Published online before print August 28, 2003, doi: 10.1161/01.RES.0000093379.61888.35
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© 2003 American Heart Association, Inc.
UltraRapid Communication |
Regulation of Connexin43 Gap Junctional Conductance by Ventricular Action Potentials
From the Department of Pharmacology, SUNY Upstate Medical University, Syracuse, NY.
Correspondence to Richard D. Veenstra, Department of Pharmacology, SUNY Upstate Medical University, 750 E Adams St, Syracuse, NY 13210. E-mail veenstrr{at}upstate.edu
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Abstract |
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Transjunctional voltage regulates cardiac gap junctional conductance, but the kinetics of inactivation were considered too slow to affect cardiac action potential propagation. Connexin43 (Cx43) is abundantly expressed in the atrial and ventricular myocardium and the rapid ventricular conduction tissues (ie, His-Purkinje system) of the mammalian heart and is important to conduction through these cardiac tissues. The kinetics of Cx43 voltage gating were examined at peak action potential voltages using simulated ventricular myocardial action potential waveforms or pulse protocols exceeding 100-mV transjunctional potentials. Junctional current responses approximate the action potential morphology but conductance calculations reveal a 50% to 60% decline from peak to near constant plateau values. Junctional conductance recovers during phase 3 repolarization and early diastole to initial values. The bases for these transient changes in junctional conductance are the rapid decay kinetics in tens of milliseconds at peak transjunctional voltages (Vj) of 130 mV and the gradual increase in junctional conductance as Vj returns toward 0 mV. The decay time constants change e-fold per 22.1 mV above the half-inactivation voltage for Cx43 gap junctions of ±58 mV. A realistic dynamic model for changes in junctional resistance between excitable and nonexcitable cells during cardiac action potential propagation was developed based on these findings. This dynamic model of cardiac gap junctions will further our understanding of the role gap junctions play in the genesis and propagation of cardiac arrhythmias. The full text of this article is available online at http://www.circresaha.org.
Key Words: gap junctions • ion channels • connexin43 • action potentials • electrophysiology
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Introduction |
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Myocardial gap junctions transmit electrical impulses via transient intercellular voltage gradients and are essential to action potential propagation. Disruption of the gap junction membrane structure terminates the transfer of cardiac action potentials across an electrically inexcitable gap.1 Targeted gene knockout studies of connexin43 (Cx43), connexin40 (Cx40), and connexin45 (Cx45) in mice produced ventricular outflow tract defects, slowed conduction, spontaneous ventricular tachycardias and sudden cardiac death, prolonged P-R intervals and bundle branch block, and lethal embryonic cardiac cushion developmental defects, respectively.2–8 Adult mammalian ventricular cardiac gap junctions are composed predominantly of Cx43 with secondary contributions from Cx45 whereas atrium and Purkinje fibers contain significant amounts of both Cx40 and Cx43.9–11 Cx43 appears to be absent from central nodal tissues.9–12
Cx40, Cx43, and Cx45 gap junctions also possess time- and Vj-dependent inactivation properties that are dependent on the transjunctional voltage (Vj).13–17 The half-inactivation voltages (V1/2) are 50 mV for Cx40, 60 mV for Cx43, and 39 mV for Cx45. The inactivation time constants of Cx43-containing ventricular myocyte gap junctions decrease from approximately 1 second near the V1/2 to 100 ms at 100 mV Vj.18,19 Conduction delays can achieve a maximum of 24 ms before complete conduction block ensues.20–22 Since the observed gap junction inactivation kinetics are at least 10-fold slower than the maximum cardiac conduction delays near the V1/2 value, Vj-gating is considered to have a negligible role in modulating action potential propagation. However, dynamic model simulations suggest that the resting junctional resistance can increase during action potential propagation.23,24 No one has yet examined the kinetics of Vj gating of Cx43 gap junctions during the cardiac action potential between excitable and nonexcitable cells. It is the purpose of this study to directly determine the effect that Vj gradients equal to the amplitude of the ventricular cardiac action potential have on Cx43 gap junctions and to develop a realistic kinetic model that can be applied to computer simulations of ventricular action potential propagation.
