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MEMBRANE TRANSPORTERS, ION CHANNELS, AND PUMPS

Dual effect of Na_i⁺ on Ca²⁺ influx through the Na⁺/Ca²⁺ exchanger in dialyzed squid axons. Experimental data confirming the validity of the squid axon kinetic model

¹Laboratorio de Biofísica, Instituto de Investigación Médica Mercedes y Martín Ferreyra, Consejo Nacional de Investigaciones Científicas y Técnicas, Córdoba, Argentina; ²Laboratorio de Fisiología Celular, Centro de Biofísica y Bioquímica, Instituto Venezolano de Investigaciones Científicas, Caracas, Venezuela; and ³Marine Biological Laboratory, Woods Hole, Massachusetts

Submitted 1 August 2007 ; accepted in final form 24 October 2007

	ABSTRACT

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
We propose a steady-state kinetic model for the squid Na⁺/Ca²⁺ exchanger that differs from other current models of regulation in that it takes into account, within a single kinetic scheme, all ionic [intracellular Ca²⁺ (Ca_i²⁺)-intracellular Na⁺ (Na_i⁺)-intracellular H_i⁺] and metabolic (ATP) regulations of the exchanger in which the Ca_i²⁺-regulatory pathway plays the central role in regulation. Although the integrated ionic-metabolic model predicts all squid steady-state experimental data on exchange regulation, a critical test for the validity of it is the predicted dual effect of Na_i⁺ on steady-state Ca²⁺ influx through the exchanger. To test this prediction, an improved technique for the estimation of isotope fluxes in squid axons was developed, which allows sequential measurements of ion influx and effluxes. With this method, we report here two novel observations of the squid axon Na⁺/Ca²⁺ exchanger. First, at intracellular pH (7.0) and in the absence of MgATP, Na_i⁺ has a dual effect on Ca²⁺ influx: inhibition at low concentrations followed by stimulation at high Na_i⁺ concentrations, reaching levels higher than those seen without Na_i⁺. Second, in the presence of MgATP, the biphasic response to Na_i⁺ disappears and is replaced by a sigmoid activation. Furthermore, the model predicts that Ca²⁺ efflux is monotonically inhibited by Na_i⁺, more pronouncedly without than with MgATP. These results are predicted by the proposed kinetic model. Although not fully applicable to all exchangers, this scheme might provide some insights on expected net Ca²⁺ movements in other tissues under a variety of intracellular ionic and metabolic conditions.

sodium/calcium exchanger

Since the simultaneous discovery of this transport mechanism in the squid axon (3) and the mammalian heart (26), both preparations have become significant tools to study its function and regulation. They were further improved by the introduction of the internal dialysis technique in the squid giant axon, whole cell and excised patch-clamp methodology in the heart, and also in heterologous systems expressing the exchangers.

Squid and heart Na⁺/Ca²⁺ exchangers show similarities and differences. The similarities are indeed striking and allow both preparations to be used in the characterization of exchanger properties and in the possible extrapolation of data to pathological conditions. These are intracellular Na⁺ (Na_i⁺) inactivation, Ca_i²⁺ regulation, intracellular H⁺ (H_i⁺) inhibition, H_i⁺- Na_i⁺ synergism, and MgATP upregulation (5). Patch-clamp experiments allow the study only of the current-producing translocation modes of the exchanger. On the other hand, the dialyzed squid giant axon and giant barnacle muscle fiber (24) are the only available preparations in which all electrogenic [extracellular Na⁺ (Na_o⁺)/Ca_i²⁺ and extracellular Ca²⁺ (Ca_o²⁺)/ Na_i⁺] and nonelectrogenic (Na_o⁺/Na_i⁺ and Ca_o²⁺/Ca_i²⁺) transport modes of the exchanger can be assayed under ionic and biochemical control of intra- and extracellular environments. Actually, the analysis of electroneutral transport modes was crucial for this. On the one hand, Na_o⁺/Na_i⁺ exchange allowed the affinity of the Ca_i²⁺-regulatory site and its interactions with cytosolic ionic and metabolic substrates to be unambiguously determined. On the other hand, it was possible to establish a voltage dependence of Ca_o²⁺/Ca_i²⁺ exchange in contrast with the voltage insensitivity of Na_o⁺/Na_i⁺ exchange (9).

At least three main kinetic models have been proposed to explain ion and ATP modulation of the Na⁺/Ca²⁺ exchanger. One of them, which accounts for H_i⁺ and (H_i⁺ + Na_i⁺) inhibition in the mammalian heart under patch-clamp conditions, was put forward by Doering and Lederer (14–16). This scheme explains well the H_i⁺ block of the outward Na⁺/Ca²⁺ exchange current in the absence of Na_i⁺ (proton block per se) and the cytoplasmic Na⁺ and intracellular pH (pH_i) interdependency in inhibiting the exchange current. The Na_i⁺-H_i⁺ synergism is the result of an increased affinity for H_i⁺ following the binding of Na_i⁺ to the exchanger. However, the binding sites were not made explicit, and any possible role of the Ca_i²⁺-regulatory site was not considered (14, 15).

