INTRODUCTION

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The Na⁺/K⁺-ATPase is an ion-translocating membrane protein. It uses the energy derived from the hydrolysis of one molecule of ATP to extrude three sodium ions and import two potassium ions against their electrochemical gradients (Glynn, 1993; Läuger, 1991). Because one positive charge per turnover is transported across the membrane, the Na⁺/K⁺-ATPase generates outward, hyperpolarizing electrical current; it is "electrogenic." The membrane potential also influences the activity of the Na⁺/K⁺-ATPase, which is stimulated at depolarized potentials and inhibited by hyperpolarization.

A great deal of research has been directed toward the identification of the electrogenic steps within the reaction cycle of the Na⁺/K⁺-ATPase (the Albers-Post model). The development of kinetic methods has contributed to a better understanding of how and when electrical charge is moved across the membrane. Whole-cell patch-clamp (Nakao and Gadsby, 1986) and giant excised inside-out patch-clamp (Hilgemann, 1994; Friedrich et al., 1996) techniques have been used to record relaxation currents after voltage jumps that were assigned to a reaction that is rate limited by Na⁺ deocclusion at the extracellular side. Current transients after a photolytically generated ATP concentration jump from caged ATP were measured with Na⁺/K⁺-ATPase-containing membrane fragments adsorbed to a black lipid membrane (BLM) (Fendler et al., 1985, 1987; Borlinghaus et al., 1987; Nagel et al., 1987). This method allowed the assignment of measured rate constants to particular steps of the Na⁺ branch of the reaction cycle (Fendler et al., 1987, 1993; Apell et al., 1987). These rate constants can be compared with the results of an optical method using potential sensitive styryl dyes in conjunction with the stopped flow technique to gain kinetic information about the reactions following phosphorylation of the Na⁺/K⁺-ATPase (Wuddel and Apell, 1995; Kane et al., 1997).

In most cases, time-resolved kinetic measurements of pump currents generated upon flash photolysis of caged ATP were performed using P³-[1-(2-nitrophenyl) ethyl] caged ATP (NPE-caged ATP), which is released with high efficiency and is commercially available. These measurements are limited to low pH values due to slow photolysis with increasing pH. At pH 7.4 ATP release from NPE-caged ATP has a time constant of ~25 ms, corresponding to a relaxation rate of 40 s¹ (McCray et al., 1980; Walker et al., 1988). Recently, a new method has been introduced, which consists of a periodic voltage perturbation of a sequence of reactions involving the phosphorylated sodium pump (Sokolov et al., 1994, 1998; Lu et al., 1995). Although this method uses caged ATP for activation of the enzyme, its time resolution is independent of the rate of release of ATP. Therefore, it allows the measurement of kinetic parameters in a wide pH range. In this paper, we have used the technique to investigate the kinetic parameters of the reactions involved in Na⁺ transport at pH 6.2-8.5.

	MATERIALS AND METHODS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX REFERENCES

Chemicals

In most cases the solutions contained 25 mM imidazole, 1 mM dithiothreitol (DTT), 3 mM MgCl₂, and 130 mM NaCl. The pH was adjusted to 6.2 (7.4, respectively) with HCl (referred to as "standard conditions"). For measurements at high pH (8.5), Tris was used instead of imidazole. In sodium-free or low-sodium solutions (Na⁺ titration of the capacitive signal), we have used a background of 50 mM imidazole and 0.25 mM EGTA. All chemicals were purchased in analytical grade or higher.

Caged ATP (P³-[1-(2-nitrophenyl) ethyl] adenosine 5'-triphosphate Na salt) was purchased from Calbiochem. For the lipid bilayers diphytanoylphosphatidylcholine (PC) (synthetic; Avanti Polar Lipids, Pelham, AL) and octadecylamine (60:1, w/v 98%; Riedel-DeHaen AG, Seelze-Hannover, Germany) were prepared 1.5% in n-decane according to the method of Bamberg et al. (1979).

Membrane fragments containing Na⁺/K⁺-ATPase (protein concentration 2-3 mg/ml) from pig kidney were prepared as described previously (Jørgensen, 1974; Fendler et al., 1985). The membrane fragments have diameters of ~100-300 nm (Scales and Inesi, 1976) and a thickness of ~4 nm.

Measuring procedure

Optically black BLMs with an area of 0.01-0.02 cm² were formed in a Teflon cell as described elsewhere (Fendler et al., 1987). Each of the two compartments of the cell was filled with 1.5 ml of electrolyte. The membrane was connected to an external measuring circuit via agar-agar salt bridges and Ag/AgCl electrodes. Fifteen microliters of the Na⁺/K⁺-ATPase-containing membrane fragments (2 mg/ml protein concentration) were added to one compartment of the cuvette and stirred for 40 min, during which the membrane fragments were adsorbed to the BLM in a sandwich-like structure.

