Characterization of intracellular pH regulation in the guinea-pig ventricular myocyte

Abstract

1. Intracellular pH was recorded fluorimetrically by using carboxy-SNARF-1, AM-loaded into superfused ventricular myocytes isolated from guinea-pig heart. Intracellular acid and base loads were induced experimentally and the changes of pH_i used to estimate intracellular buffering power (β). The rate of pH_i recovery from acid or base loads was used, in conjunction with the measurements of β, to estimate sarcolemmal transporter fluxes of acid equivalents. A combination of ion substitution and pharmacological inhibitors was used to dissect acid effluxes carried on Na⁺-H⁺ exchange (NHE) and Na⁺-HCO₃⁻ cotransport (NBC), and acid influxes carried on Cl⁻-HCO₃⁻ exchange (AE) and Cl⁻-OH⁻ exchange (CHE).

2. The intracellular intrinsic buffering power (β_i), estimated under CO₂/HCO₃⁻-free conditions, varied inversely with pH_i in a manner consistent with two principal intracellular buffers of differing concentration and pK. In CO₂/HCO₃⁻-buffered conditions, intracellular buffering was roughly doubled. The size of the CO₂-dependent component (β_CO2) was consistent with buffering in a cell fully open to CO₂. Because the full value of β_CO2 develops slowly (2·5 min), it had to be measured under equilibrium conditions. The value of β_CO2 increased monotonically with pH_i.

3. In 5 % CO₂/HCO₃⁻-buffered conditions (pH_o 7·40), acid extrusion on NHE and NBC increased as pH_i was reduced, with the greater increase occurring through NHE at pH_i < 6·90. Acid influx on AE and CHE increased as pH_i was raised, with the greater increase occurring through AE at pH_i > 7·15. At resting pH_i (7·04-7·07), all four carriers were activated equally, albeit at a low rate (about 0·15 mM min⁻¹).

4. The pH_i dependence of flux through the transporters, in combination with the pH_i and time dependence of intracellular buffering (β_i+β_CO2), was used to predict mathematically the recovery of pH_i following an intracellular acid or base load. Under several conditions the mathematical predictions compared well with experimental recordings, suggesting that the model of dual acid influx and acid efflux transporters is sufficient to account for pH_i regulation in the cardiac cell. Key properties of the pH_i control system are discussed.

Intracellular pH in mammalian myocardial cells is governed by the balance among four sarcolemmal acid-equivalent ion transporters (Sun et al. 1996). Two of these, Na⁺-H⁺ exchange (NHE) and Na⁺-HCO₃⁻ cotransport (NBC), mediate acid-equivalent efflux (acid extrusion; Dart & Vaughan-Jones, 1992; Lagadic-Gossmann et al. 1992a) while the other two, Cl⁻-HCO₃⁻ exchange (anion exchange; AE) and Cl⁻-OH⁻ exchange (CHE) mediate acid-equivalent influx (acid loading; Vaughan-Jones, 1979; Sun et al. 1996; Leem & Vaughan-Jones, 1998b). Activity of the transporters is modulated by pH. In the present work, we attempt to characterize the overall kinetics of cardiac pH_i regulation in terms of the activity of these acid/base transporters. In order to do this, we have determined experimentally the pH_i sensitivity of acid-equivalent flux through each type of transporter. Provided that all relevant transporters have been identified it should then be possible, by summing their fluxes, to reconstruct the time course of pH_i regulation following acute, intracellular acid or base loads. By inspecting the pH_i sensitivity of the four transporters, it should also be possible to deduce the relative importance of each to the control of intracellular pH, and to the maintenance of resting pH_i.

In order to investigate the kinetic properties of a transporter, we have used recordings of pH_i in isolated ventricular myocytes to estimate sarcolemmal fluxes of acid equivalents. Fluxes are calculated as the product of dpH_i/dt (the rate of change of pH_i), caused by a transporter's activity, and β_tot, which represents total intracellular buffering power. The value assumed for β_tot therefore affects the estimate of acid/base flux. Buffering comprises two components that can be summed algebraically (Roos & Boron, 1981). These are intrinsic, non-CO₂-dependent buffering (β_i) and CO₂-dependent buffering (β_CO2). The values of intrinsic and CO₂-dependent buffering power vary differently as pH_i varies. Two further points are relevant. (i) In some cell types, such as smooth muscle myocytes (Baro et al. 1989; Aickin, 1994) and CNS neurones (Amos et al. 1996), β_CO2 is reported to be essentially zero, even in the presence of physiological concentrations of CO₂, although the reason for this is far from clear and such reports remain controversial. To date, systematic measurements of β_CO2 have not been made in the cardiac ventricular cell, although clear effects of CO₂-dependent buffering on pH_i are evident (Leem & Vaughan-Jones, 1998a). (ii) In the cardiac cell, intracellular CO₂-dependent buffering equilibrates slowly, most notably following acute intracellular alkali loads (Leem & Vaughan-Jones, 1998a). This is in contrast to intracellular intrinsic buffering which, on the time scale of the experiments shown in the present work, equilibrates essentially instantaneously (Leem & Vaughan-Jones, 1998a). The slow equilibration of CO₂-dependent buffering produces pH_i transients that may be mistaken for acid transport. Estimates of transporter flux from recordings of pH_i must therefore be made when the intracellular CO₂/HCO₃⁻ buffer system is at equilibrium. In view of the complexities and uncertainties concerning intracellular buffering in cardiac cells, we have designed experiments to measure both β_i and β_CO2.

By using data from the experiments outlined above, we have formulated a mathematical model of pH_i regulation that takes into account not only pH_i-controlled acid efflux and influx through multiple types of transporter, but also intrinsic buffering and slow, intracellular CO₂-dependent buffering.

A preliminary account of some of this work has been published (Leem & Vaughan-Jones, 1996).

METHODS

Isolation of guinea-pig ventricular myocytes

The composition of solutions used for cell isolation and the details of the procedure have been described previously (Lagadic-Gossmann et al. 1992a). Briefly, single ventricular myocytes were isolated from 350-450 g albino guinea-pigs (killed by cervical dislocation) using a combination of enzymatic and mechanical dispersion (0.7 mg ml⁻¹ collagenase, Boehringer Mannheim, and 0.04 mg ml⁻¹ protease, Sigma). The cells were finally suspended in Hepes-buffered Dulbecco's modified Eagle medium and left at room temperature until use. Only myocytes displaying a rod shape and calcium tolerance were used in the study.

Measurement of intracellular pH

SNARF loading and calibration

The pH_i was measured by using acetoxymethyl ester (AM)-loaded carboxy-SNARF-1, a dual-emission, pH-sensitive fluorophore. Full details of dye loading plus pH_i measurement and dye signal calibration have been given previously (e.g. Buckler & Vaughan-Jones, 1990; Sun et al. 1996). Briefly, isolated cells were loaded for 7 min at room temperature with 10 μM carboxy-SNARF-1 AM. SNARF fluorescence from individual cells was excited at 540 ± 12 nm and measured simultaneously at 590 ± 5 and 640 ± 5 nm, with an inverted microscope (Nikon Diaphot) converted for epifluorescence. The signals were digitized at 0.25 kHz (CED 1401 plus) and then averaged over 0.5 s intervals. The emission ratio was calculated and converted to a pH value using the pH ratiometric fluorescence equation (Buckler & Vaughan-Jones, 1990; Sun et al. 1996). This calculation requires knowledge of ‘default’ pH calibration data for intracellular SNARF, obtained in situ for individual ventricular myocytes and averaged for > 10 cells from at least three animals. These default data were obtained with the nigericin (10 μM) calibration technique (see Sun et al. 1996, for details of calibration solutions). The default values were determined routinely once a month. The terms determined were maximum emission ratio at pH 5.5, minimum ratio at pH 9.5 and 9.5/5.5 pH fluorescence ratio measured at 640 nm. Typical values were 1.556, 0.129 and 2.049, respectively. These predict a pK_a for intracellular SNARF of 7.365. Default data were used in place of performing a nigericin calibration after every experiment, in order to reduce potential contamination of the cell superfusion system with nigericin. The accuracy of the in situ calibration was cross-checked regularly during experiments, by using the weak acid/base (propionate/trimethylamine) null point technique (Eisner et al. 1989; see Buckler & Vaughan-Jones (1990) for details of experimental procedure). An acceptable cross-check was one where pH_i of a myocyte determined by the null point and default data methods agreed to within 0.1 pH unit (more usually, agreement was within 0.05 pH unit).

Cleaning the superfusion apparatus

Care was taken to clean the superfusion apparatus thoroughly after a nigericin calibration (see Sun et al. 1996). The superfusion lines were replaced. The superfusion chamber and solution switcher were dismantled and soaked in ethanol for several hours, followed by a soak for at least 12 h in a 20 % solution of the detergent Decon 75 (Decon Laboratories Ltd, Hove, Sussex, UK), followed by simmering in deionized water for several hours.