Another model, also in the heart, came from excised giant patch-clamp (17–19, 21) and whole cell voltage-clamp experiments in myocytes (22). In this case, two inactive states of the carrier, I₁ and I₂, are considered. The exchanger with fully loaded Na_i⁺ transport sites can follow two routes: 1) translocation of Na⁺ to the outside or 2) entrance into an intracellular inactive state, I₁. The rate constants leading to or from I₁ are affected by the binding of Ca_i²⁺ to its regulatory site, leading to decreased inhibition; MgATP would act in a similar way. The I₂ inhibited state has no Na⁺ or Ca²⁺ bound to it, and it is precisely the binding of Ca²⁺ to its regulatory site that releases inhibition. In all cases, protons reduce the affinity for the binding of Ca²⁺ to its regulatory site.

Based on data obtained in dialyzed squid axons on unidirectional steady-state ²²Na⁺ and ⁴⁵Ca²⁺ fluxes through all partial reactions of the Na⁺/Ca²⁺ exchanger (Na_o⁺/Ca_i²⁺, Na_i⁺/Ca_o²⁺, Na_o⁺/Na_i⁺, and Ca_o²⁺/Ca_i²⁺ exchanges), we suggested a different scheme in which the Ca_i²⁺-regulatory site plays a central role in H_i⁺ interaction and metabolic upregulation by MgATP. The model predicts H_i⁺ inhibition, (H_i⁺ + Na_i⁺) synergic inhibition, and consequent Na_i⁺-dependent inactivation; it also predicts that all these processes are counteracted by Ca_i²⁺ and by MgATP_. This model of exchange regulation differs from former models in that 1) it includes all known ionic (Na_i⁺-H_i⁺-Ca_i²⁺) and MgATP interactions with the exchanger and 2) Na_i⁺-dependent inhibition takes place at sites other than Na_i⁺ transport sites (9, 10).

In the present work, the technique for isotope flux measurement in dialyzed squid axons was improved in a way that makes it possible to sequentially estimate, in the same axon, the influx and efflux of ions. We report here two novel observations that are predicted by the model for ionic and metabolic regulation of the squid Na⁺/Ca²⁺ exchanger (see the APPENDIX). First, at low pH_i (7.0) and in the absence of MgATP, Na_i⁺ has a dual effect on Ca²⁺ influx: inhibition at low concentrations followed by stimulation at high Na_i⁺ concentrations ([Na⁺]_i), reaching levels higher than those seen without Na_i⁺. Second, in the presence of MgATP, the biphasic response to Na_i⁺ disappears, being replaced by a sigmoid activation. On the other hand, Ca²⁺ efflux is monotonically inhibited by Na_i⁺, more potently without than with MgATP. This behavior can be explained by synergic H_i⁺- Na_i⁺ interactions that are antagonized by the nucleotide. In summary, the experimental results reported here on unidirectional Ca²⁺ flux measurements under steady-state conditions entirely agree with the integrated ionic-metabolic squid axon model of Na⁺/Ca²⁺ exchange.

	METHODS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
Experiments were carried out with giant axons from Loligo pealei at the Marine Biological Laboratory in Woods Hole, MA. Immediately after decapitation of the squid, giant axons were dissected from the mantle in artificial seawater. The mean axon diameter of Loligo pealei during the April-May 2007 season was 510 µm (n = 30). The experimental procedures for internally dialyzing squid axons have been described elsewhere (7). Dialysis capillaries were from regenerated cellulose acetate fiber with a molecular weight cutoff of 18,000 Da (210 µm outer diameter and 200 µm inner diameter, no. 132225 Spectra porous Spectrum, Houston, TX). The stiffness of the dialysis capillary was optimized by placing a platinum-iridium (20%) wire inside.

Solutions. The standard dialysis medium had the following composition (in mM): 385 Tris-MOPS, 40 NaCl, 1 MgCl₂, 285 glycine, and 1 Tris-EGTA; pH 7.3. The standard external solution consisted of (in mM) 440 NaCl, 0.3 CaCl₂, 60 MgCl₂, and 10 Tris·Cl; pH 7.6. The osmolarity of all solutions was adjusted to 940 mosmols. The dialysis medium for influx experiments was a modification of the standard dialysis medium in which the [Na⁺]_i was varied from 0 to 300 mM by mixing isosmolar solutions of Tris-MOPS and Na-MOPS. During flux experiments, dialysis solutions contained 10 mM [EGTA], 0.5 mM Mg²⁺, and 5 µM ionized Ca²⁺ at pH 7.0. The estimation of [Ca²⁺]_i and intracellular Mg²⁺ concentration ([Mg²⁺]_i) was made with the WinMaxc computer program (version 2.00, Chris Patton Hopkins Marine Station). The external medium contained (in mM) 440 LiCl (compensating for external NaCl), 5 CaCl₂, and 60 MgCl₂; pH 7.6. In Ca²⁺-free solutions, MgCl₂ was 65 mM. To stop any endogenous production of ATP, 1 mM NaCN was always present in external media. The addition of 3 mM ATP to the dialysis medium was made at a constant free [Mg²⁺]_i of 0.5 mM. The Ca²⁺ pump component of Ca²⁺ efflux as well as the operation of the Na⁺/K⁺ pump were eliminated by adding 100 µM vanadate to dialysis media. Since the leak of Ca²⁺ is critical in influx experiments, all radioactive influx solutions contained 300 nM TTX, which is known to block nonspecific Ca²⁺ influx by 70% (13), and 10 µM verapamil (for details, see Fig. 2). Before ⁴⁵Ca²⁺ was included in external or dialysis solutions, all axons were routinely predialyzed for 45 min with the standard medium containing 1 mM EGTA, free of Ca²⁺ and ATP. EGTA was purchased from Molecular Probes (Eugene, OR). Sodium, calcium, and magnesium salts were from Baker. [²²Na]NaCl and [⁴⁵Ca]CaCl₂ were from New England Nuclear. All other reagents were ultrapure and from Sigma (St. Louis, MO).

