Action potential repolarization enabled by Ca⁺⁺channel deactivation in PSpice simulation of smooth muscle propagation

Abstract

Abstract Background Previously, only the rising phase of the action potential (AP) in cardiac muscle and smooth muscle could be simulated due to the instability of PSpice upon insertion of a second black box (BB) into the K+ leg of the basic membrane unit. This restriction was acceptable because only the transmission of excitation from one cell to the next was investigated. Methods In the current work, the repolarization of the AP was accomplished by inserting a second BB into the Ca++ leg of the basic membrane unit. Repolarization of the AP was produced, not through an activation of the K+ channel conductance, but rather through a mimicking of the deactivation of the Ca++ channel conductance. Propagation of complete APs was studied in a chain (strand) of 10 smooth muscle cells, in which various numbers of gap-junction (gj) channels (assumed to be 100 pS each) were inserted across the cell junctions. Results The shunt resistance across the junctions produced by the gj-channels (Rgj) was varied from 100,000 MΩ (0 gj-channels) to 10,000 MΩ (1 gj-channel), to 1,000 MΩ (10 channels), to 100 MΩ (100 channels), to 10 MΩ (1000 channels), and to 1.0 MΩ (10,000 channels). Velocity of propagation (θ, in cm/sec) was calculated from the measured total propagation time (TPT, the time difference between when the AP rising phase of the first cell and the last cell crossed -20 mV), assuming a constant cell length of 200 μm. When there were no gj-channels, or only one, the transmission of excitation between cells was produced by the electric field (EF), i.e., the negative junctional cleft potential, that is generated in the narrow junctional clefts (e.g., 100 A) when the prejunctional membrane fires an AP (a fraction of a millisecond before the adjacent surface membrane). There were significant end-effects at the termination of the strand, such that the last cell (cell #10) failed to fire, or fired after a prolonged delay. This end-effect was abolished when the strand termination resistance (Rbt) was increased from 1.0 KΩ to 600 MΩ. When there were 1000 or 10,000 gj-channels, the transmission of excitation was produced by local-circuit current flow from one cell to the next through the gj-channels. Discussion In summary, it is now possible to simulate complete APs in smooth muscle cells that could propagate along a single chain of 10 cells, even when there were no gj-channels between the cells.