Effect of transverse gap-junction channels on transverse propagation in an enlarged PSpice model of cardiac muscle

BACKGROUND: In previous PSpice modeling studies of simulated action potentials (APs) in parallel chains of cardiac muscle, it was found that transverse propagation could occur between adjacent chains in the absence of gap-junction (gj) channels, presumably by the electric field (EF) generated in the narrow interstitial space between the chains. Transverse propagation was sometimes erratic, the more distal chains firing out of order. METHODS: In the present study, the propagation of complete APs was studied in a 2-dimensional network of 100 cardiac muscle cells (10 × 10 model). Various numbers of gj-channels (assumed to be 100 pS each) were inserted across the junctions between the longitudinal cells of each chain and between adjacent chains (only at the end cells of each chain). The shunt resistance produced by the gj-channels (R(gj)) was varied from 100,000 MΩ (0 gj-channels) to 1,000 MΩ (10 channels), 100 MΩ (100 channels) and 10 MΩ (1,000 channels). Total propagation time (TPT) was measured as the difference between the times when the AP rising phase of the first cell (cell # A1) and the last cell (in the J chain) crossed 0 mV. When there were no gj-channels, the excitation was transmitted between cells by the EF, i.e., the negative potential generated in the narrow junctional clefts (e.g., 100 Å) when the prejunctional membrane fired an AP. For the EF mechanism to work, the prejunctional membrane must fire a fraction of a millisecond before the adjacent surface membrane. When there were many gj-channels (e.g., 100 or 1,000), the excitation was transmitted by local-circuit current flow from one cell to the next through these channels. RESULTS: TPT was measured as a function of four different numbers of transverse gj-channels, namely 0, 10, 100 and 1,000, and four different numbers of longitudinal gj-channels, namely 0, 10, 100 and 1,000. Thus, 16 different measurements were made. It was found that increasing the number of transverse channels had no effect on TPT when the number of longitudinal channels was low (i.e., 0 or 10). In contrast, when the number of longitudinal gj-channels was high (e.g., 100 or 1,000), then increasing the number of transverse channels decreased TPT markedly. CONCLUSION: Thus, complete APs could propagate along a network of 100 cardiac muscle cells even when no gj-channels were present between the cells. Insertion of transverse gj-channels greatly speeded propagation through the 10 × 10 network when there were also many longitudinal gj-channels

Cable properties and propagation velocity in a long single chain of simulated myocardial cells

<p>Abstract</p> <p>Background</p> <p>Propagation of simulated action potentials (APs) was previously studied in short single chains and in two-dimensional sheets of myocardial cells <abbrgrp><abbr bid="B1">1</abbr><abbr bid="B2">2</abbr><abbr bid="B3">3</abbr></abbrgrp>. The present study was undertaken to examine propagation in a long single chain of cells of various lengths, and with varying numbers of gap-junction (g-j) channels, and to compare propagation velocity with the cable properties such as the length constant (<it>λ</it>).</p> <p>Methods and Results</p> <p>Simulations were carried out using the PSpice program as previously described. When the electric field (EF) mechanism was dominant (0, 1, and 10 gj-channels), the longer the chain length, the faster the overall velocity (<it>θ</it>_ov). There seems to be no simple explanation for this phenomenon. In contrast, when the local-circuit current mechanism was dominant (100 gj-channels or more), <it>θ</it>_ovwas slightly slowed with lengthening of the chain. Increasing the number of gj-channels produced an increase in <it>θ</it>_ovand caused the firing order to become more uniform. The end-effect was more pronounced at longer chain lengths and at greater number of gj-channels.</p> <p>When there were no or only few gj-channels (namely, 0, 10, or 30), the voltage change (ΔV_m) in the two contiguous cells (#50 & #52) to the cell injected with current (#51) was nearly zero, i.e., there was a sharp discontinuity in voltage between the adjacent cells. When there were many gj-channels (e.g., 300, 1000, 3000), there was an exponential decay of voltage on either side of the injected cell, with the length constant (<it>λ</it>) increasing at higher numbers of gj-channels. The effect of increasing the number of gj-channels on increasing <it>λ </it>was relatively small compared to the larger effect on <it>θ</it>_ov. <it>θ</it>_ovbecame very non-physiological at 300 gj-channels or higher.</p> <p>Conclusion</p> <p>Thus, when there were only 0, 1, or 10 gj-channels, <it>θ</it>_ovincreased with increase in chain length, whereas at 100 gj-channels or higher, <it>θ</it>_ovdid not increase with chain length. When there were only 0, 10, or 30 gj-channels, there was a very sharp decrease in ΔV_min the two contiguous cells on either side of the injected cell, whereas at 300, 1000, or 3000 gj-channels, the voltage decay was exponential along the length of the chain. The effect of increasing the number of gj-channels on spread of current was relatively small compared to the large effect on <it>θ</it>_ov.</p

