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Regulation kinetics of Na⁺-Ca²⁺ exchange current in guinea-pig ventricular myocytes

Yasutada Fujioka*, Koh Hiroe and Satoshi Matsuoka

MS 1004 Received 17 April 2000; accepted after revision 11 August 2000.

	ABSTRACT

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1. To investigate the regulation of native cardiac Na⁺-Ca²⁺ exchange by cytoplasmic Na⁺ (Na⁺_i) and Ca²⁺ (Ca²⁺_i), we recorded the Na⁺-Ca²⁺ exchange current (I_Na-Ca) from inside-out 'macro patches' excised from intact guinea-pig ventricular cells.

2. The half-maximal concentration (K_h) of Ca²⁺_i required to induce an inward I_Na-Ca was 7 µM. The K_h of Na⁺_i required to induce an outward I_Na-Ca was 21 mM, and tended to decrease at the steady state of Na⁺-dependent inactivation.

3. The time constant () of Na⁺-dependent inactivation was ~1·5 s at 100 mM Na⁺_i and 1 µM Ca²⁺_i. The K_h for Na⁺_i was 14 mM.

4. Ca²⁺_i augmented the peak outward I_Na-Ca (K_h = 0·2 µM) and attenuated Na⁺-dependent inactivation (K_h = 2·2 µM). The outward I_Na-Ca was activated by 5 µM Ca²⁺_i with a half-time to reach steady state (t_½) of ~0·4 s. This activation was composed of two exponential processes. Deactivation of the current upon Ca²⁺_i removal also consisted of two exponential processes and had a t_½ of ~0·5 s.

5. A Na⁺-Ca²⁺ exchange model, consisting of one consecutive 4Na⁺:1Ca²⁺ exchange cycle and two inactive states, well mimicked the experimental data with regard to ion dependencies and regulation kinetics.

6. These data provide detailed information on the kinetics of the Na⁺_i- and Ca²⁺_i-dependent regulation of native Na⁺-Ca²⁺ exchange. They also indicate that the regulation kinetics operate faster in macro patches than in the giant membrane patch from cardiac 'blebs', or in Xenopus oocytes expressing a cloned exchanger (NCX1.1).

	INTRODUCTION

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Na⁺-Ca²⁺ exchange is the major mechanism by which cytoplasmic Ca²⁺ (Ca) is extruded from cardiac myocytes. The Ca extrusion rate is primarily determined by electrochemical gradients of Na⁺ and Ca²⁺ across the sarcolemma. In addition to their primary role as permeating ions, cytoplasmic Na⁺ (Na⁺_i) and Ca secondarily regulate the Na⁺-Ca²⁺ exchange activity via Na⁺-dependent inactivation and Ca²⁺-dependent activation mechanisms (Hilgemann, 1990). Namely, the exchanger is inactivated by an increase in [Na⁺]_i and deactivated by removal of Ca. These regulatory mechanisms have been systematically studied in giant membrane patches excised from 'blebs' of ventricular cells (Hilgemann, 1990; Hilgemann et al. 1992a,b) and from Xenopus oocytes expressing a canine heart exchanger (NCX1.1; Matsuoka et al. 1993, 1995, 1997). An equivalent regulatory process was also demonstrated in whole-cell clamped myocytes (Matsuoka & Hilgemann, 1994). Furthermore, several domains, responsible for Na⁺- and Ca²⁺-dependent regulation, have been identified by site-directed mutagenesis of NCX1.1 (Matsuoka et al. 1993, 1995, 1997; Dyck et al. 1999).

The qualitative properties of the regulatory mechanisms in NCX1.1 were similar to those governing the cardiac bleb exchanger. However, their kinetics differed significantly. Na⁺-dependent inactivation was about fivefold faster for the cardiac bleb exchanger than for the NCX1.1 exchanger. NCX1.1 often had a large current even in the absence of regulatory Ca. Because of these differences, the regulation kinetics of the exchanger need to be studied under more physiological conditions. However, a method for recording the Na⁺-Ca²⁺ exchange current (I_Na-Ca) in inside-out membrane patches excised from intact myocytes has not been developed.

To gain more insight into the native Na⁺-Ca²⁺ exchange of the sarcolemmal membrane, we recorded I_Na-Ca in 'macro patches' excised from intact guinea-pig ventricular myoctes, and studied cytoplasmic ion dependencies and the kinetics of Na⁺- and Ca²⁺-dependent regulation. We found that the speed of regulation is substantially faster in the exchanger of macro patches than in that of the giant membrane patch from cardiac blebs, while the affinity of the exchanger for Na⁺_i and Ca is almost the same. In addition, we constructed a Na⁺-Ca²⁺ exchange model consisting of one consecutive 4Na⁺:1Ca²⁺ exchange cycle and two inactive states, in order to test how the recently suggested 4Na⁺:1Ca²⁺ exchange (Fujioka et al. 2000) is reliant upon ion dependencies and regulation kinetics.

Some of our data were presented at the 43rd annual meeting of the Biophysical Society (Fujioka et al. 1999).

	METHODS

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Isolation of myocytes

Single ventricular myocytes were isolated as described previously (Powell et al. 1980; Fujioka et al. 1998). In accordance with Kyoto University animal welfare guidelines, guinea-pigs (200-300 g) were deeply anaesthetized by an intraperitoneal injection of an overdose of pentobarbital sodium (> 0·1 mg g^-1). The ascending aorta was cannulated in situ and the heart was perfused with a control Tyrode solution under artificial ventilation. The heart was dissected and its beat stopped by switching the perfusate to a nominally Ca²⁺-free Tyrode solution. The heart was then perfused with the nominally Ca²⁺-free Tyrode solution containing collagenase (0·4 mg ml^-1, Sigma Type I) for 15 min. After perfusion of the heart with a modified Kraft-Brühe (KB) solution (Isenberg & Klöckner, 1982) to wash out the collagenase, the left ventricle was cut into small pieces and the myocytes were dispersed into the modified KB solution. The isolated myocytes were transferred to 5 mM Hepes-buffered minimal essential medium (MEM; Dainippon Pharmaceutical Co. Ltd, Japan; pH = 7·4) and used for experiments within 8 h.