The external measuring circuit (Fig. 1 A) consists of the lock-in amplifier (model 7220; EG&G Instruments, Wokingham, UK), which applies a sinusoidal alternating voltage across the compound membrane (the BLM together with the adsorbed membrane fragments). The following settings have been used on the lock-in: effective value of the alternating voltage, 10 mV; gain, 0-20 dB; slope, 12 dB/oct; output time constant, 100 ms for frequencies higher than 10 Hz, and 1 s for lower frequencies. The current generated in response to the alternating voltage can either be sent directly to the current input of the lock-in amplifier or passed through a current-voltage converter preamplifier and sent to the voltage input of the lock-in amplifier. The lock-in amplifier then displays the effective values of the two components of the input signal: l_x, in phase with the reference sinusoidal voltage, and l_y, which is 90° out of phase. The advantage of using the preamplifier is that, along with the capacitance measurements, one can also record the short-circuit currents as described by Fendler et al. (1985). The disadvantage is that the preamplifier introduces an additional phase shift and a current amplification, which are both frequency dependent, so that they have to be determined before the experiment.

View larger version (22K): [in this window] [in a new window]   FIGURE 1   (A) Bilayer set-up and electrical circuitry used for the measurement of the capacitive signal. A, Voltage input on the lock-in amplifier; B, current input on the lock-in amplifier; REF, output for the alternating voltage; P, preamplifier; BLM, black lipid membrane (with adsorbed membrane fragments containing Na+/K+-ATPase); E, Ag/AgCl electrodes. (B) Equivalent circuit describing the compound membrane. The capacitance of the membrane fragments, the underlying lipid membrane, and the uncovered lipid membrane are Cp, Cm, and Cu, respectively. The conductivity of the membrane fragments is Gp, and the access conductivity is Ga. The admittance Yp describes the contribution of the Na+/K+-ATPase to the electrical properties of the compound membrane.

The adsorption of the membrane fragments was monitored by the decrease in both the l_x and l_y components of the electrical signal on the lock-in amplifier. When the system has reached a steady state (constant values of the two components l_x and l_y), 0.2-0.3 mM caged ATP was added to the compartment containing the membrane fragments and stirred for 10 min. Then, an ATP concentration jump was generated by ATP release through flash photolysis of caged ATP. To photolyze the caged ATP, light pulses of an excimer laser (duration 10 ns, wavelength 308 nm) were focused on the lipid bilayer membrane. The intensity at the membrane surface was adjusted so that 15-20% of the caged ATP was photolyzed.

	THEORY

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX REFERENCES

A voltage-sensitive equilibrium under a periodic electrical perturbation

Consider the two-state system

(1)

Before the perturbation the system is in equilibrium with the concentrations and . If a periodic perturbation is applied, the system assumes the time-dependent concentrations c_A(t) and c_B(t). We now introduce the time-dependent equilibrium concentrations (t) and (t). These are the concentrations that would be established if the system were allowed to relax to equilibrium under the conditions prevailing at time t (Bernasconi, 1976). Using these concentrations, we define the reaction variable,

(2)

and the "driving function" (Bernasconi, 1976),

(3)

Using these definitions, we can obtain the "complete relaxation equation" with a method analogous to that of Bernasconi (1976) for a second-order system:

(4)

Let us now assume that the reaction described by Eq. 1 is voltage sensitive. The system is perturbed by applying a voltage V over the membrane. The situation can be described by introducing a voltage-dependent equilibrium constant K (Läuger, 1991):

(5)

K⁰ is the equilibrium constant in the absence of a voltage. The dimensionless parameter u = e₀V/k_BT corresponds to the "real" voltage V expressed in units of k_BT/e₀  25 mV (k_B = Boltzman constant, T = temperature, e₀ = elementary charge). Here we assume that one positive charge is transported over the total transmembrane distance of the membrane when the reaction proceeds from A to B.

Introducing the concentrations for the equilibrium constants, we obtain

(6)

Under the assumption of a small periodic perturbation (u 1) and using e^u  1 + u, we obtain

(7)

Note that the driving function is 0 if before perturbation the equilibrium is completely on side A or B. It is at maximum for  = .

The equilibrium considered above could be, e.g., a partial reaction of an integral membrane protein in which charge is translocated. The perturbation could be a voltage V applied over the membrane. What is the current response of the system when the perturbation is applied? For this we assume that one positive charge is transported over the total membrane thickness when going from A to B. The current generated per unit area is

(8)

Here the concentration c_A is a surface density (molecules per unit area). Using Eq. 8 together with Eq. 4, we obtain

(9)

If we use a sinusoidal perturbation and convert to complex numbers, the reaction variable x depends on the driving function according to the method of Bernasconi (1976):

(10)

With Eqs. 7 and 9 we obtain

(11)

The time-independent complex function relating current and voltage is the admittance Y. It depends on the frequency of the perturbation. The admittance per unit area describing the voltage-sensitive equilibrium A  B is given by

(12)

The real and imaginary parts of Y_AB () are

(13)

	RESULTS

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX REFERENCES

Using a lock-in amplifier, we have studied the behavior of Na⁺/K⁺-ATPase reconstituted on BLMs in an alternating electric field. The lock-in amplifier generates a sinusoidal alternating voltage across a compound membrane system consisting of a BLM with adsorbed membrane fragments containing purified Na⁺/K⁺-ATPase from pig kidney. The lock-in amplifier also monitors the two components of the corresponding alternating current: I_x, in phase with the voltage, and I_y, which is 90° out of phase. All experiments to be discussed further have been performed in the absence of K⁺, thus describing the partial reactions of the Na⁺/K⁺-ATPase associated with Na⁺ transport only. If not otherwise indicated, experiments were conducted under "standard conditions" as defined in Materials and Methods.