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Materials and Methods |
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Stable clones of rat Cx43-transfected of neuro2A neuroblastoma (N2A) cells were cultured as previously described.25 Double whole-cell patch-clamp recordings were achieved with dual Axopatch 200B (Axon Instruments) or BioLogic RK-400 (Molecular Kinetics/Bio-Logic) patch-clamp amplifiers using the procedures defined for correcting for junctional series resistance errors.26 Electrode resistance values after membrane patch disruption ranged from 5 to 23 M
(10.7±4.6 M) with whole-cell input resistances of 1 to 5 G and cell input capacitances of 1.5 to 3.0 pF. All experimental results included in the final analysis were limited to <5% error in the applied Vj for the entire duration of the protocol and all reported junctional conductance (gj) measurements represent corrected values according to the following expression: equation
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where Rel=the series resistance of each whole-cell patch electrode, V=the command potential for each cell, I=the whole-cell current for each cell, and -
I2 is the change in whole-cell 2 current during a voltage-clamp step applied to cell 1.26 Ij must equal zero and gj is undefined when Vj=0 mV, so gj was assigned a value of zero under these conditions (ie, Figures 2B, 2C, 3B, 4A, 7A, and 8A through 8 
F). All whole-cell current recordings were low-pass-filtered at 500 Hz (LPF-202A 4-pole bessel filter, Warner Instruments Inc) and digitized at 4 kHz using a Digidata 1320 A/D board and pClamp8.2 software (Axon, Instruments, Inc). Data analysis was performed using the Clampfit program, and junctional current and voltage calculations were performed offline. Graphs were constructed using Origin version 6.1 software (OriginLab).
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Cardiac action potential waveforms were generated using the Luo-Rudy model for the guinea pig ventricular myocyte cardiac action potential.27 Computer simulations were integrated with a 125-µsec (t) time step at constant cycle lengths (CLs) of 250, 500, 750, 1000, 1500, and 2000 ms until a steady state was achieved. The simulated action potential waveforms used for voltage clamping were provided by Dr Yoram Rudy’s laboratory at Case Western Reserve University (Cleveland, Ohio). To incorporate these six cardiac action potentials into a digital voltage stimulator (Challenger VM-2B, Kinetic Software), each action potential waveform was reduced to <200 time steps by integrating each simulated action potential with a t of 1 ms. Figure 1 illustrates the output voltage action potential waveforms applied to cell 1 (V1) at the indicated CL. The command voltage for cell 2 (V2) was set equal to the simulated diastolic resting potential that increased slightly from -88.1 to -90.2 mV with increasing CL. All results were obtained by applying a train of 200 action potentials at the appropriate frequency to a pair of Cx43-transfected N2A cells and recording both whole-cell currents following previously described procedures unless otherwise indicated.
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Results |
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Time-Dependent Changes in Ij and gj During an Action Potential
Calculated Ij traces were obtained from six experiments at a constant CL of 1000 ms for 200 seconds shortly after establishing dual whole-cell patch-clamp recording conditions. An example of the initial Ij response to the first action potential after a prolonged (>30 seconds) period of quiescence and the steady-state average of the last 100 action potentials is shown in Figure 2A. There was a 12-ms delay before the action potential voltage clamp commenced. The action potential duration at 95% repolarization (APD95) was 153 ms for CL=1000 ms. This Cx43 cell pair had a peak gj of 4.14 nS, and both Ij traces resemble the shape of the action potential but with a sharp decline from the peak to a slowly changing quasi steady-state value achieved near the midpoint of the action potential plateau. To compare the decline in gj during successive action potentials at a constant frequency, Ij was divided by the corrected Vj value during each action potential and the time-dependent changes in gj plotted during the same train of 200 action potentials (see Materials and Methods). Figure 2B illustrates that gj genuinely declined from the peak of the action potential to a minimum plateau value. The most unexpected result was that gj actually began to recover during the final phase of repolarization as Vj declined toward 0 mV. To average the results from all six experiments at CL=1000 ms, gj was normalized (Gj) to the peak gj of the first action potential in each experiment and the results were pooled (Figure 2C).
