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Frequency-dependent regulation of cardiac Na⁺/Ca²⁺ exchanger

Institute of Cardiovascular Sciences, University of Manitoba, Faculty of Medicine, St. Boniface Research Centre, Winnipeg, Manitoba, Canada

Submitted 26 October 2004 ; accepted in final form 3 June 2005

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
The activity of the cardiac Na⁺/Ca²⁺ exchanger (NCX1.1) undergoes continuous modulation during the contraction-relaxation cycle because of the accompanying changes in the electrochemical gradients for Na⁺ and Ca²⁺. In addition, NCX1.1 activity is also modulated via secondary, ionic regulatory mechanisms mediated by Na⁺ and Ca²⁺. In an effort to evaluate how ionic regulation influences exchange activity under pulsatile conditions, we studied the behavior of the cloned NCX1.1 during frequency-controlled changes in intracellular Na⁺ and Ca⁺ (Na and Ca). Na⁺/Ca²⁺ exchange activity was measured by the giant excised patch-clamp technique with conditions chosen to maximize the extent of Na⁺- and Ca²⁺-dependent ionic regulation so that the effects of variables such as pulse frequency and duration could be optimally discerned. We demonstrate that increasing the frequency or duration of solution pulses leads to a progressive decline in pure outward, but not pure inward, Na⁺/Ca²⁺ exchange current. However, when the exchanger is permitted to alternate between inward and outward transport modes, both current modes exhibit substantial levels of inactivation. Changes in regulatory Ca²⁺, or exposure of patches to limited proteolysis by -chymotrypsin, reveal that this "coupling" is due to Na⁺-dependent inactivation originating from the outward current mode. Under physiological ionic conditions, however, evidence for modulation of exchange currents by Na-dependent inactivation was not apparent. The current approach provides a novel means for assessment of Na⁺/Ca²⁺ exchange ionic regulation that may ultimately prove useful in understanding its role under physiological and pathophysiological conditions.

sodium/calcium exchange; coupled inactivation; ionic regulation; giant excised patch

The transport substrates Na⁺ and Ca²⁺ also promote entry into, or exit from, distinct inactive states of the Na⁺/Ca²⁺ exchanger, analogous to the gating of ion channels (10, 17, 19, 25). For outward currents, the presence of Na⁺ on the cytoplasmic surface of the exchanger leads to its partitioning between active and inactive configurations. This type of ionic regulation is termed intracellular Na⁺ (Na)-dependent, or I₁, inactivation and exhibits a K_1/2 for Na of 15 mM (19). At low levels of Ca(e.g., nM range), Na⁺/Ca²⁺ exchanger molecules can enter into a second inactivated state, termed Ca-dependent, or I₂, inactivation. The transition of exchangers into and out of I₂ is regulated by [Ca²⁺]_i, with a K_1/2 of 0.3 µM (17).

Although conventional electrophysiological and fluorescence-based approaches have established the existence and operation of ionic regulatory mechanisms (11, 21, 23, 28), only recently have efforts become focused on a thorough understanding of these dynamic processes. For example, Weber et al. (39) recently demonstrated allosteric regulation of the cardiac Na⁺/Ca²⁺ exchanger (NCX1.1) by Ca on a beat-to-beat basis. Moreover, these investigators measured submembrane [Ca²⁺] levels during the course of a cardiac action potential, allowing inference on the transport behavior of the exchanger during an excitation-contraction/relaxation cycle (40). Studies using fluorescence resonance energy transfer (FRET) have shown conformational changes of the exchanger associated with contractile activity in myocytes (31). In addition to this mounting evidence suggesting a dynamic modulation of exchange activity that is responsive to Ca oscillations, it was recently proposed that persistent Ca²⁺ activation can occur beyond the period when cytosolic Ca²⁺ is elevated (8, 34).

The giant excised patch technique (14, 15) has been very useful in characterizing the kinetic aspects of ionic regulation of the Na⁺/Ca²⁺ exchanger (10, 17, 19), as well as in helping define the structural components underlying their operation (9, 24–26). However, nearly all studies using this technique have evaluated the dynamics of Na⁺/Ca²⁺ exchange activity over prolonged time periods (e.g., 10–30 s). In the present study, we have used rapid solution pulses to investigate the role of ionic regulation in modulating the activity of NCX1.1.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
Purified cRNA encoding NCX1.1 was prepared for injection into Xenopus laevis oocytes as previously described (10, 25). Briefly, X. laeves were generally anesthetized with benzocaine, and oocytes were harvested, teased apart, and washed in a buffered isotonic solution. Oocytes were then incubated with collagenase to disperse the eggs, followed by a defolliculation solution to remove the follicles that surround each cell. After being washed, stage V–VI (i.e., mature) eggs were selected for injection with 23 ng of cRNA.