Solutions

Hepes-buffered Tyrode solution contained (mM): 135 NaCl, 4.5 KCl, 1 MgCl₂, 2 CaCl₂, 11 glucose and 20 Hepes (pK_a= 7.5). For Na⁺-free Tyrode solution, Na⁺ was replaced by 145 mM N-methyl-D-glucamine (NMDG). Cl⁻-free Tyrode solution contained (mM): 140 sodium gluconate, 4.5 potassium gluconate, 4 calcium gluconate, 2 magnesium gluconate, 11 glucose and 20 Hepes. The pH of all solutions was adjusted to 7.4 at 37°C using 4 M NaOH, except for Na⁺-free Tyrode solution, which was adjusted with 5 M HCl, and Cl⁻-free, Na⁺-free Tyrode solution, which was adjusted using glucuronic acid. CO₂/HCO₃⁻-buffered Tyrode solutions were saturated with 5 % CO₂-95 % air and contained (mM): 120 NaCl, 4.5 KCl, 1 MgCl₂, 2 CaCl₂, 11 glucose and 22 NaHCO₃. For Na⁺-free Tyrode, NaCl and NaHCO₃ were replaced isosmotically by NMDG and the pH of the CO₂-saturated solution adjusted to 7.4 at 37°C with HCl.

When acetate was added either to Hepes- or HCO₃⁻-buffered solutions, an equimolar amount of anion (either Cl⁻ or gluconate) was omitted.

Drugs and chemicals

Carboxy-SNARF-1 AM was bought from Molecular Probes. Hoe 694 was kindly provided by Drs W. Scholz and H. Lang of Hoechst Aktiengesellschaft (Germany). Dimethyl amiloride (DMA) was bought from Research Biochemicals International. All other general chemicals were from Merck or Sigma.

Calculation of sarcolemmal acid flux (J_H)

Following activation of a transporter, the product of dpH_i/dt and intracellular buffering power (β) gives the net rate of intracellular acid or base loading. The value selected for β depends on intrinsic (non-CO₂) buffering (β_i) and (where appropriate) CO₂-dependent buffering (β_CO2). The former value was calculated from eqn (1) in Results, and the latter value was estimated as:

(Roos & Boron, 1981). It is important to realize that this latter equation assumes CO₂/HCO₃⁻ buffer equilibrium and therefore will not be applicable to out-of-equilibrium periods such as those that occur for 2-3 min following the imposition of an intracellular alkali load induced by the acetate prepulse technique (Leem & Vaughan-Jones, 1998a). The equation also assumes equality of pK_a for CO₂/HCO₃⁻ and equality of CO₂ solubility and CO₂ concentration on both sides of the sarcolemma. When [HCO₃⁻]_o is calculated from the Henderson-Hasselbalch equation, the effect of saturated water vapour pressure on the pK_a of CO₂/HCO₃⁻ must be taken into account. Under these conditions, pK_a for CO₂/HCO₃⁻ becomes 6.15 at 37°C (Leem & Vaughan-Jones, 1998a).

Rates of change of pH_i (dpH_i/dt) from an intracellular acid or alkali load were obtained by computer from the first time differential of the best fit polynomial equation (SigmaPlot III) to the experimental data points sampled at 0.5 s intervals. A 4th order polynomial fit was used and was confirmed by a P value > 0.99, obtained from Student's paired t test (Leem & Vaughan-Jones, 1998a;r² usually > 0.98). All statistical data are expressed as means ±s.e.m.

RESULTS

Intrinsic buffering

In previous work with guinea-pig ventricular myocytes, β_i was estimated in the pH_i range 7.3-6.8 (Lagadic-Gossmann et al. 1992a). For the present experiments, we computed acid flux over a considerably wider pH_i range (6.2-7.7). Intrinsic buffering was determined in cells superfused with Hepes-buffered Tyrode solution, i.e. nominally free of CO₂/HCO₃⁻. The protocol consisted of acid loading a cell by using the ammonium prepulse technique, and then recording the resulting fall of pH_i (Roos & Boron, 1981). The experiments were performed in Cl⁻-free (gluconate substituted) solution to inhibit CHE (Leem & Vaughan-Jones, 1998b). Thirty micromolar Hoe 694 was included in all superfusates to inhibit NHE (Loh et al. 1996). In order to estimate β_i over a sufficiently wide range of pH_i values, the extracellular ammonium concentration during the prepulse was reduced in 5 mM steps from 30 mM to zero (cf. the protocol in Fig. 9 of Lagadic-Gossmann et al. 1992a). One such experiment is illustrated in Fig. 1A. Because solutions were Cl⁻ free, (NH₄)₂SO₄ was superfused rather than NH₄Cl. Ba²⁺ (2 mM) was also present throughout the experiment to reduce transmembrane NH₄⁺ movement through K⁺ channels. The successive decreases in pH_i produced by stepping down the extracellular ammonium concentration were used to estimate β_i (mM) as β_i=Δ[NH₄⁺]_i/ΔpH_i, where [NH₄⁺]_i=[NH₄⁺]_o× 10^(pH_o-pH_i), assuming that the pK of ammonium dissociation is the same in the extracellular and intracellular compartment (Roos & Boron, 1981; Lagadic-Gossmann et al. 1992a). The increase of intracellular acid equivalents produced by extracellular ammonium reduction was assumed to equal the calculated reduction of intracellular [NH₄⁺]. The value of β_i was assigned to the mid-point of each step decrease in pH_i.

Figure 9. Integrated plot of intracellular pH regulation.

A, the plots are taken from Fig. 4 for Cl⁻-HCO₃⁻ exchange (AE,▾) and Cl⁻-OH⁻ exchange (CHE, ▿) and from Fig. 6 for Na⁺-H⁺ exchange (NHE, ○) and Na⁺-HCO₃⁻ cotransport (NBC, •). For simplicity, the standard error bars have not been re-plotted. The vertical dotted lines that enclose the shaded area delineate the ‘permissive range’ of pH_i control. This is the range (defined arbitrarily) where flux magnitude through all the transporters is notably low (see Discussion for further details). B, close-up view of permissive range. Data taken from A with the additional inclusion of NHE and NBC flux activity at the mean resting pH_i of 7.07 (the single open square above the pH_i axis defines the identical activity for each transporter). The flux activity for the AE and CHE transporters at this same pH_i is also represented by the single open square plotted below the pH_i axis. These additional data are derived from Fig. 8B.

Figure 1. Intracellular intrinsic buffering.

A, experimental protocol: stepwise, intracellular acid loads were induced sequentially by superfusing 15 mM (NH₄)₂SO₄ and then reducing extracellular ammonium concentration in 5 mM steps (i.e. 2.5 mM step reductions of (NH₄)₂SO₄) to zero. All solutions were Cl⁻ free (gluconate substituted), contained in 30 μM Hoe 694 and were buffered (pH_o 7.40) with 20 mM Hepes (nominally free of CO₂/HCO₃⁻). Each stepwise fall of pH_i was used to calculate intracellular intrinsic buffering power (β_i). The resulting value is listed for the mid-point of each step fall in pH_i. B, •, β_i averaged over successive 0.2 unit pH_i bins, starting for the range 6.1-6.3, 6.3-6.5 and so on, where the number of determinations in each bin is n = 2, 5, 3, 4. From pH_i 6.9 and above, data have been averaged over successive 0.1 pH_i ranges, and n = 4, 7, 7, 7, 12, 22, 17, 17, 12. Data were taken from a total of 28 cells. The continuous line through the averaged data was calculated from eqn (1) in Results. This line represents the sum of two component buffers whose buffering powers (pK and concentration) vary with pH_i in accordance with the two intersecting biphasic curves plotted in the lower part of the figure.

Figure 1B pools data obtained from several experiments. As in previous work (Vaughan-Jones & Wu, 1990a;Lagadic-Gossmann et al. 1992a), we find that β_i declines as pH_i rises. Furthermore, in the range 6.8 to 7.3 the β_i values are very similar to those reported previously for this cell type (Lagadic-Gossmann et al. 1992a) and decline roughly linearly. Over a wider pH_i range, however, it is apparent that the decline is non-linear. As shown in Fig. 1B, this can be conveniently described by assuming contributions from two principal buffer species (A and B):

(1)

where [TA] and [TB] are total concentration of buffer A and buffer B, respectively. By using SigmaPlot to fit the β_ivs. pH_i curve, the following values were obtained: [TA]= 84.22 ± 5.37 mM, [TB]= 29.38 ± 1.32 mM, pK_A= 6.03 ± 0.08 and pK_B= 7.57 ± 0.08 (goodness of fit: r²= 0.78).