The average behavior of the Cx43 gap junction to constant pacing at a frequency of 1 Hz closely resembles the behavior of the single experiment shown in Figures 2A and 2B (Figure 2C). Gj declined by 42% during the first 25 ms of the action potential and remained essentially constant at 0.44 of the maximum (peak) Gj during the plateau phase of the action potential. From its time-dependent minimum, Gj slowly began to increase after Vj had declined below 85 mV, achieving the value of 0.70 at the APD95 for CL=1000 ms. Gj recovered to its full initial value over the next 60 ms, 167 ms after the onset of the action potential. The results from one low gj (
0.8 nS) experiment are illustrated in Figure 3, where 10 of 68 Ij traces along with the ensemble averages of those 10 and all 68 traces are displayed (Figure 3A). The Ij recordings from this low gj experiment illustrate the variability in the responses of the estimated maximum eight 100-pS Cx43 gap junction channels present in this experiment (Figure 3B). The ensemble average of as few as 10 Ij traces recapitulates the behavior of the higher gj recordings where discrete fluctuations are less obvious due to the activity of 
10 gap junction channels. On average in this experiment, there were approximately five 100-pS channels open initially with only two equivalent channels remaining open during the plateau phase of the action potential. It is not possible to resolve whether the channels closed completely or to a subconductance state owing to the multichannel behavior of this recording. The activities of the inactivated channels begin to recover during phase 3 repolarization. These data provide direct evidence for the Vj-dependent gating of individual Cx43 gap junction channels during the action potential and indicate that this is the primary mechanism for the modulation of Gj.
These procedures were followed for the five other CLs examined and the results are summarized in Figure 4A. The steady-state Gj was calculated for the APD95 of each frequency-dependent action potential since the Gj calculations became more variable as limVj
0. Therefore, the last 6 to 7 mV of final repolarization were excluded from the Gj analysis. Gj declined to 0.37 to 0.45 of the maximum except at CL=250 ms, which only achieved a minimum time-dependent Gj of 0.50 owing to the shorter APD. In all cases, Gj increased toward initial peak values as Vj decreased from 85 mV toward 0 mV. Gj returned to the peak value when Vj10 mV during the recovery phase of the CL-dependent Gj curve. The mean gj (±SD) was 4.17±2.99 for all experiments (n=32).
The steady-state Gj-Vj curve for Cx43 was obtained by pooling the ensemble average of five 200-ms/mV Vj ramps from 0 to ±100 mV from four different experiments (Figure 4B). The average Gj-Vj curve was fitted with a Boltzmann function: equation
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where Gssmax=1 (Gj=gj/gj, max)=the resting normalized slope conductance between ±2 and ±25 mV for each experiment, Gssmin=the minimum value of gj/gj, max, A=the slope factor for the Boltzmann curve=zF/RT, and V1/2=the half-inactivation voltage. The slope factor is proportional to the gating charge movement (z) of the state transition.13,14 For the curve shown in Figure 4B that best describes the averaged data, Gssmin=0.18 and 0.18, V1/2=-59 and +57 mV, and z=-3.2 and +2.8 elementary charges for negative and positive Vj values. These results are similar to prior results for Cx43 using Vj pulse protocols.18,19,28 The minimum Gj achieved during the action potential plateau does not achieve the Gssmin of the Cx43 steady-state Gj-Vj curve, yet the recovery phase of the CL-dependent Gj curves is correlated with the sloped portion of the steady-state Gj-Vj curve from Vj<85 mV.