Na⁺/Ca²⁺ exchange currents were measured with the giant excised patch-clamp technique (14). To effectively eliminate the effects of solution mixing within our perfusion devices, solution pulses were alternately applied with two perfusion devices oriented symmetrically with respect to the patch pipette. For fast-frequency studies, solutions were applied either continuously for 32 s or for varying durations at frequencies of 0.5, 1, and 2 Hz in such a manner that each solution was applied for one-half of the total duty cycle. For example, under conditions in which pure outward-mode exchange was studied at 0.5 Hz, patches were exposed to a Na⁺-based solution pulse for 1 s to allow for the development of outward Na⁺/Ca²⁺ exchange current, followed by the application of a Li⁺-based solution for 1 s, which does not generate current. Alternatively, the ratio of time during the duty cycle that patches were exposed to the Na⁺- vs. the Li⁺-based solution was altered at a constant frequency. In these experiments, the ratio of time that patches were exposed to Na⁺ vs. Li⁺ [stimulatory phase (t_st)/inactive phase (t_in)] is referred to as .

"Intracellular" solution switching was accomplished with a PC running pCLAMP6 software (Axon Instruments) interfaced with an eight-channel solenoid driver that controlled gravity-driven solution reservoirs for the two temperature-controlled perfusion devices. For pure outward Na⁺/Ca²⁺ exchange current measurements, pipettes contained (in mM) 100 N-methyl-D-glucamine-MES, 30 HEPES, 30 tetraethylammonium (TEA)-OH, 16 sulfamic acid, 8.0 CaCO₃, 6 KOH, 0.25 ouabain, 0.1 niflumic acid, and 0.1 flufenamic acid [pH 7.0 at room temperature (RT) with MES], and currents were elicited by rapidly switching from Li⁺- to Na⁺-based bath solutions containing (in mM) 100 [Na⁺ + Li⁺]-aspartate, 20 CsOH, 20 MOPS, 20 TEA-OH, 10 EGTA, 0–9.91 CaCO₃, and 1.0–1.5 Mg(OH)₂ (pH 7.0 at 30°C with MES or LiOH) to generate free [Ca²⁺]_i of 0.3, 1.0, and 3.0 µM. For pure inward Na⁺/Ca²⁺ exchange current measurements, pipettes contained (in mM) 100 Na-MES, 20 CsOH, 20 TEA-OH, 10 EGTA, 10 HEPES, 8 sulfamic acid, 4 Mg(OH)₂, 0.25 ouabain, 0.1 niflumic acid, and 0.1 flufenamic acid (pH 7.0 at RT with MES), and currents were activated by switching between the Ca²⁺-free and 10 µM Ca²⁺-containing, Li⁺-based bath solutions described above. For combined inward-outward current measurements, pipettes contained (in mM) 100 Na-MES, 20 CsOH, 20 HEPES, 20 TEA-OH, 4 sulfamic acid, 2 CaCO₃, 0.25 ouabain, 0.1 niflumic acid, and 0.1 flufenamic acid (pH 7.0 at 30°C with MES), and outward and inward currents were activated with the same solutions used for initiating pure outward and inward currents described above. For brevity, only the Na⁺ and Ca²⁺ concentrations of pipette and bath solutions are given in RESULTS. Minor deviations from the above are indicated where appropriate. Free Mg²⁺ and Ca²⁺ concentrations were calculated as described previously (4, 10). Pooled data are presented as means ± SE. Two-tailed Student's t-tests were used for comparison of unpaired data, and P < 0.05 was considered significant.

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
Rapid solution pulses. Figure 1 shows a comparison of pure outward NCX1.1 exchange currents activated by continuous or pulsatile solution applications. During continuous solution application with 100 mM Na⁺ and 0.3 µM Ca²⁺, outward current peaked rapidly, followed by a slow decay to steady-state levels (Fig. 1A). Previous work has shown that peak current levels under these experimental conditions reflect the availability of Na⁺/Ca²⁺ exchangers before activation, whereas steady-state current levels reflect the overall balance of exchangers moving into and out of the I₁ inactive state (17, 19). Substantially different results were obtained when activating/nonactivating solutions were pulsed intermittently. In these tracings, Na⁺-containing solutions were present for half of each pulse and Li⁺-containing solutions were present for the remainder of the duty cycle. As demonstrated in Fig. 1, B–D, peak outward currents progressively decayed with successive solution pulses, and the extent and time course of this decline were strongly dependent on the stimulation frequency.