ATP concentration jumps

We have recorded changes in the values of I_x and I_y associated with activation of Na⁺/K⁺-ATPase through fast ATP concentration jumps generated by flash photolysis of an inactive precursor, caged ATP. As shown in Fig. 2 A, ATP release from caged ATP leads to an increase in both the I_x and the I_y components (I_x and I_y) of the alternating current to a new steady state. The current increment I_y will be used in the following for further analysis. Note that the current increment is rather small: at 20 Hz I_y is only 0.35% of the total component I_y.

View larger version (45K): [in this window] [in a new window]   FIGURE 2   (A) Fast increase in the Ix and Iy components of the alternating current recorded with the lock-in amplifier upon flash photolysis of caged ATP. Standard conditions, pH 6.2, Na+/K+-ATPase 20 µg/ml, caged ATP 0.4 mM. The alternating potential generated by the lock-in was V = 10 mV,  = 20 Hz. Stirring is stopped ~10 s before the laser flash and is resumed ~20 s after the laser flash. The noise associated with stirring is due to mechanically induced capacitance fluctuations of the black lipid membrane. (B) Inhibition of the signals Ix and Iy by 150 µM digitoxigenin (same conditions as in A).

When stirring is resumed, we notice a decrease in I_x and I_y toward the initial values (before the flash). This can be explained by the depletion of ATP in the region adjacent to the Na⁺/K⁺-ATPase-containing membrane fragments due to stirring. The noise associated with stirring is due to capacitance fluctuations of the BLM mechanically induced by stirring. Therefore, for a better signal-to-noise ratio, stirring was stopped during the ATP-releasing laser flash.

Before the flash, in the presence of 130 mM NaCl, the enzyme is stabilized in the E₁ conformation. Upon flash photolysis of caged ATP, the Na⁺/K⁺-ATPase binds and hydrolyzes ATP and undergoes a conformational transition to the E₂P state. In the absence of K⁺, the dephosphorylation is very slow (5 s¹; Hobbs et al., 1988). Therefore, we can assume that upon activation with ATP the phosphorylated Na⁺/K⁺-ATPase exists in a voltage-dependent equilibrium, E₁P  E₂P. Application of an alternating voltage with amplitude V and a frequency  (or an angular frequency  = 2) results in a periodic perturbation of the equilibrium (see Theory), which can be described by an additional admittance. This can be expressed in terms of a capacitance and a conductance increment C_p and G_p in parallel with the conductance G_p and capacitance C_p of the membrane fragments (Eq. A5).

Experimentally, only the total admittance increment Y of the compound membrane can be determined, which can be calculated from the in-phase and the out-of-phase components I_x and I_y of the measured current increment. Using complex notation, we obtain I_x = V·ReY and I_y = V·lmY, where ReY is the real part and lmY is the imaginary part of Y. In a limited frequency range a simple approximate relationship exists between lmY and C_p (Eq. A5), which enables us to calculate C_p from the measured quantity I_y:

(14)

A similar equation can be derived for G_p, but it yields no additional information. In addition, C_m and C_p are not precisely known. Therefore, only relative values for C_p may be obtained, which makes I_y/ a sufficient and convenient quantity for our analysis.

Inhibition of the capacitive signal by digitoxigenin

Digitoxigenin (a membrane-permeant analog of ouabain) (150 µM) was added under stirring to the compartment containing the Na⁺/K⁺-ATPase-containing membrane fragments. After 5 min, flash photolysis of caged ATP produced a transient increase in the current (Fig. 2 B). After subsequent laser flashes the transient was absent, and only a small stationary increment of the I_y (or I_x) component was observed, which was ~10-20% of the value before the addition of digitoxigenin (Fig. 3). An interesting feature is the presence of a transient signal upon the first laser flash after the addition of the inhibitor (Fig. 2 B). This can be explained by the fact that cardiac glycosides bind preferentially to and immobilize the enzyme in the E₂P conformation of the pump (Glynn, 1985), which requires phosphorylation by ATP.

View larger version (16K): [in this window] [in a new window]   FIGURE 3   Contribution of ATP release from caged ATP to the capacitive signal. Standard conditions, pH 6.2, caged ATP 0.3 mM. Angular frequency spectra were measured in the absence of Na+/K+-ATPase (), upon the addition of 20 µg/ml Na+/K+-ATPase (), and upon further addition of 50 µM digitoxigenin (). V = 10 mV,  = 10 Hz.

The experiments demonstrate that the capacitive signal is indeed due to the activity of the Na⁺/K⁺-ATPase. In particular, the possibility is eliminated that the capacitance increment represents charge separation at the membrane surface due to ATP release from caged ATP. An additional control experiment is shown in Fig. 3. There we have performed flash photolysis experiments in the presence of 0.3 mM caged ATP and no Na⁺/K⁺-ATPase in the cuvette. Under these conditions we found small increments I_y of 2.5 pA at 20 Hz. The angular frequency spectra of the corresponding capacitance increments (I_y/; see above) showed no angular frequency dependence in the range between 10 and 1015 Hz (below 10 Hz the signal was too noisy to be recorded).

