Effect of myocyte-fibroblast coupling on the onset of pathological dynamics in a model of ventricular tissue

Managing lethal cardiac arrhythmias is one of the biggest challenges in modern cardiology, and hence it is very important to understand the factors underlying such arrhythmias. While early afterdepolarizations (EAD) of cardiac cells is known to be one such arrhythmogenic factor, the mechanisms underlying the emergence of tissue level arrhythmias from cellular level EADs is not fully understood. Another known arrhythmogenic condition is fibrosis of cardiac tissue that occurs both due to aging and in many types of heart diseases. In this paper we describe the results of a systematic in-silico study, using the TNNP model of human cardiac cells and MacCannell model for (myo)fibroblasts, on the possible effects of diffuse fibrosis on arrhythmias occurring via EADs. We find that depending on the resting potential of fibroblasts (VFR), M-F coupling can either increase or decrease the region of parameters showing EADs. Fibrosis increases the probability of occurrence of arrhythmias after a single focal stimulation and this effect increases with the strength of the M-F coupling. While in our simulations, arrhythmias occur due to fibrosis induced ectopic activity, we do not observe any specific fibrotic pattern that promotes the occurrence of these ectopic sources.

1. Fig S1: Fibroblasts are inserted randomly between myocytes on a system of size 1024 × 1024. 10 percent of the lattice points are occupied by fibroblasts (black squares) while the remaining points are occupied by myocytes. (b) Schematic diagram illustrating diffuse fibrosis with a lattice of myocytes (circles) interspersed with fibroblasts (ellipses) coupled to the each other via gap-junctions (broken lines).
2. Fig S2: The effect of coupling with Fibroblast-1 (a) and Fibroblast-2(b) on a single cell action potential for xG CaL = 5.0 and yG Kr = 0.4 for the case of no coupling (solid line), Gs = 0.5 nS (broken line) and Gs = 2.0 (dot-dash line).
3. Fig S3: Phase diagram for the different forms of action potentials in the xG CaL -yG Kr parameter space for the case of one myocyte coupled to 5 fibroblasts as a function of strength of M-F coupling (Gs), with x and y corresponding to the factor by which the maximal conductance of I Kr and I CaL are multiplied. The top row (a-c) correspond to the case with fibroblast parameters (V F R = −49.7 mV and C = 6.3 pF) while the bottom row (d-f) corresponds to the case with parameters (V F sR = −24.5 mV and C = 50 pF). Cases that do not describe any reversal of the action potential before complete repolarization are represented as NO EAD, while those that show such a reversal are denoted EAD. OSC corresponds to action potentials that oscillate without returning to their resting state.
4. Fig S4: Fraction of simulations leading to the different dynamical states observed in Fig.5 for both Fibroblast-1 (a) and Fibroblast-2 (b) are shown as a function of the M-F coupling strength (Gs). For ease of comparison the results for the case without fibroblasts is also plotted.
5. Fig S5: Fraction of simulations leading to the different dynamical states observed in Fig.6 for both Fibroblast-1 (a) and Fibroblast-2 (b) are shown as a function of the M-F coupling strength (Gs). For the sake of comparison the results for the case without fibroblasts is also plotted.
6. Fig S6: The value of parameter xG CaL at which the transition from NO EAD to EAD state occurs is plotted as a function of the strength of M-F coupling for values of yG Kr = 0.4 (a, d), 0.8 (b, e) and 1.2 (c, f) respectively for the case C = 6.3 pF (circle), C = 14.5 pF (diamond) and C = 50 pF (square). Panels (a, b, c) correspond to resting membrane potential V F R = 49.7 mV, while panels (d, e, f) correspond to the case when V F R = 24.5 mV.
7. Fig S7:Illustration of the effect of MF coupling on action potentials of myocyte (a) and fibroblast (b), current flowing from a myocyte to (N = 5) coupled fibroblasts I M toF (c) and myocyte L-type calcium current (d) for the cases of MF coupling to zero fibroblast (solid line), 5 fibroblasts with V F R = −49.7mV (broken line) and V F R = −24.5mV (dot-dash line). Fibroblast capacitance C F = 50 pF and strength of MF coupling is Gs = 1nS. The current flowing between myocyte and fibroblasts is where V M yo and V F are myocyte and fibroblast voltages respectively and C m = 185 pF is the myocyte membrane capacitance. For the parameters used here (xG CaL = 2.0 and yG Kr = 0.4) while no EADs are observed even in the presence of coupling, depending on the value of V F R the myocyte action potential duration either shortens (broken line) or lengthens (dot-dash line).
where V M yo and V F are myocyte and fibroblast voltages respectively and C m = 185 pF is the myocyte membrane capacitance. For the parameters used here (xG CaL = 3.0 and yG Kr = 0.4), EAD occurs only in the presence of MF coupling (broken line).   , with x and y corresponding to the factor by which the maximal conductance of I Kr and I CaL are multiplied. The top row (a-c) correspond to the case with fibroblast parameters (V F R = −49.7 mV and C = 6.3 pF) while the bottom row (d-f) corresponds to the case with parameters (V F sR = −24.5 mV and C = 50 pF). Cases that do not describe any reversal of the action potential before complete repolarization are represented as NO EAD, while those that show such a reversal are denoted EAD. OSC corresponds to action potentials that oscillate without returning to their resting state.
(f) (e) (d) Figure 6: The value of parameter xG CaL at which the transition from NO EAD to EAD state occurs is plotted as a function of the strength of M-F coupling for values of yG Kr = 0.4 (a, d), 0.8 (b, e) and 1.2 (c, f) respectively for the case C = 6.3 pF (circle), C = 14.5 pF (diamond) and C = 50 pF (square). Panels (a, b, c) correspond to resting membrane potential V F R = 49.7 mV, while panels (d, e, f) correspond to the case when V F R = 24.5 mV.