Voltage-Dependent Changes in Ij Decay Constants
To determine the basis for the rapid decline in gj during the early phases of the cardiac action potential until quasi steady-state conditions were achieved, Vj pulses between -40 and -140 mV were applied to Cx43 gap junctions to determine the decay constants at fixed Vj values. A train of five Vj pulses of equal magnitude were applied once every 30 seconds, and the ensemble-averaged current was fitted with an exponential function. The decay time constants of selected Vj pulses from a single experiment are shown in Figure 5A. Only the initial 400 ms of the 2.5-second duration pulses are displayed to better illustrate the rapid decay phase of the Ij signal recorded from cell 2. At some Vj values, there was a second slower decay phase with a time constant ranging from 0.5 to 1.5 seconds that amounted to <20% of the total decay in Ij (data not shown). The decay time constants became progressively faster with increasing Vj and closely match the data in amplitude and time. The results from 3 to 12 experiments at the absolute value of each Vj (|Vj|) were averaged and the reciprocals of the decay time constants (mean±SD) were plotted in Figure 5B. The observed >1000-ms decay constants reported for Vj values near the V1/2 (ie, 40 to 60 mV) of the steady-state Gj-Vj curves of cardiac connexin gap junctions declined to 10 ms at potentials equivalent to the peak of the cardiac action potential. The curved line indicates the best fit of the data by the equation:
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The decay constants decline e-fold per 22.1±0.8 mV (=
) from an initial amplitude (A0) of 0.00046±0.00007 ms-1 (
=2175 ms) at Vj=40 mV. Only examining Vj±100 mV made this newly observed decline in the Ij decay constants possible. The rapid decay kinetics may explain the decline in gj observed during the first 50 ms or more of the action potential leading to the quasi steady-state plateau values. These results suggest that the fast Vj gating properties of Cx43 can play a role in regulating gj during the time course of a cardiac action potential.
Time-Dependent Recovery of Ij and Gj
A second observation of probable importance in the CL-dependent Gj curves is the recovery of Gj during the late phases of the cardiac action potential. The significance of this phenomenon was examined further by applying full amplitude premature action potentials of varying delay to Cx43 gap junctions at a CL of 1000 ms. Figure 6A demonstrates in a single experiment that gj is truly increasing during the repolarization and early diastolic phases of the cardiac action potential. Each Ij trace is the ensemble average of 20 sweeps for each stimulus delay, and the premature stimulus delay was increased from 120 to 190 ms from the onset of the normal CL=1000-ms action potential. The amplitude of Ij increased progressively with incrementally increasing 10-ms delays. The average Gj from six experiments is illustrated in Figure 6B and is indicative of a consistent increase in Gj from the minimum Gj obtained during the action potential to 82% of the initial Gj value during the first 30 ms of the diastolic interval. These observations confirm the observed increase in Gj albeit with a reduced slope relative to the continuous Gj curve (Figure 6B, dashed line) obtained in Figures 2C and 4
A. The discrepancy between the peak Gj of the premature stimuli and the recovery phase of the CL=1000-ms Gj curve may result from the differences in Vj used to calculate Gj.
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80 mV achieved during a CL=1000-ms action potential. Again, each Ij trace is the ensemble average of 20 sweeps. Exponential time constants ranged from 30 to 96 ms (see
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A pulse protocol that stepped to fixed Vj values between +70 and 0 mV from the plateau action potential Vj of near 80 mV revealed that Ij increased in a time-dependent manner with time constants ranging between 30 and 95 ms for Vj70 mV (Figure 6C and Table 1). On average, Gj increased in a Vj-dependent manner from the plateau of the action potential to the start of the Vj pulse (Figure 6D, solid lines) and approximated steady-state values at the end of the 125-ms duration Vj pulse (Figure 6D, dashed arrows). The time constants were weakly correlated with the Vj of the recovery pulse (r=0.80 or 0.91 for linear or exponential fits). There is general agreement that the recovery time constants are on the order of tens of milliseconds in the 10- to 70-mV Vj range, at least 10-fold faster than the decay time constants at these same voltages. These time constant measurements further reinforce the concept that both the inactivation and recovery kinetics of Cx43 gap junctions can achieve values of 10 ms, depending on Vj.