View larger version (17K): [in this window] [in a new window]   Fig. 1. Diagram of the experimental influx-efflux chamber. A: lateral view across the middle of the central slot. B: top view. The isotope entering the central compartment (shaded area) exits through the guard outflows. The lateral compartments were kept at infinite dilution by the isotope free inlet and outlet systems (see METHODS). Note that 45Ca2+ influx and efflux were measured over the same area of the axon.

View larger version (15K): [in this window] [in a new window]   Fig. 2. Intracellular Ca2+ (Cai2+)-dependent Ca2+ influx and extracellular Ca2+ (Cao2+)-dependent Ca2+ efflux (Cao2+/Cai2+ exchange) consecutively measured in a single dialyzed squid axon. The ordinate shows Ca2+ influx and Ca2+ efflux (in pmol·cm–2·s–1); the abscissa shows time (in min). Note the following: 1) the internal and external solutions were Na+ free; 2) all Ca2+ influx is Cai2+ dependent and all Ca2+ efflux is Cao2+ dependent (Ca2+/Ca2+ exchange); and 3) the influx and efflux values were very similar (flux ratio: 1:1), which is to be expected for a Ca2+/Ca2+ exchange mode. Axon diameter was 550 µm. Temperature was 19°C. Lio, extracellular Li+; pHi, intracellular pH.

We adapted the original influx chamber (7) to the dimensions of the efflux chamber (13), making it possible to measure both influx and efflux in the same axon. This eliminates natural variations between axons, and, since the area exposed to the radioactive external and internal media is the same, it is possible to precisely measure the influx-to-efflux ratio or net Ca²⁺ flux (Ca²⁺ influx – Ca²⁺ efflux). The new influx-efflux chamber is shown in Fig. 1, A and B. The procedure for influx-efflux sequential measurements is to measure the influx first. ⁴⁵Ca²⁺ enters the central compartment through the isotope inlet (influx; see Fig. 1A, lateral view), at first rapidly, at a rate of 1.2 ml/min to obtain a good mix, and then slowly, at 2.3 ml/h. A glass cover is placed on the top of the central compartment, restricting its opening to the sides (see Fig. 1, A and B); in this way, the isotope filling the central compartment leaks out to the lateral ones, where it is collected by the isotope-free outlet guard. The isotope confined to the dialyzed region is shown as a shaded area in Fig. 1, A and B.

To keep the extremes of the axon free of isotope, an isotope-free medium (similar to the external medium) is perfused through the isotope-free inlet (influx; Fig. 1, A and B) and removed by the outer guards located in the lateral compartment (Fig. 1B, outer guard) at a rate of 0.750 ml/min. To check that no significant amounts of isotope were leaking to the lateral compartments, samples were taken and counted during the course of an experiment. Well-defined boundaries between the center (isotope) and lateral (isotope free) compartments could be easily viewed by the addition of phenol red (0.5 mM) to the radioactive medium. To avoid changes in hydrostatic pressure between the lateral compartments that could cause a flow of isotope-free solution into the central compartment, the whole chamber was closed by a rectangular bath covering the entire axon [Fig. 1A, external solution level (influx)] (7).

For influx experiments, we used a high specific activity in the external medium (600,000 counts·min^–1·µl^–1, representing 120 counts·min^–1·fmol^–1 for 5 mM Ca²⁺). This allows the estimation of fluxes as low as a few femtomoles per centimeter squared per second of Ca²⁺ entering the axon. During influx experiments, the dialysis capillary was perfused at a rate of 3 µl/min, and the solution was collected at the end (periods of 3 min) and counted online. For subsequent Ca²⁺ efflux measurement, the glass cover was removed, the inlet (efflux)-outlet (efflux) guards were turned on, and the lateral compartments was turned off (Fig. 1B). Immediately, the dialysis medium was changed to one containing the radioactive material and perfused at a rate of 3 µl/min (8, 9). Influx was always measured first to avoid the build up of significant amounts of intracellular isotope during the course of an efflux experiment. For efflux measurements, the external medium was perfused at a rate of 3 ml/min (inlet and outlet efflux; Fig. 1B) for counting online. Influxes and effluxes were carried out at a room temperature of 19°C.

