Intracellular Na+ Modulates Pacemaking Activity in Murine Sinoatrial Node Myocytes: An In Silico Analysis

Figure 1. Reparameterization of the Kharche et al. model of the murine SAM. (A) Experimental (top panels) and simulated (bottom panels) voltage-dependence of peak ICaL [24], peak Ito [25], and If availability [26]. (B) Parameter scaling factors yielded by the global optimization process aimed at minimizing the differences between average measured and simulated AP characteristics (shown in the schematic in the inset). Definition of both model parameters and AP characteristics is reported in Appendix A. (C) Time course of membrane voltage in a representative experimental trace and in simulations performed with the original Kharche et al. model (orange) and our optimized dataset-specific reparameterization (blue). (D) Comparison between experimentally measured AP characteristics [23] and the outputs predicted with original and optimized models.

Figure 2. Properties of the newly developed dataset-specific model of the murine SAM. (A) Time course of AP, Ca2+ and Na+ concentrations, and main ion currents in the optimized model. (B) Simulated and experimentally observed effects on FR induced by complete block of INa1.1 and INa1.5 [28,29], Ito and Isus [29], ICaT [30], ICaL [31], NCX [32], and NKA [33]. “Stop” indicates interruption of spontaneous firing activity.

Figure 3. NKA and NCX reductions can both enhance SAM automaticity and impair pacemaking activity depending on the degree of block. (A) Bar graph showing the relative contribution of NKA, NCX, INa1.1, INa1.5, Ist, INaB, and If to total Na+ influx and removal during a beat cycle in the optimized murine SAM model. (B) Average FR upon simulation of various extents of NKA block. Insets show voltage traces obtained simulating 40%, 60%, and 70% block. (C) Average FR upon simulation of various extents of NCX block. Insets show voltage traces obtained simulating 50%, 75%, and 80% block. Thin gray traces in insets correspond to the voltage traces simulated in the absence of the block.

Figure 4. Mild block of NKA has positive chronotropic and isotropic effects. (A) Time course of membrane potential, [Ca2+]i, NKA current, [Na+]i, and FR predicted upon sudden 40% block of NKA maximal transport rate (at t = 10 s). Black traces are obtained clamping [Na+]i to the initial value, while blue traces are obtained simulating the normal condition in which [Na+]i is free to change. (B) Comparison between the time course before applying the block and at the end of the simulation for membrane potential, [Ca2+]i, NKA current, NCX current, ICaL, and its Ca2+-dependent inactivation. CDI values were calculated from the state variable Fca, representing the gate describing CDI in the Hodgkin-Huxley type ICaL model in the Kharche et al. framework (CDI = 1 − Fca, with Fca varying from 0 to 1).

Figure 5. Excessive Na+ accumulation and consequent Ca2+ overload upon NKA block impair SAM automaticity. (A) Time course of membrane potential, [Ca2+]i, [Na+]i, and FR simulated upon 60% block of NKA (at t = 10 s). Blue traces are obtained simulating the baseline condition in which [Na+]i is free to change. Purple and green traces are obtained by clamping [Na+]i to either the maximal or the minimum values in the blue trace. The inset shows the FR-[Na+]i phase plot obtained during the bistable regime. (B) Time course of membrane potential, [Ca2+]i, [Na+]i, FR, and CDI of ICaL obtained upon simulation of 70% block of NKA (at t = 10 s). Green traces are obtained by clamping [Na+]i to 12 mM after t = 60 s; orange traces are obtained by imposing (after t = 60 s) the values of CDI predicted before NKA block; blue traces are obtained simulating the model without any constrain on [Na+]i or CDI.

Figure 6. Ca2+-dependent ICaL inactivation upon NCX block impairs SAM automaticity. (A) Time course of membrane potential, [Ca2+]i, [Na+]i, and FR upon simulation of 75% block of NCX (at t = 10 s). The inset shows the FR-[Na+]i phase plot obtained when the model enters the bursting regime. (B) Time course of membrane potential, [Ca2+]i, [Na+]i, FR, and CDI of ICaL upon simulation of 80% block of NCX (at t = 10 s). In both panels, orange traces are obtained by imposing (after t = 60 s) the values of CDI predicted before NCX block; blue traces are obtained simulating the model without any constrain on CDI.

Figure 7. Combining NKA and NKA block facilitates disruption of SAM automaticity. (A) Time course of membrane potential, [Ca2+]i, [Na+]i, and FR upon simulation of combined 50% block of NKA and NCX. (B) Average FR (top panel) and its standard deviation (bottom panel) were assessed upon combinations of concomitant NKA and NCX block.

Figure 8. Increased GCaL and leftward shift of ICaL voltage-dependence counteracts disruption of SAM automaticity induced by combined NKA and NCX block. Average FR (A) and FR standard deviation (B) were assessed upon combinations of concomitant NKA and NCX block with normal or altered ICaL function. Changes in ICaL include modulation of maximal conductance (±50%) and shifts in the voltage-dependence of activation and inactivation (±4 mV).

Figure 9. Feedback of Na+ and Ca2+ signals and membrane clock modulates SAM automaticity. (A) Schematic of the relationships linking Na+ and Ca2+ signaling and SAM automaticity. (B) FR-[Na+]i phase plots showing FR and [Na+]i values predicted over time upon 40%, 60%, and 70% NKA block (blue lines), during quasi-steady-state [Na+]i-clamp simulations in which [Na+]i is slowly (i.e., 0.33 mM/min) increased from 8 to 17 mM and then reduced to 8 mM (orange lines), and at steady-state in voltage-clamp simulations in which the FR is controlled (dotted black lines with dots).

Figure 10. Hypercalcemia facilitates disruption of SAM automaticity. Average FR (top panels) and FR standard deviation (bottom panels) were assessed upon combinations of concomitant NKA and NCX block at different levels of extracellular [Ca2+]. Note that the baseline [Ca2+]o used in our simulations is 1.8 mM.