Subsequently, on the same BLM, we have added Na⁺/K⁺-ATPase-containing membrane fragments to a concentration of 20 µg/ml in one compartment of the cuvette. After 30 min of continuous stirring, flash photolysis of caged ATP induced a much larger change in the I_y component of the alternating current (18 pA at 20 Hz), and the angular frequency spectra of the corresponding capacitance increment displayed a characteristic "Lorentzian" behavior (Fig. 3). Then, 50 µM digitoxgenin was added to the same compartment as the Na⁺/K⁺-ATPase-containing membrane fragments, and upon stirring for 10 min, the signal due to flash photolysis of caged ATP was decreased to the value before the addition of Na⁺/K⁺-ATPase. Moreover, the angular frequency spectra were similar to that obtained without Na⁺/K⁺-ATPase in the cuvette (Fig. 3). Therefore, a fraction of the signal (~12% at low frequencies, up to 22% at 1015 Hz) is probably due to ATP release from caged ATP, but most of the signal, as well as the characteristic "Lorentzian" shape of the angular frequency spectra, reflects the contribution of the Na⁺/K⁺-ATPase.

Capacitive signal in the presence of monensin and the protonophore 1799

The question was addressed whether the increase in the membrane capacitance can be due to charge accumulation within the space between the attached membrane fragments and the BLM. Upon the addition of 10 µM monensin (a H⁺/Na⁺,K⁺ exchanging agent) and 2.5 µM protonophore 1799 the membrane conductance increased by ~1000 times (from 80 pS to 0.1 µS). Fig. 4 A shows the short circuit current recorded as described by Fendler et al. (1985), before and after the addition of ionophores. The trace obtained in the presence of ionophores is characterized by the presence of a small stationary current due to the slow cycling of the pumps in the absence of K⁺. In particular, the negative phase observed in the absence of ionophores, which represents backflow of charge from between the membrane fragments and the BLM (Fendler et al., 1985), is abolished. Fig. 4 B shows the corresponding capacitive signals under the same conditions as in Fig. 4 A. The difference between the two signals is restricted to the decaying phase when stirring is resumed. In particular, the fast increase and the stationary phase of the I_y component that are associated with changes in the capacitance of the membrane fragments upon flash photolysis of caged ATP are not affected by the presence of the ionophores, which would prevent any charge accumulation after activation of the ion pumps.

View larger version (25K): [in this window] [in a new window]   FIGURE 4   (A) Transient currents before and after the addition of ionophores. Standard conditions, pH 6.2, Na+/K+-ATPase 20 µg/ml, caged ATP 0.225 mM, monensin 10 µM, 1799 2.5 µM. (B) Signals recorded on the lock-in amplifier corresponding to the transients presented in A (same conditions). The alternating potential generated by the lock-in was characterized by V = 10 mV,  = 20 Hz.

Na⁺ dependence of the capacitive signal

A NaCl titration of the I_y component of the alternating current was performed, at both low (10 Hz) and high (1015 Hz) frequencies. The result is shown in Fig. 5. The starting solution contained 3 mM MgCl₂, 50 mM imidazole, 0.25 mM EGTA, and 1 mM DTT at pH 6.2. Although half-saturation of the titration curves occurs at ~90 mM, a simultaneous fit according to the model described in the Discussion gave a binding constant of 900 mM. The low affinity suggests that the Na⁺ dependence of the I_y component of the measured current describes the effect of sodium ions on the E₁P  E₂P equilibrium at the extracellular binding sites.

View larger version (18K): [in this window] [in a new window]   FIGURE 5   Na+ dependence of the capacitive signal at 10 Hz () and 1015 Hz. (). Initial conditions: MgCl2 3 mM, DTT 1 mM, imidazole 50 mM, EGTA 0.25 mM, Na+/K+-ATPase 20 µg/ml, caged ATP 0.3 mM, pH 6.2, V = 10 mV. For fitting procedure see Discussion.

To exclude the influence of ionic strength on the capacitive signal, the I_y component of the current was measured at 10 and 1015 Hz, using a buffer that contained 50 mM NaCl and increasing amounts of choline chloride (other buffer components were as described above for the Na⁺ titration). As a reference, a NaCl dependence has been obtained as described above, but starting at 50 mM NaCl. The two dependencies are shown in Fig. 6 (top). They have been normalized to the low frequency value (10 Hz) at 50 mM NaCl. The comparison demonstrates that ionic strength does not affect the high and low frequency capacitive signal at total salt concentrations ([NaCl] + [choline chloride]) up to 630 mM. It also rules out a lyotropic effect of the Cl anions in this concentration range.