Figure 2 shows a representative experiment in which ⁴⁵Ca²⁺ influx and ⁴⁵Ca²⁺ efflux were measured consecutively in the same axon in the absence of Na_i⁺ and Na_o⁺ and without ATP. With 5 mM Ca_o²⁺, the influx of Ca²⁺ in the absence of Ca_i²⁺ was very low (a leak of 50 fmol·cm^–2·s^–1) and similar to that reported previously in dialyzed squid axons containing no intra- or extracellular K⁺ and superfused with 300 nM TTX (13). Raising Ca_i²⁺ to 5 µM caused a fast activation of Ca²⁺ influx to 3.4 pmol·cm^–2·s^–1 (Ca_i²⁺-activated [⁴⁵Ca²⁺]_o influx via Ca_o²⁺/Ca_i²⁺ exchange); this uptake returned to initial values when [Ca²⁺]_i was removed. After the extracellular radioactive solution was washed out and the axon was dialyzed with the standard dialysis medium for 25 min while the chamber was prepared for an efflux measurement, the addition of the radioactive dialysis solution containing 5 µM Ca_i²⁺ caused the efflux of Ca²⁺ to reach a value of 3.2 pmol·cm^–2·s^–1 (Ca_o²⁺-activated [⁴⁵Ca²⁺]_i efflux via Ca_o²⁺/Ca_i²⁺ exchange), which was completely abolished upon the removal of external Ca²⁺. The almost exact match of the Ca²⁺ influx and efflux values indicates that the fluxes were collected over a similar area of the axon, thus confirming the validity of the experimental procedure. Na⁺ efflux experiments were carried out with the same chamber as previously described (9).

	RESULTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
Effects of [Na⁺]_i on Ca²⁺ influx and efflux at pH 7.0 and in the absence of ATP. Figure 3 shows an experiment in which, in the same axon, both Ca²⁺ influx (left) and efflux (right) were measured as a function of [Na⁺]_i at a pH_i of 7.0 and in the absence of ATP. Na⁺ was always absent in the external medium, where it was replaced with 440 mM LiCl. The relevant baselines of the fluxes were as follows: Ca_i²⁺-dependent Ca²⁺ influx (left) and Ca_o²⁺-dependent Ca²⁺ efflux (right), both in the presence of 5 mM Ca_o²⁺, 5 µM Ca_i²⁺, and without Na_i⁺ and MgATP; i.e., via the Ca_o²⁺/Ca_i²⁺ exchange mode. Figure 3 shows that, in the absence of [Na⁺]_i, the influx of Ca²⁺ reached a value of 3.6 pmol·cm^–2·s^–1. The addition of 25 mM Na_i⁺ caused a large drop in this influx to a steady level of 1.35 pmol·cm^–2·s^–1 (63% inhibition). A subsequent rise in [Na⁺]_i resulted in a progressive increase in Ca²⁺ uptake, which, at 300 mM Na_i⁺_, almost quadrupled the rate seen under the Ca_o²⁺/Ca_i²⁺ exchange mode. As expected, the efflux of Ca²⁺ through the Ca_o²⁺/Ca_i²⁺ exchange mode had a value practically identical to that of the influx. However, in this case, Na_i⁺ did not have a biphasic effect and led only to inhibition of Ca²⁺ efflux, which was 75% at 25 mM and almost complete at 50 mM. The results of six different axons are summarized in Fig. 4.

View larger version (13K): [in this window] [in a new window]   Fig. 3. Effects of intracellular Na+ (Nai+) concentration ([Na+]i) on 45Ca2+ influx and efflux in the same dialyzed axon at pHi 7.0 in the absence of ATP. The ordinate shows Ca2+ fluxes (in pmol·cm–2·s–1); the abscissa shows time (in min). Note the following: 1) Ca2+ influx at 5 µM Cai2+ (starting in the Ca2+/Ca2+ exchange mode) was inhibited at 25 mM Nai+ and then progressively activated upon increasing [Na+]i to 50, 100, and 300 mM, surpassing Ca2+/Ca2+ exchange values; and 2) the Cao2+-dependent Ca2+ efflux was strongly inhibited Nai+, reaching full inhibition at 50 mM. Axon diameter was 510 µm. Temperature was 19°C.

View larger version (12K): [in this window] [in a new window]   Fig. 4. Summary of five different dialyzed squid axons in which the Nai+ dependency of Ca2+ influx and Ca2+ efflux were consecutively measured in the absence of ATP and at a pHi of 7.0. The ordinate shows Ca2+ influx and Ca2+ efflux (in pmol·cm–2·s–1); The abscissa shows [Na+]i (in mM). Note the following: 1) the external solution was Na+ free; 2) Nai+ had a dual effect on Ca2+ influx (inhibition at 25 mM followed by activation at higher concentrations); and 3) Ca2+ efflux was monotonically inhibited by Nai+ inhibition with a K0.5 of 10 mM. Points represent means ± SE; n = 5 axons. Temperature was 19°C.

Effects of [Na⁺]_i on Ca²⁺ influx and efflux at pH 7.0 and in the presence of ATP. The inhibition of the squid Na⁺/Ca²⁺ exchanger by H_i⁺ and Na_i⁺ is such that, at pH_i = 7.0, relatively low [Na⁺]_i are strongly inhibitory and effectively antagonized by MgATP (9, 10). Therefore, if part of the inhibitory effects described above are related to H_i⁺-Na_i⁺ synergism, it should be reduced or abolished in the presence of MgATP. Figure 5 shows a single experiment where this hypothesis was tested. After a steady-state influx of Ca²⁺ of 3.8 pmol·cm^–2·s^–1 was obtained in the presence of 5µM Ca_i²⁺, 5 mM Ca_o⁺, no Na_i⁺, and no ATP, the addition of 3 mM ATP caused an increase in Ca²⁺ influx close to 4.3 pmol·cm^–2·s^–1. The subsequent addition of Na_i⁺ monotonically increased Ca²⁺ influx.

