Tortuous Cardiac Intercalated Discs Modulate Ephaptic Coupling

Figures

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  Figure 1. Different finite element geometries and meshes. (A) Schematic representation of the model for voltage clamp (left) and current clamp protocols (right). The extracellular potential (Ve) at the rim of the disc was set to zero (red). The schematic was modified from Hichri et al. [14]. (B) Intercalated disc mesh consisting of concentric folds parametrized by amplitude A and number of folds N. In this example, A = 1/8 RID and N = 4. (C) Intercalated disc mesh consisting of radial folds parametrized by A and N. In this example, A = 1/8 RID and N = 4. (D) Reference mesh of a flat intercalated disc.

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  Figure 2. Effects of the number of folds N and the amplitude of folds A for concentric folds on INa and minimal Ve for a uniform distribution of gNa. The intracellular potential of the pre-junctional cell was subjected to a voltage clamp protocol with Vstep = −25 mV (left) and Vstep = −50 mV (right) while the intracellular potential of the post-junctional cell was clamped at resting membrane potential. The cleft width was set to 30 nm and gap junctional coupling was set to zero. Continuous and dotted curves correspond to INa in the pre- and post-junctional membranes, respectively. Dashed-dotted lines represent minimal Ve. Reference simulations with a flat intercalated disc (ID) are shown in black. (A) The amplitude of the folds was kept constant (A = 1/4 RID) while the number of folds was varied from 1 to 4. (B) The number of folds was kept constant (N = 4) while their amplitude was varied from 1/16 RID to 1/2 RID. Arrows: I: self-attenuation of INa in the pre-junctional membrane; II: self-activation in the pre-junctional membrane; III: self-activation in the post-junctional membrane.

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  Figure 3. Time course of total INa with INa density and Ve at different positions in the intercalated disc for a uniform distribution of gNa. Intercalated disc with concentric folds (A = 1/4 RID and N = 4). The cleft width was 30 nm. The intracellular nodes were subjected to a voltage clamp protocol with Vstep = −25 mV (left) and Vstep = −50 mV (right). Top: total INa in the tortuous intercalated disc (purple). For comparison, total INa in the pre-junctional membrane without any ephaptic coupling (free membrane) is shown in grey. Middle: INa density at different distances from the center of the intercalated disc (inset). Continuous and dotted curves correspond to total INa and INa density in the pre- and post-junctional membranes, respectively. Bottom: Ve at the corresponding positions in the intercalated disc.

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  Figure 4. Effects of jointly changing the number N and amplitude A of concentric folds such that their product remains constant (A ∙ N = 1/2 RID) on ephaptic coupling (uniform distribution of gNa). The intracellular nodes were subjected to a voltage clamp protocol with Vstep = −25 mV (left) and Vstep = −50 mV (right). (A) The cleft width was set to 30 nm. Continuous and dotted curves correspond to INa in the pre- and post-junctional membranes, respectively. Reference simulations with a flat intercalated disc (ID) are shown in black. (B) Peak INa and peak minimal Ve for the same combinations of A and N (color coding as in A) when cleft width was varied from 10 to 100 nm in steps of 10 nm.

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  Figure 5. Effects of changing the number N and amplitude A of radial folds on INa and minimal Ve for a uniform distribution of gNa. Contains the same simulations and figure layout as in Figure 2 but now shows results for an intercalated disc mesh with radial folds. (A) The amplitude of the folds was kept constant (A = 1/4 RID) while the number of folds was varied from 2 to 8. (B) The number of folds was kept constant (N = 4) while their amplitude was varied from 1/16 RID to 1/2 RID. Dotted arrows: I: self-attenuation of INa in the pre-junctional membrane; II: self-attenuation and less self-activation in the pre-junctional membrane; III: less self-activation in the post-junctional membrane.

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  Figure 6. Effects of changing the number N and amplitude A of concentric folds on Vi, INa and minimal Ve with Na+ channels clustered in the center of the intercalated disc (Rc = 1/8 RID). The intracellular node of the pre-junctional cell was subjected to a current clamp protocol with a rectangular current pulse (intensity: 11.5 nA; duration: 0.5 ms). On the intracellular node of the post-junctional cell, a current clamp protocol with zero current was applied. Gap junctional coupling was set to zero. Continuous and dotted curves correspond to INa in the pre- and post-junctional membranes, respectively. Reference simulations with a flat intercalated disc (ID) are shown in black. (A) The cleft width was set to 30 nm. First row: The amplitude of the folds was kept constant (A = 1/4 RID) while the number of folds N was varied from 1 to 4. Second row: The number of folds was kept constant (N = 4) while their amplitude A was varied from 1/16 RID to 1/2 RID. (B) The cleft width was set to 40 nm. Number and amplitude of folds were varied as in panel A.

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  Figure 7. Effects of changing the number N and amplitude A of radial folds on Vi, INa and minimal Ve with Na+ channels clustered in the center of the intercalated disc (Rc = 1/8 RID). Contains the same simulations and figure layout as in Figure 6 but now shows results for an intercalated disc mesh with radial folds. (A) The cleft width was set to 30 nm. First row: The amplitude of the folds was kept constant (A = 1/4 RID) while the number of folds N was varied from 2 to 4. Second row: The number of folds was kept constant (N = 4) while their amplitude A was varied from 1/16 RID to 1/2 RID. (B) The cleft width was set to 40 nm. Number and amplitude of folds were varied as in panel A.

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  Figure 8. Comparison of the effects of concentric and radial folds in the presence of clustered Na+ channels in the center of the intercalated disc (Rc = 1/8 RID). (A) Response of the post-junctional cell for radial (left) and concentric folds (right) and for different combinations of cleft width and tortuosity (i.e., value of A ∙ N). The responses were categorized as subthreshold depolarization (green), action potential (red) or no depolarization (blue). Note that for some combinations of A and N, two different responses occurred (double-colored dots). Note also that for radial folds, simulations with A ∙ N = 1/16 RID were not run because this involves simulations with N = 1 (which corresponds to an oblique but flat intercalated disc). (B) Delay (measured at Vi = 0 mV) between the action potential upstrokes of the pre- and post-junctional cells for radial (left) and concentric folds (right) as a function of A and N. The cleft width was set to 30 nm. The zero on the abscissas correspond to the flat intercalated disc.