Reduced gap junction coupling amplifies the effects of cardiomyocyte variability and destabilizes the heartbeat

Figures

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  FIGURE 1. Action potentials and calcium transients in simulations of 15 × 5 randomly distributed cells of two different types (blue: Normal, healthy cells, red: Cells with no IKr, double gCaL, and 75% reduced gK1), Case 1 in Table 1. In the leftmost panel, the cells are strongly connected (600 nS) like in normal healthy tissue. The cell connections are gradually reduced in the right panels, as indicated in the panel titles. In the case with G g = 0 nS, the cells are completely disconnected. The lower panel illustrates the distribution of cell types in the cell collection, and the yellow circles mark the cells whose action potentials and calcium transients are reported in the upper panels. The gap junction coupling is the same between all cells in the collection.

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  FIGURE 2. Action potentials recorded in six different cells in a simulation of 15 × 20 cells. The cell collection consists of two different types of cell (blue: Normal, healthy cells, red: Cells with no IKr, double gCaL, and 75% reduced gK1), Case 2 in Table 1. The cell types are evenly distributed throughout the domain such that every other cell is normal and every other cell is perturbed (see lower panel). The gap junction conductance is set to 2 nS for all cell connections. In the upper left panel, we compare the action potential of the two cell types for cells located in the center of the cell collection (marked with yellow circles in the lower panel). In the upper center panel, we compare the action potential of the two cell types for cells located at sides of the cell collection (marked with turquoise circles in the lower panel). Finally, in the upper right panel, we compare the action potential of the two cell types for cells located in corners of the cell collection (marked with purple circles in the lower panel).

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  FIGURE 3. Simulations of 25 × 25 cells with different degrees of gap junction coupling variations and different average gap junction conductances (Case 3 in Table 1). Upper panel: Time of arrival (ToA) for the depolarization and repolarization waves for cell number 10 in the x‐direction and each of the cells in the y‐direction. The cell properties are the same for all cells, but the degree of gap junction coupling variation increases for each plot row. The different lines correspond to different values of the average gap junction conductance, Gg* (see legends). Note that the ToA axis covers different time points in the different plots, but the scaling of the axis is the same in all cases. Lower panel: Illustration of cell collections with 0%, 25% and 50% variations in the gap junction coupling. The color of the cell connections indicate the strength of the gap junction coupling between cells, β, in the sense that Gg=1+βGg*.

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  FIGURE 4. Simulations of 25 × 25 cells with different degrees of cell variations and different average gap junction conductances (Case 4 in Table 1). Upper panel: Time of arrival (ToA) for the depolarization and repolarization waves for cell number 10 in the x‐direction and each of the cells in the y‐direction. The degree of variation of cell properties are increased for each plot row, but the gap junction conductance is the same for all cell connections. The different lines correspond to different values of the average gap junction conductance, Gg* (see legends). Note that the ToA axis covers different time points in the different plots, but the scaling of the axis is the same in all cases. Lower panel: Illustration of the cell collections with 0%, 25% and 50% variations in the cell properties. The color of the cells indicate the APD50 value of the cell if it was not connected to other cells. Note, however, that the variation in cell parameters affect several different cell properties, not only the APD50 value.

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  FIGURE 5. Simulations of 25 × 25 cells with 50% variation in gap junction coupling, different degrees of cell variations and different average gap junction conductances (Case 5 in Table 1). Upper panel: Time of arrival (ToA) for the depolarization and repolarization waves for cell number 10 in the x‐direction and each of the cells in the y‐direction. The degree of variation of cell properties are increased for each plot row. The different lines correspond to different values of the average gap junction conductance, Gg* (see legends). Note that the ToA axis covers different time points in the different plots, but the scaling of the axis is the same in all cases. Lower panel: Illustration of the cell collections with 0%, 25% and 50% variations in the cell properties. The color of the cells indicate the APD50 value of the cell if it was not connected to other cells. Note, however, that the variation in cell parameters affect several different cell properties, not only the APD50 value. The color of the cell connections indicate the strength of the gap junction coupling between cells.

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  FIGURE 6. Maximum variation in the time of arrival (ToA) for the depolarization and repolarization waves as functions of the average gap junction conductance, Gg*, for the simulations described in Figures 3, 4, 5 (Cases 3–5 in Table 1).

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  FIGURE 7. Action potentials, calcium transients and sarcomere length (SL) shortening for two different cells in a collection of 25 × 25 cells with 50% variation in cell properties and gap junction coupling (Case 5 in Table 1, Figure 5). We plot the properties of the two cells along the same x‐values with the largest difference in the action potential duration (APD50) for the G*g = 4 nS case. The lower panel displays the parameter adjustments, αi,k (see (7)), corresponding to the two cells.

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  FIGURE 8. Time of arrival (ToA) for the depolarization and repolarization waves at cell number 13 in the x‐direction and each of the cells in the y‐direction in simulations of 25 × 25 cells with four different gap junction conductances (see legends). The strength of the gap junction coupling and the cell properties are the same for all cells, except that a perturbation current, Ip, that is constant in time, is included for each cell (Case 6 in Table 1). This current is given on the form Ip=rα, where α∈−1A/F1A/F varies randomly between cell (see right panel), and r is increased for each row. Note that the ToA axis covers different time points in the different plots, but the scaling of the axis is the same in all cases.

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  FIGURE 9. Simulation of a collection of 15 × 5 cells modeled using the O'Hara‐Rudy model with 53% IKr block, 4×gCaL and 0.25 Hz pacing. We consider five different values of the average gap junction conductance (column titles). The cell properties are the same for all cells. The gap junction conductance is constant in the upper row and varies randomly between cell connections within ±25% and ±50% of the average gap junction conductance, respectively, in the center and lower rows (Case 3 in Table 1). We plot the action potential in the cells along a line in the x‐direction. In the lower left panel, these cells are circled with a color corresponding to the color of the plotted action potentials.

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  FIGURE 10. Simulation of a collection of 15 × 5 cells modeled using the O'Hara‐Rudy model with 53% IKr block, 4×gCaL and 0.25 Hz pacing. We consider five different values of the average gap junction conductance (column titles). The cell properties varies randomly from cell‐to‐cell (Case 4 in Table 1), and the isolated single cell APDs corresponding to 1 Hz pacing and no parameter adjustments are displayed in the lower panel. The degree of variation of cell properties are increased for each plot row. The gap junction conductance is the same, Gg, between all cells. We plot the action potential in the cells along a line in the x‐direction. In the lower left panel, these cells are circled with a color corresponding to the color of the plotted action potentials.

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  FIGURE 11. Simulation of a collection of 15 × 5 cells modeled using the O'Hara‐Rudy model with 53% IKr block, 4×gCaL and 0.25 Hz pacing. We consider five different values of the average gap junction conductance (column titles). The cell properties varies randomly from cell‐to‐cell, and the isolated single cell APDs corresponding to 1 Hz pacing and no parameter adjustments are displayed in the lower panel. The degree of variation of cell properties are increased for each plot row. The gap junction conductance varies randomly between cell connections within ±50% of the average gap junction conductance, Gg*. We plot the action potential in the cells along a line in the x‐direction. In the lower left panel, these cells are circled with a color corresponding to the color of the plotted action potentials.

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  FIGURE 12. Action potentials and ICaL currents in the cell marked with a dark blue circle in the lower panel of Figure 11. We consider the case of 50% cell variation and 50% gap junction variation (Case 5 in Table 1).