Modeling Time- and Vj-Dependent Changes in Gj
Figure 7A illustrates the concept that the primary phase of Gj inactivation occurs during the peak Vj values after the upstroke and early repolarization phases (0 and 1) of the cardiac action potential. The average Gj curves for all six CLs were best fit by a double-exponential function with major component having a time constant of -25 to -30 ms and a second component with a time constant of -5 to -6 ms. Conversely, the recovery of Gj coincides with the rapid phase 3 repolarization and final slow repolarization that continues during early diastole (phase 4) of the cardiac action potential. The Vj dependence of the inactivation and recovery phases of Gj are better illustrated in Figure 7B where the average CL=1000-ms Gj is plotted relative to Vj. Figure 7B clearly illustrates that the Vj-dependent inactivation of Gj occurs above 90 mV with the majority of the inactivation occurring above 115 mV. The small curl in Gj at peak Vj values results from the time lag between the peak Gj and peak Vj calculations obtained from the whole-cell recordings during the first few milliseconds of the action potential. It was routinely observed that the double-exponential decay of Ij in time was best described by a single Vj-dependent Boltzmann distribution.
In order to relate two time-dependent decay components to a single voltage-dependent Boltzmann distribution, the time-dependent decay of Ij was modeled with the following expressions: equation
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and
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The initial conditions for each inactivation component were defined by
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and
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where
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Each time-dependent inactivation component (G1t and G2t) was assumed to have a Gmin equal to the Gmin of the steady-state Gj Boltzmann curve (Equation 2 and Figure 4B) and the Vj-dependent time constants were computed based on the exponential decay time constants described in Figure 5B. To adequately describe the rapid inactivation of Gj during the action potential, the faster inactivation component, G1t, was assigned a rate five times greater than the slower inactivation component, (G2t), in accordance with the two fitted time components of the CL-dependent Gj curves. G2t was assigned the initial value of A0 (=0.00046) at 40 mV in accordance with Equation 3.
The numerical solution to Equations 4 and 5 is illustrated in Figure 8 for each CL. The exact values of the parameters used to generate the inactivation graphs for each component are listed in Table 2. In all cases, the A0 and Gmin values were kept constant except as indicated for CL=250 and 2000 ms, respectively. The Gmax1 and Gmax2 values were modified for each CL to produce a more precise fit of the data. However, Gmax1 was relatively constant and averaged 0.49±0.04 across all CLs. Gmax2 was observed to increase slightly from 0.10 at CL500 ms to an average of 0.18±0.02 for CL750 ms.
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The recovery phase of the Gj curve always coincided with the two rates of repolarization of approximately 2.6 mV/ms during phase 3 and approximately one-tenth that amount during the final tail of repolarization below 10-mV Vj that terminated during diastole. As Figure 6 and Table 1 indicate, there is a time dependence to the Vj-dependent recovery in Ij and Gj. However, the time constants varied only slightly with Vj, so it was not possible to obtain reliable Vj-dependent time constants for the recovery phase of Gj. To define the Gj recovery phase as a function of Vj, it was observed that a double-exponential function of voltage adequately described the change in Gj relative to Vj (Figure 7B). These two components coincided with the two phases of repolarization as observed in Figure 7A. The two components to the recovery phase of Gj were defined by the expressions: equation
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and
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where
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and
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are the final values of R1t and R2t. The values for Gmax1 and Gmax2 are listed in Table 2, the amplitudes for Rmax1, Rmax2, AR1, and AR2 are given in Table 3, and the numerical solutions to Equations 9 and 10 are illustrated in Figure 8. At CL=250 ms, there was only one component (R1t) to the recovery phase whereas the contribution of R2t steadily increased with increasing CL.
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Equations 9 and 10 are time-independent, whereas the increase in Gj likely depends on the rate of repolarization of the action potential. Given that the dt for the data is 0.25 ms, and the observed time constants range from 30 to 50 ms, the solution to (dt/Vj)=would range from 0.0083 to 0.0050, meaning that any time dependence would increase Gj by less than 1% per dt. The primary observations are that the Gj recovery is dependent on the two rates of repolarization evident in the action potential and that final repolarization is more significant at longer CLs than phase 3 repolarization. All of the Gj recovery at the highest frequency examined (240 bpm) occurs during phase 3 repolarization. Since the two rates of repolarization were nearly the same for all six CLs examined, how the rates of Gj recovery vary with the phase 3 and final repolarization rates remains to be determined.