View larger version (24K): [in this window] [in a new window]   Fig. 1. Frequency dependence of pure outward Na+/Ca2+ exchange currents. Pure outward currents were generated either by continuous (A) or rapid solution pulses applied at a stimulus frequency () of 0.5 (B), 1 (C), and 2 (D) Hz. The "intracellular" (bath) solution contained 100 mM Na+ and 0.3 µM regulatory Ca2+, and the pipette contained 8 mM Ca2+. Continuous and frequency-dependent current records were obtained from the same patch. Dashed lines represent zero-current levels. E: pooled data for frequency dependence of cumulative charge movement during the stimulus train (Q) relative to that occurring during a continuous solution application (defined as 100%), the ratio of peak current for the last and first pulses in the stimulus train (ss), and the ratio of the steady-state current over the peak current for continuous solution application (Fss), which is represented by the dotted line positioned slightly above the x-axis. Scale bars represent 100 pA and 10 s for A–D, respectively.

The degree of cumulative inactivation during repetitive solution pulses was quantified by taking the ratio of peak current for the first and last pulses in the stimulus train, defined as _ss. As shown in Fig. 1E, there was an inverse relationship between _ss and stimulation frequency. At no point, however, was _ss smaller than F_ss, because partial recovery of exchangers from I₁ inactivation always occurred during the interpulse interval (i.e., when the Li⁺-based solution was applied; see APPENDIX). In addition, there was also a small increase in the rate constant for the decay of peak currents (l) with increased pulse frequency: l was 0.18 ± 0.02 s^–1 (n = 4) at 0.5 Hz, 0.20 ± 0.02 s^–1 (n = 5) at 1 Hz, and 0.23 ± 0.01 s^–1 (n = 3) at 2 Hz. Therefore, stimulation frequency affected both the rate and magnitude of pure outward Na⁺/Ca²⁺ exchange current decay during repetitive solution pulses.

The influence of pulsatile solution application on Na⁺/Ca²⁺ exchange activity can be quantified by integrating the cumulative charge carried during successive solution pulses, defined as _Q (6, 7). Here, we measured the total charge carried during a continuous solution application to serve as a reference point defined as 100% (e.g., Fig. 1A). In the absence of regulatory mechanisms, simply dividing this continuous trace into active and inactive components would reduce the cumulative charge to 50%, because current would only be produced during the active periods. As shown in Fig. 1E for 0.5-Hz stimulation, the amount of cumulative charge moved during pure outward currents was 93 ± 10% (n = 4) of that calculated for a continuous solution pulse. Increasing the frequency of solution pulses led to a gradual decrease in the ratio of charge movement to 83 ± 8% (n = 5) and 77 ± 3% (n = 3) at 1 and 2 Hz, respectively. Thus, in the presence of 0.3 µM regulatory Ca²⁺, _Q at the fastest frequency examined was nearly 80% of that measured for a continuous solution pulse. This augmentation of current during pulsatile flow reflects the recovery of exchangers from Na-dependent inactivation that occurs during the nonconducting period (see APPENDIX).

In contrast with pure outward Na⁺/Ca²⁺ currents, pure inward currents were relatively less affected by frequency-controlled solution pulses. The current trace from a representative patch is shown in Fig. 2, where inward currents were activated by 10 µM Ca(in the absence of Na) during continuous and pulsatile solution application at 0.5, 1, and 2 Hz. Figure 2, left, shows data from intact, regulated patches, whereas Fig. 2, right, shows data from the same patches after limited proteolysis with -chymotrypsin (-ChT) for 1 min to deregulate exchange currents. Note that maximal current levels were achieved within several pulses of the train. Moreover, the pulsed tracings showed a square appearance similar to that observed during continuous solution application, although there was a noticeable decline in peak currents at the highest frequency examined (2 Hz). Similar results were obtained in a total of six patches. Thus there was a substantial difference in the effects of rapid solution pulsing on unidirectional Na⁺/Ca²⁺ exchange currents depending on whether inward or outward currents were evaluated.