CO₂-dependent buffering

The experiment shown in Fig. 2A illustrates the effect of CO₂/HCO₃⁻ on intracellular buffering power. All solutions were again made Cl⁻ free in order to inhibit acid influx carriers (Leem & Vaughan-Jones, 1998b). For the first part of the trace, an intracellular alkali load was imposed in Hepes-buffered conditions, by using the acetate prepulse (20 mM) technique. Total intracellular buffering power (β_tot) under these conditions (nominally free of CO₂/HCO₃⁻) equals non-CO₂ intrinsic buffering power (β_i). Buffering power was calculated as β_tot=Δ[Acetate⁻]_i/ΔpH_i, where [Acetate⁻]_i=[Acetate⁻]_o× 10^(pH_i-pH_o), assuming that the pK_a of acetic acid is the same in both the extracellular and intracellular compartment. In Fig. 2A, β_i determined from the rise of pH_i following the first acetate removal was 21.2 mM, a value similar to that determined previously (Fig. 1) over a comparable pH_i range (7.0-7.35). The superfusate was then switched to one buffered with 5 % CO₂/HCO₃⁻ (same pH_o of 7.40), and a second acetate pulse applied. This time a higher acetate concentration (40 mM) was used. Acetate removal again produced a rise of pH_i. Two points should be noted. Firstly, the rise was followed by a rapid but only partial recovery of pH_i. This recovery was not caused by sarcolemmal acid influx on the AE or CHE carriers since it was occurring in Cl⁻-free solution. It was caused by the slow equilibration of intracellular CO₂-dependent buffering following the alkali loading procedure (Leem & Vaughan-Jones, 1998a), a process completed in about 2.5 min. Secondly, the rise in steady-state pH_i upon acetate removal was about the same as that seen previously in Hepes buffer despite the fact that twice the concentration of acetate had been removed. This result indicates that total intracellular buffering power had been approximately doubled in the presence of CO₂/HCO₃⁻. A similar increase of intracellular buffering power in CO₂/HCO₃⁻ was observed in four further experiments like that shown in Fig. 2A. The value of β_tot calculated from the rise of pH_i in CO₂/HCO₃⁻ solution in Fig. 2A was 48.3 mM. This value (β_tot) comprises the algebraic sum of β_i and β_CO2. Subtracting the buffering power determined initially in Hepes solution (21.2 mM) therefore delivers the value of β_CO2. In Fig. 2A, this was 27.1 mM.

Figure 2. Intracellular CO₂-dependent buffering.

A, intracellular buffering doubles on switching from Hepes to CO₂/HCO₃⁻-buffered conditions. The trace shows a ratiometric recording of pH_i. Superfusates were Cl⁻ free (gluconate substituted). An acetate prepulse (20 mM) was performed initially in Hepes, then (40 mM) in CO₂/HCO₃⁻-buffered solutions (same pH_o= 7.40). B, total intracellular buffering power (β_tot) in CO₂/HCO₃⁻-buffered conditions. Experimental protocol: a 40 mM acetate prepulse was executed in Cl⁻-free, 5 % CO₂/HCO₃⁻-buffered solution (pH_o 7.40) and the subsequent steady-state rise of pH_i used to calculate intracellular buffering power (β_tot). This has been plotted versus pH_i at the mid-point of the rise of intracellular HCO₃⁻ following acetate removal (see text for details). Data have been pooled from several cells and averaged for the following 0.1 pH_i ranges (•) starting at pH 6.90, with sample sizes, n = 8, 9, 6, 19 and 20. Also plotted (lower continuous line) is the relationship between intrinsic buffering capacity (β_i) and pH_i over the same pH_i range (6.90-7.38) calculated from eqn (1) in Results. C,β_CO2 in the cardiac cell. At a given pH_i, the difference between the mean experimental values of β_tot (• in B) and the value of β_i determined from eqn (1) (continuous curve in B) gives β_CO2. This difference has been plotted versus pH_i in C (○). The continuous line drawn through the data is the theoretical value of β_CO2vs. pH_i for a cell open to CO₂, and has been calculated from eqn (2) in Results.

Figure 2B shows a plot of total intracellular buffering power (β_tot; filled circles) as a function of intracellular pH, averaged for 62 buffer determinations from 31 cells bathed in CO₂/HCO₃⁻-buffered solution. Since total intracellular buffering power contains a large component attributable to β_CO2, and since intracellular CO₂-dependent buffering power theoretically increases exponentially with pH_i (assuming the cell is open to CO₂), we could not assign a calculated buffer value to the mid-point pH_i value following acetate removal. Instead, we assigned it to the mid-point of the rise in [HCO₃⁻]_i calculated for the rise of steady-state pH_i, on the grounds that full CO₂-dependent buffering is linearly related to intracellular bicarbonate (Roos & Boron, 1981) in accordance with the equation:

(2)

The pH_i value corresponding to the mid-point for the bicarbonate rise was obtained using the following equation:

(3)

where pH_start was the pH_i value just before acetate removal and pH_end was the steady-state pH_i after acetate removal.

Figure 2B shows that, over the pH_i range 6.9-7.4, total intracellular buffering power increases with a rise of pH_i. The continuous line drawn in Fig. 2B plots the relationship between intrinsic buffering power (β_i) and pH_i, as determined previously (eqn (1)) in Hepes-buffered solutions. Over the same pH_i range, β_i falls rather than rises, and the relationship is roughly linear. The value of β_i at any given pH_i (calculated from eqn (1)) was then subtracted from the averaged values of β_tot shown in Fig. 2B, thus giving β_CO2. In Fig. 2C the derived values of β_CO2 have been plotted as a function of pH_i.

The value of β_CO2 rises with increasing pH_i. The continuous line fitted to the data in Fig. 2C shows the theoretical relationship calculated for a cell open to CO₂, assuming CO₂ buffering is at equilibrium. The theoretical value for β_CO2 was calculated for a given pH_i by using eqn (2) (see legend to Fig. 2C for further details). Note that the experimental and theoretical values for β_CO2 are in reasonably close agreement. This indicates that intracellular CO₂-dependent buffering is fully expressed in the cardiac cell.

In all subsequent work we have assumed that intracellular buffering power, β_tot, equals the sum of β_i and β_CO2, where β_i conforms to eqn (1) and β_CO2 conforms to eqn (2).

Protocols for activating acid extruders and acid loaders

Hepes buffer

The trace shown in Fig. 3A, one of eight similar experiments, demonstrates the activation of acid-equivalent efflux and influx in the presence of a Hepes-buffered superfusate (nominally free of CO₂/HCO₃⁻). The first part of the trace shows pH_i recovery from an acid load (loading induced by ammonium prepulse). The recovery is known (Lagadic-Gossmann et al. 1992a) to be mediated by acid extrusion on Na⁺-H⁺ exchange (NHE). The second part of the trace shows pH_i recovery from an alkali load (loading induced by acetate prepulse). We have recently proposed (Leem & Vaughan-Jones, 1998b) that this latter recovery is mediated by acid-equivalent influx on a Cl⁻-OH⁻ exchanger (CHE), or alternatively by influx on an H⁺-Cl⁻ cotransporter (note that these alternative modes of transport cannot readily be distinguished). Consistent with this hypothesis, pH_i recovery from alkalosis is inhibited in Hepes-buffered, Cl⁻-free solution (note, for example, the lack of recovery from alkalosis following an acetate prepulse in the first part of the trace in Fig. 2A; see also Leem & Vaughan-Jones, 1998b). In Fig. 3A, the alkali recovery phase occurred in the presence of Hoe 694 (30 μM), a high affinity NHE-1 inhibitor, confirming that the acid influx is independent of NHE activity. Note also that this recovery continued to pH_i levels lower than control but that on removal of the NHE inhibitor the fall was terminated, pH_i rising again towards control levels. The same result was seen in seven other experiments. The result suggests that, at normal resting pH_i, both acid extrusion and acid loading fluxes must be active. We return to this point later in the Results section.

Figure 3. Activating sarcolemmal acid efflux and influx.

A, Hepes-buffered solution (pH_o 7.40). Ratiometric recording of pH_i. A 10 mM ammonium prepulse was succeeded by a 40 mM acetate prepulse. Hoe 694 (30 μM) was added, as indicated by bar, to inhibit Na⁺-H⁺ exchange. B, 5 % CO₂/HCO₃⁻-buffered solution (pH_o 7.40). The first bar above the pH trace indicates application of 10 mM ammonium chloride. The second bar indicates application of 80 mM acetate. Shortly before removal of the acetate, Na⁺_o was withdrawn (replaced by NMDG), in order to inhibit acid extrusion on Na⁺-H⁺ exchange and Na⁺-HCO₃⁻ cotransport.

