Insights into the molecular mechanisms of bradycardia-triggered arrhythmias in long QT-3 syndrome

Congenital long QT syndrome is a rare disease in which the electrocardiogram QT interval is prolonged due to dysfunctional ventricular repolarization. Variant 3 (LQT-3) is associated with mutations in SCN5A, the gene coding for the heart Na⁺ channel α subunit. Arrhythmias in LQT-3 mutation carriers are more likely to occur at rest, when heart rate is slow. Several LQT-3 Na⁺ channel mutations exert their deleterious effects by promoting a mode of Na⁺ channel gating wherein a fraction of channels fails to inactivate. This gating mode, termed “bursting, ” results in sustained macroscopic inward Na⁺ channel current (I_sus), which can delay repolarization and prolong the QT interval. However, the mechanism of heart-rate dependence of I_sus has been unresolved at the single-channel level. We investigate an LQT-3 mutant (Y1795C) using experimental and theoretical frameworks to elucidate the molecular mechanism of I_sus rate dependence. Our results indicate that mutation-induced changes in the length of time mutant channels spend bursting, rather than how readily they burst, determines I_sus inverse heart-rate dependence.

Patient genotyping is becoming increasingly common as a method to search for molecular explanations of seemingly idiopathic syndromes (1, 2). However, it is difficult to make the connection between gene defects and abnormal function at the cellular level that underlies distinct syndromes. Cystic fibrosis, idiopathic ventricular fibrillation, and long QT syndrome are examples of clinical syndromes that arise from defects in ion channels (3–7). Ion channel mutations may exert their deleterious effects through alterations in gating kinetics, loss of ion selectivity, or dominant negative current suppression (2, 8, 9). Investigation of inherited defects in ion channels may lead to improved understanding of the mechanistic basis of disease.

Congenital long QT syndrome, a rare disease in which the QT interval of the electrocardiogram is prolonged due to dysfunctional ventricular repolarization, is associated with syncope and sudden death (10, 11). Congenital long QT syndrome is associated with mutations in genes coding for at least six ion channel subunits (11). These mutations result in cardiac events with various triggers (10). Long QT syndrome variant 3 (LQT-3) is associated with mutations in SCN5A, the gene coding for the α subunit of the voltage-gated Na⁺ channel (7), and LQT-3 mutation carriers are at greater risk of cardiac events during rest or bradycardia than during exercise when heart rate is elevated (10). Rhythm disturbances arising from some LQT-3–linked SCN5A defects stem from a gain of Na⁺ channel function that promotes the conduction of Na⁺ ions for prolonged periods at depolarized membrane potentials (7, 12, 13). Most defects have been shown to reduce the stability of inactivation of the cardiac Na⁺current (I_Na) during prolonged depolarization, when wild-type (WT) channels typically enter an absorbing inactivation state (7, 12, 13). This mutation-induced destabilization of inactivation increases sustained Na⁺ channel inward current (I_sus) during the action potential (AP) plateau, which disrupts the delicate balance of membrane currents required for regulation of AP duration (APD). Excess inward current via inactivation-deficient Na⁺ channels can thus prolong APD and facilitate the development of arrhythmogenic early afterdepolarizations (14, 15) at the cellular level. These cellular effects are consistent with mutation-induced QT prolongation and arrhythmia risk at the systems level.

Patients afflicted with SCN5A-linked LQT-3 have been observed to experience cardiac events that are strongly dependent on heart rate (1, 16). At slow heart rates during rest or relaxation, patient phenotypes are marked by prolonged QT intervals and susceptibility to polymorphic tachyarrhythmias (16). To date, the molecular mechanism by which the severity of LQT-3 phenotype worsens at slow heart rates is not known at the level of mutation-induced changes in single ion channel kinetic properties. Previous work (14, 15) has demonstrated mutation-induced rate dependence of APD using a theoretical modeling approach, but has lacked the required precision for detailed analyses of the molecular mechanism of I_sus stimulation-rate dependence. Previously, the paucity of single-channel records precluded extraction of actual time constants of entry into and exit from the burst mode. As a result, a thorough understanding of the rate dependence of channel bursting has been elusive.