View larger version (34K): [in this window] [in a new window]   Fig. 2. Frequency dependence of pure inward Na+/Ca2+ exchange currents. Currents were activated by alternating between a 0 and 10 µM Ca2+ containing 100 mM Li+-based solution applied to the cytoplasmic surface of the patch continuously or at 0.5, 1, and 2 Hz. The pipette contained 100 mM Na+. Traces on left were obtained from an intact (i.e., regulated) patch, and traces on right were obtained in an -chymotrypsin (-ChT)-treated (i.e., deregulated) patch.

View larger version (26K): [in this window] [in a new window]   Fig. 3. Effects of changes in duty cycle on pure outward Na+/Ca2+ exchange current. Outward currents were activated by applying 100 mM Na+ to the cytoplasmic surface of the patch in the continuous presence of 0.3 µM regulatory Ca2+. The pipette contained 8 mM Ca2+. A: outward current elicited by a continuous solution pulse. B–D: outward currents elicited by a series of rapid solution pulses applied at 1 Hz. The fraction of the duty cycle () spent in a Na+-based solution to that spent in a Li+-based solution was varied such that the duration of exposure of patches to Na+ during the 1-s solution pulse was increased from 200 (B; = 0.25) to 500 (C; = 1) and then 800 (D; = 4) ms. Currents in A–D were generated in the same patch. E: ratio dependence of ss at = 0.25 (n = 2), 1 (n = 5), and 4 (n = 2). Dotted line represents the average value of Fss from the continuous solution pulses that preceded the fast-frequency trials. Scale bars represent 40 pA and 10 s for A–D.

View larger version (33K): [in this window] [in a new window]   Fig. 4. Cytoplasmic Ca2+ dependence of Fss and ss at a pulse frequency of 1 Hz. A: pure outward currents elicited by continuous solution pulses containing 100 mM Na+ and various regulatory Ca2+ concentrations, as indicated. The concentration of Ca2+ in the pipette solution was 8 mM. Note that elevation of regulatory Ca2+ modulates both peak and steady-state current levels. B–D: representative traces from the same patch as in A of pure outward Na+/Ca2+ exchange current generated by rapid solution pulses applied at 1 Hz in the presence of 0.3, 1, and 3 µM regulatory Ca2+. E and F: pooled data on the Ca2+ dependence of Fss, ss, and Q during 1-Hz stimulation. Dotted line in F represents the theoretical Q value for outward current in the absence of ionic regulation for an unregulated exchanger spending equal time in conducting and nonconducting states. Scale bars represent 100 pA and 10 s for A–D.

View larger version (14K): [in this window] [in a new window]   Fig. 5. Coupling of inactivation for inward and outward modes of Na+/Ca2+ exchange during a continuous solution pulse. The pipette contained 100 mM Na+ and 2 mM Ca2+. The patch was exposed first to a solution eliciting outward Na+/Ca2+ exchange current by applying 100 mM Na+ and 1 µM regulatory Ca2+ (trace a), followed by a 32-s recovery period. A solution containing 100 mM Li+ and 10 µM Ca2+ was then applied to induce an inward Na+/Ca2+ exchange current (trace b). Outward current was then initiated directly from the inward current mode (trace c). Once a steady-state level of outward current was attained, an inward current was then initiated (trace d). Scale bars represent 100 pA and 10 s. Inset: recovery from Na-dependent (I1) inactivation developed during outward currents slows the rate of activation of inward Na+/Ca2+ exchange currents.

View larger version (40K): [in this window] [in a new window]   Fig. 6. Inactivation coupling for inward and outward transport modes of Na+/Ca2+ exchange current during rapid solution pulsing. A: influence of inactivation of outward currents on inward currents is evident during alternating transport modes at 0.5 and 1 Hz. The pipette solution contained 100 mM Na+ and 2 mM Ca2+. Outward currents were induced by perfusing patches with a solution containing 100 mM Na+ and 1 µM Ca2+. Inward currents were elicited with a Li+-based bath solution containing 10 µM regulatory Ca2+. The dotted baseline near the middle of the current waveforms represents the zero-current level. Dashed lines represent a least-squares fit of the outward and inward current peaks to a single-exponential function. The fitted decay rate constants at 0.5 Hz were 0.19 ± 0.03 (n = 9) and 0.24 ± 0.03 (n = 7) s–1 for outward and inward current peaks, respectively, whereas those at 1 Hz were 0.24 ± 0.02 (n = 4) and 0.35 ± 0.10 (n = 4) s–1 for outward and inward current, respectively. B: effect of -ChT on inward and outward Na+/Ca2+ exchange currents elicited by continuous and rapid solution pulses. Patches were exposed to 1 mg/ml -ChT for 30 s before current recording to remove both I1 and Ca-dependent (I2) regulation. Na+/Ca2+ exchange currents were elicited by a continuous solution pulse for 32 s (left) or rapid solution pulses applied at 0.5 (middle) and 1 (right) Hz. The time-dependent declines of outward and inward currents were completely abolished by -ChT. Scale bars represent 50 pA and 10 s.