Electrophysiology

Inside-out 'macro patches' were formed as described in our recent study (Fujioka et al. 2000). An ion concentration jump of cytoplasmic solution was achieved using a theta capillary mounted on a piezo translator (Fujioka et al. 2000). The holding potential was 0 mV. The membrane current was filtered at 50-500 Hz using a low-pass filter, and sampled at 50-100 Hz with an A/D converter (ADX-98H, Canopus, Japan; or ADM-640AT, Micro Science, Japan). The current-voltage (I-V ) relationship was recorded using ramp voltage pulses (dV/dt = 0·72 V s^-1) as previously described (Fujioka et al. 1998), and the membrane current was filtered at 500 Hz and sampled at 1·6 kHz.

The temperature of the cytoplasmic solution at the theta capillary outlet was 36-37°C.

Solutions and chemicals

The control Tyrode solution contained (mM): NaCl, 140; KCl, 5·4; CaCl₂, 1·8; MgCl₂, 0·5; NaH₂PO₄, 0·33; glucose, 5·5; and Hepes, 5 (pH = 7·4/NaOH). The modified KB solution (high-K⁺, low-Cl^- solution) contained (mM): KCl, 25; glutamate, 70; KH₂PO₄, 10; taurine, 10; EGTA, 0·5; glucose, 11; and Hepes, 10 (pH = 7·3/KOH).

The compositions of the pipette and cytoplasmic solutions were essentially the same as those described previously (Fujioka et al. 2000). The pipette solution used to record the outward I_Na-Ca contained (mM): N-methyl-D-glucamine (NMDG), 100; aspartate, 100; Hepes, 5; TEA-Cl, 20; ouabain, 0·05; CaCl₂, 5; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0·002 (pH = 7·4/NMDG). The pipette solution used to record the inward I_Na-Ca contained (mM): NaOH, 100; aspartate, 100; Hepes, 5; TEA-Cl, 20; ouabain 0·05; EGTA, 0·1; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0·002 (pH = 7·4/NMDG). The standard pipette solution used to record both the outward and inward I_Na-Ca in a patch contained (mM): NaOH, 145; aspartate, 145; Hepes, 5; TEA-Cl, 20; ouabain 0·05; CaCl₂, 2; MgCl₂, 2; CsCl, 2; BaCl₂, 2; and nicardipine, 0·002 (pH = 7·4/HCl).

The standard cytoplasmic solution with 100 mM Na⁺ contained (mM): NaOH, 100; EGTA, 10; Hepes, 20; aspartate, 100; TEA-Cl, 20; CsCl, 20; CaCl₂, 8·79; and MgCl₂, 1·11 (pH = 7·2/NMDG). The [Na⁺]_i was changed by replacing Na⁺ with Li⁺. The free Ca²⁺ and Mg²⁺ concentrations were calculated to be 1·0 µM and 1·0 mM, respectively, using software developed by Bers et al. (1994). The free Mg²⁺ concentration was always fixed at 1 mM when the free Ca²⁺ concentration was varied.

I_Na-Ca was isolated as Na⁺_i- or Ca-induced current. As demonstrated in our previous studies (Fujioka et al. 2000), background current contamination of I_Na-Ca is small under the present experimental conditions.

The relationship between the amplitude of I_Na-Ca and a given ion concentration was obtained by fitting the Hill equation to data:

where I_max is the maximum current, [C] is the Na⁺ or Ca²⁺ concentration, n_H is the Hill coefficient and K_h is the half-maximal concentration.

Regulatory Ca dependence was determined by adding I_Na-Ca in the absence of Ca (I_0Ca) to the Hill equation as follows:

To study the relationship between the ratio of steady-state I_Na-Ca to peak I_Na-Ca (F_ss) and [Ca²⁺]_i, the following equation was used:

where F_ss,max is the maximal F_ss value and F_ss,0Ca is the F_ss value in the absence of regulatory Ca.

In the pooled data, data from each patch were normalized to the fitted maximal value (I_max or F_ss,max). All statistical data are shown as means ± S.D.

	RESULTS

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Cytoplasmic ion dependencies of the transport reaction

To characterize the cytoplasmic ion-binding site of the exchanger, the dependence of I_Na-Ca on Ca was studied by recording the Ca-induced inward I_Na-Ca (forward mode of the exchange). When the pipette solution contained 100 mM Na⁺ (Na⁺_o) and 0 mM Ca²⁺ (Ca), application of 1, 10 and 30 µM Ca induced inward I_Na-Ca, as shown in Fig. 1. The onset time course of the current was usually determined by the speed of solution change, and was almost instantaneous (Fujioka et al. 2000). In some patches, as shown in Fig. 1A, a slow and small activation phase lasting 3-5 s followed the initial current jump. Difference currents in the absence and presence of 1, 10 and 30 µM Ca are plotted in Fig. 1B. The I-V relationship was exponential, unlike the almost linear I-V relationship observed in the giant membrane patch (Matsuoka & Hilgemann, 1992). The [Ca²⁺]_i dependence of the inward I_Na-Ca is shown in Fig. 1C. The amplitude of I_Na-Ca was measured at various [Ca²⁺]_i at 0 mV, and normalized to a fitted maximal value in each patch. The K_h for Ca was 7·3 µM and n_H was 1·7.

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Figure 1. Inward INa-Ca A, Ca2+i-induced inward INa-Ca (100 mM Na, 0 mM Ca2+o and 0 mM Na+i). Ca2+i was applied during the period indicated below the traces. Currents induced by 1, 10 and 30 µM Ca2+i are shown superimposed. B, I-V relationships of the Ca2+i-induced INa-Ca. Difference currents in the presence and absence of Ca2+i are shown. C, [Ca2+]i dependence of inward INa-Ca. The number of patches was 11-15 at each [Ca2+]i. The continuous line is a fitted function.