Here we combine theoretical and experimental approaches to illuminate the mechanism of the rate dependence of I_sus at the cellular level through analyses of experimentally measured mutation-altered single-channel gating. We first focused on an LQT-3 mutation (Y1795C) that had been previously described at the whole-cell level (17). We selected the Y1795C mutation because QT prolongation is pronounced at slow heart rates in mutation carriers, and previous analysis revealed a strong inverse pulse-rate dependence of Y1795C channel I_sus amplitude (17). We performed detailed kinetic analyses of single Y1795C channels and used these data to extract transition rate constants of bursting of single Na⁺ channels. These rate constants were then incorporated into a Markov model of I_Na (15) that recapitulates the features of experimentally measured current amplitude and rate dependence.

Our computational analysis suggests that the amount of time mutant channels spend bursting (burst mode dwell time), rather than how readily they burst (latency to burst), is primarily responsible for rate-dependent changes in single-channel bursting and macroscopic I_sus. This prediction was tested and validated by the analysis of another LQT-3 mutation, ΔKPQ. These results provide an explanation of the molecular mechanism for bradycardia-induced QT prolongation in patients carrying LQT-3 mutations.

The amplitude of Y1795C mutant channel I_sus depends on stimulation rate. Figure 3 illustrates sustained macroscopic Na⁺ inward current (I_sus) recorded in cells expressing Y1795C mutant Na⁺ channels. The upper panel of the figure shows currents measured at high gain in response to the voltage protocol shown schematically in the figure. Currents recorded in response to trains of voltage pulses applied at different interpulse intervals are illustrated under steady-state conditions. The lower panel shows currents measured in this manner at two experimental interpulse intervals to mimic bradycardia (1-second interpulse interval) and tachycardia (20-millisecond interpulse interval). In all examples, a dotted line is included to indicate the zero current baseline. There is an eightfold increase in magnitude of I_sus, current that would contribute to a delay in ventricular repolarization, that occurs simply by increasing the interpulse interval. Consequently, mutation carriers would be expected to experience more severe QT prolongation at slower heart rates, consistent with clinical observations. What is the basis of this heart rate–dependent change in I_sus at the level of single-mutant Na⁺ channels?

Figure 3

Influence of stimulation rate on Y1795C I_sus. Experimental recordings of TTX-sensitive current (see Methods) are shown at high gain in cells expressing Y1795C mutant channels. Currents shown are in response to voltage pulses (500 milliseconds, –10 mV) applied from a holding potential of –100 mV. Y1795C I_sus during the initial depolarizing pulse is shown in the top panel. Below are steady-state traces recorded after a train of depolarizing pulses with different interpulse intervals (t) to mimic bradycardia (left, t = 1 second) and tachycardia (right, t = 20 milliseconds).

The LQT-3 Y1795C mutation affects background and bursting gating modes. Figure 4 illustrates unitary current recordings from WT and Y1795C (17) mutant channels in the background gating mode during brief depolarization. Both WT and Y1795C channels open and then enter an absorbing inactivated state, as evidenced by the failure of channels to reopen. However, prolonged channel openings are apparent for Y1795C (Figure 4a, sweeps four and seven, right) compared with WT channels in the illustrated sweeps. The experimental open-time histograms (Figure 4b, top row) confirm that this is a significant effect, revealing a mutation-induced near-doubling of channel MOT (Y1795C, 0.97 ± 0.05 milliseconds, n = 6; WT, 0.50 ± 0.05 milliseconds, n = 7; P < 0.01). This time constant was extracted by fits to the experimentally determined histograms (Figure 4b, top row, dashed curves). Because transitions from open state to inactivated state (UO → UIF) dominate at this voltage (–30 mV), the mutation-induced doubling of MOT is likely due to a reduction in the transition rate of open-state inactivation. Thus, this experimentally derived time constant was used to estimate the transition rate of open-state inactivation for mutant and WT channels in the background gating mode (Figure 4b, bottom row). The MOT is determined theoretically by the single exponential function e^–t/τ (see Methods) where τ = 1/sum of transition rates out of the open state. These changes in open-state inactivation account for the previously reported slowing of the onset of inactivation of macroscopic Y1795C currents, but not the mutation-induced increase in I_sus (17), since the MOT histogram indicates that all Y1795C channels inactivate within 6 milliseconds.