Transverse propagation of action potentials between parallel chains of cardiac muscle and smooth muscle cells in PSpice simulations

BACKGROUND: We previously examined transverse propagation of action potentials between 2 and 3 parallel chain of cardiac muscle cells (CMC) simulated using the PSpice program. The present study was done to examine transverse propagation between 5 parallel chains in an expanded model of CMC and smooth muscle cells (SMC). METHODS: Excitation was transmitted from cell to cell along a strand of 5 cells not connected by low-resistance tunnels (gap-junction connexons). The entire surface membrane of each cell fired nearly simultaneously, and nearly all the propagation time was spent at the cell junctions, the junctional delay time being about 0.3 – 0.5 ms (CMC) or 0.8 – 1.6 ms (SMC). A negative cleft potential (V(jc)) develops in the narrow junctional clefts, whose magnitude depends on the radial cleft resistance (R(jc)), which depolarizes the postjunctional membrane (post-JM) to threshold. Propagation velocity (θ) increased with amplitude of V(jc). Therefore, one mechanism for the transfer of excitation from one cell to the next is by the electric field (EF) that is generated in the junctional cleft when the pre-JM fires. In the present study, 5 parallel stands of 5 cells each (5 × 5 model) were used. RESULTS: With electrical stimulation of the first cell of the first strand (cell A1), propagation rapidly spread down that chain and then jumped to the second strand (B chain), followed by jumping to the third, fourth, and fifth strands (C, D, E chains). The rapidity by which the parallel chains became activated depended on the longitudinal resistance of the narrow extracellular cleft between the parallel strands (R(ol2)); the higher the R(ol2 )resistance, the faster the θ. The transverse resistance of the cleft (R(or2)) had almost no effect. Increasing R(jc )decreases the total propagation time (TPT) over the 25-cell network. When the first cell of the third strand (cell C1) was stimulated, propagation spread down the C chain and jumped to the other two strands (B and D) nearly simultaneously. CONCLUSIONS: Transverse propagation of excitation occurred at multiple points along the chain as longitudinal propagation was occurring, causing the APs in the contiguous chains to become bunched up. Transverse propagation was more erratic and labile in SMC compared to CMC. Transverse transmission of excitation did not require low-resistance connections between the chains, but instead depended on the value of R(ol2). The tighter the packing of the chains facilitated transverse propagation

Propagation velocity profile in a cross-section of a cardiac muscle bundle from PSpice simulation