Influence of "coupled" inactivation. Figure 7 shows pooled data illustrating the differential effects of inactivation coupling on outward and inward current characteristics. The chart shows steady-state levels of peak currents (_ss) and the overall current integral for the train of pulses expressed as a ratio of that obtained during continuous solution application (_Q). In this instance, "uncoupled" inactivation refers to conditions in which only pure inward or outward Na⁺/Ca²⁺ exchange currents were elicited. For "coupled" inactivation, exchange currents alternated between inward and outward transport directions. As shown in Fig. 7A, where currents were driven in alternate transport modes (i.e., coupled inactivation), we found that outward currents were augmented both in terms of their steady-state levels (_ss) achieved and the value of the overall current integral (_Q), compared with the same protocol where pure outward currents were solely elicited (i.e., uncoupled). An opposite response was observed for inward currents, as shown in Fig. 7B. Here, the presence of coupled inactivation led to significant decreases in both parameters.

View larger version (14K): [in this window] [in a new window]   Fig. 7. Quantitative analyses of Na+/Ca2+ exchange currents under conditions allowing for the development of pure inward or pure outward current (uncoupled inactivation) or under conditions allowing the exchanger to alternate between transport modes (coupled inactivation). A: effect of rapid solution pulses applied at 1 Hz on ss and Q for uncoupled (open bars) and coupled (gray bars) outward exchange currents. The number of patches studied under each condition is given in parentheses. B: pooled data for inward Na+/Ca2+ exchange currents labeled as in A. *P < 0.03.

The following experiments were designed to crudely approximate the changes in ionic conditions that occur during diastole and systole, with full recognition of the limitations and oversimplifications of this approach. Figure 8 illustrates alternating inward and outward Na⁺/Ca²⁺ exchange currents before (Fig. 8A) and after (Fig. 8B) deregulation of the exchangers with -ChT. Pipettes contained 140 mM Na⁺ and 2 mM Ca²⁺ to mimic physiological extracellular ion concentrations. Diastole and systole were "simulated" by applying 0.1 and 3 µM Ca²⁺, respectively, to the cytoplasmic surface of the patch in the continuous presence of 10 mM Na⁺. Here, large inward currents were elicited under "systolic" conditions (i.e., 3 µM Ca), whereas small outward currents were generated under "diastolic" conditions (i.e., 0.1 µM Ca). Notably, the application of voltage pulses would dramatically influence the behavior of the exchanger under these experimental conditions, although efforts to include voltage pulses have been hindered by patch instability. Under these conditions, a small inactivation of outward currents is apparent in regulated patches, whereas these currents are larger and stable after -ChT treatment. In addition, the rate of current development in either direction was considerably accelerated after deregulation (Fig. 8, C and D). These results illustrate the operation of ionic regulation under slightly more realistic physiological ionic conditions. Notably, no evidence was found for Na-dependent regulation of exchange currents under these ionic conditions.

View larger version (43K): [in this window] [in a new window]   Fig. 8. Representative current traces are shown from an intact patch (A) and a patch subjected to limited proteolysis by 1 mg/ml -ChT (B). In these experiments, pipettes contained 140 mM Na+ and 2 mM Ca2+. To crudely approximate ionic conditions during diastole and systole, currents were activated by applying 0.1 µM and 3 µM Ca, respectively, in the continuous presence of 10 mM Na. The dotted lines illustrate zero-current levels. C: overlapping current traces on an expanded time scale taken from the middle of each trace. Note that after proteolysis (dashed line) the rate of current development was faster during the development of both inward and outward currents. D: time constants for current development during the transitions that occurred on increasing and decreasing cytoplasmic Ca2+ levels. Time constants were obtained as the slopes of the Boltzmann function used for fitting data as shown in C. For the transition from outward to inward current, t = 0.099 ± 0.007 (n = 5) vs. 0.052 ± 0.010 s (*P = 0.0062) for intact and proteolized patches (n = 5), respectively. For the transition from inward to outward current, t = 0.032 ± 0.001 vs. 0.014 ± 0.003 s (P = 0.0008) for intact and proteolized patches (n = 5), respectively.