The affinity of the ion-binding site for Na⁺_i was studied by measuring the outward I_Na-Ca (reverse mode of the exchange). In the presence of 0 mM Na⁺_o and 5 mM Ca, application of 6-100 mM Na⁺_i induced an outward I_Na-Ca. The current onset was within the solution change. The current rapidly inactivated (Na⁺-dependent inactivation; Hilgemann et al. 1992b), so that the steady-state currents almost overlapped at [Na⁺]_i greater than 25 mM. The I-V relationships of the Na⁺_i-induced current near its peak (0·5 s after the Na⁺_i application) are plotted in Fig. 2B. The I-V relationships were relatively linear, and similar to those observed for the bleb exchanger (Matsuoka & Hilgemann, 1992). The [Na⁺]_i dependence of the peak current is plotted in Fig. 2C (; n = 3). The K_h for Na⁺_i and n_H were 21·3 mM and 2·1, respectively. The apparent Na⁺_i affinity of the steady-state current (; n = 3) tended to be higher than that of the peak current. The K_h for Na⁺_i was 6·7 mM when n_H was fixed at 1 (dotted line). This finding indicates that the apparent affinity for Na⁺_i depends on the Na⁺-dependent inactivation.

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Figure 2. Outward INa-Ca A, Na+i-induced outward INa-Ca (0 mM Na, 5 mM Ca2+o and 1 µM Ca2+i). Na+i was applied during the period indicated below the traces. Currents induced by 6, 12, 25, 50 and 100 mM Na+i are shown superimposed. B, I-V relationships of the Na+i-induced INa-Ca. Difference currents in the presence and absence of 12, 25 and 100 mM Na+i are shown. The I-V relationships in the presence of Na+i were obtained 0·5 s after Na+i application ( in the chart recording shown in the inset). C, [Na+]i dependence of outward INa-Ca. Current amplitudes were measured at the peak () and steady state (). The continuous and dotted lines represent fitted Hill equations at the peak and steady state, respectively. Three patches were studied at each [Na+]i.

Na⁺-dependent inactivation

Na⁺-Ca²⁺ exchange activity is influenced by Na⁺-dependent inactivation, as demonstrated in Fig. 2. The kinetics of Na⁺-dependent inactivation were therefore studied. In a majority of the patches, Na⁺-dependent inactivation could be fitted by a single exponential function (Fig. 3A; continuous line). The time constant () at 100 mM Na⁺_i was 1·5 ± 0·4 s (n = 25; [Ca²⁺]_i = 1 µM), and the ratio of steady-state current to peak current (F_ss) was 0·27 ± 0·11 (n = 25). The time constant was about half of that observed for the exchanger of cardiac bleb membrane ( = 2·8 ± 1·1 s with 8 mM Ca; Hilgemann et al. 1992b), and one-sixth of that observed for NCX1.1 expressed in oocytes ( = 8·9 ± 2·3 s with 8 mM Ca; Matsuoka et al. 1997).

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Figure 3. Na+-dependent inactivation A, single exponential fit of the Na+i-dependent inactivation. A fitted exponential (continuous line) was superimposed over the 100 mM Na+i-induced INa-Ca (dotted trace); 0 mM Na, 5 mM Ca2+o and 1 µM Ca2+i. B, relationship between Fss and [Na+]i. Kh was 13·5 mM, nH was 2·0 and the saturating Fss value was 0·14. C, [Na+]i dependence of the reciprocal of the time constant (1/). Kh was 21 mM, nH was 2·6 and the maximum value was 1·0 s-1.

The [Na⁺]_i dependence of the inactivation is summarized in Fig. 3B and C. The F_ss value decreased as [Na⁺]_i was increased, and became nearly saturated at 50 mM Na⁺_i. The K_h for Na⁺_i was 13·5 mM (n_H = 2·0) when F_ss was assumed to be 1 at 0 mM Na⁺_i. Reciprocal values of the time constant (1/) also increased as [Na⁺]_i was increased and became saturated at 50 mM Na⁺_i (K_h = 21 mM and n_H = 2·6). These properties are similar to those observed for the exchanger in cardiac bleb membranes and NCX1.1 expressed in oocytes (Matsuoka et al. 1996).

Recovery from the Na⁺-dependent inactive state was studied using a paired-pulse protocol (Fig. 4). The outward I_Na-Ca was twice induced by 50 mM Na⁺_i and the interval between Na⁺_i applications was changed from 50 to 1 s. As the interval shortened, the second current decreased. The ratio of the amplitude of the second peak to that of the first reflects the fraction of the exchanger that is in an active state immediately after the recovery interval. This ratio is plotted in Fig. 4B as a function of the interval period (). The amplitude of the first current increased slightly during the course of the experiment, but the F_ss values () did not change significantly. Therefore, this spontaneous increase in current amplitude could not have significantly affected our measurements. The recovery was fitted by an exponential function and was 7·3 s (5·4 ± 1·2 s; n = 4).

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Figure 4. Recovery from Na+-dependent inactivation A, paired-pulse protocol. The outward INa-Ca was first induced by 50 mM Na+i, followed by a second set of currents induced by a second application of 50 mM Na+i after an interval of 1-50 s; 0 mM Na, 5 mM Ca2+o and 1 µM Ca2+i. B, fraction of the active exchanger. The ratio of the second peak to the first peak is plotted against interval time (). Fss values for the first current are plotted at time 0 (). The continuous line is a fitted exponential: 0·17 + 0·83(1 - e-t/7·3), where t is the interval period (in s).