BACKGROUND: The effect of depth on propagation velocity within a bundle of cardiac muscle fibers is likely to be an important factor in the genesis of some heart arrhythmias. MODEL AND METHODS: The velocity profile of simulated action potentials propagated down a bundle of parallel cardiac muscle fibers was examined in a cross-section of the bundle using a PSpice model. The model (20 × 10) consisted of 20 chains in parallel, each chain being 10 cells in length. All 20 chains were stimulated simultaneously at the left end of the bundle using rectangular current pulses (0.25 nA, 0.25 ms duration) applied intracellularly. The simulated bundle was symmetrical at the top and bottom (including two grounds), and voltage markers were placed intracellularly only in cells 1, 5 and 10 of each chain to limit the total number of traces to 60. All electrical parameters were standard values; the variables were (1) the number of longitudinal gap-junction (G-j) channels (0, 1, 10, 100), (2) the longitudinal resistance between the parallel chains (R(ol2)) (reflecting the closeness of the packing of the chains), and (3) the bundle termination resistance at the two ends of the bundle (R(BT)). The standard values for R(ol2 )and R(BT )were 200 KΩ. RESULTS: The velocity profile was bell-shaped when there was 0 or only 1 gj-channel. With standard R(ol2 )and R(BT )values, the velocity at the surface of the bundle (θ(1 )and θ(20)) was more than double (2.15 ×) that at the core of the bundle (θ(10), θ(11)). This surface:core ratio of velocities was dependent on the values of R(ol2 )and R(BT). When R(ol2 )was lowered 10-fold, θ(1 )increased slightly and θ(2)decreased slightly. When there were 100 gj-channels, the velocity profile was flat, i.e. the velocity at the core was about the same as that at the surface. Both velocities were more than 10-fold higher than in the absence of gj-channels. Varying R(ol2 )and R(BT )had almost no effect. When there were 10 gj-channels, the cross-sectional velocity profile was bullet-shaped, but with a low surface/core ratio, with standard R(ol2 )and R(BT )values. CONCLUSION: When there were no or few gj-channels (0 or 1), the profile was bell-shaped with the core velocity less than half that at the surface. In contrast, when there were many gj-channels (100), the profile was flat. Therefore, when some gj-channels close under pathophysiological conditions, this marked velocity profile could contribute to the genesis of arrhythmias

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

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 (R(gj)) 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 (R(bt)) 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

Propagated repolarization of simulated action potentials in cardiac muscle and smooth muscle

BACKGROUND: Propagation of repolarization is a phenomenon that occurs in cardiac muscle. We wanted to test whether this phenomenon would also occur in our model of simulated action potentials (APs) of cardiac muscle (CM) and smooth muscle (SM) generated with the PSpice program. METHODS: A linear chain of 5 cells was used, with intracellular stimulation of cell #1 for the antegrade propagation and of cell #5 for the retrograde propagation. The hyperpolarizing stimulus parameters applied for termination of the AP in cell #5 were varied over a wide range in order to generate strength / duration (S/D) curves. Because it was not possible to insert a second "black box" (voltage-controlled current source) into the basic units representing segments of excitable membrane that would allow the cells to respond to small hyperpolarizing voltages, gap-junction (g.j.) channels had to be inserted between the cells, represented by inserting a resistor (R(gj)) across the four cell junctions. RESULTS: Application of sufficient hyperpolarizing current to cell #5 to bring its membrane potential (V(m)) to within the range of the sigmoidal curve of the Na(+ )conductance (CM) or Ca(++ )conductance (SM) terminated the AP in cell #5 in an all-or-none fashion. If there were no g.j. channels (R(gj )= ∞), then only cell #5 repolarized to its stable resting potential (RP; -80 mV for CM and -55 mV for SM). The positive junctional cleft potential (V(JC)) produced only a small hyperpolarization of cell #4. However, if many g.j. channels were inserted, more hyperpolarizing current was required (for a constant duration) to repolarize cell #5, but repolarization then propagated into cells 4, 3, 2, and 1. When duration of the pulses was varied, a typical S/D curve, characteristic of excitable membranes, was produced. The chronaxie measured from the S/D curve was about 1.0 ms, similar to that obtained for muscle membranes. CONCLUSIONS: These experiments demonstrate that normal antegrade propagation of excitation can occur in the complete absence of g.j. channels, and therefore no low-resistance pathways between cells, by the electric field (negative V(JC)) developed in the narrow junctional clefts. Because it was not possible to insert a second black-box into the basic units that would allow the cells to respond to small hyperpolarizing voltages, only cell #5 (the cell injected with hyperpolarizing pulses) repolarized in an all-or-none manner. But addition of many g.j. channels allowed repolarization to propagate in a retrograde direction over all 5 cells