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

Ionic regulatory mechanisms. The giant excised patch clamp technique, developed by Hilgemann (15), has been invaluable in understanding how Na and Ca regulate the activity of the Na⁺/Ca²⁺ exchanger beyond their role as transport substrates. Numerous studies have documented how both Na- and Ca-dependent regulatory mechanisms can dramatically influence Na⁺/Ca²⁺ activity, presumably through alteration of the active exchanger population (9, 10, 15, 17, 19). For example, in response to a prolonged pulse of Na, the exchange current transient can decay by 90% (15). Similarly, in the absence of Ca, outward exchange currents can be nearly eliminated despite highly favorable electrochemical gradients supporting exchange activity (15, 25, 27). The majority of studies using this technique to date have typically used long (i.e., >30 s) continuous solution application, enabling the kinetic features of Na⁺/Ca²⁺ transport and regulation to be identified and quantified (9, 10, 15, 17, 19). Although giant excised patch clamping has become an essential tool in helping to define the extremes of exchanger regulation, identification of what proportion of the exchanger population is active under more realistic (i.e., physiological or pathophysiological) conditions has yet to be established.

The rich kinetic details revealed from giant excised patch-clamp studies have been difficult to extrapolate into understanding cellular Na⁺/Ca²⁺ exchange operation. Specifically, it remains unclear as to how the entire exchanger population is regulated to match requirements for cellular Ca²⁺ efflux (and possibly influx). Similar to L-type Ca²⁺ channels, whose numbers exceed that required for an individual contraction (1, 2, 22), it is likely that Na⁺/Ca²⁺ exchangers are also present in considerable excess of the number required to facilitate myocyte relaxation and maintain Ca²⁺ homeostasis. Na⁺/Ca²⁺ exchange is generally thought to remove the same quantity of Ca²⁺ that enters through the L-type Ca²⁺ channel on a beat-to-beat basis (3, 7). Depending on the species examined, this constitutes roughly 7–28% of the Ca²⁺ removal required to return Ca to diastolic levels (2). However, the exchanger is also capable of mediating relaxation completely independent of the sarcoplasmic reticulum, albeit at slightly slower rates (2), implying that there is a considerable excess of exchangers over that required to remove Ca²⁺ during regular patterns of stimulation.

Several recent studies have highlighted the involvement of Ca²⁺-dependent (I₂) regulation of Na⁺/Ca²⁺ exchange in controlling cellular Na⁺/Ca²⁺ exchange activity (8, 31, 34, 39). Here, there is reasonable evidence to suggest that increased cytosolic Ca²⁺ levels grade exchange activity, presumably through the I₂ regulatory mechanism. However, there is no equivalent information regarding a potential role for Na-dependent (I₁) inactivation. In large part, uncertainty as to the relevance of Na-dependent inactivation resides in the fact that this regulatory mechanism is only apparent at [Na⁺]_i far in excess of those thought to occur physiologically. Despite this uncertainty, however, there is sufficient circumstantial evidence to suggest an, as yet, undiscovered role for Na-dependent inactivation. For example, the XIP region of the Na⁺/Ca²⁺ exchanger is highly conserved across the entire superfamily of cloned exchangers, including the unique gene products NCX2 and NCX3 (9). Alternative splicing of the NCX1 family leads to marked alterations in Na-dependent inactivation (10, 30), and prominent interactions between Na- and Ca-dependent regulatory mechanisms have been extensively described (17, 19, 25). Phosphatidylinositol 4,5-bisphosphate signaling strongly influences Na⁺/Ca²⁺ exchange activity (13, 16, 18), presumably through its only identified interaction with the exchanger's XIP region and the subsequent modification of I₁ inactivation (12). All of these observations indicate that further investigation of the Na-dependent inactivation mechanism is warranted, despite present uncertainty as to its specific physiological or pathophysiological role.

In an effort to advance our understanding of physiological Na⁺/Ca²⁺ exchange regulation, we have characterized the kinetic features of Na- and Ca-dependent regulatory mechanisms for the cardiac Na⁺/Ca²⁺ exchanger NCX1.1 under pulsatile conditions. The most salient features of ionic regulation apparent from examining continuous solution application were readily apparent under pulsatile conditions. That is, both Na- and Ca-dependent regulation prominently modified outward Na⁺/Ca²⁺ exchange currents but were not discernible for inward currents. Notably, several other features were also revealed that are not readily apparent by simple examination of continuous solution traces. For example, changing the frequency of solution application over the range of 0.5–2 Hz prominently modified the extent of Na-dependent inactivation both for pure outward currents and during oscillations between inward and outward currents. Na-dependent inactivation that arose during outward currents strongly influenced the rate and magnitude of inward currents. These observations were made under conditions designed to optimize the appearance of ionic regulation, so that the effects could be readily discerned. However, under more realistic ionic conditions crudely approximating diastole and systole, evidence for Na-dependent regulation was not apparent. Here, in the presence of 10 mM Na, we observed that the rate of current development was accelerated after deregulation of exchangers with -ChT, but no evidence for Na-dependent regulation was apparent.