Since the inward I_Na-Ca was almost time independent in the absence of Na⁺_i (Fig. 1), the inactivation probably occurs due to the presence of Na⁺_i, as was first described for the exchanger in the giant membrane patch (Hilgemann et al. 1992b). If this hypothesis can also be applied to the exchanger in the macro patch, then inward I_Na-Ca (forward mode of the exchange) should be inactivated by the presence of Na⁺_i. In Fig. 5, the outward and inward I_Na-Ca were both recorded in a patch (145 mM Na⁺_o and 2 mM Ca). The left panel shows a control membrane current obtained in the absence of both Na⁺_i and Ca. In the right panel, an inward I_Na-Ca was first induced by 1 µM Ca. The difference between the control and the inward current was -1·0 pA. The exchange immediately converted to reverse mode upon the application of 50 mM Na⁺_i, and an outward I_Na-Ca was generated (peak amplitude = +2·0 pA). This current decayed rapidly until it reached a steady level (+0·6 pA, F_ss = 0·3). Upon removal of Na⁺_i, the exchange switched back to forward mode and an inward I_Na-Ca was again induced. After an initial jump in current, the inward I_Na-Ca exhibited a slow increase. This slow reactivation logically reflects its recovery from the inactive state. The ratio of the initial inward I_Na-Ca (-0·4 pA) to the steady-state I_Na-Ca (-1·0 pA) was 0·4, suggesting that 60 % of the exchanger entered the inactive state during the Na⁺ application. This ratio is close to the F_ss value of the outward I_Na-Ca (0·3), which suggests that 70 % of the exchanger entered into the inactive state. These findings support the idea that the exchanger enters an inactive state from the Na⁺_i-loaded configuration (Hilgemann et al. 1992b).

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Figure 5. Recovery of inward INa-Ca from Na+-dependent inactivation The pipette solution contained 145 mM Na and 2 mM Ca2+o. Left panel, control membrane current in the absence of both Na+i and Ca2+i. Right panel, inward and outward INa-Ca were both induced by cytoplasmic solution changes indicated below the trace. The dotted line represents the mean control current. See text for details.

Ca²⁺ activation

So far the Na⁺-dependent inactivation has been studied at a constant [Ca²⁺]_i (1 µM). Ca augmented the outward I_Na-Ca in the giant membrane patch from the bleb (Hilgemann, 1990) and the oocyte expressing NCX1.1 (Matsuoka et al. 1993). The effect of Ca on I_Na-Ca was therefore studied. With 0 mM Na⁺_o and 5 mM Ca in the pipette solution, 100 mM Na⁺ was applied to induce an outward I_Na-Ca at [Ca²⁺]_i ranging from 0 to 30 µM. The outward I_Na-Ca was very small in the absence of Ca, but the peak and steady-state currents became augmented as [Ca²⁺]_i was increased. The increase in peak current was attributed to the exchanger's recovery from a Na⁺-independent inactive state, termed the I₂ state by Hilgemann et al. (1992a). The Na⁺_i-dependent inactivation (I₁ inactivation) was attenuated by an increase in [Ca²⁺]_i to 30 µM. It should be noted that the holding current in the absence of Na⁺_i did not change as [Ca²⁺]_i was increased, which suggests that the background conductance was not affected by Ca. The I-V relationships of the Na⁺-induced outward I_Na-Ca at various [Ca²⁺]_i are shown in Fig. 6B. The amplitude of I_Na-Ca increased at all membrane potentials.

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Figure 6. Ca2+i-dependent activation A, outward INa-Ca at different regulatory [Ca2+]i (0 mM Na and 5 mM Ca2+o). Outward INa-Ca was induced by 100 mM Na+i in the continuous presence of 0, 0·1, 1 and 30 µM Ca2+i. B, representative I-V relationships of INa-Ca at different regulatory [Ca2+]i. The I-V relationships in the presence of Na+i were measured near the peak ( in the inset). Difference currents in the absence and presence of 100 mM Na+i are shown (0, 0·1 and 1 µM Ca2+i). The inset shows a chart recording at 1 µM Ca2+i.

The [Ca²⁺]_i dependencies of the peak and steady-state outward I_Na-Ca are summarized in Fig. 7A and B (n = 7). The peak amplitude mainly reflects I₂ regulation, because it is assumed that no exchanger exists in the I₁ state before Na⁺_i is applied. The K_h for activation of the peak current by Ca was 0·2 µM (n_H = 0·8). The affinity for Ca was tenfold lower at the steady state than at the peak current (K_h = 2·0 µM and n_H = 1·6).

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Figure 7. Regulatory [Ca2+]i dependence of outward INa-Ca A, [Ca2+]i dependence of the peak current. Normalized peak current (Ipeak; ) is plotted against [Ca2+]i. The continuous line is a fitted function. Imax = 1·01, Kh = 0·2 µM, nH = 0·80 and I0Ca = 0·00. B, [Ca2+]i dependence of the steady-state current. Normalized steady-state current (Iss; ) is plotted against [Ca2+]i. The continuous line is a fitted function. Imax = 0·94, Kh = 2·0 µM, nH = 1·60 and I0Ca = 0·04. C, [Ca2+]i-Fss relationship. Fss,max = 0·69, Kh = 2·2 µM, nH = 1·87 and Fss,0Ca = 0·14. D, [Ca2+]i- relationship. The reciprocal of is plotted against [Ca2+]i.

The [Ca²⁺]_i dependence of I₁ inactivation was studied by plotting F_ss values against [Ca²⁺]_i (Fig. 7C). The K_h for Ca was 2·2 µM (n_H = 1·9). This value is compatible with steady-state [Ca²⁺]_i dependence (Fig. 7B). Therefore, steady-state Ca²⁺ dependence is primarily determined by the I₁ inactivation. At saturated [Ca²⁺]_i (30 µM), a small transient current component was always observed (F_ss = 0·82 ± 0·05), suggesting that regulatory Ca cannot induce a full recovery from I₁ inactivation. The reciprocal of the time constant (1/) of the I₁ inactivation increased as [Ca²⁺]_i was increased, but did not become saturated (Fig. 7D).