View larger version (13K): [in this window] [in a new window]   Fig. 5. Effects of [Na+]i on 45Ca2+ influx and efflux in an axon dialyzed at pHi 7.0 and in the presence of 3 mM ATP. The ordinate shows Ca2+ fluxes (in pmol·cm–2·s–1); the abscissa shows time (in min). Note the following: 1) the external solution was Na+ free; 2) at 5 µM Cai2+, Ca2+ influx was monotonically stimulated by [Na+]i; and 3) Cao2+-dependent Ca2+ efflux was monotonically inhibited by Nai+ with a much lower affinity that in the absence of ATP. Axon diameter was 510 µm. Temperature was 19°C.

View larger version (12K): [in this window] [in a new window]   Fig. 6. Summary of four different dialyzed squid axons in which the Nai+ dependency of Ca2+ influx and Ca2+ efflux were consecutively measured at a pHi of 7.0 and in the presence of 3 mM ATP. The ordinate shows Ca2+ influx and Ca2+ efflux (in pmol·cm–2·s–1); the abscissa shows Nai+ (in mM). Note the following: 1) all extracellular solutions were Na+ free; 2) the influx of Ca2+ was monotonically stimulated by Nai+; and 3) the efflux of Ca2+ was monotonically inhibited by Nai+ with a K0.5 of 75 mM. Points represent means ± SE; n = 4 axons. Temperature was 19°C.

View larger version (12K): [in this window] [in a new window]   Fig. 7. Activation of Cao2+-dependent 22Na+ efflux (reverse Na+/Ca2+ exchange) by [Na+]i at a pHi of 7.0 in the absence and presence of 3 mM ATP. The ordinate shows Cao2+-dependent Na+ efflux (in pmol·cm–2·s–1); the abscissa shows time (in min). Note the following: 1) extracellular solutions were Na+ free; 2) at all concentrations, Nai+ activated reverse exchange (Cao2+/ Nai+ exchange); and 3) the apparent affinity for that Nai+ stimulation was lower in the absence than in the presence of ATP. Axon diameter was 490 µm. Temperature was 19°C.

View larger version (12K): [in this window] [in a new window]   Fig. 8. Summary of three different dialyzed squid axons in which activation of the Cao2+-dependent Na+ efflux (reverse Na+/Ca2+) exchange by [Na+]i was followed at pHi 7.0 in the absence and presence of 3 mM ATP. The ordinate shows Cao2+-dependent Na+ efflux in the absence and in the presence of 3 mM MgATP (in pmol·cm–2·s–1); the abscissa shows [Na+]i (in mM). Note the following: 1) external solutions were Na+ free; 2) Nai+ stimulated Cao2+-dependent Na+ efflux through a sigmoid curve; and 3) K0.5 for Nai+ activation was 80 mM in the absence of ATP and 37 mM in the presence of ATP. Points represent means ± SE; n = 3 axons. Temperature was 19°C.

View larger version (12K): [in this window] [in a new window]   Fig. 9. Overall cycling kinetic model for ionic and ATP modulation of the squid Na+/Ca2+ exchanger. Definitions and values of unidirectional rate constants as well as other relevant information are listed in the APPENDIX. This model is based on a kinetic scheme proposed previously (9).

View larger version (13K): [in this window] [in a new window]   Fig. 10. A: model simulation of the effects of Nai+ on the influx of Ca2+ in an axon with an internal solution containing 5 µM Ca2+, a pH of 7.0 with and without 3 mM ATP, and variable [Na+]i. The extracellular solution was Na+ free and contained 5 mM Ca2+. The ordinate shows Ca2+ influx (in arbitrary units); the abscissa shows [Na+]i (in mM). Note the following: 1) Nai+ inhibition was observed in the absence but not in the presence of ATP; and 2) the simulation adequately reproduced the results shown in Figs. 4 and 6. B: model simulation of the activation by Nai+ of the efflux of Na+ through the reverse mode of the Na+/Ca2+ exchange. The intracellular solution contained 5 µM Ca2+, a pH of 7.0 with and without 3 mM ATP, and variable [Na+]i; the extracellular medium was free of Na+ and contained 5 mM Ca2+. Note the following: 1) Nai+ activated reverse exchange (Cao2+/ Nai+) through a sigmoid curve in both instances; 2) the apparent affinity for Nai+ was lower in the absence than in the presence of ATP; and 3) the simulation adequately reproduced the results shown in Fig. 8. All simulations were carried out with the kinetic model described in Fig. 9 using the values and procedures listed in the APPENDIX.

	DISCUSSION

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

However, there is an additional inhibitory effect of Na_i⁺, and that is on the efflux of Ca²⁺. In this case, although only a monotonic inhibition curve is to be expected, it will be made up of the sum of two different actions: one due to the formation of the H₂EiNa state and the other due to the competition of Na_i⁺ with Ca_i²⁺ for the intracellular transport sites. According to the model discussed here (Fig. 9 and APPENDIX), the expectations are that, at pH_i 7.0, the first mechanism will prevail without MgATP and be much reduced or abolished with MgATP. This is exactly what was found when Figs. 3 and 4 were compared with Figs. 5 and 6 (see Ref. 9). Also, simulations with the model presented here show that alkaline pH_i acts similarly to MgATP in abolishing the dual effect of Na_i⁺ on Ca²⁺ influx (not shown).