Figure 4

Background gating properties of WT and Y1795C mutant channels. (a) Experimentally observed WT (left) and Y1795C (right) single channels in the background mode. (b) MOTs of experimentally measured (top) and simulated (bottom) channels in the background mode (i.e., non-burst mode) at –30 mV. Histograms (bin size = 200 microseconds) were generated from all events (500–1,000 sweeps) for each construct. Only patches containing fewer than three channels were used to generate histograms. MOT was determined by single exponential fits to the experimental data. The time constants extracted from the fits were: Y1795C, 0.97 ± 0.05 milliseconds, n = 6; WT, 0.50 ± 0.05 milliseconds, n = 7. The computation (lower panel) accurately simulates mutation-induced prolongation of MOT (Y1795C, 1.01 milliseconds; WT, 0.50 milliseconds). The MOT is determined theoretically by the single exponential function e^–t/τ where τ = 1/sum of transition rates out of the open state. τ, time constant.

Figure 5 summarizes experiments in which we investigated the effects of the Y1795C mutation on single-channel activity during prolonged depolarization to determine effects of the mutation on modal gating and to derive theoretical transition rate constants (probabilities) of entry into and exit from the burst mode. In each panel of Figure 5a, arrows are shown to indicate entry into (left arrow) and exit from (right arrow) the bursting mode during repetitively applied pulses (–30 mV, 100 milliseconds, 2.0 Hz). As seen in the illustrated traces in Figure 5a, bursting can be detected for WT channels, albeit infrequently (left column), but in Y1795C channels, bursting occurs more often and appears to last longer (right column). Importantly, it is apparent that once initiated, bursting can persist from pulse to pulse despite an interpulse interval (of 400 milliseconds) at –120 mV. This finding suggests that bursting is not voltage dependent, an observation incorporated into the model.

A histogram of the latency to burst of WT and Y1795C mutant channels (Figure 5b) reflects the likelihood of entry into the burst mode. This was used to compute the burst mode entry rate (≈10^–6 ms^–1). Figure 5c shows histograms of burst mode dwell times measured for WT (left) and Y1795C channels (right). Two components are apparent in both histograms. A fast component most likely reflects background reopenings, which occur infrequently for both WT and mutant channels. We estimated the dwell time in the burst mode affected by the mutation by extracting exponential fits to the slow component of the Y1795C histogram (Figure 5c). Clearly the Y1795C mutation has two effects on bursting: it increases the propensity to burst (reduced latency to burst) and the dwell time of bursting channels (increased dwell time). While both of these mutation-altered gating properties are clearly important in determining the amplitude of I_sus, are these effects at the single-channel level sufficient to account for Y1795C macroscopic channel activity? Can we determine whether one or both of these properties underlies the observed reverse rate dependence of I_sus?

Single-channel properties predict equilibrium macroscopic gating. Figure 6 compares experimental and simulated records at high gain to emphasize the combined effect of the increase in channel bursting and the reduction in the transition rate of open-state inactivation (UO → UIF) on macroscopic current under steady-state conditions (100 milliseconds pulses to –10 mV, 0.5 Hz). The reduced transition rate of open-state inactivation decreases the speed of decay in the simulated macroscopic Y1795C current (arrow) compared with WT currents. Notably, the decay speed in the simulation, determined from the experimental single-channel MOT, can account for the macroscopic decay observed experimentally (Figure 6, a and b, arrows, right panels). Moreover, the burst mode entry rate and burst mode exit rate derived from the single-channel records resulted in simulated sustained current amplitude very similar to that observed in the macroscopic recordings. Slight adjustments on the order of less than 10^–7 for burst mode entry rate and less than 10^–5 for burst mode exit rate were implemented to exactly match the experimentally observed macroscopic amplitudes (I_sus/I_peak) at the end of 100 milliseconds of depolarization (see Table 1, model parameters). The Y1795C mutation results in a simulated increase of approximately fivefold in sustained current compared with WT (0.5% vs. 0.1%, respectively), in agreement with experimentally determined currents (shown in Figure 6c).