CO₂/HCO₃⁻ buffer

Figure 3B illustrates an experiment similar to that shown in Fig. 3A, but performed in CO₂/HCO₃⁻ buffer. Recovery of pH_i from the acid load (induced by ammonium prepulse) was now mediated by a combination of NHE and Na⁺-HCO₃⁻ cotransport (NBC) (Dart & Vaughan-Jones, 1992; Lagadic-Gossmann et al. 1992a), while recovery >2.5 min after inducing an alkali load (acetate prepulse) was caused (Leem & Vaughan-Jones, 1998b) by acid equivalent influx on a combination of CHE plus Cl⁻-HCO₃⁻ exchange (AE). In this latter case, the recovery from alkalosis was observed in Na⁺-free solution (NMDG substituted) in order to ensure that it was independent of the activity of NHE or NBC (both of which are Na⁺ dependent). The pH_i recovery again continued to levels lower than control. Re-adding Na⁺ to the external superfusate, and thus restoring NHE and NBC activity, terminated this fall of pH_i, which promptly returned to control levels. The same result was seen in seven other experiments.

Characterization of acid loaders

The pH_i dependence of CHE and AE

Because the recoveries from intracellular alkalosis illustrated in Fig. 3A and B were recorded in the absence of acid extruder activity, they were used to characterize the pH_i sensitivity of acid influx. Figure 4 pools data derived from several such experiments. Acid equivalent influx was computed >2.5 min after acetate removal in order to ensure complete CO₂/HCO₃⁻ buffer equilibration following the alkali load (Leem & Vaughan-Jones, 1998a).

Figure 4. pH_i dependence of dual acid influx.

•, total acid influx (dpH_i/dt×β_tot), measured from pH_i recovery rate from intracellular alkalosis (acetate prepulse) in CO₂/HCO₃⁻-buffered conditions (Na⁺-free conditions; Na⁺_o replaced by NMDG). ○, acid influx measured in Hepes buffered conditions (i.e. influx through Cl⁻-OH⁻ exchange; dpH_i/dt×β_i; 30 μM Hoe 694 or 30 μM DMA was present to inhibit acid extrusion through NHE). □, total influx - CHE flux therefore plots the CO₂/HCO₃⁻-dependent acid influx (caused by AE activity). Flux values in CO₂/HCO₃⁻ (•) have been averaged over successive 0.025 pH_i ranges starting (left to right) with 7.025-7.05; n = 114, 108, 94, 109, 122, 130, 110, 96, 63, 41, 17, 9, 5. Flux values in Hepes (○) have been averaged over successive 0.025 pH_i ranges starting with 7.05-7.075; n = 126, 128, 113, 109, 113, 113, 83, 75, 76, 71, 68, 50, 42, 32, 23, 22, 18, 17. Data taken from a total of 8 cells.

Inspection of Fig. 4 shows that in Hepes (open circles) acid influx is low at pH_i 7.06 and doubles as pH_i increases by about 0.3 units (from pH_i 7.06 to 7.35). This must represent the pH_i sensitivity of CHE-mediated acid influx. In CO₂/HCO₃⁻ buffer (filled circles), influx is again low at pH_i 7.06 and increases steeply with rising pH_i. These latter measurements must represent the pH_i sensitivity of acid influx occurring via a combination of AE and CHE activity. Subtracting the CHE curve (open circles) from the combination curve (CHE + AE; filled circles) provides an estimate of the pH_i sensitivity of AE alone (open squares). Inspection of this latter curve reveals that acid influx through AE is much more pH_i sensitive than that through CHE, increasing nearly tenfold in response to a 0.3 unit rise in pH_i.

Characterization of acid extruders

The pH_i dependence of NHE and NBC

Although a preliminary description of this has been presented for the guinea-pig ventricular myocyte (Lagadic-Gossmann et al. 1992a), a full analysis averaged for several cells has so far not been undertaken. The experiments shown in Fig. 5 illustrate the two components of acid extrusion in the myocardial cell (NHE and NBC). In the first part of Fig. 5A, acid extrusion in Hepes buffer is revealed as an amiloride-inhibitable pH_i recovery from intracellular acidosis (loading induced by ammonium prepulse). This confirms the functional expression of NHE activity. The later part of the trace shows activation of an amiloride-insensitive pH_i recovery following replacement of the superfusate's Hepes buffer by CO₂/HCO₃⁻ buffer. The amiloride-insensitive recovery has been ascribed to the NBC carrier (Dart & Vaughan-Jones, 1992; Lagadic-Gossmann et al. 1992a).

Figure 5. Dual acid efflux.

A, the first part of the experiment was performed in Hepes-buffered solutions. The second part, as indicated, was performed in 5 % CO₂/HCO₃⁻. The pH_o was 7.40 throughout. Note the amiloride-resistant pH_i recovery from an intracellular acid load (15 mM ammonium withdrawal) in CO₂/HCO₃⁻ buffer. B, CO₂/HCO₃⁻ -buffered solutions throughout (pH_o 7.40). Note that pH_i recovery from an intracellular acid load (15 mM ammonium withdrawal) was slowed by DMA.

Figure 5B dissects out the dual extrusion system in a different way. Here, in CO₂/HCO₃⁻ buffer, pH_i recovery from an acid load (loading by ammonium prepulse) was observed first in the presence of the high affinity NHE inhibitor dimethyl amiloride (DMA) and then in its absence. Recovery was much faster in the absence of DMA, confirming that NHE contributes significantly but not exclusively to pH_i recovery. Note that following acute intracellular acid loading, intracellular CO₂-dependent buffering should re-equilibrate reasonably rapidly (10-20 s) unlike following acute intracellular base loading where equilibration is much slower (a few minutes; Leem & Vaughan-Jones, 1998a). Slow CO₂-dependent buffering will not therefore significantly distort estimates of transporter flux derived from pH_i recovery from acid loads.

Figure 6 pools data obtained from several experiments like those shown in Fig. 5B. Acid extrusion (dpH_i/dt×β_tot) has been plotted versus pH_i for results in CO₂/HCO₃⁻ buffer containing 30 μM DMA (open circles). This therefore describes the pH_i dependence of acid efflux through NBC. Also plotted in Fig. 6 is acid extrusion in CO₂/HCO₃⁻ buffer in the absence of DMA (filled circles). This latter graph provides the pH_i dependence of acid extrusion through a combination of NHE plus NBC. The difference between the two curves (filled circles minus open circles) therefore provides a description (open squares) of the pH_i sensitivity of extrusion through NHE alone, determined in the presence of a CO₂/HCO₃⁻ buffer system. Inspection of the flux data in Fig. 6 indicates that, in the pH_i range 7.0-6.5, NHE activity increases much more steeply than that of NBC.

Figure 6. pH_i dependence of dual acid efflux.

Data derived from 22 cells exposed to experimental protocols like that shown in Fig. 4B.•, total acid efflux derived from pH_i recovery from an intracellular acid load. ○, acid efflux through Na⁺-HCO₃⁻ cotransport (NBC), derived from pH_i recovery from an acid load in the presence of 30 μM DMA. □, acid efflux through Na⁺-H⁺ exchange (NHE), derived from the difference between the recovery rate with and without DMA. Data derived from experiments like that shown in Fig. 5B.•, fluxes averaged over successive 0.05 pH_i ranges, starting with 6.55-6.60, n = 2, 2; and averaged over successive 0.025 pH_i-ranges, starting with 6.65-6.70, n = 2, 3, 6, 7, 13, 16, 22, 29, 36, 49, 40, 66, 92, 108, 94, 115. ○, fluxes averaged over 0.05 pH_i bins starting with 6.55-6.60, n = 14, 16; and averaged over successive 0.025 pH_i ranges starting with 6.65-6.75, n = 16, 6, 31, 43, 49, 60, 82, 72, 83, 87, 100, 140, 108, 112, 156, 146.

Note that the ordinate in Fig. 6 refers to net acid efflux, i.e. the fluxes ascribed to NHE and NBC activity have not been corrected for possible simultaneous acid influx activity. This is considered below, in the section on ‘flux overlap’.

The pH_i dependence of acid extrusion was further derived in a separate set of experiments that employed a different protocol. Net extrusion was computed from the rate of pH_i recovery after an ammonium prepulse performed first in Hepes (for NHE) and then in CO₂/HCO₃⁻ buffer (for NHE plus NBC). A sample ammonium prepulse and subsequent pH_i recovery in the two conditions is shown in Fig. 7A. Note that recovery was faster in CO₂/HCO₃⁻ despite the fact that total intracellular buffering power is greater than in Hepes. Data averaged from several such experiments have been plotted in Fig. 7B. Acid extrusion in CO₂/HCO₃⁻ buffer (open circles; total extrusion) is consistently larger than that estimated in Hepes buffer (filled circles; NHE). The difference between these two plots gives an estimate of the pH_i dependency of NBC flux. This is plotted (open squares) along with the NHE data (filled circles) in the inset to Fig. 7B. The pH_i sensitivity of NHE and NBC derived in this way is very similar to that seen in Fig. 6, again consistent with NBC activity complementing that of NHE in CO₂/HCO₃⁻ buffer. The results in Fig. 7 therefore support the results of the pharmacological dissection (with DMA) illustrated in Fig. 6.

Figure 7. pH_i dependence of acid efflux determined without pharmacological dissection.