The Vj-dependent solutions to Equations 4, 5, 9, and 10 provide an accurate description of the phasic changes in Cx43 Gj observed during the ventricular cardiac action potential over frequencies ranging from 30 to 240 bpm (Figure 8). The final expression for Gj is as follows: equation
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This equation can be solved for continuously in time and lends itself to incorporation into existing models of cardiac action potential propagation where each intercellular gap junction is presently assigned a static Rj value. It should be noted that Gjt stabilizes to a value of one during diastole since gap junctions are normally considered to be open at rest.
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Discussion |
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According to the Luo-Rudy model, the average ventricular myocyte is approximately 11 µm in diameter, 100 µm long, and has a capacitive membrane surface area of 1.5x10-4 cm2.27 This calculates to an input capacitance of 150 pF assuming a specific capacitance of 1 µF/cm2. Isolated ventricular myocytes have an input resistance of 40 M
, which yields a specific membrane resistivity of 6.0, k-cm2, within the experimental range of 2.4 to 7.3 k-cm2.29,30 To depolarize an isolated myocyte from -90 mV to the threshold for the sodium current of -60 mV requires approximately 4.5 pC of charge. To activate the cell in 100 µs will require 45 nA of current, or approximately 80% of the 57 nA of peak fast sodium current (INa) produced by the average ventricular myocyte (380 µA/µF).27 Given a peak Vj of 130 mV, a gj of 346 nS (Rj of less than 29 M) is required for this to occur. Rj measurements between isolated pairs of adult ventricular myocytes estimate an Rj of 1.7 M (gj=590 nS), nearly a 20-fold excess of gap junction channels.20,31 A conduction velocity of 0.5 m/s in the ventricular myocardium translates into a conduction time of approximately 200 µs/cell. Given that the peak sodium current can deliver enough charge to activate a ventricular myocyte in a minimum of 80 µsec, the rest of the delay must reflect cellular activation times, junctional delay, and the two-dimensional (transverse [radial] and longitudinal) pattern of intercellular current flow. Thus, in well-coupled tissues, Rj and other factors account for 50% of the intercellular conduction time. This is in close agreement with the results obtained from one- and two-dimensional cables of cultured neonatal rat ventricular myocytes where junctional conduction times of 89 to 118 ms accounted for 22% to 51% of the total intercellular conduction time.32 In cardiac tissues, cell cultures, and in ventricular myocyte cell pairs, these 100-µs conduction times have been observed to increase to several milliseconds under conditions of partial uncoupling.20–22,33–36 Activation times in excess of 20 ms are required for complete conduction block to develop. It is consistently observed that increasing junctional resistance can produce slower conduction velocities than reductions in excitability prior to the development of conduction failure.35,37 Most recently, it was demonstrated that heterogeneous Cx43 coupling in the ventricle produces decreased cardiac contractility in addition to the conduction disturbances.38 During these delayed activation times, the L-type calcium current (ICa,L) plays an increasingly important role in sustaining the propagation of the cardiac action potential since it is the major excitatory ionic current during this conduction delay.37,39,40
Our results demonstrate that Cx43 gj can inactivate by as much as 40% within this 25-ms time period required for action potential transfer. Simulations and membrane potential (Vm) recordings indicate that nearly the entire action potential amplitude exists as a Vj gradient between the activated and nonactivated regions during this time period, certainly in excess of 100 mV where the inactivation time constants become less than 100 ms. If electrotonic interactions are large enough to approach the action potential peak or plateau voltages, Vj will become negligible, causing the amount of inactivation to become abbreviated and gj to recover sooner. Previous investigations similarly reported that the fast decay time constants (f) decrease from approximately 500 to 100 ms with increasing Vj from ±70 to ±100 mV in cardiac ventricular gap junctions.18,19 Our results in N2A cells extend these observations to Vj values equal to the action potential amplitude and demonstrate that f decreases exponentially with Vj to a minimum value of 20 ms at 140 mV. It is possible that changes in cellular conditions can affect the gj kinetics and that the rates of inactivation may be different between N2A cells expressing Cx43 and native ventricular cardiomyocytes despite similar f values.18,19 The voltage constant () for these changing kinetics is 22.1±0.8 mV and the calculated (f) values are in close agreement with experimental observations (Figure 5). However, we observed that a second time constant was required to fit the time-dependent gj curves (Figure 8). This second exponential component, which we will call the ultrafast time constant (uf), was five times faster than f but had the same Vj dependency (Table 2). The contributions of (f) and (uf), to the inactivation of Cx43 gj, were modeled using Equations 4 and 5 , (G1t+1 and G2t+1).