Figure 6

Experimental and simulated macroscopic sustained current. (a) Shown are experimental recordings of TTX-sensitive currents in response to depolarization (–10 mV, 100 milliseconds) from a –100 mV holding potential recorded in cells expressing WT (left) and Y1795C (right) channels. (b) Simulated WT (left) and Y1795C (right) currents generated using the Na⁺ channel Markov model shown in Figure 1. The reduced rate of open channel inactivation (UO → UIF) due to Y1795C is reflected in the longer time course of the macroscopic current decay (a and b, arrows). (c) Sustained current, normalized to peak current, is plotted as percent peak current for WT and Y1795C channels. The left panel is a summary of experimentally recorded I_sus (–10 mV, 100 milliseconds). The values are: WT, 0.07% ± 0.01 %, n = 7; Y1795C, 0.40% ± 0.04%, n = 10. The right panel shows the values simulated by the model using the gating parameters described in the text. In both the experimentally recorded and simulated currents, the sustained current (I_sus) relative to peak current (I_peak) is increased in Y1795C (I_sus/peak = 0.5%) compared with WT (I_sus/I_peak ≤ 0.1%).

These changes in MOT and burst mode gating do not affect computed voltage dependence of activation or inactivation (Figure 7, a and b, right panels), consistent with experimental measurements for Y1795C channels (Figure 7, a and b, left panels). However, the increase in experimentally determined single-channel MOT, which is due to reduced transition rates of open-state inactivation, is simulated by the model to result in an increase in macroscopic current density at membrane potentials above the inactivation threshold (above –40mV) (Figure 7c, right). The longer MOTs of the mutant channels afford greater opportunity for the passage of Na⁺, thereby resulting in larger current density. The 15% increase simulated by the model fits the experimentally observed trend (a 20% increase) shown in Figure 7c, left. Thus the model, with critical parameters determined solely from MOT and burst mode gating experiments, accurately simulates steady-state macroscopic current properties. We next tested model predictions of channel activity under nonequilibrium conditions.

Figure 7

Macroscopic current properties of experimental and simulated WT and Y1795C channels. Shown in each panel is a summary of experimentally determined records (left) and simulated current (right). In the experimental records, open circles are WT (n = 8) and filled circles are Y1795C (n = 9) channels. Theoretical symbols overlap except in c (where the thick line represents Y1795C channels in the right panel). (a) Shown is the voltage dependence of inactivation following 500-millisecond conditioning pulses. Normalized current is plotted versus conditioning pulse voltage. (b) The Y1795C mutation does not affect the voltage dependence of activation (see Methods). (c) The Y1795C mutation increases peak experimentally determined (left) and computed current (right). Experimental currents were measured in lowered extracellular Na⁺ to ensure voltage control. In the simulation, the slowing of the transition rate from open to inactivation states acts to increase open-state probability in the Y1795C mutant compared with WT, resulting in an increase in macroscopic I_Na. WT macroscopic I_Na is about 20% and 15% less than Y1795C I_Na in the experiment and the simulation, respectively. Note that simulated density is larger because it is computed in a simulated cardiac myocyte in full Na⁺ solutions. μA, microAmps; μF, microfarad.