A, recovery of pH_i from an intracellular acid load (15 mM ammonium prepulse) in Hepes- and CO₂/HCO₃⁻-buffered conditions. B, plot of acid efflux versus pH_i derived from pH_i recoveries like those shown in A, for Hepes-buffered (•, NHE activity) and CO₂/HCO₃⁻ -buffered conditions (○, combined activities of NHE and NBC). Data derived from a total of 7 cells. •, buffer values averaged over successive 0.05 pH_i ranges, starting with 6.55-6.60, n = 1, 3, and then averaged over successive 0.025 pH_i ranges starting with 6.65-6.675, n = 11, 8, 17, 18, 24, 33, 34, 48, 58, 77, 100, 153, 203, 163, 25. ○, buffer values averaged over successive 0.05 pH_i ranges starting with 6.55-6.6; n = 5, 9; and successive 0.025 pH_i ranges starting with 6.65-6.675, n = 17, 11, 16, 24, 39, 52, 71, 68, 72, 88, 124, 97, 89, 98, 28. Inset to B plots as a function of pH_i (□) the difference between the values for total efflux and NHE-mediated efflux (data taken, at common pH_i values, from the main graph of B). This gives the pH_i dependence of NBC. For comparison, the data for NHE activity are also re-plotted (•, data taken from main graph of B).

The setting of steady-state pH_i: overlap between acid extrusion and loading

Resting (steady-state) pH_i of the ventricular myocyte was virtually identical in Hepes and CO₂/HCO₃⁻ buffer. It was 7.07 ± 0.01, n = 134 in Hepes; and 7.04 ± 0.01, n = 78 in CO₂/HCO₃⁻. Although the difference between the values is statistically significant (P < 0.05; unpaired t test), it amounts to only 0.03 pH units. The analysis of acid influx shown in Fig. 4 suggests that, at these resting pH_i values, there will be a small but significant activation of CHE and also (in CO₂/HCO₃⁻ buffer) of AE. This implies that there must also be a simultaneous low level of acid extrusion, or pH_i would not be in a steady state. The simultaneous activity of loading and extrusion transporters at resting pH_i is consistent with the previous observation (Fig. 3A and B) that, in the absence of extrusion, the acid loaders drive pH_i below its resting value.

We have examined further the nature of the background acid loading that operates at the resting pH_i. In Hepes buffer, background loading can be revealed by inhibiting Na⁺-H⁺ exchange, as illustrated by the experiment shown in Fig. 8A. Dimethyl amiloride (DMA) was added to block NHE, producing a slow fall of resting pH_i that was reversed upon DMA washout. The middle and right-hand columns in Fig. 8B compare this acid loading (hatched column) with that measured during pH_i recovery from an intracellular alkali load (open column; data gathered in the presence of the NHE inhibitor Hoe 694, 30 μM). At a pH_i of 7.07 (equivalent to normal, resting pH_i) the two values are identical. Since pH_i recovery from an intracellular alkali load is, in Hepes, mediated by CHE (recovery is abolished almost entirely in Cl⁻-free solution; Leem & Vaughan-Jones, 1998b), the above result indicates that background acid loading revealed by adding DMA to a resting cell is also CHE mediated.

Figure 8. Background acid loading.

A, background acid loading (i.e. fall of pH_i) revealed in Hepes-buffered solutions by adding DMA to inhibit NHE activity. B, open column, acid influx measured at pH_i 7.07 in Hepes-buffered solution, estimated from pH_i recovery rate from an intracellular alkali load (40 mM acetate prepulse; cf. Fig. 3A) imposed in the presence of Hoe 694 (30 μM). Hatched column, background acid loading at pH_i 7.07 in Hepes-buffer, measured from the rate of fall of pH_i upon addition of 30 μM DMA to resting cells (as in A). Filled column, acid influx at pH_i 7.07 in CO₂/HCO₃⁻-buffered solution, measured from pH_i recovery rate from an intracellular alkali load (80 mM acetate prepulse; cf. Fig. 3B) imposed in Na⁺-free solution (NMDG-substituted, to inhibit acid extruders). ** Significant difference, P < 0.01; N.S., not significant, P > 0.05.

The left-hand column in Fig. 8B (filled column) shows that background acid loading measured at pH_i 7.07 in Na⁺-free, CO₂/HCO₃⁻ buffer was twice that seen in Hepes. Data were taken from experiments like that shown in Fig. 3B. The Na⁺_o was replaced by NMDG about 30 min before taking measurements so that Na⁺_i would also have been negligible (Ellis, 1977). The absence of Na⁺ inhibits acid extrusion on both NHE and NBC. Since background acid loading in the isolated ventricular myocyte requires the presence of extracellular Cl⁻ (Leem & Vaughan-Jones, 1998b), the increased rate of acid loading on adding extracellular HCO₃⁻ must have been caused by activation of the AE transporter. Thus at resting pH_i in CO₂/HCO₃⁻ buffer, CHE and AE must mediate background acid loading about equally. Since resting pH_i in Hepes and CO₂/HCO₃⁻ is essentially the same (differing by no more than 0.03), the above result implies that, in CO₂/HCO₃⁻, NHE and NBC carriers must also mediate acid extrusion about equally, in order to maintain a constant pH_i. Thus, at steady-state pH_i, all four acid equivalent carriers are equally active, each operating at a rate of about 0.15 mM min⁻¹.

Plotting pH_i regulation

The pH_i dependence of acid flux through all four transporters has been combined on a common pH_i axis in Fig. 9A (upper panel). Figure 9B (lower panel) shows the central pH_i region of the plots on an expanded scale. In both panels, the points are taken from Figs 4 and 6 but, for clarity, the standard error bars have been omitted. Acid efflux (open circles, NHE; filled circles, NBC) has not been corrected for possible simultaneous acid influx activity (but see below for consideration of this). In contrast, acid influx (open triangles, CHE; filled triangles, AE) needs no correction since it was estimated in the absence of extruder activity. In the present work, acid influx was not measured at pH_i values less than 7.03, but activity of CHE and AE is low at this pH_i, being 0.15 mM min⁻¹ and presumably declining to zero as pH_i decreases to about 6.70, which is the estimated equilibrium pH_i for both carriers (Sun et al. 1996). Indeed in past work, background acid loading at pH_i 6.95 has been shown to be negligible in these cells in Hepes or CO₂/HCO₃⁻ buffer (Lagadic-Gossmann et al. 1992b). At pH_i < 7.03, background loading is therefore sufficiently small to have little effect on measurements of acid efflux, and so was ignored. For acid extrusion at pH_i > 7.03, however, simultaneous acid influx is increasingly likely to contaminate significantly the efflux measurements. In this pH_i range, acid efflux is regulated down to low levels while influx increases. The acid efflux through NHE and NBC at the resting pH_i of 7.07 (0.15 mM min⁻¹ through each carrier) has therefore been included in Fig. 9B (for convenience represented by the single open square above the pH_i axis). Similarly the influx through CHE and AE at this pH_i (0.15 mM min⁻¹ through each carrier) has also been included as the single open square plotted below the pH_i axis. The data shown in Fig. 9B therefore emphasize the region of overlap between efflux and influx at pH_i levels close to the steady-state value.

A final point to note in Fig. 9 is that unidirectional acid extrusion at pH_i > 7.2, although not plotted, must be close to zero because in this range pH_i recovery rate from an alkali load is unaffected by the presence or absence of Na⁺ (Leem & Vaughan-Jones, 1998b).

Reconstructing pH_i regulation

The pH_i activation of acid loading and extrusion fluxes shown in Fig. 9 provides sufficient detail to permit a full reconstruction of pH_i regulation in the ventricular myocyte. Such reconstruction is an important means of testing the accuracy of our proposed four-transporter scheme for pH_i control. Some parts of the model, notably those for intracellular CO₂-dependent buffering and for the kinetics of acetate prepulsing, have been published already (Leem & Vaughan-Jones, 1998a). In the present work we have selected best-fit polynomial expressions for the pH_i activation of NHE, NBC, CHE and AE, derived from the data shown in Figs 4 and 6 (see dashed lines fitted to data in Fig. 9A and B). By combining these polynomial expressions with our previous computations for intracellular CO₂-dependent H⁺ buffering, we have arrived at an integrated model of pH_i regulation in the guinea-pig myocyte. In the computations, we have used the presently derived equation for intrinsic intracellular buffering (eqn (1) and Fig. 1), and we have extended the model to include details of the ammonium prepulse technique. These additions to the 1998 Leem & Vaughan-Jones model are given in the Appendix.

Figure 10A illustrates a simulation of an intracellular acidosis that activates the acid extruders. It shows, firstly, an ammonium prepulse and the subsequent NHE-mediated pH_i recovery from acidosis in Hepes buffer. This is followed by a second ammonium prepulse, but in this case NHE in the model has been switched off (equivalent, experimentally, to acid loading in the presence of an NHE inhibitor such as amiloride). Note the lack of pH_i recovery from the acid load. There is then a switch in the model to CO₂/HCO₃⁻ buffer in order to activate NBC. This leads to the onset of a pH_i recovery from acidosis that is independent of NHE. The simulation in Fig. 10A should be compared with the original experimental trace shown in Fig. 10B.