It might be argued that the data presented here could plausibly be interpreted solely in terms of Na⁺ interactions with the translocation sites on the basis of the model proposed for the cardiac Na⁺/Ca²⁺ exchanger. Several reasons indicate that this is not the case. On the one hand, the effects of pH_i, MgATP, and (H_i⁺ + Na_i⁺) synergic inhibition on the regulatory site of the heart system are well documented (5, 18, 19); to ignore these interactions and focus only on translocation sites seems an oversimplification. On the other hand, some working assumptions would require different translocation rates of the reversal Na⁺/Ca²⁺ and Ca²⁺/Ca²⁺ exchanges, where the first should be slower. Actually this is not the case for the squid axon, where the only limiting branch for translocation, including that at alkaline pH_i (8.8), is the entry of Ca²⁺ (8, 12). Other experimental results in dialyzed squid axons also unambiguously show that, provided the Ca_i²⁺-regulatory site is saturated, neither MgATP nor pH_i has any effect on the affinity of the intracellular transport sites for Ca²⁺ or Na⁺. In addition, those affinities are not affected by protons in the presence of MgATP or by MgATP at alkaline pH_i (Ref. 11 and Beaugé and DiPolo, unpublished observations). Furthermore, the comparison of Figs. 4 and 6 of this work shows that, at pH_i 7.0, inhibition of Ca²⁺ efflux by Na_i⁺ is much more effective in the absence than in the presence of MgATP. Therefore, the Na⁺-Ca²⁺ competition at the transport site(s) is seen in the presence of MgATP, while, without the nucleotide, Na_i⁺ inhibition must occur somewhere else. With no changes in the intrinsic affinities of the intracellular transport sites for Na⁺ or Ca²⁺, the only feasible explanation seems to involve effects on the Ca_i²⁺-regulatory site. Actually, this differential inhibition of Ca²⁺ efflux by Na_i⁺ is predicted not only by the steady-state overall cycling scheme described here (see below) but also by the more restricted fast equilibrium scheme of the squid axon model (9, 12).

The complete transport cycle of the squid Na⁺/Ca²⁺ exchanger and the simulation data are shown in Figs. 9 and 10. The values and rationale for the rate constants used are indicated in the APPENDIX. The simulations, described in Fig. 10, show that the model in fact predicts the experimental flux data. In Fig. 10A, the dual effect of Na _i⁺ on the influx of Ca²⁺ (inhibition at low and activation at high [Na⁺]_i), seen at pH_i 7.0, is replaced by a monotonic activation in the presence of 3 mM ATP (compare with Fig. 4). Other simulations not shown here demonstrate that, at alkaline pH_i, inhibition by Na_i⁺ is no longer observed even without ATP. In Fig. 10B, the simulation curves of Na⁺ efflux as a function of [Na⁺]_i reproduce the experiments shown in Fig. 8.

An obvious advantage of the squid model is that it takes into account and explains, in a single kinetic scheme, the behavior of steady-state Na⁺/Ca²⁺ exchange fluxes under a whole variety of ionic and metabolic conditions investigated up to the present in this preparation (6, 9, 25). It is important to notice that the squid scheme also predicts the existence of a pre-steady-state Na_i⁺ inactivation that is enhanced at low pH_i and counteracted by alkalinization, ATP, and an increase in [Ca²⁺]_i (10, 11).

The question is to what extent it can be applied to other exchangers, particularly that of the mammalian heart. And that is far from straightforward. Compared with the cardiac exchanger, the squid scheme fails to predict the experimental findings, sustained by other theoretical models, of an increased rate of Na_i⁺ inactivation upon increasing [Na⁺]_i and the still high fraction of steady-state inactivation at 1–3 µM [Ca²⁺]_i (17, 21). Also, although the final targets for MgATP effects in the squid axon and in the heart are related to the Ca_i²⁺-regulatory site, it must be remembered that the metabolic pathways for that modulation are completely different in both preparations (5, 10).

Another important difference between the squid axon and mammalian heart is in the effects on extracellular monovalent cations. Thus, whereas in the squid axon, Li⁺, K⁺, Rb⁺, and Cs⁺ stimulate all Na⁺/Ca²⁺ exchange modalities in which external Ca²⁺ is the transported species (Ca²⁺/Ca²⁺ and reverse exchange) (1, 3, 4), they fail to do so in cardiac cells under giant patch conditions (21). Based on this, it is not unlikely that both systems do have kinetic differences. Nevertheless, and although not fully applicable to all exchangers, the scheme presented here might provide some insights on expected net Ca²⁺ movements in other tissues under a variety of intracellular ionic and metabolic conditions, leading to modifications in the concentrations of intracellular regulatory ligands (Ca_i²⁺-Na_i⁺-H_i⁺ and MgATP).

Finally, some considerations about methodology seem appropriate. The efflux of Na⁺ in exchange for Ca²⁺ in either direction is an electrogenic event. Nowadays, a lot has been learned about this system, in particular ligand interactions related to Na_i⁺ inactivation, by measuring Na⁺/Ca²⁺ exchange currents in the reverse mode (see Ref. 5 for references). However, even such a powerful approach will be of no use for detecting the inhibition of the Na⁺/Ca²⁺ exchanger by low [Na⁺]_i at low pH_i and without ATP, as described here. To that aim, methods other than the current measurements must be applied.