The time course of deactivation and activation by Ca is shown in Fig. 8. The steady-state current was augmented by increasing [Ca²⁺]_i to 5 µM. The pipette solution contained 0 mM Na⁺_o and 5 mM Ca. At steady state, after 50 mM Na⁺_i was applied, 5 µM Ca was removed (Fig. 8A) and reapplied (Fig. 8B) in the continuous presence of 50 mM Na⁺_i. The activation and deactivation processes could be fitted by two exponentials (continuous lines), which are superimposed on the current traces (dotted traces). In the lower panels of Fig. 8, the two exponentials are shown in semilogarithmic plot (two continuous lines). The original current after subtraction of the steady-state component is shown (right dotted data), together with the fast component (left dotted data), which was obtained by subtraction of the fitted slow component from the original current. The time constants of fast and slow deactivation were 0·4 and 3·8 s, respectively, and those of fast and slow activation were 0·1 and 3·2 s, respectively. We observed a delay of Ca diffusion (about 0·1-0·4 s) when the [Ca²⁺]_i was increased from 0 to 1 µM, which could be due to Ca²⁺ trapping by EGTA (Fujioka et al. 2000). Therefore, the actual fast component of activation might be much faster than our estimation. In a total of four patches, the time constants for the fast and slow components were 0·19 ± 0·16 and 2·10 ± 1·25 s, respectively, for deactivation, and 0·08 ± 0·06 and 2·39 ± 1·39 s, respectively, for activation.

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Figure 8. Time course of outward INa-Ca responding to the removal and addition of regulatory Ca2+i The pipette solution contained 0 mM Na and 5 mM Ca2+o. [Na+]i = 50 mM. A, removal of regulatory Ca2+i. The current response to the removal of 5 µM Ca2+i is shown (dotted data). Fitted exponentials are superimposed (continuous line). The lower panel depicts the semilogarithmic plots of the membrane current and the fitted exponentials. B, readdition of regulatory Ca2+i. The current response to the addition of 5 µM Ca2+i is shown (dotted data). The data are presented in a similar manner to A. See text for details.

These data are not consistent with previous data obtained in the giant membrane patch from the bleb (Hilgemann et al. 1992b), in which only a slow component was observed. With regard to the cloned NCX1.1, this process involved two components, but its overall time course was extremely slow (Matsuoka et al. 1993, 1995, 1997).

	DISCUSSION

Top Abstract Introduction Methods Results Discussion References

In this study, we investigated details of regulation kinetics and cytoplasmic ion dependencies of the native Na⁺-Ca²⁺ exchanger in inside-out macro patches excised from intact ventricular myocytes. The exchanger in both the forward and the reverse mode inactivated as [Na⁺]_i was increased (Na⁺-dependent inactivation: I₁). Ca augmented the peak outward I_Na-Ca, most probably by facilitating the exchanger's recovery from Na⁺-independent inactivation (I₂). In addition, Ca increased steady-state outward I_Na-Ca by attenuating I₁ inactivation. The Ca affinity of I₂ regulation (K_h = 0·2 µM) was approximately one log unit higher than that of I₁ regulation (K_h = 2·2 µM). These properties are similar to those of the exchanger in the cardiac bleb, and NCX1.1 expressed in the oocyte. However, the speed of regulation was substantially faster in the macro patch. Our data suggest that the Na⁺_i- and Ca-dependent regulation mechanisms provide negative feedback under physiological conditions. In particular, the Ca regulation mechanism may be important in the prevention of excessive Ca²⁺ extrusion via Na⁺-Ca²⁺ exchange.

Regulation kinetics

Regulation kinetics have been systematically studied in the giant membrane patch excised from the cardiac bleb, and the NCX1.1-expressing oocyte. When compared with studies performed under similar experimental conditions (100 mM Na⁺_i and 1 µM Ca), of I₁ inactivation (1·5 ± 0·4 s with 5 mM Ca) in the macro patch was about half of that for the bleb giant patch (2·8 ± 1·1 s with 8 mM Ca; Hilgemann et al. 1992b), and one-sixth of that for NCX1.1 (8·9 ± 2·3 s with 8 mM Ca; Matsuoka et al. 1997). The degree of I₁ inactivation (F_ss) was 0·27 ± 0·11 in the macro patch, which was similar to the value obtained from the bleb giant membrane patch. For NCX1.1, the degree of I₁ inactivation tended to be smaller (F_ss = 0·4 ± 0·1; Matsuoka et al. 1997).

The steady-state outward I_Na-Ca responded much faster to the removal and reapplication of regulatory Ca. The half-time to reach steady state (t_½) was 0·47 ± 0·19 and 0·42 ± 0·24 s upon the removal and readdition of 5 µM Ca, respectively ([Na⁺]_i = 50 mM). In the bleb giant patch, the t_½ of both reactions was 5 s ([Na⁺]_i = 100 mM and [Ca²⁺]_i = 2 or 0·3 µM; Hilgemann, 1990; Hilgemann et al. 1992a). The response of NCX1.1 was much slower, with a t_½ of 10 s ([Na⁺]_i = 100 mM and [Ca²⁺]_i = 1 µM; Matsuoka et al. 1997). The activation by the I₂ regulation process should be rapid, because the activation of inward I_Na-Ca was usually instantaneous (Fig. 1A). Therefore, the fast component upon the removal and addition of regulatory Ca²⁺ may reflect the I₂ process. The slow component probably reflects the regulatory action of Ca on I₁ inactivation. A site-directed mutagenesis study in the exchanger inhibitory peptide (XIP) region supports this idea (Matsuoka et al. 1997). In wild-type, the response of I_Na-Ca upon the removal and addition of regulatory Ca²⁺ consisted of slow and fast components. In mutants that lacked I₁ inactivation, the fast component became predominant.