It is now established that Na levels are elevated in cardiac hypertrophy and during heart failure (33, 38). Far more dramatic increases in Na occur during ischemia-reperfusion injury (29, 37), well into the range of [Na⁺]_i at which Na-dependent inactivation would become prominent. Presumably, regulation of the Na⁺/Ca²⁺ exchanger under these conditions will fall intermediate between the extremes we have documented in this study. Continued efforts and refinement of the current approach should prove useful toward determining the specific [Na⁺]_i at which this type of regulation becomes significant.

Limitations of study. The majority of our study was conducted under conditions designed to maximize the extent of ionic regulation. Specifically, we used ionic conditions to examine unidirectional transport by the exchanger and/or supranormal levels of Na to promote outward currents. At present, we cannot routinely apply voltage pulses coincident with anticipated membrane potential changes during diastole and systole, because these dramatically reduce patch stability. Similarly, there are temporal restrictions in our ability to change ion concentrations, preventing optimal simulation of physiological excitation-contraction coupling. Notably, however, there are no current means of assessing Na⁺/Ca²⁺ exchange activity that are not hindered by similar limitations. Despite these limitations, the current approach represents a useful starting point for evaluation of Na⁺/Ca²⁺ exchanger regulation that should assist in understanding its physiological and pathophysiological regulation.

	APPENDIX

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
Assuming that the regulation of Na⁺/Ca²⁺ exchange accompanying changes in cytoplasmic Na⁺ concentration occurs at slower rates than changes in the bulk and membrane subsurface concentrations, we based our analysis of current-time transients during fast repetitive solution changes on the two-state model of Na⁺ inactivation described by Hilgemann et al. (17, 19). A similar analysis was applied to describe ligand binding to periodically accessible receptors in a model of phasic ion channel blockade (35, 36).

The repetitive pulsatile train comprises a number of single episodes (i.e., complete cycles), each of which has the duration = t_st + t_in, where t_st is the time interval when cytoplasmic Na⁺ is present (i.e., stimulatory phase) and t_in is the time interval when cytoplasmic Na⁺ is absent (i.e., interstimulus or inactive phase). Accordingly, the frequency of the train is = 1/.

According to the Na⁺-dependent, or I₁, inactivation model (17, 19), we consider that the transition of fully active exchangers into the I₁ inactive state occurs from the 3 Na-loaded conformation of the exchanger, E_3ni:

where and are inactivation and recovery rate constants, respectively. The molar fractions of exchangers in the active () and inactive (I₁) states constitute the total exchanger population, so I₁ + = 1.

During the stimulatory phase of a cycle, entry into and recovery from the inactive state is occurring. Accordingly, the rate of change of the fraction, '_j, of the total exchanger population being in an active state during the jth stimulatory phase is given by:

(A1)

where f_3ni is the fraction of active exchangers with 3 bound Na⁺ facing the cytoplasmic side of the membrane. The solution to Eq. A1 is:

(A2)

where = (f_3ni + ) is a current decay rate constant, '_j,o is the initial fraction of active exchangers at the beginning of the jth stimulatory phase, and ' = / is the steady-state fraction of active exchangers assuming an infinitely long stimulatory interval.

Because f_3ni = 0 in the absence of cytoplasmic Na⁺, the fraction (''_j) of the entire exchanger population being in an active state during the jth inactive phase is given by the equation:

(A3)

where t is time. The solution to Eq. A3 reads:

(A4)

where ''_j,o is the initial fraction of active exchangers at the beginning of the jth inactive phase, and '' is the steady-state fraction of active exchangers in the case of an infinitely long recovery interval.

The current transients generated during pulsatile solution switching are described by a sequence of recurrent equations because the initial fraction of active exchangers for the jth stimulus is determined by that attained at the end of the previous, i.e., (j – 1)th, inactive phase, and the initial fraction of active exchangers for the jth inactive phase is determined by that attained at the end of the jth stimulatory phase.