	APPENDIX

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
The model shown in Fig. 9 is an overall cycling scheme based on that initially proposed for the squid Na⁺/Ca²⁺ exchanger (9). The set of simultaneous differential equations was solved by using the chemical reaction facility of the Scop simulation program for steady-state conditions. As shown in Fig. 9, "f" means forward rate constant for transport (Ca_i²⁺ exit and Na_o⁺ entry) or the "on" rate constant for a ligand binding, whereas "b" means backward rate constant for transport (Ca_o²⁺ entry and Na_i⁺ exit) or the "off" rate constant for a ligand binding. External ligands and externally facing binding sites of the exchanger are labeled with an "o"; conversely, intracellular ligands and internally facing binding sites are labeled with an "i." For the sake of simplicity, all on rate constants were arbitrarily taken as equal to 10⁸ M^–1·s^–1. The other constants were chosen to obtain the experimental results, and obviously it is very likely that more than one set would work.

Other points to mention here are as follows. First, the lower value for the backward Ca²⁺ translocation constant is sustained from experimental results in squid axons (12). Second, to maintain microscopic reversibility (for thermodynamic reasons) in the closed loop, the product of the clockwise and counterclockwise rate constants must be equal. Therefore, the following equality

can be reduced to

The values of the off binding and translocation rates constants were as follows: bci = 2 x 10⁴ s^–1; bni = 5 x 10⁵ s^–1; brc = 10 s^–1; bh10 = 8 x 10^–1 s^–1; bh20 = 1 x 10^–1 s^–1; bninhib0 = 1 x 10⁵ s^–1; bco = 3 x 10⁴ s^–1; bno = 7.5 x 10⁶ s^–1; fc = 1 x 10³ s^–1; bc = 1 x 10² s^–1; fn' = 1 x 10⁴ s^–1; and bn = 1 x 10⁴ s^–1.

Finally, the protecting effect of ATP by reducing the affinity for the binding of Na_i⁺ and H⁺ to their inhibitory sites was arbitrarily assumed to be equal for both ligands and to act by increasing the off rate constants by the same factor in the following way (9):

where factor_ATP_bh1 = 5.0, factor_ATP_bh2 = 5.0, factor_ATP_ bninhib = 5.0.

The K_m for ATP (KmATP) was taken as 2 x 10^–4 M.

The following chemical kinetic equations were transformed by the program into differential equations:

The equation

was eliminated on the basis of the conservation equation

The ligand concentrations were as follows:

Integration was performed with the Sparse numerical solver, and fluxes were estimated by the following simplification:

At first sight, it may seem that the values of the rate constant chosen here will give apparent affinity values for the ligands that are too different from those expected from the available data. However, it must be remembered that in the steady solution of multiple step systems (like that described here), those apparent affinities are a complex function of several rate constants and cannot be predicted from the off-to-on constant ratio (27). Actually, simulations performed with the values of this work adequately predict previous experimental results in dialyzed axons (9). Among others, they include the following: pH_i effects on Na_o⁺-dependent Ca²⁺ efflux in the absence and presence of ATP, Na_i⁺ inhibition of forward Ca²⁺ exchange and pH_i 6.9 without and with ATP, and Ca_i²⁺ activation of Na⁺/Na⁺ exchange as a function of pH_i and ATP (results not shown).

	GRANTS

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
This work was supported by United States National Science Foundation Grant MCB 0444598, Fondo Nacional de Ciencia y Tecnología Grants S1-9900009046 and G-2001000637 (Venezuela), Fundación Polar (Venezuela), and AFONCYT Grant PICT-05-12397 (Argentina), and Consejo Nacional de Investigaciones Científicas y Técnicas Grant PIP 5118 (Argentina).

	FOOTNOTES

 

Address for reprint requests and other correspondence: R. DiPolo, Laboratorio de Fisiología Celular, Centro de Biofísica y Bioquímica, Instituto Venezolano de Investigaciones Científicas, Apartado Postal 21827, Caracas 1020-A, Venezuela (e-mail: dipolor{at}ivic.ve)

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.

	REFERENCES

TOP ABSTRACT METHODS RESULTS DISCUSSION APPENDIX GRANTS REFERENCES

 
1. Allen TJ, Baker PF. Comparison of the effects of potassium and membrane potential on the calcium-dependent sodium efflux in squid axons. J Physiol 378: 53–76, 1986.[Abstract/Free Full Text]

2. Annunziato L, Pignataro G, Di Renzo GF. Pharmacology of brain Na⁺/Ca²⁺ exchanger: from molecular biology to therapeutic perspectives. Pharmacol Rev 56: 633–654, 2004.[Abstract/Free Full Text]

3. Baker PF, Blaustein MP. Sodium-dependent uptake of calcium by crab nerve. Biochim Biophys Acta 150: 167–170, 1968.[Medline]

4. Beaugé L, DiPolo R. Effects of monovalent cations on Na-Ca exchange in nerve cells. Ann NY Acad Sci 639: 147–155, 1991.[Web of Science][Medline]

5. Blaustein MP, Lederer JN. Sodium/calcium exchange: its physiological implication. Physiol Rev 79: 763–854, 1999.[Abstract/Free Full Text]

