Reciprocal Modulation of IK1-INa Extends Excitability in Cardiac Ventricular Cells

Abstract

The inwardly rectifying potassium current (I_K1) and the fast inward sodium current (I_Na) are reciprocally modulated in mammalian ventricular myocytes. An increase in the expression of channels responsible for one of these two currents results in a corresponding increase in expression of the other. These currents are critical in the propagation of action potentials (AP) during the normal functioning of the heart. This study identifies a physiological role for I_K1-I_Na reciprocal modulation in ventricular fiber activation thresholds and conduction. Simulations of action potentials in single cells and propagating APs in cardiac fibers were carried out using an existing model of electrical activity in cardiac ventricular myocytes. The conductances, G_K1, of the inwardly rectifying potassium current, and G_Na, of the fast inward sodium current were modified independently and in tandem to simulate reciprocal modulation. In single cells, independent modulation of G_K1 alone resulted in changes in activation thresholds that were qualitatively similar to those for reciprocal G_K1-G_Na modulation and unlike those due to independent modulation of G_Na alone, indicating that G_K1 determines the cellular activation threshold. On the other hand, the variations in conduction velocity in cardiac cell fibers were similar for independent G_Na modulation and for tandem changes in G_K1-G_Na, suggesting that G_Na is primarily responsible for setting tissue AP conduction velocity. Conduction velocity dependence on G_K1-G_Na is significantly affected by the intercellular gap junction conductance. While the effects on the passive fiber space constant due to changes in both G_K1 and the intercellular gap junction conductance, G_gj, were in line with linear cable theory predictions, both conductances had surprisingly large effects on fiber activation thresholds. Independent modulation of G_K1 rendered cardiac fibers inexcitable at higher levels of G_K1 whereas tandem G_K1-G_Na changes allowed fibers to remain excitable at high G_K1 values. Reciprocal modulation of the inwardly rectifying potassium current and the fast inward sodium current may have a functional role in allowing cardiac tissue to remain excitable when I_K1 is upregulated.

Keywords: cardiac cells; mathematical model; reciprocal modulation.

Figure 1

Action potential propagation in a cardiac fiber. (A) Schematic view of three cells in a fiber. In addition to a number of sodium, potassium, and calcium currents in the cell membrane, each cell has non-selective gap junction channels that allow currents to flow down the fiber. The gap junction current, I_gj, allows a depolarized cell to drive electrical activity in a neighboring cell. (B). Equivalent circuit representation of the three cells in (A). Each cell has a capacitance associated with the cell membrane and ionic currents represented by a conductance and a battery for the Nernst potential for the corresponding ion. The inward rectifier potassium current, I_K1, current has a non-linear conductance (see Methods) with a maximal conductance, G_K1, and its reversal potential is the potassium Nernst potential, E_K. The fast sodium current, I_Na, has a time-dependent conductance with the maximal conductance, G_Na, and its reversal potential is the sodium Nernst potential, E_Na. (C) Simulations showing cell membrane potential, V_m, and ion channel currents, I_K1 and I_Na, for a subthreshold stimulus (dashed curves) and suprathreshold stimulus (solid curves). Results shown are for the 5th cell in a fiber of 100 cells with 0.2 ms-duration current stimuli administered at the 5 ms mark to the first 4 cells. A subthreshold stimulus brings V_m to about −60 mV after which V_m declines (dashed curve) back to its resting membrane potential of about −90 mV; the I_K1 waveform due to a subthreshold stimulus is larger than the suprathreshold case (solid curve) because the subthreshold V_ms are more negative and thus less inward rectified. I_Na is partially activated (dashed curve) for a subthreshold stimulus and fully activated (solid curve) for the suprathreshold stimulus; the fully activated I_Na is what triggers the full depolarization of V_m to about +20 Mv.

Figure 2

Independent and reciprocal modulation of I_K1 and I_Na in single cells and fibers. By standard convention, inward (depolarizing) stimulus currents are negative. (A). Changes in single cell threshold due to independent modulation of G_Na. These results indicate that as G_Na is increased, the magnitude of the threshold is lowered. G_K1 was held at its default value of 0.5 μS. (B) Fiber threshold was also lowered as G_Na was increased. G_K1 was held at 0.5 μS and G_gj was held at 10 μS. (C) Fiber conduction velocity increased as G_Na was increased (same conditions as B). (D) Changes in single cell threshold due to independent modulation of G_K1: as G_K1 is increased, the magnitude of the threshold is raised. G_Na was held at 0.5 μS. (E) Fiber threshold was raised as G_K1 was increased. For values of G_K1 larger than 1.3 μS, the fiber was inexcitable. G_Na was held at its default value of 0.5 μS and G_gj was held at 10 μS. (F) Fiber conduction velocity decreased as G_K1 was increased (same conditions as D). (G) Changes in single cell threshold due to reciprocal modulation of G_K1 and G_Na. Cell threshold increased monotonically with the tandem changes in G_K1:G_Na. Three different ratios for G_K1:G_Na were used: 1:2, 1:1, and 2:1; the X-axis shows the G_K1 values, the corresponding G_Na value depends on the ratio used. (H) Fiber threshold changes due to reciprocal modulation of G_K1 and G_Na. Three different ratios for G_K1:G_Na were used (1:2, 1:1, and 2:1) while G_gj was held at 10 μS. The X-axis shows the G_K1 values, the corresponding G_Na value depends on the ratio used. (I) Fiber conduction velocity increased with reciprocal modulation of G_K1 and G_Na (same conditions as D). The X-axis shows the G_K1 values, the corresponding G_Na value depends on the ratio used.

Figure 3

Effects of reciprocal modulation of I_K1 and I_Na and changes in gap junction conductance, G_gj, on fiber thresholds. (A) Changes in fiber threshold due to reciprocal modulation of G_K1–G_Na (1:1 ratio). At any particular value of G_K1–G_Na, increasing G_gj raises the threshold for initiating a propagating action potential. The curves for G_gj = 0.1 and 0.2 μS (top two curves) overlap considerably. Magnitudes of current thresholds increase monotonically with increasing G_K1–G_Na for G_gj = 0.1–1 μS while higher values of G_gj result in biphasic dependence. (B) Changes in fiber conduction velocity due to reciprocal modulation of G_K1–G_Na. At any particular value of G_K1–G_Na, increasing G_gj increases the conduction velocity of propagating action potentials. Markers are the same as panel A: top curve is for G_gj = 20 μS.

Figure 4

Effects of independent and reciprocal modulation of I_K1 and I_Na and changes in gap junction conductance, G_gj, on fiber space constant. (A) Changes in fiber space constant due to independent modulation of G_K1 and G_Na: the space constant is insensitive to changes in G_Na alone (G_K1 held at 0.5 μS–flat line) but is very sensitive to alterations in G_K1 (G_Na held at 0.5 μS–curve). (B) Changes in fiber space constant due to reciprocal modulation of G_K1–G_Na (1:1 ratio). Each curve is for a different value of G_gj from 0.1 to 20 μS.