These equations accurately describe the time and Vj dependence of Cx43 gj based on the first-order decay kinetics and steady-state Gj-Vj curve for Cx43. A previous attempt to develop a dynamic gap junction model qualitatively demonstrated that transient reductions in gj can alter conduction times and produce conduction block at higher resting gj values than previously simulated estimates.21–24 This model assumed four different conductance states (two would be identical for a homotypic gap junction channel) based essentially on the steady-state Gj-Vj curve for Cx43 but assuming distinct Boltzmann distributions for the open probabilities of the fully open (high, H) and residual subconductance (low, L) states for each hemichannel of the gap junction.23,24 According to this formulation, Gmin is predicted by the number of gap junction channels in the LL state at either extreme of Vj and Gmax by the number of gap junction channels in the HH state at very low Vj values. The ensemble average of fewer than 10 Cx43 gap junction channels reveals that the sum of all channel states present in this homotypic gap junction recapitulates the behavior of the macroscopic gj curves (Figure 3). Thus, the present model accounts for the behavior of all channel conductance states regardless of the relative proportions of fully open, subconductance, or even the previously assumed nonexistent closed state. Furthermore, the present model was derived from experimental data on Cx43 gap junctions and provides the first description of actual time-dependent changes in Cx43 gj during a ventricular action potential, including different frequencies of stimulation. The equations describing the inactivation process are also readily solved using numerical integration methods. Therefore, this model should be more readily incorporated into existing models of ventricular action potential propagation and provide a more accurate account of the transient changes in gj experienced in this tissue. Electrotonic interactions will also be accounted for in this model since the gj calculations are determined by Vj. These transient reductions in gj associated with the leading edge of excitation would be expected to favor antegrade and inhibit retrograde conduction during normal patterns of excitation.
It has long been known that cardiac excitability exhibits "refractoriness" to additional excitatory stimulation. The "effective refractory period" refers to the time period when a second excitatory stimulus cannot elicit another action potential.41 This is followed by the "relative refractory period" when a suprathreshold stimulus can elicit a less than full amplitude action potential response. These phases of non- or reduced excitability are temporally correlated with phase 1 to mid phase 3 and the latter half of phase 3 repolarization, respectively. Numerical simulations have also described a "vulnerable window" in time and voltage when extrasystoles are most effective in inducing unidirectional conduction block and reentrant excitation, a major source of cardiac arrhythmias.42,43 Decreasing gj widens this vulnerable window during phase 3 repolarization, just as it slows conduction velocity and increases electrical dispersion. The early phase of Gj recovery (R1t) (Equation 9) occurs during phase 3 repolarization and is most closely correlated with the relative refractory period of the cardiac action potential (Figure 7). The late phase of Gj recovery (R2t) (Equation 10) is most closely correlated with the "supernormal period" of cardiac excitability when a subthreshold stimulus can elicit a premature action potential.
The amplitudes of the Ij responses to premature (albeit full response) action potential stimuli with increasing delay bears a striking resemblance to the recovery of maximum upstroke velocity (d
/dt) of the premature action potential with increasing stimulus delay (Figures 6A and 6B).44 These data strongly suggest a correlation between cardiac excitability and intercellular coupling with important implications regarding electrical inhomogeneity and arrhythmogenesis. The increased cellular uncoupling that occurs during the action potential will further promote electrical heterogeneity. Following an action potential, the d/dt normally does not begin to recover until Vm has repolarized to at least -70 mV.44 This is due to the slow recovery from inactivation of INa.45 By contrast, Gj begins to recover when Vj decreases below 90 mV, or near a Vm of 0 mV. However, Gj does not recover to its full resting value until Vj declines to <10 mV, ie, when Vm remains slightly depolarized after an action potential.