The experimental conditions, such as the temperature and composition of solutions, were slightly different among the three experimental systems. The temperature was 36-37°C in the cardiac macro patch, 34-36°C in the bleb giant patch and 30°C in the NCX1.1-expressing oocyte. In our preliminary experiments, we measured I_Na-Ca from the cardiac bleb at the same temperature (37°C), using experimental solutions of the same composition (5 mM Ca) as that for the present macro patch experiments. The I₁ inactivation ( = 3 to 4·5 s with 100 mM Na⁺) was still slower than that for the macro patch (data not shown). The speed of I₁ inactivation of NCX1.1 increased slightly when the temperature was raised to 35°C, but was not comparable to that of the cardiac macro patch. Therefore, the temperature and composition of the solution cannot fully account for the observed differences.

NCX1.1 was cloned from canine heart, while both the macro patch and the bleb giant patch were excised from guinea-pig ventricular cells. However, the amino acid sequence of the canine NCX1.1 shared 98 % identity with that of the guinea-pig exchanger (Tsuruya et al. 1994). Therefore, the differences are probably not due to primary structure.

The environment surrounding the exchanger, such as membrane lipid composition, the amount of cytoplasmic ATP and other unknown factors, may significantly influence its regulation kinetics. Membrane-related lipids, such as phosphatidylserine and phosphatidylinositol-4',5'-bisphosphate (PIP₂), stimulate I_Na-Ca in the bleb giant patch by attenuating I₁ inactivation (Hilgemann & Collins, 1992; Hilgemann & Ball, 1996). The composition of the membrane lipids may vary among the three patch membranes. Hilgemann & Ball (1996) have proposed that ATP stimulates the exchanger by increasing the formation of PIP₂. In our preliminary experiments in the macro patch, 1 mM cytoplasmic MgATP had only a small stimulatory effect on I_Na-Ca, while ATP strongly augmented I_Na-Ca in the bleb membrane patch (Hilgemann, 1990) and did not stimulate the I_Na-Ca of NCX1.1 under control conditions (He et al. 1998). These findings support the above hypothesis.

In this study, the Ca regulation kinetics were only studied with regard to the outward I_Na-Ca (reverse mode), because the regulatory and permeating actions of Ca can be easily separated. The regulatory action of Ca on the inward I_Na-Ca (forward mode) was demonstrated in a site-directed mutagenesis study (Matsuoka et al. 1995). Several mutations within the regulatory Ca²⁺-binding regions altered the Ca affinity of the inward I_Na-Ca. Therefore, it is likely that Ca also regulates the inward I_Na-Ca (forward mode) in the native exchanger.

We suggested recently that the stoichiometry of the cardiac exchanger is 4 or variable (Fujioka et al. 2000). The data presented here do not provide direct evidence to support this finding. However, our data provide clues to an important problem raised by a stoichiometry of 4. Namely, if the stoichiometry is 4, one would expect the steady-state intracellular Ca²⁺ concentration to fall to a extremely low level, because the 4Na⁺:1Ca²⁺ exchange should provide a stronger driving force for Ca²⁺ extrusion than that of the 3Na⁺:1Ca²⁺ exchange. However, the Ca-regulation mechanism may provide negative feedback. When the intracellular Ca²⁺ concentration falls into the submicromolar range, the exchanger should rapidly deactivate to prevent excessive Ca²⁺ extrusion. In fact, the 'off' time course of Ca regulation is of the order of a hundred milliseconds, and its range of action corresponded to the physiological concentrations of intracellular Ca²⁺. Therefore, it is likely that Ca regulation plays an important role in a beat-to-beat manner. The physiological relevance of these regulatory processes was demonstrated in a study involving transgenic mice (Maxwell et al. 1999). In transgenic mice overexpressing a deletion mutant of NCX1.1 (680-685), in which the I₁ and I₂ regulations were both eliminated, the potentiation of post-rest force was greater than in wild-type overexpressing mice. These data suggest that regulatory processes function in wild-type under physiological conditions, although the underlying mechanism governing this phenomenon is unknown.

Cytoplasmic ion dependence

Cytoplasmic ion dependencies were similar among the three membrane patches. The apparent Na⁺_i affinity of the transport cycle was evaluated by measuring the peak outward I_Na-Ca immediately after Na⁺_i application at a nearly saturating concentration of Ca for I₂ regulation (1 µM). We estimated that 80 % or more of the exchanger recovers from the I₂ inactive state (see Fig. 7A). The K_h for Na⁺_i was 21·3 mM (n_H = 2·1). In the bleb giant patch, the K_h was 16 mM (n_H = 2·6, [Ca²⁺]_i = 0·3 µM; Hilgemann, 1990) and in NCX1.1 it was 28·1 mM (Matsuoka et al. 1997). The apparent Ca affinity of the transport cycle was evaluated by measuring the inward I_Na-Ca in the absence of Na⁺_i. The K_h for Ca was 7·3 µM (n_H = 1·7). This value mainly reflects that of the transport cycle, because the absence of Na⁺_i suppresses I₁ inactivation and the Ca affinity of I₂ regulation is one log unit higher. The observed K_h value was slightly larger than that for the bleb giant patch (3·4 µM, n_H = 1·0; Hilgemann et al. 1992b), but close to that for NCX1.1 expressed in oocytes (6·9 µM, n_H = 1·1; Matsuoka et al. 1995). Therefore, the ion dependencies of the transport cycle are similar among the three different membrane patches, though the exchanger of the bleb membrane patch has a tendency to exhibit higher affinities for Na⁺_i and Ca.