Single-channel gating mode kinetics account for stimulation rate–dependent changes in I_sus. We tested the predictions of our model based on experimentally obtained kinetic parameters under pacing conditions (i.e., nonequilibrium gating). Figure 8 compares experimental (left panels) and simulated (right panels) macroscopic Y1795C mutant current shown during trains of 20 pulses (–10 mV for 500 milliseconds with interpulse voltage of –100 mV). Currents measured in response to pulses applied at an interpulse interval of 20 milliseconds are shown in Figure 8, a and b. Each graph shows the superposition of current in response to the first and 20th pulses in the train. After 20 pulses (Figure 8a), I_sus is markedly reduced in both the experimental (left) and theoretical (right) records. The experimentally measured percentage of I_sus at the end of each 500-millisecond depolarization (I_susn) relative to the I_sus amplitude of the first pulse (I_sus1) is summarized in Figure 8b, left, as (I_susn/I_sus1) × 100. The corresponding simulation is shown in Figure 8b, right, indicating good agreement between theory and experiment. This pulse-dependent reduction in I_sus is less in both experimental and simulated records when the interpulse interval is increased to 1 second. These results confirm that I_sus carried by Y1795C channels is augmented at slow heart rates, and furthermore, that the single-channel data incorporated into the model are sufficient to account for the stimulation-rate dependence of I_sus.

Figure 8

Stimulation-rate dependence of Y1795C channel sustained current (I_sus): agreement between simulated and experimental data. (a) The panels compare experimental (left) and simulated (right) records of Y1795C channel sustained current (I_sus) during trains (20 pulses) of repetitive voltage pulses applied after a pulse-free period. Shown is the superposition of current in response to the first and 20th pulses (–10 mV, 500 milliseconds). The experimental records are TTX-sensitive currents (see Methods). The interpulse interval was 20 milliseconds. (b) Pulse-dependent changes in I_sus during rapid stimulation. I_sus during successive pulses (I_susn) was normalized to I_sus recorded (left) or computed (right) during the first pulse (I_sus1) of the pulse train and plotted versus pulse number. The interpulse interval was 20 milliseconds. (c) Pulse-dependent changes in I_sus in response to slow stimulation rate. I_sus was measured, computed, and plotted as in b, but in this case the interpulse interval was 1 second. CL, cycle length.

Are the burst mode entry rate and the burst mode exit rate equally important in determining the stimulation-rate dependence of I_sus? In order to determine whether the burst mode entry rate (latency to burst) or the burst mode exit rate (burst mode dwell time) determines rate-dependent changes in I_sus, we simulated a range of possible burst mode entry and exit rates. If one transition rate is exclusively responsible for the stimulation rate–dependent changes in I_sus, then variation in the other transition rate should not affect stimulation-rate dependence of I_sus.

Using the model, we tested this idea (Figure 9) at two stimulation rates with the fast (20-millisecond interpulse interval, left) and slow (1-second interpulse interval, right) protocols described for Figure 8. The burst mode entry rate was fixed at 10^–4, 10^–5, or 10^–6 ms^–1 (10), while each graph shows three burst mode exit rates (10^–6 ms^–1 to 10^–4 ms^–1). At the fast stimulation rate (left), I_sus does not decrease in a pulse-dependent manner when the burst mode exit rate is 10^–6 ms^–1, regardless of the burst mode entry rate (Figure 9, a–c, open circles). In contrast, increasing the burst mode exit rate (10^–5 ms^–1 and 10^–4 ms^–1) results in pulse-dependent reduction of I_sus at each of the three entry rates (Figure 9, a–c, left panels). These simulations suggest that the burst mode exit rate primarily determines the rate dependence of I_sus.

Figure 9

Simulations predict that the burst mode dwell time, rather than latency to burst, determines the stimulation-rate dependence of I_sus. The figure illustrates the effect on I_sus of changing the burst mode exit rates (open circles, 10^–6 ms^–1; dashes, 10^–5 ms^–1; filled diamonds, 10^–4 ms^–1) with fixed entry rates. In each panel, computations are shown for fast (interpulse interval, 20 milliseconds, left) and slow (interpulse interval, 1 second, right) stimulation rates (protocol described in Figure 8 legend). I_sus at the end of each depolarization pulse (I_susn) is plotted as a percentage of I_sus at the end of the first pulse (I_sus1). The pulse-dependent reduction of I_sus for each burst mode exit rate is unchanged regardless of the fixed entry rate (10^–4 ms^–1 in a, 10^–5 ms^–1 in b, and 10^-6 ms^–1 in c).