Figure 10. Modelling intracellular pH regulation: dual acid extrusion.

A, results of the modelling. Initially NBC and AE fluxes are switched off in the model while β_tot is set to equal β_i (simulating CO₂-free conditions). Following the second (15 mM) ammonium prepulse, NHE activity in the model is switched off, thus simulating the addition of amiloride. In the final part of the simulation, CO₂/HCO₃⁻ buffer conditions are initiated in the model, thus mimicking the addition of 5 % CO₂. Intracellular buffering is now assumed to include contributions from the time-dependent CO₂/HCO₃⁻ buffer system. The NBC and AE transporters are also switched on in the model. B, specimen record; this shows, for comparison, the experimental trace (taken from Fig. 5A) that has a protocol similar to that in the modelling shown in A.

Figure 11A shows a simulation of an intracellular alkalosis that activates the acid loading transporters. The first part of the trace simulates an acetate prepulse in CO₂/HCO₃⁻ buffer. This is followed by a rapid recovery from alkalosis. The recovery is attributable firstly to slow CO₂-dependent intracellular buffering and secondly to acid influx activity on CHE and AE. The simulated addition of DIDS (which inhibits AE and NBC activity; these carriers are thus switched off in the model) reduces the rate of acidification observed during the slow phase of recovery from the alkali load. Finally, a switch from CO₂/HCO₃⁻ to Hepes buffer is simulated. This produces initially a large intracellular alkalosis caused through the loss of intracellular CO₂, followed by a pH_i recovery from alkalosis due to stimulation of acid influx (base efflux) on the CHE transporter. The simulation in Fig. 11A should be compared with the specimen experimental trace shown in Fig. 11B.

Figure 11. Modelling intracellular pH regulation: dual acid loading.

A, results of the modelling. The first part of the trace is modelled for 5 % CO₂/HCO₃⁻-buffered conditions (pH_o 7.40), showing the addition and subsequent removal of (80 mM) extracellular acetate. A second acetate prepulse (80 mM) was modelled while simultaneously switching off AE and NBC activity (equivalent to adding the drug DIDS). Finally, withdrawal of 5 % CO₂/HCO₃⁻ buffer (constant pH_o of 7.40) is simulated by setting P_CO2 to zero in the model and switching off AE and NBC activity. B, for comparison, a specimen experimental recording of pH_i is shown with a protocol similar to that modelled in A. The dose of DIDS applied was 0.1 mM. The acetate applications were made at a concentration of 80 mM.

DISCUSSION

The present work characterizes the pH_i dependence of acid-equivalent flux through the four sarcolemmal transporters responsible for pH_i regulation in the cardiac cell. While pH_i dependence for NHE has been characterized for various cardiac preparations (e.g. Lazdunski et al. 1985; Vaughan-Jones & Wu, 1990b), full kinetic analyses for guinea-pig ventricular NHE, NBC, AE and CHE have not so far been presented. All four pH_i activation curves have now been determined experimentally and, in combination with new data on intrinsic and CO₂-dependent buffering power, have been integrated into a computational model of intracellular pH regulation. This is the first full model of pH_i regulation in heart although results of an earlier and simpler version have recently been presented, based on experimental data culled from the present work (Ch'en et al. 1998). A quantitative model of pH_i control was first formulated over 20 years ago for another cell type, the squid giant axon, by Boron & de Weer (1976). Their model incorporated a single acid-equivalent transporter (an acid extruder), but while the issue of slow CO₂-dependent buffering was alluded to, it was not specifically addressed. The present scheme is therefore the first to incorporate multiple efflux-influx transporters plus time-dependent buffering. By using this approach we are able to predict with reasonable accuracy the pH_i transients following intracellular acid and alkali loads, both in the presence and absence of CO₂/HCO₃⁻ buffer.

AE and CHE

The two transporters display very different sensitivities to intracellular pH. The AE carrier (Cl⁻-HCO₃⁻ exchange) shows a modest increase in activity in the pH_i range up to 7.15, but above this value it activates steeply with pH_i. In contrast, the CHE carrier (Cl⁻-OH⁻ exchange) displays a modest, near-linear increase in activity over the whole pH_i range tested, from 7.05 to 7.50. These considerable differences in pH_i activation of AE and CHE reinforce previous evidence for the existence of a dual acid loading system in the cardiomyocyte.

AE activation

The steep activation of AE at pH_i > 7.15 (Fig. 4) is comparable to that reported recently by Xu & Spitzer (1994) for the ventricular myocyte. In the latter work the activation was fitted most simply by a linear function whereas the present pH_i dependence is clearly curvilinear. Saturation of AE activity at high pH_i has not yet been seen but Leem & Vaughan-Jones (1998a,b) have pointed out the danger of analysing acid fluxes at high pH_i immediately following a weak acid prepulse (when CO₂/HCO₃⁻ buffering is out of equilibrium for 2-3 min). In the present work this has limited our assessment of AE activity to a maximum pH_i of 7.35 (Fig. 4). We therefore do not exclude flux saturation at higher pH_i values.

The cause of the steep activation of cardiac AE by pH_i is not known but it is unlikely to be due simply to increased binding of bicarbonate to the internal transport site. At constant P_CO2 (5 %), raising pH_i from 7.05 to 7.35 (at CO₂/HCO₃⁻ equilibrium) increases intracellular HCO₃⁻ concentration by about twofold (from 9.3 to 19.6 mM). Assuming an AE transport stoichiometry of 1 HCO₃⁻ : 1 Cl⁻ this would, at most, double bicarbonate efflux, provided there were non-saturating, first-order kinetics at the HCO₃⁻ binding site. In reality, net efflux of HCO₃⁻ through AE increases by twelvefold in this pH_i range (see Fig. 4). The simplest explanation for this is that HCO₃⁻ efflux is regulated allosterically by pH_i or even by intracellular HCO₃⁻ (in addition to HCO₃⁻ binding to the transport site). In this case, AE activation would be triggered by deprotonation and/or by binding of bicarbonate to an intracellular modifier site. Evidence for a deprotonation model has emerged recently from site-directed mutagenesis of cDNA of AE-1 and AE-2 isoforms (Sekler et al. 1995; Zhang et al. 1996).

Physiological roles for AE and CHE

Both carriers assist pH_i regulation during intracellular alkalosis (Leem & Vaughan-Jones, 1998b) and both contribute significantly to the sensitivity of pH_i to a fall of pH_o (Sun et al. 1996). Moreover, as discussed below, both are activated equally at the resting pH_i. Nevertheless, the steeper pH_i sensitivity of AE indicates that it is the major system for protecting pH_i from alkali overload.

An additional physiological role for cardiac anion exchangers is in the control of intracellular Cl⁻ (Vaughan-Jones, 1979, 1986). Both the AE and CHE transporters will mediate Cl⁻ uptake. It is notable that a DIDS-insensitive, Na⁺-independent Cl⁻ uptake system has been described recently in both cardiac and smooth muscle (Chipperfield et al. 1997), in addition to uptake via Cl⁻-HCO₃⁻ exchange and the Na⁺-K⁺-2Cl⁻ cotransporter. A candidate for this novel Cl⁻ transporter may therefore be CHE.

Molecular identity of acid loading

We have previously suggested (Sun et al. 1996) that CHE may be an AE-related protein. A similar suggestion has been made for a CHE-like transporter in intestinal epithelial tissue (Alvarado & Vasseur, 1996) although in this latter case the carrier is described as a H⁺-Cl⁻ cotransporter rather than a Cl⁻-OH⁻ exchanger. Whichever ion species is involved (H⁺ or OH⁻), an AE protein that reproduced wild-type CHE activity in the cardiac cell would have to fulfil the conditions of transporting OH⁻ (or H⁺) in preference to bicarbonate, and of being relatively insensitive to DIDS (Leem & Vaughan-Jones, 1998b), combined properties that have yet to be demonstrated for any AE isoform. As for the AE isoform responsible for functional Cl⁻-HCO₃⁻ exchange in heart, a strong candidate must be AE-3b or 3c (Yannoukakos et al. 1994) although Puceat et al. (1995) have suggested that, in the adult rat ventricular myocyte, it is AE-1 and that AE-3 may serve a structural rather than a pH_i regulatory role.

NHE and NBC

Both transporters are active at resting pH_i and are activated further by a fall of pH_i. It is clear, however, that the greater activation occurs on NHE once pH_i has fallen below 6.90. Over the pH_i range tested (7.03-6.55, a fall of about 0.5 units) NHE activity increases 30-fold. Such steep activation is consistent with previous work on this carrier, which displays positive allosteric stimulation by intracellular H⁺ once pH_i dips below typical resting values (Aronson, 1985; Vaughan-Jones & Wu, 1990b). In contrast, activity of NBC activates roughly linearly with decreasing pH_i. Whether allosteric stimulation is involved here is not known.