Two forms of triggered activity, early afterdepolarizations (EADs) and delayed afterdepolarizations (DADs) occur during the relative refractory and supernormal periods, respectively.46 EADs primarily occur at longer cycle lengths and depend on ICa,L as the excitatory current.47 A simulation study demonstrated that EADs can be suppressed by high gj or their propagation facilitated by intermediate amounts of electrical coupling.48 EADs are thought to be the primary mechanism for the torsades de pointes arrhythmia characteristically associated with long-QT (LQT) syndromes. There are five genetically linked LQT syndromes identified to date, and they are associated with loss-of-function mutations in the rapid and slow delayed rectifier potassium channels (IKr and IKs) or the gain of function in INa.49 Conversely, DADs are potentiated by increasingly rapid rates of stimulation and interventions that result in rises in intracellular calcium ion concentrations ([Ca]i) and occur when Vm is almost fully repolarized. Elevated [Ca]i levels increase net Ca2+ influx across the sarcolemma by decreasing Ca2+ efflux via the Na+-Ca2+ exchanger and by activating a nonspecific inward cation current (Ins(Ca)), resulting in a transient inward current (Iti).50 However, at the most rapid rates of stimulation, the late phase of Gj recovery is absent, presumably due to the reduced amount and duration of inactivation present at the shorter cycle lengths (Figure 8). It is quite apparent that Gj recovery is temporally correlated with key phases of cardiac excitability often associated with the genesis of arrhythmias.
The numerical model for the modulation of Cx43 gj by action potential generated Vj gradients was developed from constant pacing at a single CL using a steady-state action potential waveform (Figure 1). Hence, frequency transitions may present additional factors not modeled in the present investigation. However, since the model is Vj-driven, the gradual changes in APD associated with frequency transitions may not produce any new phenomena. Alterations in the rates of inactivation are readily accounted for by increasing the value of A0, A1, and A2 in Equations 3 through 5 (Table 2, Figure 8). Lower Gmin values can also account for the minimum Gj attained at prolonged APDs associated with longer cycle lengths for stimulation. What we anticipate being the most likely limitation of the present model is the recovery of gj during action potential repolarization. Provided that the Vj dependence of Gj (Figures 4B and 6D) is the underlying basis for inactivation and recovery, then slower rates of repolarization could allow for more gj recovery during phase 3 repolarization (Figures 7A and 7B). This mechanistic hypothesis for the recovery of Gj merits consideration because slower rates of repolarization would increase the vulnerable window and enhance the probability of early afterdepolarizations. The initial Gj recovery component is, therefore, potentially arrhythmogenic and should be further investigated.
We do not claim to know what the structural bases of Cx43 are for these dual inactivation and recovery components of Gj. It has been hypothesized that charged amino acid residues on the cytoplasmic amino terminal domain of the connexins act as the "voltage sensor" for gating, but the precise mechanism of channel closure is still undetermined.51,52 The recovery from this Vj-dependent closure is even less well studied. The new observations about Vj gating that are advanced by this investigation suggest that "fast Vj gating" may play a more important role in cardiac electrophysiology than previously considered. The longer-term changes in Rj associated with hypoxia and acidosis may involve the "slow chemical gating" of gap junction channels modulated by intracellular pH, calcium, and posttranslational modification (eg, protein kinase–dependent phosphorylation).53
In conclusion, this dynamic model for the physiological modulation of Cx43 gj by action potential–generated Vj gradients will permit the development of more realistic models of ventricular conduction, delay, and block and provide new insights into the role that gap junctions play in the genesis of arrhythmias.
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Acknowledgments |
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This study was supported by NIH grants HL-42220 and HL-45466 to R.D.V. The simulated action potential waveforms used for voltage clamping were provided by Dr Yoram Rudy’s laboratory at Case Western Reserve University.
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Footnotes |
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Original received June 10, 2003; resubmission received July 23, 2003; revised resubmission received August 20, 2003; accepted August 20, 2003.
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