In Figure 9, a–c, right panels, the simulations were repeated at the slow stimulation rate as described above. While the stimulation rate–dependent reduction in I_sus is much weaker than at the fast rate, it is again primarily determined by the burst mode exit rate. The simulations strongly suggest that it is the burst mode exit rate calculated from the burst mode dwell time, rather than burst mode entry rate determined by the latency to burst, that mainly governs the rate dependence of I_sus.

To validate this prediction, we investigated the stimulation-rate dependence of I_sus and single-channel bursting in another LQT-3 mutation, ΔKPQ, the first LQT-3 mutation reported to promote channel bursting (5, 7). Figure 10 illustrates experimental data for the ΔKPQ channels, and Table 2 summarizes key findings for both constructs studied. The records for the ΔKPQ channels shown in Figure 10 strongly resemble those for the Y1795C channel: channel bursting is apparent (Figure 10a) and the mutation increases the dwell time in the burst mode (Figure 10b). ΔKPQ channels burst more readily than do Y1795C channels, as indicated by the reduced latency to burst for ΔKPQ channels (Table 2). Macroscopic ΔKPQ currents measured in response to repetitive pulsing decrease in a pulse-by-pulse manner remarkably similar to Y1795C channels (Figure 10, c and d). Like the Y1795C mutation, the ΔKPQ mutation reduces the burst mode exit rate (increases the burst mode dwell time, Table 2), and consistent with predictions of the model, exhibits a very similar rate-dependent reduction in I_sus (Figure 10d). Thus, these results support the theoretical analysis and indicate that mutation-induced change in the burst mode exit rate is the primary determinant of stimulation-rate dependence of I_sus.

Figure 10

Experimental investigation of the reversed stimulation dependence of ΔKPQ I_sus. (a) Cell-attached single-channel activity in a cell expressing ΔKPQ channels. Shown are consecutive sweeps. (b) The dwell time of bursting activity was measured as in Figure 5 and was used to generate the histogram shown (bin size = 500 milliseconds). The smooth curve is the best fit double exponential function best fit to the histogram (see Table 2 for values). (c) TTX-sensitive macroscopic current is shown at high gain in response to the first and 20th pulses (–10 mV, 500 milliseconds, holding potential –100 mV) of a pulse train (20-millisecond interpulse interval). (d) Mean ± SEM ΔKPQ I_sus (open circles, n = 6) normalized to I_sus1 and plotted as a function of pulse number during the pulse train (interpulse interval, 20 milliseconds). The dotted line replots the experimental data for Y1795C channels shown in Figure 8b for comparison.

Mutation-induced changes in single-channel kinetics account for inverse rate-dependent prolongation of APD. Finally, we investigated the effect of the Y1795C mutation on the rate dependence of APD using a theoretical model of the cardiac ventricular AP during pacing (15). Figure 11 illustrates the 19th and 20th APs (upper rows) and corresponding I_Na high gain (lower rows) from virtual cells containing WT (left) and Y1795C (right) channels. Figure 11a compares APs and currents after pacing at a cycle length of 300 milliseconds from resting steady state (see Methods). The Y1795C mutation clearly results in larger I_sus (arrow) compared with WT that becomes progressively larger as the pacing rate is slowed (Figure 11b, cycle length of 1,200 milliseconds). This stimulation rate–dependent increase of I_sus in the mutant channel underlies the preferential APD prolongation at slow rates, a result that is consistent with the clinical observation that Y1795C carriers are susceptible to arrhythmia events during bradycardia.