It is notable that for relatively modest acid loads (i.e. to pH_i 6.90), both NHE and NBC are stimulated about equally (Fig. 6). Thus, at pH_i values within the normal physiological range, both carriers are equally important for mediating acid extrusion.

Molecular identity of acid extrusion

While the functional NHE isoform in heart is known to be NHE-1 (Scholz et al. 1995; Fliegel & Dyck, 1995; Loh et al. 1996), the molecular identity of the cardiac NBC carrier is not known. A renal Na⁺-HCO₃⁻ cotransport (labelled NBC-1) has recently been cloned and expressed from salamander, rat and human (Romero et al. 1997, 1998; Burnham et al. 1997, 1998). It is possible that mammalian cardiac NBC is related to this, especially since mRNA fragments of renal NBC-1 have been provisionally identified in cardiac tissue. The functional properties of renal and cardiac NBC seem very different since the former is an acid loader and the latter an acid extruder. This need not, however, imply greatly different molecular structures. Functional differences could result from differences in Na:HCO₃⁻ transport stoichiometry influencing the equilibrium pH_i of the carrier and hence its direction of operation across the surface membrane. For example, renal NBC-1 has a (probable) equivalent stoichiometry (n) of 3 HCO₃⁻:1 Na⁺ (i.e. n = 3; Romero et al. 1997) and thus a low equilibrium pH_i (about 6.0), biasing it in favour of acid loading under physiological conditions. In contrast, cardiac NBC was originally suggested to have a stoichiometry ranging between n = 1 and n = 2 (Lagadic-Gossmann et al. 1992a) and thus a higher equilibrium pH_i which, under most conditions, would favour acid extrusion (i.e. HCO₃⁻ ion influx). A stoichiometry of n = 2 has been proposed recently for cardiac NBC in cat papillary muscle and the rat ventricular myocyte (Camilion de Hurtado et al. 1995; Aiello et al. 1998), where it is suggested that NBC activity is both electrogenic and voltage dependent. It should be noted that the assumption of an electrogenic (n = 2) or electroneutral (n = 1) NBC stoichiometry would not alter the pH_i dependence of acid efflux through NBC reported in the present work (Fig. 6) as this was determined simply from changes in pH_i recovery rate.

The setting of steady-state pH_i

When pH_i is in a steady state, all four acid transporters are activated to the same extent. This implies that physiological changes in resting pH_i may be achieved by modulation of the activity of any or all of the carriers. Sarcolemmal receptor-activated modulation has been reported variously for NHE, NBC and AE in cardiac cells (e.g. Lagadic-Gossmann et al. 1992b;Desilets et al. 1994; Matsui et al. 1995), but it is not known if CHE is also receptor coupled.

‘Permissive range’ of pH_i control

The activity of the four transporters (Fig. 9A) is regulated down to low levels in the pH_i range 6.95-7.25. Outside these limits, net acid-equivalent flux activates steeply, thus safeguarding the cell from extreme acidosis or alkalosis. In the central pH_i region (6.95 to 7.25), however, the low transporter fluxes mean that small acid/base loads or small shifts in the pH_i sensitivity of an individual acid/base transporter will relatively easily produce displacements of pH_i. The central region (Fig. 9A and B) may therefore represent a permissive range within which small pH_i displacements are tolerated, at least transiently. Such an arrangement could provide a control system that permits some forms of pH_i signalling in the cardiac cell while still, in the longer term, overseeing pH_i regulation. It is notable, for example, that a number of cardioactive hormones and neurotransmitters, such as catecholamines (Lagadic-Gossmann et al. 1992b;Desilets et al. 1994), angiotensin (Matsui, et al. 1995) and endothelin (Wu & Tseng, 1993) trigger changes of pH_i within the permissive range that may be of functional importance.

Intracellular buffering

The present work provides a comprehensive examination of intracellular buffering power in the ventricular myocyte. A convenient fit to the pH_i dependence of intrinsic buffering (Fig. 1B) could be achieved by assuming two main intracellular buffers of differing concentration and pK_a (pK values of 6.03 and 7.57). The identity of the two putative buffers is not known, although intracellular histidine residues may contribute to the higher pK, while intracellular ATP and inorganic phosphate may contribute to the lower pK. The possibility remains that the results actually represent the effects of several rather than just two intracellular buffer moieties with a whole range of overlapping pK values. Whatever the mechanism of intrinsic buffering, its high power at low extremes of pH_i presents powerful protection against acute intracellular acid overload, a feature also complemented by the steep activation of NHE in this pH_i range.

An important finding in the present work is that CO₂-dependent intracellular buffering is readily demonstrable in the ventricular myocyte. Moreover, this component of buffering conforms quantitatively to that expected for a cell fully open to CO₂. Although such buffering has now been observed in several cell types (Thomas, 1976; Zhao et al. 1995; Leem & Vaughan-Jones, 1998a), there are some notable and puzzling reports of little or no CO₂-dependent buffering in other cells such as those of vascular smooth muscle (Baro et al. 1989; Aickin, 1994) and mammalian CNS neurones (Amos et al. 1996). Possible causes of the lack of detection of CO₂ buffering in these latter cell types have been discussed by Leem & Vaughan-Jones (1998a).

Model of intracellular pH regulation

The model (Figs 10 and 11) predicts the features of pH_i regulation in the cardiac myocyte remarkably well including the presence of significant HCO₃⁻-dependent and HCO₃⁻-independent mechanisms for recovery of pH_i from acid and alkali loads. The model also predicts the presence of fast and slow phases of pH_i recovery from an alkali load although in some experiments (e.g. Fig. 11B) the fast phase (largely due to CO₂-dependent buffering, Leem & Vaughan-Jones, 1998a) is less pronounced than in the model (Fig. 11A). In other experiments, however, clear ‘fast phase’ followed by ‘slow phase’ recoveries are evident (see e.g. Fig. 3B of present paper, and see Figs 2, 5 and 7 of Leem & Vaughan-Jones, 1998b). Some differences between experiment and simulation can be seen in the time course of pH_i recovery from an acid as well as an alkali load (Fig. 10). These temporal discrepancies most likely occur because averaged data have been used in the model so that an exact match with any individual experiment cannot be expected. What is encouraging, however, is that the principal features of cardiac pH_i control are reproduced so well and that the overall predicted time course of control is reasonable.

Another important feature of both the model and the experimental results is that the pH_i dependency of the four types of transporter is the key factor in determining steady-state pH_i. It might have been argued, for example, that other mechanisms contribute to the ‘background acid loading’ of the cell and therefore to the setting of resting pH_i. Such mechanisms could be the metabolic production of acid within the cell (cf. Bountra et al. 1988) or an influx of acid on other carriers such as sarcolemmal Ca²⁺-H⁺-ATPase (Naderali et al. 1997). These possibilities are unlikely to have played a significant role since pH_i recovery from intracellular alkalosis is virtually absent in Cl⁻-free solution, i.e. background loading is Cl⁻_o dependent (Leem & Vaughan-Jones, 1998b), consistent with contributions from CHE and AE.

Similar model for all mammalian cardiac cells?

It seems probable that the four-transporter model will account for pH_i regulation in cardiac cells from mammalian species other than guinea-pig, as well as in non-ventricular types of cardiac cell, such as atrial and Purkinje cells, although the levels of functional expression of each transporter may be expected to vary regionally and developmentally. NHE has been identified in all cardiac cells examined to date. NBC has been positively identified in guinea-pig (Lagadic-Gossmann et al. 1992a), rat (Le Prigent et al. 1997) and cat (Camilion de Hurtado et al. 1995) as well as, originally, in the sheep Purkinje fibre (Dart & Vaughan-Jones, 1992). AE activity was first described in the sheep Purkinje fibre (Vaughan-Jones, 1979, 1986) and has since been identified in ventricular cells of guinea-pig and rat (Lagadic-Gossmann et al. 1992a;Xu & Spitzer, 1994). CHE activity has so far been investigated only in ventricular cells of guinea-pig and rat (e.g. Sun et al. 1996; Leem & Vaughan-Jones, 1998b).

Future refinements to the model

Important features that are currently absent from the present model and which must be incorporated once suitable experimental data become available are the overall sensitivity of the integrated pH_i control system to extracellular pH, and its sensitivity to extracellular agonists such as hormones and neurotransmitters. A preliminary coupling of pH_i control to other cardiac cellular models of excitation and contraction has already been undertaken (Ch'en et al. 1998), and is providing insight into the role of acid-equivalent transporters in generating inotropic and arrhythmogenic patterns of behaviour in the myocardium.