View larger version (26K): [in this window] [in a new window]   FIGURE 6   The capacitive signal at 10 Hz (, , ) and 1015 Hz. (, , ) at different concentrations of added salts. Initial conditions: MgCl2 3 mM, NaCl 50 mM, DTT 1 mM, imidazole 50 mM, Na+/K+-ATPase 20 µg/ml, caged ATP 0.3 mM, pH 6.2, V = 10 mV. (Top) Addition of choline chloride (, ). (Bottom) Addition of NaClO4 (, ). For comparison a reference measurement generated by the addition of NaCl has been included in both graphs (, ). The results are normalized to the value obtained at 10 Hz before the addition of salt.

Lyotropic anions modulate the properties of the Na⁺/K⁺-ATPase (Suzuki and Post, 1997; Ganea et al., 1999). The effect of the lyotropic anion ClO₄ is shown in Fig. 6 (bottom). This is a titration similar to that described above starting at 50 mM NaCl. But in this case NaClO₄ was added. These data were normalized to the reference NaCl dependence used in Fig. 6 (top) as described. A pronounced effect of the replacement of Cl by ClO₄ is found and can be explained by a shift of the conformational equilibrium to the E₁P form induced by the lyotropic anion as described before (Suzuki and Post, 1997).

ATP dependence of the capacitive signal

The ATP dependence of the capacitive signal has been determined in two different ways, using a titration protocol described previously for transient currents generated by the Na⁺/K⁺-ATPase (Nagel et al., 1987). First, a caged ATP titration of the signal was performed by successive caged ATP additions. The ATP concentration upon flash photolysis of caged ATP was calculated from the light intensity at each caged ATP concentration as described elsewhere (Friedrich et al., 1996). The signal displayed a saturating behavior, with a K_0.5 of 0.35 µM ATP. Subsequently, the concentration of released ATP was decreased by decreasing the released fraction at a constant saturating caged ATP concentration of 400 µM via a reduction of the light intensity. Under these conditions the ATP dependence had a K_0.5 of 24 µM. This behavior is typical for competitive binding of caged ATP to the ATP binding site (Nagel et al., 1987).

Frequency spectra of the capacitive signal

We have recorded capacitive signals at frequencies of the applied sinusoidal voltage between 3 and 1015 Hz. The limits of this frequency domain have been chosen to maintain a direct proportionality between the small changes in the capacitance of the adsorbed membrane fragments and the corresponding small changes in the I_y component of the current (see Discussion). The lower frequency is limited by the time constant of the compound membrane, while the upper limit is determined by the access resistance through the agar bridges and the electrolyte solution. Lowering the access resistance allows the extension of the frequency domain toward higher values. Under the conditions of the experiment the low and the high frequency limits were ~3 Hz and ~1000 Hz, respectively.

In Fig. 7 the capacitive signal is plotted as a function of the angular frequency  at three different pH values. Under these conditions, the frequency dependence of the capacitive signal reflects the voltage-dependent equilibrium E₁P  E₂P. It can be shown (Eqs. 13 and 14) that the measured quantity C_p is proportional to a Lorentzian function 1/(1 + ²²), where  represents the relaxation time of the equilibrium. It is obvious from Fig. 7 that this is not sufficient to describe the data, and an additional constant term has to be added. Therefore, for a fit of the experimental results, the following model function was used:

(15)

As shown in Fig. 7, at pH 7.4 the maximum value for the relaxation rate was obtained, ¹ = 323 s¹. At pH 8.5, ¹ decreased to 114 s¹, and at pH 6.2 it decreased to 192 s¹. These values are compiled in Table 1. Note that the data for pH 7.4 shown in the figure are the same as those of Ganea et al. (1999). There, a somewhat larger value of ¹ = 393 ± 51 s¹ was obtained because of a different fitting procedure.

View larger version (18K): [in this window] [in a new window]   FIGURE 7   Frequency spectra of the capacitive signal at pH 6.2 (), pH 7.4 (), pH 8.5 (). Conditions: NaCl 130 mM, MgCl2 3 mM, DTT 1 mM, imidazole 25 mM (or Tris 25 mM, for pH 8.5), Na+/K+-ATPase 20 µg/ml, caged ATP 0.225 mM. The spectra were fitted with Iy/ = A + B/(1 + 22). The relaxation rates 1 obtained were 192 s1 (pH 6.2), 323 s1 (pH 7.4), and 114 s1 (pH 8.5).

View this table: [in this window] [in a new window]   TABLE 1   Kinetic parameters for the E1P  E2P transition and for extracellular Na+ binding at three different pH values

The amplitudes of the capacitive signal at different pH

The high and the low frequency limits of the capacitive signal (in the following these will be referred to as amplitudes) were measured at several pH values. The pH was varied by successive additions of HCl or NaOH, starting at different pH values (Fig. 8). The measurements were carried out at two different frequencies, 10 Hz and 1015 Hz. The amplitude values were normalized to the maximum value at 10 Hz for each experiment. The low frequency amplitude (10 Hz) displays a more pronounced pH dependence, with a maximum amplitude close to pH 8. The amplitude of the high-frequency component (1015 Hz) is almost constant between pH 6 and 8 and starts to decline at higher pH values.

