Coupling and heterogeneity modulate pacemaking capability in healthy and diseased two-dimensional sinoatrial node tissue models

Figures

• 

  Fig 1. Schematic of multicellular study design. A multiscale mathematical modeling approach was employed to study the mechanisms of sinoatrial node excitability. The effect of cell-to-cell coupling and cellular heterogeneity on tissue synchronization were evaluated in both healthy sinoatrial nodes and those that mimicked Sinus Node Disease. Blue inset in central top panel shows that cells were connected to 4 neighbors using ohmic resistances that modeled gap junctions between adjacent myocytes.

• 

  Fig 2. Features extracted from sinoatrial node AP simulations. A schematic AP trace is annotated with characteristic features. The full waveform is divided into the AP phase (solid line) and diastolic phase (dashed line) based on the criteria described. Critical voltages and durations are defined as labeled. Abbreviations: APA, action potential amplitude (mV); APD, action potential duration (ms); CL, cycle length (ms); DD, diastolic depolarization (ms); MDP, maximum diastolic potential (mV); OS, overshoot (mV); TOP, take off potential (mV).

• 

  Fig 3. Cell categorization. Cells forming the tissue have been divided into different categories, depending on whether they exhibited action potentials, or not, under both coupled and uncoupled conditions. Alterations in intercellular coupling can cause an individual cell to switch categories, for instance from dormant at one value of coupling to driven at another value.

• 

  Fig 4. Modeling conductance heterogeneity using virtual populations of isolated SAN cells. (A) The effect of heterogeneous ionic channel expression on the automaticity of SAN cells was compared across models. In all three models the percentage of dormant cells rose with increasing levels of heterogeneity. (B) The effect of heterogeneity on the SA node AP properties was evaluated in spontaneously beating cells, by measuring cycle length (CL), AP amplitude (APA) and AP duration (APD) at varying σ levels. Outliers (values more than three median absolute deviations) were removed from distributions. (C) Logistic regression analysis was utilized to deduce which specific ionic currents across the three models are responsible for SA node cell’s automaticity. Positive values indicate that an increase in the parameter increases the probability of the cell to be spontaneously beating.

• 

  Fig 5. SAN cells synchronize their electrical properties when coupled in a tissue. (A) When coupled together heterogeneous SAN cells give rise to a spontaneously beating tissue. The only exception occurs at very high values of heterogeneity (σ equal to 0.4 and 0.5, with 0.5% and 2.8% of dormant cells respectively) and very high levels of intercellular resistance (R = 10,000 MΩ). (B-D) The population of cells synchronizes its AP metrics: cycle length (CL), action potential amplitude (APA) and action potential duration (APD) when well-connected in tissue.

• 

  Fig 6. Certain coupling conditions restore automaticity to a prevalently dormant SA node tissue. (A) Effect of Ca2+ blockade in the Fabbri model with published parameters. (B) Distribution of PCaL in the tissue at varying degrees of Ca2+ blockade (cellular heterogeneity factor σ equals 0.1). (C) Comparison of the electrical activity of a cell within the tissue (σ equals 0.1) before and after blockade of Ca2+ by 50%. (D) Dormant cells within the tissue beat at intermediate values of coupling. (E) Quantification of the average tissue CL, APA and APD at varying degrees of Ca2+ blockade.

• 

  Fig 7. Pathophysiological changes in ionic currents lead to a pattern of tissue automaticity dependent on the degree of intercellular coupling. (A) Effect of L-type Ca2+ current (ICaL) perturbation in the Fabbri tissue model (σ equal to 0.1). (B) Effect of perturbation in ICaL and Na+/K+ pump (INaK) in the Maltsev-Lakatta tissue model (σ equal to 0.4). (C) Effect of combined ICaL, rapid delayed rectifier K+ current (IKr), and INaK perturbation in the Severi tissue model (σ equal to 0.2).

• 

  Fig 8. A small cluster of pacemaker cells can drive a prevalently dormant tissue. (A-top) (A) In the random tissue configuration dormant and pacemaker cells are interspersed in the matrix. (A-bottom) In the cluster configuration pacemaker cells are confined to a small portion of the matrix surrounded by dormant cells. Here dormant cells are cells that fail to depolarize after inhibition of ICaL by 50%. (B) The range of intercellular coupling compatible with AP generation and entrainment, i.e. reduced percentage of dormant cells, is wider in the cluster tissue configuration compared to the random. Results shown here were obtained with Fabbri human model (σ equal to 0.1).

• 

  Fig 9. Coupling between a spontaneous cell and a dormant cell. (A) Average Inet and Igj were extracted from the central 80% portion of the first occurrence of DD (from the beginning of the simulation to the first TOP); TOP Inet and Igj were sampled at the time of the TOP. (B) Inet and Igj trends during diastole (top) for Cell 1 (spontaneous) and at TOP (bottom) for Cell 2 (dormant) with respect to different degrees of cellular coupling. Igj is plotted in green for Cell 1 in both panels (the positive sign indicates an outward current, supplied to Cell 2). (C) Behavior of the two cells depending on coupling: both cells are beating periodically only for intermediate coupling values.

• 

  Fig 10. Coupling spontaneous cells with dormant cells inside a tissue. (A) Percentages of cells composing each category at different degrees of intercellular coupling. (B) Inet trends during diastole (top) and at TOP (bottom) with respect to different degrees of intercellular coupling for every cell category. Average value (symbol) ± standard deviation (dashed line). (C) Electrical activity of 50 cells (4th column of the 2D tissue matrix) when they are coupled with different intercellular resistances.