Figure 11

The reverse stimulation-rate dependence of Y1795C on I_sus and APD. (a) The 19th and 20th APs from virtual cells containing WT (left) and Y1795C (right) channels with corresponding I_Na (at high gain, bottom) (see Methods). The Y1795C mutation clearly results in larger I_sus (arrow) compared with WT that becomes progressively larger as the stimulation rate is slowed, as indicated by the APs shown in (b) (stimulation rate, 1,200 milliseconds). (c) Computed APD for cells expressing WT and Y1795C channels plotted against simulated stimulation cycle length (CL). As the cycle length becomes progressively longer (simulating slowing of heart rate), the WT and Y1795C adaptation curves diverge, indicating that the Y1795C mutation exerts its deleterious effects preferentially at slow stimulation rates.

Mutation-induced alteration in modal gating dwell time underlies inverse rate-dependent increase in macroscopic current. Rhythm disturbances resulting from gene-specific mutation-induced long QT syndrome vary widely in response to heart rate (1, 16). LQT-1 mutations due to defects in KvLQT1 are strongly associated with β-adrenergic stimulation and cardiac events during rapid pacing (1, 22). Recently, it has been demonstrated that a frequently occurring LQT-1 mutation results in the disruption of a signaling complex required for channel phosphorylation that increases the amplitude (23) of the slowly activating component of the delayed rectifier K⁺ current (I_Ks). The signaling complex is crucial for APD shortening during rapid pacing. LQT-2 patients that have defects in HERG are equally likely to exhibit cardiac events at fast and slow rates (1) that likely stem from different mechanisms (24). Na⁺ channel–linked LQT-3 symptoms typically manifest at slower heart rates where patient phenotypes are marked by rhythm disturbances that may act as precursors to sudden cardiac death (1), although a recent study in the ΔKPQ mutation expressed in a transgenic mouse model demonstrated arrhythmogenic events at very fast pacing rates (25). The understanding of the mechanism of these variable rate dependencies is crucial for the development of therapeutic interventions.

Previous analysis of an LQT-3 mutant Na⁺ channel (Y1795C) demonstrated that the persistent non-inactivating I_Na, I_sus, exhibits implicit stimulation-rate dependence even in the absence of neural influence (17). These results suggest that gating properties of I_Na may be sufficient to account for the stimulation-rate dependence of I_sus. In this study we have combined experimental and theoretical approaches in order to elucidate the mechanism of the stimulation rate–dependent reduction in I_sus associated with the bradycardia dependence of Na⁺ channel–linked long QT syndrome. Recordings from single channels allow for the derivation of theoretical entry rates into and exit rates from the bursting mode of gating. Our results indicate that mutation-induced changes in the amount of time that mutant channels spend bursting (burst mode dwell time), rather than how readily they burst (latency to burst), primarily determine the inverse heart-rate dependence of I_sus. We experimentally confirmed this prediction by analysis of ΔKPQ mutant channels for which the burst mode exit rate (determined by the burst mode dwell time) was found to be very similar to the derived rate for Y1795C channels. Based on our theoretical analysis, this suggested that the stimulation rate–dependent reduction in I_sus should be similar for ΔKPQ and Y1795C channels, a prediction confirmed by the data presented in Figure 10d. Thus pharmacological control of the burst mode exit rate becomes a novel therapeutic strategy for rate-dependent regulation of APD in the heart (see below for structural targets).

Mechanistic insights from the computational model. The cardiac ventricular AP is a complex cellular event with multiple interconnected pathways contributing to the balance of ionic currents that control its waveform (26). Hence, extrapolation from mutation-induced changes in gating of a single ion channel to effects on AP waveform is not obvious, and in many cases requires computer-based simulations that can estimate the contributions from multiple pathways (27). It must be noted, however, that modeling of complex biological processes is not without limitations. By definition, a model is a simplification of the actual biological process that allows insight and understanding but may result in the exclusion of details necessary for absolute understanding of biological complexity and mechanism (28, 29). Nonetheless, the value of this approach is illustrated by the results presented in Figure 11. We demonstrated that the Y1795C channels result in larger macroscopic I_sus than do WT channels, and that this current becomes progressively larger as the stimulation rate is slowed. However, at sufficiently rapid stimulation rates (Figure 11a), despite the larger mutant-channel sustained inward current (Figure 11a, arrow), the mutation has little effect on APD (compare WT and Y1795C APs in Figure 11a). What mechanism underlies this apparent contradiction?

