Gap-junction channels inhibit transverse propagation in cardiac muscle

Abstract

The effect of adding many gap-junctions (g-j) channels between contiguous cells in a linear chain on transverse propagation between parallel chains was examined in a 5 x 5 model (5 parallel chains of 5 cells each) for cardiac muscle. The action potential upstrokes were simulated using the PSpice program for circuit analysis. Either a single cell was stimulated (cell A1) or the entire chain was stimulated simultaneously (A-chain). Transverse velocity was calculated from the total propagation time (TPT) from when the first AP crossed a Vm of -20 mV and the last AP crossed -20 mV. The number of g-j channels per junction was varied from zero to 100, 1,000 and 10,000 (Rgj of infinity, 100 MOmega, 10 MOmega, 1.0 MOmega, respectively). The longitudinal resistance of the interstitial fluid (ISF) space between the parallel chains (Rol2) was varied between 200 KOmega (standard value) and 1.0, 5.0, and 10 MOmega. The higher the Rol2 value, the tighter the packing of the chains. It was found that adding many g-j channels inhibited transverse propagation by blocking activation of all 5 chains, unless Rol2 was greatly increased above the standard value of 200 KOmega. This was true for either method of stimulation. This was explained by, when there is strong longitudinal coupling between all 5 cells of a chain awaiting excitation, there must be more transfer energy (i.e., more current) to simultaneously excite all 5 cells of a chain.

Figure 1

The 5 × 5 model for cardiac muscle, consisting of 5 parallel strands (A-E) of 5 cells each (1–5) (total of 25 cells). Each muscle cell was represented by a block of 4 basic units: 2 units representing the surface membrane (one upward-facing and one downward-facing) and one unit for each of the two junctional membranes. For simplicity, the lumped resistance of the gap-junctions is not indicated here, but is shown in Fig. 2. Transverse propagation is sequential activation of chains A to B to C to D to E.

Figure 2

Blow-up of a small portion of the 5 × 5 model to show the electrical circuit for each basic unit, including the "black-box" required for excitability. R_ol2 represents the longitudinal resistance of the interstitial fluid between the parallel chains; the higher the resistance, the tighter the packing of the chains. Depolarizing current (0.25 nA) is applied to the interior of either the first cell or the entire chain (A-chain) simultaneously. When gap-junction channels were added, a resistor (R_gj) was inserted across each cell junction, from the interior of one cell to the interior of the next one.

Figure 3

Transverse propagation of simulated action potentials (APs; rising phase) for cardiac muscle (5 × 5 models) with stimulation of one cell only (cell A1; first cell of the A-chain). A: R_gj = ∞ (0 channels). R_ol2 = 200 KΩ. Standard conditions. All 25 cells responded. B: R_gj = 1.0 MΩ (10,000 channels). R_ol2 kept unchanged. The last 2 chains (D, E) failed to respond. All 5 cells of each chain that responded (A, B, C) fired simultaneously because of the strong cell coupling. C: With R_gj held at 1.0 MΩ, raising R_ol2 to 10 MΩ (representing tighter packing of the parallel chains) now allowed all 5 chains to respond. Thus, adding gj-channels inhibited transverse propagation, but this inhibition could be overcome by raising R_ol2.

Figure 4

Transverse propagation of simulated APs for cardiac muscle with stimulation simultaneously of the entire A-chain. This was done as a better assessment of transverse propagation for comparison with stimulation of only one cell of the A-chain. A: R_gj = ∞ (0 channels). R_ol2 = 200 KΩ. Standard conditions. All 5 chains responded. B: R_gj = 1.0 MΩ (10,000 channels). With R_ol2 kept at 200 KΩ, chains C, D, and E failed to respond. C: With R_gj held at 1.0 MΩ, raising R_ol2 to 10 MΩ (representing tighter packing of the chains) now allowed all 5 chains to respond. All 5 cells of each chain responded simultaneously because of the strong coupling. Thus, adding gj-channels inhibited transverse propagation, but this inhibition was overcome by raising R_ol2.

Figure 5

Summary of the transverse propagation experiments. Graphic plot of the number of chains responding as a function of R_gj for cardiac muscle, with stimulation of only one cell (cell A1) (panel A) or with stimulation of the entire A-chain (panel B). Data for various R_ol2 values (0.2, 1.0, 5.0, and 10 MΩ) are indicated. Four different R_gj values were tested: ∞ (0 channels), 100 MΩ (100 channels), 10 MΩ (1,000 channels), and 1.0 MΩ (10,000 channels). Thus, transverse propagation was depressed when there were many gj-channels (1000 or 10,000), but elevation of R_ol2 could overcome this depression.

Figure 6

Special experiment to test why presence of many gap-junction channels inhibits transverse propagation. Stimulated Cell A1 only. R_ol2 of 1.0 MΩ. A: Uniform value for R_gj of 1.0 MΩ (10,000 channels) in all 5 chains. Chains D and E failed to respond. Compare with Fig. 3B for the standard R_ol2 of 0.2 MΩ. B: The R_gj values in chains D and E only were changed to infinity (0 channels). Now chains D and E responded. See text for details. This demonstrates that removing the gj-channels in the two chains awaiting excitation (D, E) increased the safety factor for transverse propagation.