6. DiPolo R. The influence of nucleotides on calcium fluxes. Fed Proc 35: 2579–2582, 1976.[Web of Science][Medline]

7. DiPolo R. Calcium influx in internally dialyzed squid giant axons. J Gen Physiol 73: 91–113, 1979.[Abstract/Free Full Text]

8. DiPolo R, Beaugé L. Characterization of the reverse Na/Ca exchange in squid axons and its modulation by Ca_i and ATP. Ca_i-dependent Na_i-Ca_o and Na_i-Na_o exchange modes. J Gen Physiol 90: 505–525, 1987.[Abstract/Free Full Text]

9. DiPolo R, Beaugé L. MgATP counteracts intracellular proton inhibition of the sodium-calcium exchanger in dialyzed squid axons. J Physiol 539: 791–803, 2002.[Abstract/Free Full Text]

10. DiPolo R, Beaugé L. Sodium-calcium exchanger: influence of metabolic regulation on ion carrier interactions. Physiol Rev 86: 155–203, 2006.[Abstract/Free Full Text]

11. DiPolo R, Beaugé L. The squid preparation as a general model for ionic and metabolic Na/Ca exchange interactions. Physiopathological implications. Ann NY Acad Sci 1099: 135–151, 2007.[CrossRef][Web of Science][Medline]

12. DiPolo R, Berberián G, Beaugé L. Phosphoarginine regulation of the squid nerve Na⁺/Ca²⁺ exchanger: metabolic pathway and exchanger-ligand interactions different from those seen with ATP. J Physiol 554: 387–401, 2004.[Abstract/Free Full Text]

13. DiPolo R, Rojas H, Beaugé L. Ca entry at rest and during prolonged depolarization in dialyzed squid axons. Cell Calcium 3: 19–42, 1982.[CrossRef][Web of Science][Medline]

14. Doering AE, Lederer WJ. The mechanism by which cytoplasmic protons inhibit the sodium-calcium exchanger in guinea pig heart cells. J Physiol 466: 481–499, 1993.[Abstract/Free Full Text]

15. Doering AE, Lederer WJ. The action of Na⁺ as a cofactor in the inhibition by cytoplasmic protons of the cardiac Na⁺-Ca²⁺ exchanger in the guinea pig. J Physiol 480: 9–20, 1994.[Abstract/Free Full Text]

16. Doering AE, Eisner DA, Lederer WJ. Cardiac Na-Ca exchange and pH. Ann NY Acad Sci 779: 182–198, 1996.[Web of Science][Medline]

17. Fujioka Y, Hiroe K, Matsuoka S. Regulation kinetics of Na⁺-Ca²⁺ exchange current in guinea-pig ventricular myocytes. J Physiol 529: 611–623, 2000.[Abstract/Free Full Text]

18. Hilgemann DW, Collins A, Matsuoka S. Steady-state and dynamic properties of cardiac sodium-calcium exchange. Secondary modulation by cytoplasmic calcium and ATP. J Gen Physiol 100: 933–961, 1992.[Abstract/Free Full Text]

19. Hilgemann DW, Matsuoka S, Nagel GA, Collins A. Steady-state and dynamic properties of cardiac sodium-calcium exchanger. Sodium-dependent inactivation. J Gen Physiol 100: 905–932, 1992.[Abstract/Free Full Text]

20. Iwamoto T, Inoe Y, Ito K, Sakaue Y, Kita S, Katsuragi T. The exchanger inhibitory peptide region-dependent inhibition of Na⁺/Ca²⁺ exchange by SN-6 [2-(4-nitrobenzyloxy)thiazolidine-4-carboxylic acid ethyl ester], a novel benzyloxyphenyl derivative. J Mol Pharmacol 66: 45–55, 2004.[CrossRef]

21. Matsuoka S, Hilgemann DW. Steady-state and dynamic properties of cardiac sodium-calcium exchange. Ion and voltage dependencies of the transport cycle. J Gen Physiol 100: 963–1001, 1992.[Abstract/Free Full Text]

22. Matsuoka S, Hilgemann DW. Inactivation of outward Na⁺-Ca²⁺ exchange current in guinea pig ventricular myocytes. J Physiol 476: 443–458, 1994.[Abstract/Free Full Text]

23. Philipson KD, Nicoll DA. Sodium-calcium exchange. A molecular perspective. Annu Rev Physiol 62: 111–133, 2000.[CrossRef][Web of Science][Medline]

24. Rasgado-Flores H, Espinosa-Tanguma R, Tie J, de Santiago J. Voltage dependence of Na-Ca exchange in barnacle muscle cells. 1. Na-Na exchange activated by -chymotrypsin. Ann NY Acad Sci 779: 236–248, 1996.[Web of Science][Medline]

25. Requena J. Calcium efflux from squid axons under constant sodium electrochemical gradient. J Gen Physiol 72: 443–470, 1978.[Abstract/Free Full Text]

26. Reuter H, Seitz N. The dependence of calcium efflux from cardiac muscle on temperature and external ion composition. J Physiol 195: 451–470, 1968.[Abstract/Free Full Text]

27. Segel IH. Enzyme Kinetics. New York: Wiley, 1975.

28. Shigekawa M, Iwamoto T. Cardiac Na⁺-Ca²⁺ exchange: molecular and pharmacological aspects. Circ Res 88: 864–876, 2001.[Abstract/Free Full Text]

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