The apparent Na⁺_i affinity of I₁ inactivation was determined by examining the [Na⁺]_i-F_ss relationship ([Ca²⁺]_i = 1 µM). The K_h was 13·5 mM (n_H = 2·0), which was smaller than the K_h value for the transport cycle (21·3 mM). This tendency was also observed in the giant patch from the cardiac bleb and the NCX1.1-expressing oocytes. For NCX1.1, the K_h was 8·1 mM (Matsuoka et al. 1997). The apparent Ca affinity of I₂ inactivation was determined by the [Ca²⁺]_i-peak outward I_Na-Ca relationship. The K_h for Ca was 0·2 µM (n_H = 0·8), which is similar to the value obtained in the bleb giant patch (0·1 µM; Hilgemann, 1990) and in the NCX1.1-expressing oocyte (0·2 µM; Matsuoka et al. 1997). The apparent Ca affinity of I₁ inactivation was evaluated by the [Ca²⁺]_i-F_ss relationship. The K_h for Ca was 2·2 µM (n_H = 1·9). In the bleb giant patch, the K_h was 1·8 µM (n_H = 1·4 with 90 mM Na⁺; Hilgemann et al. 1992a). In the oocyte giant patch, the value was 2·3 µM (Matsuoka et al. 1997). Thus, the ion dependencies involved in I₁ and I₂ regulation are quite similar among the three membrane patches.

Model consideration

The regulation kinetics of the exchanger in the bleb giant membrane patch were well simulated by a consecutive 3Na⁺:1Ca²⁺ exchange model with two independent inactive states (I₁ and I₂; Hilgemann et al. 1992a,b). Here, we constructed a 4Na⁺:1Ca²⁺ exchange model to test whether a 4Na⁺:1Ca²⁺ exchange is possible in terms of the ion dependence and regulation kinetics of I_Na-Ca. The model consisted of a consecutive 4Na⁺:1Ca²⁺ exchange cycle and two inactive states. A two-state consecutive cycle was used for simplicity. Details of this model are described in the Appendix.

Figure 9A shows a simulated inward I_Na-Ca and its [Ca²⁺]_i dependence, corresponding to Fig. 1. The current was almost time independent. Figure 9B shows a simulated outward I_Na-Ca. In the lower panel, the [Na⁺]_i dependence of the simulated peak (continuous line) and steady-state I_Na-Ca (dotted line) are presented. Corresponding experimental data can be found in Fig. 2. [Na⁺]_o and [Ca²⁺]_o dependencies were also simulated and are shown in Fig. 9C and D. The experimental data were obtained from the whole-cell clamped experiments of Kimura et al. (1987) and Ehara et al. (1989). The affinity for Ca of this model was slightly lower than that stated in the whole-cell experiments.

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Figure 9. Simulation of cytoplasmic and extracellular ion dependencies A, simulated inward INa-Ca. [Na+]o = 100 mM, [Ca2+]o = 0 mM and [Na+]i = 0 mM. One, 10 and 30 µM Ca2+i-induced inward INa-Ca are shown in the upper panel, and correspond to Fig. 1A. The simulated [Ca2+]i dependence is shown in the lower panel (continuous line). Experimental data () are taken from Fig. 1C. B, simulated outward INa-Ca. [Na+]o = 0 mM, [Ca2+]o = 5 mM and [Ca2+]i = 1 µM. Six, 12, 25, 50 and 100 mM Na+i-induced INa-Ca are shown in the upper panel. Corresponding experimental data are in Fig. 2A. The simulated [Na+]i dependence of the peak (continuous line) and steady-state (dotted line) currents is shown in the lower panel. Experimental data of the peak current () are taken from Fig. 2C. C, simulated [Na+]o dependence. [Ca2+]o = 1 mM, [Na+]i = 0 mM and [Ca2+]i = 430 nM. Data () are from Kimura et al. (1987). D, simulated [Ca2+]o dependence. [Na+]o = 140 mM, [Na+]i = 40 mM and [Ca2+]i = 55 nM. Data () are from Ehara et al. (1989).

A simulation of the augmentation of the outward I_Na-Ca by regulatory Ca is shown in Fig. 10A. The Ca affinity of the peak current (continuous line) was higher than that of the steady-state current (dotted line) by about one log unit. Figure 10B shows that entrance into and recovery from I₁ inactivation were well simulated. The ratio of the inward I_Na-Ca to the peak outward I_Na-Ca was about 1, while the experimental value was about 0·5 (see Fig. 5). This is probably because the affinity for Ca is lower in this model. Figure 10C shows the simulation of the response of I_Na-Ca to regulatory Ca. The time course was similar to that of the corresponding data (Fig. 8).

		View larger version [in this window] [in a new window]
Figure 10. Simulation of INa-Ca A, simulated regulatory [Ca2+]i dependence of outward INa-Ca. [Na+]o = 0 mM, [Ca2+]o = 5 mM. The upper panel shows 100 mM Na+i-induced currents at 0, 0·1, 1 and 30 µM Ca2+i. Corresponding data are in Fig. 6A. The [Ca2+]i dependence of the peak (continuous line) and steady-state (dotted line) currents is simulated in the lower panel. Experimental data of the peak () and steady-state currents () are taken from Fig. 7A and B. The simulation and experimental data were normalized to the amplitude obtained at 10 µM Ca2+i. B, simulated recovery from Na+-dependent inactivation. [Na+]o = 145 mM, [Ca2+]o = 2 mM and [Ca2+]i = 1 µM. Corresponding data are in Fig. 5. C, simulated responses to the removal and readdition of regulatory Ca2+. [Na+]o = 0 mM, [Ca2+]o = 5 mM and [Na+]i = 50 mM. Corresponding data are in Fig. 8.

The model was able to simulate well experimental data obtained in the macro patch, suggesting that 4Na⁺:1Ca²⁺ exchange is possible in terms of ion dependence and regulation kinetics. However, this model could not simulate the actual I-V relationship of the outward I_Na-Ca (Fig. 2), which yields a relatively linear relationship. To reconstruct the accurate I-V relationship, it may be necessary to hypothesize electrogenic ion occlusions and electrogenic Ca⁺ translocation, as described by Matsuoka & Hilgemann (1992).