View larger version (24K): [in this window] [in a new window]   FIGURE 8   pH dependence of the capacitive signal (Iy/) at 10 Hz and 1015 Hz. Five different experiments were performed: 1) Starting solution: imidazole 25 mM, pH 7.4. The pH was decreased by the addition of HCl (). 2) Using the same starting solution as in (1), the pH was increased by the addition of NaOH (). 3) and 4) Starting solution: Tris 25 mM, pH 8.5. The pH was decreased by the addition of HCl ( and ). 5) Starting solution: imidazole 25 mM, pH 6.2. The pH was increased by the addition of NaOH (). In all experiments the electrolyte solutions contained NaCl 130 mM, MgCl2 3 mM, DTT 1 mM, Na+/K+-ATPase 20 µg/ml, and caged ATP 0.3 mM. The amplitude values were normalized to the maximum value at 10 Hz for each experiment.

	DISCUSSION

TOP ABSTRACT INTRODUCTION MATERIALS AND METHODS THEORY RESULTS DISCUSSION APPENDIX REFERENCES

In which frequency range is the approximation valid?

The ion pumps are electrically characterized by an increment of the complex admittance, Y_p() = G_p + iC_p, of the membrane fragments. Y_p() is part of a complicated RC network describing the electrical properties of the compound membrane (see Fig. 1 B), which consists of the supporting bilayer and the adsorbed membrane fragments (Bamberg et al., 1979). The compound membrane has the total admittance Y(). Using the lock-in amplifier, we determine changes in the total admittance, Y() = ReY + ilmY, upon activation of the ion pumps. To calculate Y_p() from Y(), we exploit the fact that these two quantities are approximately proportional (see Eq. A5 in the Appendix). This relationship is only valid in a limited frequency range that will be determined in the following.

To test the response of the equivalent circuit at the different frequencies, we calculated the total admittance of the equivalent circuit before (Y_p = 0) and after activation of the Na⁺/K⁺-ATPase by photolytic release of ATP (Y_p() = G_p + iC_p), as described in the Appendix. A constant, frequency-independent value was assumed for the real (G_p) and for the imaginary (C_p) parts of Y_p (corresponding to the situation at the characteristic frequency  = 1/; see Eq. 13). The difference in total admittance before and after activation yields the increment Y(). From ReY and ImY the real and the imaginary components of Y_p() can be calculated according to the approximation A5 and can be compared to the exact values as shown in Fig. 9.

View larger version (14K): [in this window] [in a new window]   FIGURE 9   Comparison of the exact solution with the approximation given in Eq. 16. ---, Gp; - · - · -, Cp. The horizontal solid line corresponds to the exact solution.

The horizontal solid line in Fig. 9 at 1.5 pAV¹ corresponds to the exact value of G_p and C_p as chosen for the calculation. The dashed lines show the result of the approximation (Eq. A5). It is clear that the approximation is valid only for a certain frequency range. If we define the lower and the upper bound of the range as the angular frequency at which the approximate value is 50% of the exact value, we obtain from Fig. 9 2 s¹   2500 s¹ for C_p and for 10 s¹   10000 s¹ G_p.

The low frequency limit is reached when the condition C_p G_p, as used in the approximation, no longer holds. With a typical capacitance of the membrane fragments of ~1 µF/cm² and a conductance of ~3 µS/cm², the ratio G_p/C_p is ~3 s¹. This agrees well with Fig. 9. Another limit exists at high frequencies because in the approximation the access resistance 1/G_a was neglected. This resistance is composed of the resistance of the solution and the salt bridges and the input resistance of the lock-in amplifier and has a value of ~40 k. Together with the capacitance of the compound membrane, this represents a low-pass RC network that limits the range of the measurement to angular frequency values below G_a/C_tot. The total capacitance of the compound membrane C_tot has a typical value of ~2 nF, yielding an upper limit of   1.25 × 10⁴ s¹. This crude estimation is somewhat higher than the value obtained by the calculation of C_p shown in Fig. 9, which is   2.5 × 10³ s¹ (but agrees with the upper limit for G_p).

The analysis shown in Fig. 9 demonstrates that the real component or the imaginary component of Y can be used to characterize the ion pumps contained in the membrane fragments. We have chosen to use ImY, which gives a range of 2 s¹   2500 s¹ in which Eqs. A5 and 14 apply and in which C_p() can be calculated. This "angular frequency window" also gives us the range of relaxation times that can be determined. The range given above shows that the method is well suited for relaxation times of 100-400 s¹ as determined here.

The capacitive signal reflects an electrogenic reaction of the Na⁺/K⁺-ATPase

Digitoxigenin is a membrane-permeant analog of ouabain, a specific inhibitor of the Na⁺/K⁺-ATPase. Upon the addition of 150 µM digitoxigenin to the same compartment as the Na⁺/K⁺-ATPase, a drastic reduction in the lock-in signal, on both I_x and I_y components and at both low (10 Hz) and high (1015 Hz) frequencies, was observed. The remaining signal is comparable to the signal in the absence of Na⁺/K⁺-ATPase and is probably due to the polarization of the membrane-liquid interface after the release of ATP from caged ATP. It shows no frequency dependence between 10 and 1015 Hz (Fig. 3) and will be neglected in the following. In addition, the measurements carried out in the presence of ionophores (Fig. 4) demonstrate that the signal must be attributed to charge movements associated with partial reactions of the Na⁺/K⁺-ATPase, and not to charge accumulation as a result of overall pumping activity. We can, therefore, assign the capacitive signal to a charge-translocating reaction in the reaction cycle of the Na⁺/K⁺-ATPase. In the following, we will discuss the assignment of this process to a well-defined partial reaction of the ion pump.