APPENDIX

Modelling pH_i regulation

Results of the modelling are shown in Figs 10 and 11. The model includes the ammonium- and acetate-prepulse techniques, used for inducing intracellular acid and base loads, respectively. These techniques have been modelled using a general approach similar to that adopted by Boron & de Weer (1976). The present model also contains formulations for intracellular intrinsic and CO₂-dependent buffering and for the pH_i dependence of transporter activity (NHE, NBC, AE and CHE). Our modelling of the acetate prepulse and of CO₂-dependent buffering has been presented previously (Leem & Vaughan-Jones, 1998a) and so is reproduced here only briefly.

pH_i recovery from an acid load

Ammonium prepulse technique

We make the following assumptions. (i) The stability constant for ammonium ions is the same inside and outside the myocyte. (ii) NH₃ diffuses readily through the lipid sarcolemmal phase (in accordance with Fick's Law; eqn (1)) whereas, for NH₄⁺, there is a low constant field channel conductance (eqn (2)). (iii) The apparent intracellular pK_a for CO₂/HCO₃⁻ is the same as in extracellular Tyrode solution (i.e. 6.12; see Table 1). (iv) Except for the CO₂ hydration reaction, all other reactions are instantaneous. (v) There is no membrane conductance for H⁺, OH⁻ or HCO₃⁻ (note that pH_i in cardiomyocytes is voltage independent, arguing for low conductances for these ions; Lagadic-Gossmann et al. 1992a,b;Sun et al. 1996).

Table 1.

Parameters used in the simulations

Parameter	Value	Reference
Myocyte volume	28 148 × 10−12 cm3	Campbell et al. 1987
Myocyte surface-area/volume ratio	2017 cm−1	Leem & Vaughan-Jones, 1998a
Non-ionized acetate permeability (PHA)	1.44 × 10−3 cm s−1	Klocke et al. 1972
Ionized acetate permeability (PA−) *	6.77 × 10−9 cm s−1	—
NH3 permeability (PNH3)	1.08 × 10−2 cm s−1	Klocke et al. 1972
NH4+ permeability (PNH4+) †	1.408 × 10−2 cm s−1	—
CO2 permeability	0.58 cm s−1	Forster, 1969
Ionization constant of acetate	10−4.528	Harned & Hickey, 1937
Ionization constant of ammonium	10−9.03	Klocke et al. 1972
Equilibrium constant of CO2	reaction 10−6.12	Leem & Vaughan-Jones, 1998a
CO2 hydration rate constant	0.365	Leem & Vaughan-Jones, 1998a

^*We calculated this value from the constant field equation, on the arbitrary assumption that acetate ion current is 5 pA at a resting membrane potential of −80 mV and [A⁻]_i and [A⁻]_o are 0.03 mol and 0.08 mol, respectively. This anion current is lower than that assumed in earlier modelling (50 pA, Leem & Vaughan-Jones, 1998a) but is still within an acceptable range for cardiac cells.

^†We calculated this value from the constant field equation, on the arbitrary assumption that the ammonium ion current is 20 pA at a resting membrane potential of −80 mV with 0 mm [NH₄⁺]_i and 5 mm [NH₄⁺]_o. This is a reasonable assumption since ammonium can act as a Congener for K⁺ channels.

Upon adding an extracellular ammonium salt, the influx of NH₃ (M_NH3) is given by:

(A1)

The influx of NH₄⁺ ions (M_NH4⁺) is given by:

(A2)

where P_NH3 and P_NH4⁺ are permeability coefficients for each form; V_m is the membrane potential; ε represents exp(-V_mF/RT); and F, R, and T have their usual meanings. Upon withdrawal of the extracellular ammonium salt, NH₃ efflux will acidify the cell. Note that any simultaneous efflux of NH₄⁺ (M_NH4⁺) will blunt this acidification. The net rate of intracellular proton addition (dQ_H⁺/dt) due to the combined effluxes M_NH3 and M_NH4⁺ is given by:

(A3)

where α=[H⁺]_i/([H⁺]_i+K), ρ is the area/volume ratio of the cell, and K is the dissociation constant of NH₄⁺.

In the presence of a constant P_CO2, rapid changes of pH_i caused by ammonium prepulsing may transiently drive the intracellular CO₂/HCO₃⁻ buffer system out of equilibrium. Re-equilibration of this buffer leads to a change of intracellular H⁺ and HCO₃⁻. This is given by (see Leem & Vaughan-Jones, 1998a):

(A4)

where k₁ and k_-1 are the combined forward and backward rate constants, respectively, for the hydration of CO₂ to HCO₃⁻ and H⁺.

Intracellular changes of [H⁺] will also occur due to the activity of sarcolemmal carriers. The net intracellular proton addition during ammonium withdrawal in the presence of transporter activity is given by:

(A5)

(A6)

where J_Na⁺-H⁺, J_{Na⁺-HCO3⁻}, J_Cl⁻-OH⁻ and J_{Cl⁻-HCO3⁻} are, respectively, the acid-equivalent fluxes through the four sarcolemmal transporters at a given level of pH_i. Complete formulations for the pH_i dependence of transporter flux are given below. Note that the AE and NBC transporters produce bicarbonate rather than H⁺ or OH⁻ fluxes. These fluxes are taken from the pH_i activation of acid-equivalent flux plotted in Figs 4 (for AE) and 6 (for NBC), determined when intracellular CO₂/HCO₃⁻ buffer was at equilibrium, assuming that bicarbonate flux = acid-equivalent flux.

Combining eqns (A4) and (A5) gives the rate of recovery of pH_i from an intracellular acid load:

(A7)

where β_i is the intracellular intrinsic buffering power, given by (see Results):

(A8)

Since differential eqn (A7) cannot be solved for pH_i, numerical methods are used. We calculate the time course of pH_i changes as:

(A9)

where:

(A10)

and where:

(A11)

CO₂ addition and removal

In the case where P_CO2 is changed, the following relationships are valid:

(A12)

where P_CO2 is the membrane permeability coefficient for CO₂ and:

(A13)

The procedure for determining the time course of pH_i change caused by CO₂ removal is the same as that used in the ammonium prepulse simulations (eqns (A9), (A10), (A11)), except that dQ_H⁺ (the change in intracellular proton equivalents) is given by:

(A14)

When simulating pH_i regulation in Hepes-buffered (CO₂-free) conditions, the flux components J_{Na⁺-HCO3⁻} and J_{Cl⁻-HCO3⁻} are set to zero. When simulating the addition of a specific transport inhibitor drug, the relevant transporter flux is set to zero.

pH_i recovery from an alkali load

Acetate prepulse technique

Here, the basic assumptions are the same as for simulating the ammonium prepulse technique. (i) The stability constant for acetate ions is the same inside and outside the myocyte. (ii) Non-ionized acetic acid diffuses readily through the lipid sarcolemmal phase (in accordance with Fick's Law, eqn (A15)) whereas, for the acetate anion, there is a low constant field channel conductance (eqn (A16)).

Upon adding extracellular acetate, the influx of undissociated acetate (HA) is given by:

(A15)

The influx of acetate ions (A⁻) is given by:

(A16)

where M_HA and M_A⁻ represent the net inward fluxes of each form; P_HA and P_A⁻ are permeability coefficients for each form. The net rate of intracellular proton depletion (-dQ_H⁺/dt) due to the combined influxes M_A⁻ and M_HA is:

(A17)

where α=[H⁺]_i/([H⁺]_i+ K) and K is the dissociation constant of acetic acid.

In addition to any weak acid transport, the intracellular proton change due to sarcolemmal transporter activity is as follows:

(A18)

(A19)

The procedure for calculating the time course of pH_i change induced by the acetate prepulse technique is the same as that used in the ammonium prepulse simulation (eqns (A9), (A10), (A11)) except that the change of intracellular proton equivalents (dQ_H⁺) is given by:

(A20)

Flux equations for the sarcolemmal transporters

We fitted the flux data plotted for each sarcolemmal transporter in Figs 4 and 6 by using polynomial equations. The fits to the data are illustrated by the dashed lines in Fig. 9. The best fit flux equations are as follows:

All acid-equivalent influx (i.e. on AE and CHE) is assumed to be zero at pH_i 6.70 (this is the estimated equilibrium pH_i for these transporters; Sun et al. 1996) and assumed to remain zero at lower pH_i values. All acid-equivalent efflux (i.e. on NHE and NBC) is assumed to be zero at pH_i values higher than 7.25 (Leem & Vaughan-Jones, 1998b). For convenience, it is assumed that acid-equivalent influx on AE and on CHE declines linearly from pH_i 7.07 (the value of resting pH_i), to zero at pH_i 6.70, while acid-equivalent efflux on NHE and on NBC is assumed to decline linearly from pH_i 7.07 to zero at pH_i 7.25. Finally, in the absence of any experimental data for AE and CHE activity at very high pH_i we have, for convenience, assumed saturation of AE flux at pH_i > 7.45 and of CHE flux at pH_i > 7.55.