured for t vc = 1, 100, and 1000 μs.

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  FIGURE 2. IVT‐surfaces at different t vcs. IV curves were measured as explained in Figure 1 at different t vcs and aligned along the T‐axis to reconstruct the IVT surfaces (step V m = 2 mV, step T = 2 ms) in figure, for an AP conditioned at CL = 800 ms. (a, left) The IVT surface measured with t vc = 1 ms with (a, right) selected IV curves taken at the times T indicated by transparent gray IV planes in the left panel. (b) IVT surfaces measured for different t vcs with the corresponding IV curves taken at the same times T. IV curves taken at times T = 50, 200, and 350 ms are reported in figure with light gray, dark gray, and black respectively. The dot on each curve represents the (I,V)‐state of the AP at the corresponding time T.

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  FIGURE 3. Projections on the 3 orthogonal planes. The projection of the 3D AP curve (bold black line) of the IVT surface (a) on the V,T plane provides the AP trajectory (b), on the I,V plane the phase‐plot (c), and on the I,T plane the time course of I ion flowing during the AP repolarization (d). Red and blue curves in panels a, c, and d represent the way I ion is modified when V m of the AP, at each time T, is quasi‐instantly (1 ms) depolarized or hyperpolarized by 10 mV respectively (b).

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  FIGURE 4. Ion currents contributions to the AP surface. The IVT1ms surface is reported in left (a). The projection on the IT plane of the (I,V,T)‐states of the AP (black curve on the surface) represents the time course of I ion during the AP and is reported on the right of the same panel, like in Figure 3d. IVT surfaces for I CaL (b), I Na (c), and I Kr, are also reported in figure. The projection of the (I,V,T)‐states of the AP (red curve on each surface) on the IT plane provides the time course of the corresponding currents during the AP. These are reported in the right side of panels b, c, and d in red, superimposed with the total ion current (gray).

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  FIGURE 5. Voltage threshold for excitation. IVT5ms surfaces were measured during simulations of sub‐threshold (a, b), threshold (c), and supra‐threshold (d) 5 ms depolarizing current injections. The (I,V,T)‐states of the membrane are reported, during the injections, on each surface as a black curve. The (I,V)‐state of the membrane at the end of current injection (T = 5 ms) is reported as a red dot on each IV curve. On the bottom of each panel, the IV curve taken at T = 5 ms is reported for total I ion (black), I Na (blue), and I K1 (red). The V m threshold is given in bottom panel c by the V m value (~ −58 mV) where the total IV curve (black) intersects the zero‐current level. On the right of each panel, current injections (bottom) and V m displacements (top) are also reported.

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  FIGURE 6. Absolute refractory period. Top view of the same IVT1ms surface of Figure 4a for I ion (a) and for I Na (b). (c) Strength‐interval curve measured by injecting, right after an AP (same initial conditions as in a) and as the interval with respect to the preceding AP decreases, depolarizing current pulses of increasing amplitude. The liminal current corresponding to each interval is reported in figure. White double arrows in each panel show the absolute refractory time window.

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  FIGURE 7. Voltage threshold for AONR. (a, b) Side and top view of the IVT5ms surface. For T < 80 ms, threshold for AONR (yellow dot) is found where voltage displacement of the (I,V,T)‐state (withe dot) reaches the value where the negative sloping limb of the corresponding IV curve cuts the zero current level (left panel c). For 80 ≤ T ≤ 150 ms local minima of the corresponding IV curve (middle and right panels c) mark V m values that, when reached and overcome by anodal stimuli, can make repolarization self‐regenerating. (d) Transition to SRR was also measured by voltage clamping V m a different times T during plateau for 1 ms, and by measuring the average value of the V m derivative in the first 100 ms after the clamp release (light blue bars). The V m of the transition was taken as the first value (highlighted white dots in panels e) when the derivative start to decrease abruptly after a linear increase (green arrows).

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  FIGURE 8. Voltage thresholds during late repolarization. The presence of thresholds is investigated at later times during AP. For 150 ≤ T ≤ 250 ms the (I,V,T)‐states of the membrane are already on a negative sloping limb of the corresponding IV curves (red dots in panels a–c), and repolarization is therefore self‐regenerative. In the first half of this window, no other thresholds are present. In the second half, for 200 ≤ T ≤ 260 ms, a threshold for I CaL‐driven AP is available in depolarizing direction when the curve crosses the zero‐current axis. For T ≥ 270 ms the (I,V,T)‐state of the membrane is at its rest (white dot on right panel c) and a threshold for I Na‐driven AP is available in depolarizing direction. Explanation of panels d and e like in Figure 7.

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  FIGURE 9. Summary of thresholds. Top panel: A summary of thresholds identified on the IVT5ms‐surface is reported. Region I identifies a time window when SRR can be induce, either through a threshold (yellow dots) or only by reaching the negative‐sloping limb of isochronal IV curves (orange dots). No V m thresholds are available in region II, where (I,V,T)‐states (red dots) belong to the negative‐sloping limb of IV curves and repolarization is self‐regenerating. Voltage threshold for I CaL activation is available during region III at depolarized potentials. Cathodal current injections at this time can bring V m to this state and elicit I CaL‐driven APs. The voltage threshold for I Na activation is available in region IV at depolarized potentials. Bottom panel: Sub‐threshold voltage displacements are reported as broken lines, supra‐threshold as continuous lines, for anodal (region I) and cathodal (regions III and IV) current injections. The inset of bottom panel indicates (blue arrow) the narrow time window (between 260 and 270 ms) when bi‐stability, between calcium‐ or sodium‐driven APs can take place.

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  FIGURE 10. Membrane resistance during the AP: Positive values. (a) R m values during AP are measured by taking the reciprocal of the angle of the IVT1ms surface along IV planes (gray in figure). (b) Vertical lines represent the times T1, T2, and T5 (50, 100, and 350 ms respectively) when R m was measured, and the red dots their values in MΩ (right axis). (c) IV curves at times T1, T2, and T5. Corresponding R m value reported in each panel. (d) Corresponding IV curves for I Kr (red), I K1 (green), and I CaL (blue) at the 3 T values considered.

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  FIGURE 11. Membrane resistance during the AP: Negative values. Same as Figure 10; the diastolic value at T5 is the same for comparison. At times T3 = 180 and T4 = 220 ms, the slope of the surface along IV planes (gray shaded angles in panel a), and therefore that of the corresponding IV curves (panel c), is negative, and so are the R m values measured at these times. (d) Corresponding IV curves for I Kr (red), I K1 (green), and I CaL (blue) at the 3 T values considered.

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  FIGURE 12. Summary of membrane resistance. (a) The IVT5ms surface and thresholds already reported in Figure 9. The top panel of the inset shows region III from a different angle, the lower panel the corresponding IVT‐surface for I K1. White arrows and dots show the (I,V,T)‐state where IV‐curves pass from negative‐ to positive‐slope. (b) The slope of the surface was measured along IV planes at every 2 ms during the AP and provided the R m values, reported as a black curve, with the area under the positive part of the curve in red, and that under the negative part in blue. The former coincide with regions I and IV defined in Figure 9, the latter with regions II and III. (c) Effect of varying t vc (on the ordinate axis) on the distribution of positive‐ (red) and negative‐ (blue) sloping regions of the IVT surface.