The capacitive signal contains contributions from a slow and a fast reaction

From a single electrogenic reaction a Lorentzian frequency dependence of the capacitive signal is expected (see Eq. 13) that decays to zero at high frequencies. However, as shown in Fig. 7, at high frequencies the capacitive signal attains a constant amplitude of ~30% of the value at low frequency. This component is clearly a result of the enzymatic activity of the Na⁺/K⁺-ATPase (Fig. 3). A similar behavior has been observed previously (Lu et al., 1995; Sokolov et al., 1998). It has been interpreted in terms of an electrogenic reaction with a relaxation rate outside the experimental frequency spectrum, possibly the movement of Na⁺ ions inside a putative access channel (Lu et al., 1995).

From the frequency dependence (Fig. 7) we have to conclude that two reactions contribute to the capacitive signal: 1) a slow reaction, which at pH 7.4 has a relaxation rate of ¹ = 323 s¹ (Fig. 7); 2) a fast reaction, for which only a lower limit for the relaxation rate of ¹ > 7000 s¹ can be given. In the following we analyze the amplitude of the capacitive signal at high frequency (1015 Hz), C_p¹⁰¹⁵, and at low frequency (10 Hz), C_p¹⁰, at different Na⁺ concentrations and pH. It is shown that the behavior of the amplitudes is compatible with the assumption that the slow step is the E₁P  E₂P transition, while the fast reaction is extracellular Na⁺ binding/release.

The capacitive signal and the reaction cycle of the Na⁺/K⁺-ATPase

Before the laser flash, in the presence of 130 mM NaCl, the Na⁺/K⁺-ATPase is in the NaE₁ state, according to the Albers-Post model. Upon flash photolysis of caged ATP and ATP release, the pumps bind and hydrolyze ATP, become phosphorylated, and occlude Na⁺, forming (Na)E₁P. Then they undergo a conformational transition to the E₂PNa state (for simplicity called the E₁P  E₂P transition) and finally release Na⁺. The reaction sequence can be described in a simplified model: NaE₁ + ATP  NaE₁ATP  (Na)E₁P  E₂PNa  E₂P + Na⁺. The three transported Na⁺ ions have been proposed to be sequentially released at the extracellular side (Stürmer et al., 1991; Hilgemann, 1994). However, these reactions are probably very fast (>250,000 s¹, Hilgemann, 1994; >300,000 s¹, Lu et al., 1995, at 37°C). For the purposes of our experimental technique, which is of limited time resolution (<2500 s¹; see above), these steps may be lumped together into a single Na⁺ dissociation reaction.

In the absence of K⁺ the dephosphorylation is slow (<7 s¹ at pH 6-9; Forbush and Klodos, 1991) compared to the formation of the phosphoenzyme (>100 s¹ at pH 6.2-8.5; Kane et al., 1997). Therefore, we may assume that immediately after the flash most of the pumps are in a phosphorylated state and remain there for many seconds until the released ATP in the vicinity of the membrane starts to decrease. The increase in the components of the observed current upon flash photolysis of caged ATP reflects the existence of a voltage-dependent equilibrium between the phosphorylated intermediates as proposed previously, based on whole-cell patch-clamp measurements on cardiac myocytes (Nakao and Gadsby, 1986; Lu et al., 1995) and electrical measurements on membrane fragments from rabbit kidney (Sokolov et al., 1998).

When the capacitive signal was recorded at increasing concentrations of caged ATP, its amplitude displayed a saturating behavior with a K_0.5 of 0.35 µM ATP. In contrast, pre-steady-state kinetic measurements have yielded a binding constant for ATP of ~10 µM from the ATP dependence of the relaxation rate (Fendler et al., 1987; Kane et al., 1997). How can this discrepancy be explained? Our present method is a steady-state relaxation technique, and the amount of phosphorylated protein formed is controlled not only by the concentration of ATP, but also by the rate of recovery of the E₁ state upon dephosphorylation. As a consequence of slow dephosphorylation in the absence of K⁺, very low ATP concentrations are sufficient to saturate the capacitive signal, which yields a higher apparent affinity for ATP.

The kinetic model

In the following we analyze the Na⁺ dependence of the amplitudes of the capacitive signal on the basis of a simplified kinetic model that comprises the E₁P  E₂P conformational transition and a Na⁺ binding/release step as shown in Fig. 10. Here it is assumed that all Na⁺ binding sites must be occupied before E₁P can be formed, and Na⁺ represents all three transported Na⁺ ions.

View larger version (14K): [in this window] [in a new window]   FIGURE 10   Relative basic free energy levels for states of the Na+/K+-ATPase involved in sodium translocation at pH 6.2, 7.5, and 8.5 (bottom to top), calculated according to the kinetic parameters from Table 1. Free energies of the levels are given in kJ/mol. (Bottom) Kinetic model for Na+ translocation.