Figure 11 shows a state diagram of the Na⁺-Ca²⁺ exchange model. E₁ and E₂ are states in which the ion-binding site faces the cytoplasmic and extracellular side, respectively. E₁·4Na is the cytoplasmic 4Na⁺-loaded exchanger and E₁·Ca the cytoplasmic 1Ca²⁺-loaded exchanger. E₂·4Na is the extracellular Na⁺-loaded exchanger and E₂·Ca is the extracellular Ca²⁺-loaded exchanger. E₁·0 and E₂·0 are the states in which no ion binds to the exchanger. The 4Na⁺-loaded exchanger bears two positive charges and the Na⁺ translocation step is electrogenic. In this study, we simulated I_Na-Ca at a membrane potential (V_m) of 0 mV. Na⁺ and Ca²⁺ ions were considered to bind to the E₁ and E₂ states of the exchanger in a sequential and instantaneous manner (Fig. 11B). Within the E₁ state, the fractions of exchanger that locate in E₁·4Na (F_E1·4Na) and E₁·Ca (F_{E1 · Ca}) are as follows:

where D_i = Na⁴_i × K_ci + Na³_i × K_4ni × K_ci + Na²_i ×

Na_i and Ca_i are the cytoplasmic Na⁺ and Ca²⁺ concentrations, respectively; and K_1ni, K_2ni, K_3ni, K_4ni and K_ci are the dissociation constants of the 1st Na⁺_i, 2nd Na⁺_i, 3rd Na⁺_i, 4th Na⁺_i and Ca, respectively. K_ci = 0·01 mM, K_1ni = 700 mM, K_2ni = 9 mM, K_3ni = 9 mM and K_4ni = 8 mM. In the E₂ state, the fractions of exchanger that locate in E₂·4Na (F_E2·4Na) and E₂·Ca (F_{E2· Ca}) can be calculated in a similar manner.

		View larger version [in this window] [in a new window]
Figure 11. Na+-Ca2+ exchange model A, state diagram of the Na+-Ca2+ exchange model. B, ion binding in the E1 state. See text for details.

To maintain microscopic reversibility, we postulated the following relationships between the dissociation constants of the extracellular ions and those of the intracellular ions.

where K_1no, K_2no, K_3no, K_4no and K_co are the dissociation constants of the 1st Na⁺_o, 2nd Na⁺_o, 3rd Na⁺_o, 4th Na⁺_o and Ca, respectively, and asym is a constant (= 80).

Rate constants (s^-1) for the transport cycle are as follows:

where k_Vm = e^2V_m/53·08, and V_m = 0 mV.

The exchanger enters into the I₁ inactive state from the E₁·4Na state. We assumed that the exchanger enters into the I₂ inactive state from any conformation of the E₁ state, but not from the E₂ state, in order to reconstruct the whole-cell experimental data (Matsuoka & Hilgemann, 1994). To simulate the attenuation of I₁ inactivation by Ca and the I₂ regulation, we assumed an instantaneous binding of regulatory Ca²⁺, as described in the previous model (Hilgemann et al. 1992a). The fraction of exchanger that regulatory Ca²⁺ bound (F_Ca(act)) is:

where K_Ca(act) (= 0·004 mM) is the dissociation constant of regulatory Ca²⁺. The forward (₁) and backward (₁) rate constants for entry into the I₁ state were obtained as follows:

₁ = F_E1·4Na(F_Ca(act) × _1,Ca(on) + (1 - F_Ca(act)) × _1,Ca(off)),

₁ = F_Ca(act) × _1,Ca(on) + (1 - F_Ca(act)) × _1,Ca(off),

where _1,Ca(off) and _1,Ca(off) are rate constants in the absence of regulatory Ca²⁺, and _1,Ca(on) and _1,Ca(on) are rate constants in the presence of regulatory Ca²⁺. _1,Ca(off) = 1·5 s^-1, _1,Ca(off) = 0·0005 s^-1, _1,Ca(on) = 2 s^-1 and _1,Ca(on) = 1·2 s^-1.

Similarly, the forward (₂) and backward (₂) rate constants for entry into the I₂ state were calculated as follows:

₂ = F_Ca(act) × _2,Ca(on) + (1 - F_Ca(act)) × _2,Ca(off),

₂ = F_Ca(act) × _2,Ca(on) + (1 - F_Ca(act)) × _2,Ca(off),

where _2,Ca(off) = 10 s^-1, _2,Ca(off) = 0·1 s^-1, _2,Ca(on) = 0·03 s^-1 and _2,Ca(on) = 90 s^-1.

The rate of change of each state was determined as follows:

dF_E1/dt = F_E2 × (k₂ + k₃) + F_I1 × ₁ + F_I2 × ₂ -

F_E1 × (k₁ + k₄ + ₁ + ₂),

dF_I1/dt = F_E1 × ₁ - F_I1 × ₁,

dF_I2/dt = F_E1 × ₂ - F_I2 × ₂,

where F_E1, F_E2, F_I1 and F_I2 are the fractions of the exchanger in each state.

The differential equations were resolved using Runge-Kutta's method and the Na⁺-Ca²⁺ exchange current (I_Na-Ca) was obtained as follows.

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Acknowledgements

We are very grateful to Professor A. Noma for his encouragement and valuable discussion, and to Mr M. Fukao for his excellent technical support. This work was supported by a Grant-in-Aid for Scientific Research from the Ministry of Education, Science and Culture of Japan, and by a Japan Heart Foundation and IBM Japan Research Grant (to S.M.).

Corresponding author

S. Matsuoka: Department of Physiology and Biophysics, Kyoto University Graduate School of Medicine, Yoshida-Konoe, Sakyo-ku, Kyoto 606-8501, Japan.

Email: matsuoka{at}card.med.kyoto-u.ac.jp

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