From Eq. A2, at the end of the jth stimulatory phase, the fraction of active exchangers is given by:

(A5)

Assuming that the entire population of exchangers is fully active before Na_i⁺ application, the initial fraction of active exchangers for the first episode, _o, is taken to be equal to 1.

From Eq. A4, at the end of the jth inactive phase, the fraction of active exchangers is given by:

(A6)

Obviously, '' = ''_o = 1.

By combining Eqs. A5 and A6, the initial fraction of active exchangers for the (j + 1)th pulse (starting from the second pulse) after the jth inactive phase is expressed by:

(A7)

where = (t_in + t_st) is the positional decay rate constant for the pulsatile train of peak currents, as opposed to the temporal decay rate constant that will be defined below. The member representing the sum of exponentials is a geometric series. Therefore, Eq. A7 can be rewritten as:

(A8)

From Eq. A8, the steady-state value of ' is given by:

(A9)

Assuming that all the current transients reflect the time-dependent processes of inactivation and recovery, the first peak current in the train, I_peak,1, and the peak current attained at steady state (experimentally, the peak current always attains its steady-state value within a 32-s pulsatile train), I_peak,, are given by:

(A10)

where N is the number of exchangers and i is the unitary current of the fully active Na⁺/Ca²⁺ exchanger.

In the case of continuous 32-s current transients, the expressions for the peak (I_peak) and steady-state (I_ss) currents are given by (30):

(A11)

where is the steady-state fraction of active exchangers.

From Eq. A11, the ratio of steady-state to peak current, F_ss, is equivalent to the steady-state fraction of active exchangers and therefore can be used to determine the proportion of inactivated exchange current, i.e., 1 – F_ss. The inactivation rate constant and the inactivation recovery rate constant are given by:

(A12)

During fast-frequency solution changes, the analogous ratio of the steady-state value of the peak current attained after many pulses to the first peak current, termed _ss, can be expressed from Eq. A10 as:

(A13)

where '_,o is given by Eq. A9.

From Eqs. A8 and A13, the current-pulse number relationship for the peak currents attained during consecutive pulses is described as a single-exponential decay:

(A14)

where _j is the jth peak current normalized to the first peak current. Equation A14 can be used as a fitting function for the determination of _ss and from experimental pulsatile trains. However, unless is required, a good approximation for _ss can be obtained simply as the ratio of the last peak in a pulse train to the first.

The time dependence of the decay of peak currents during the pulsatile train can be derived from Eq. A14. With the following substitution:

one can obtain:

(A15)

where l = is the temporal decay rate constant for the pulsatile train of peak currents.

In terms of the inactivation rate constant and the inactivation recovery rate constant , one can write using Eqs. A9, A12, and A13:

(A16)

where

(A17)

Note that the first member of the sum in Eq. A16, F_ss, represents the fraction of the total exchanger population remaining active after a continuous stimulation, and the second member, (1 – F_ss), represents the fraction of active exchangers recruited from the pool of inactive exchangers because of recovery during the interstimulus intervals. Therefore, the factor can be referred to as a recruitment coefficient.

With the following substitutions:

where is the ratio of the duration of the stimulatory phase to the duration of the interstimulus interval (i.e., = t_st/t_in), the recruitment coefficient can thus be expressed as a function of and :

(A18)

It follows from Eqs. A16 and A18 that, at constant and 0, = 1 and _ss = 1, corresponding to the full recovery of the exchanger population during pulsatile stimulation at very low frequency. Conversely, at constant and very high frequency (i.e., ), and _ss approach the limits:

Moreover, at constant and 0, = 1 and _ss = 1, which corresponds to full recovery of the exchanger population after a very long interstimulus interval. It can be seen that = 0 and _ss= F_ss only where , a condition that is kinetically satisfied during the development of outward current elicited by a continuous solution pulse. Otherwise, as illustrated in Fig. 1E, the condition _ss > F_ss holds.

	GRANTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
This work was supported by operating grants from the Canadian Institutes of Health Research and the Heart and Stroke Foundation of Manitoba. L. V. Hryshko was supported by a Canada Research Chair.

	FOOTNOTES

 

Address for reprint requests and other correspondence: L. V. Hryshko, Inst. of Cardiovascular Sciences, Univ. of Manitoba Faculty of Medicine, St. Boniface Research Centre, 351 Tache Ave., Winnipeg, MB, Canada R2H 2A6 (e-mail: lhryshko{at}sbrc.ca)

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

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