The question of which of the steps of the Na⁺ transport reaction are electrogenic has been the subject of discussion (Rakowski et al., 1997). Complications in the assignment of the electrogenic steps arise from the fact that if a very rapid Na⁺ binding/release step is assumed (_Na  0), the model shown in Fig. 10 is kinetically equivalent to the simple one-step model, (Na)E₁P  X_Na. The forward rate constant is k⁺, and the backward rate constant is Na⁺ concentration (c_Na) dependent,  = kc_Na/(c_Na + K_Na). X_Na comprises the E₂PNa and E₂P intermediates. This simple model shows how with increasing Na⁺ concentration the equilibrium is shifted in favor of (Na)E₁P. Under conditions in which the experimental time resolution is not sufficient to resolve a rapid Na⁺ binding/release step, the assumption _Na  0 holds. Consequently, the kinetic system behaves according to a one-step electrogenic reaction without the possibility of assessing whether the E₁P  E₂P conformational transition or the Na⁺ binding/release step or both are electrogenic. Therefore, electrogenicity of a single partial reaction cannot be inferred from a relaxation experiment alone. However, the Na⁺ dependence of the effect can contribute additional information. This approach has been used in the past (Gadsby et al., 1993) and will also be applied to the capacitive measurements presented here.

It became clear very early from voltage jump measurements on cardiac myocytes that only the reverse reaction of the electrogenic reaction is voltage sensitive (Gadsby et al., 1992). This would be a straightforward result of the kinetic model (Fig. 10) if it is assumed that only the Na⁺ binding reaction is electrogenic. Also, the voltage dependence of Na⁺/Na⁺ exchange on squid axon could be explained using an electrogenic Na⁺ binding reaction, rate limited by an electroneutral E₁P  E₂P transition (Gadsby et al., 1993). In addition, using fast current recording equipment, current transients were observed on cardiac myocytes, membrane fragments from rabbit kidney, and squid giant axons, which were assigned to a fast Na⁺ dissociation reaction (Hilgemann, 1994; Wuddel and Apell, 1995; Rakowski et al., 1997). This has been supported by capacitance measurements on cardiac myocytes (Lu et al., 1995). On the other hand, there seems to be indirect evidence from experiments using lyotropic anions for an electrogenic E₁P  E₂P transition (Ganea et al., 1999). However, the results of the latter study do not rule out the possibility that the contribution of the E₁P  E₂P transition to the overall charge translocation across the entire membrane might be small, as proposed by various studies (Wuddel and Apell, 1995; Gadsby et al., 1993). The results of Ganea et al. (1999) could perhaps be explained by a large local electric field effect of lyotropic anions on a small charge translocation during the E₁P  E₂P transition.

The selection of an appropriate model is crucial, because conclusions from a kinetic analysis are, in general, model dependent. In the following, we will analyze the capacitive signals on the basis of the kinetic model shown in Fig. 10, with emphasis on the Na⁺ dependence of the amplitudes. The relaxation of the Na⁺ binding reaction is assumed to be much faster than the applied periodic perturbation (  (_Na)¹). The data presented here and those by other groups (Lu et al., 1995; Sokolov et al., 1998) clearly rule out the E₁P  E₂P transition as the exclusive electrogenic step. In addition, its contribution to the overall electrogenicity of Na⁺ transport is probably small, as discussed above. We have therefore chosen to use a kinetic model with an electroneutral conformational transition. This model is a convenient basis for our kinetic analysis for the following reasons. The data presented in this study are consistent with such a model (but also with one that attributes part of the electrogenicity to the conformational transition). An electrogenic E₁P  E₂P transition would require an additional parameter, namely the relative electrogenicity of the conformational transition, which cannot be determined on the basis of our experimental data. An electroneutral conformational transition keeps the mathematics simple. For completeness, we discuss below in a qualitative way the effect of additional electrogenicity in the conformational transition.

The amplitudes of the capacitive signal

The interpretation of the Na⁺ dependence of the amplitudes is complex because different effects contribute. On the one hand, it is the amount of phosphoenzyme that controls the amplitudes of the capacitive signal. On the other hand, the ratio of the E₁P and the E₂P concentrations also determines the magnitude of the signal. The latter is apparent from the frequency-independent term in Eq. 13. Therefore, we have to take into account the following processes: 1) In the low concentration range, more and more E₁P and E₂P intermediate is formed with increasing Na⁺ concentration as it binds to its cytoplasmic binding site, thereby allowing phosphorylation. 2) In the high concentration range, binding of Na⁺ to the extracellular binding sites speeds up the back-reaction of the E₁P  E₂P equilibrium and drives the enzyme into the E₁P state. 3) High Na⁺ concentrations require high anion concentrations (Cl in our case), which increase E₁P via a lyotropic effect (Suzuki and Post, 1997; Ganea et al., 1999). 4) At high concentrations Na⁺ can replace K⁺ in dephosphorylating the enzyme (Nagel et al., 1987). Via rephosphorylation this effect also increases the E₁P concentration.

Formation of the phosphoenzyme (process 1) takes place at low concentrations of Na⁺. The half-saturation concentration of this