The simulation suggests that it is the summation of the mutation-induced inward current along with critical time-dependent potassium current that yields the overall rate-dependent effects of the mutation on the AP. As the stimulation rates become progressively slower, the WT and Y1795C adaptation curves diverge (Figure 11c), indicating that the Y1795C mutation exerts its deleterious effects preferentially at slow rates. At fast rates, I_Ks dominates the rate-dependent adaptation of APD (30, 31). Fast pacing results in short diastolic intervals that prevent complete deactivation of I_Ks, resulting in the buildup of instantaneous I_Ks repolarizing current at the AP onset. This effect overwhelms I_sus caused by Y1795C. At slower rates, less repolarizing current exists during each AP due to sufficient time between beats to allow complete deactivation of I_Ks. This effect, coupled with the reverse rate-dependent increases in I_sus due to Y1795C, gives rise to preferential prolongation at slow rates, consistent with the clinical observation that Y1795C carriers are susceptible to arrhythmia events during bradycardia.

Insights into structural control of channel bursting: novel targets for drug development. The structural basis of failed inactivation is poorly understood. Mutations in the III-IV linker region, both naturally occurring and experimentally induced, have been shown to disrupt the inactivation process (32) and underlie long QT syndrome (7, 12). The III-IV linker is thought to act as a blocking particle that moves into and occludes the pore following voltage-induced channel opening. More recently, LQT mutations in the C-terminus of SCN5A have been shown to affect inactivation gating, thereby implicating a role for the C-terminus in channel inactivation (17, 18, 33, 34). This focus on a possible role of the C-terminus in control of inactivation has been extended by chimeric analysis of brain and heart Na⁺ channels (35), site-directed mutagenesis of cardiac Na⁺ channels (36), and a structural analysis of the C-terminal tail of the cardiac Na⁺ channel (37).

Analysis of mutations Y1795C and ΔKPQ provides insight into a possible structural basis for mutation-induced modulation of inactivation that is reflected in modal gating. It is possible that regions of the C-terminus act as a “docking station” for the III-IV linker at voltages that are unfavorable to inactivation. During depolarization, allosteric movements may help to release the linker and allow blockage of the pore. In this way, a charged portion of the C-terminus may act as an inactivation voltage sensor. Allosteric movement of the sensor, induced by depolarization, might release the blocking particle, allowing for inactivation. Mutations in this region may disrupt the sensor, making release of the linker less likely, thereby increasing the likelihood of failed inactivation. This is consistent with the proposal that the inactivation particle is semipermanently docked when channels are closed and that this docking interaction may be modified by some C-terminal mutations. The nearly identical effects of the ΔKPQ and Y1795C mutations on burst mode dwell time provide evidence for the symmetry in C-terminus and III-IV linker interactions in the control of inactivation gating.

Understanding the structural basis of the mechanism of Na⁺ channel gating properties is crucial for the development of specifically targeted pharmacological interventions, and the present results strongly suggest that either the C-terminus and/or the inactivation gate (III-IV linker) are candidate molecular targets for the development of drugs intended to control APD in the heart, not by blocking of potassium channels, but through modulation of Na⁺ channels via control of modal gating.

This work was supported by NIH National Heart Lung and Blood Institute grants R01 HL-56810-05 and P01 HL-67849-01.

Colleen E. Clancy and Michihiro Tateyama contributed equally to this work.

Conflict of interest: No conflict of interest has been declared.

Nonstandard abbreviations used: long QT syndrome variant 3 (LQT-3); Na⁺current (I_Na); wild type (WT); sustained Na⁺ channel inward current (I_sus); action potential (AP); AP duration (APD); human embryonic kidney (HEK); tetrodotoxin (TTX); mean open time (MOT).

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