Voltage dependence of the apparent affinity for external Na(+) of the backward-running sodium pump

Abstract

The steady-state voltage and [Na(+)](o) dependence of the electrogenic sodium pump was investigated in voltage-clamped internally dialyzed giant axons of the squid, Loligo pealei, under conditions that promote the backward-running mode (K(+)-free seawater; ATP- and Na(+)-free internal solution containing ADP and orthophosphate). The ratio of pump-mediated (42)K(+) efflux to reverse pump current, I(pump) (both defined by sensitivity to dihydrodigitoxigenin, H(2)DTG), scaled by Faraday's constant, was -1.5 +/- 0.4 (n = 5; expected ratio for 2 K(+)/3 Na(+) stoichiometry is -2.0). Steady-state reverse pump current-voltage (I(pump)-V) relationships were obtained either from the shifts in holding current after repeated exposures of an axon clamped at various V(m) to H(2)DTG or from the difference between membrane I-V relationships obtained by imposing V(m) staircases in the presence or absence of H(2)DTG. With the second method, we also investigated the influence of [Na(+)](o) (up to 800 mM, for which hypertonic solutions were used) on the steady-state reverse I(pump)-V relationship. The reverse I(pump)-V relationship is sigmoid, I(pump) saturating at large negative V(m), and each doubling of [Na(+)](o) causes a fixed (29 mV) rightward parallel shift along the voltage axis of this Boltzmann partition function (apparent valence z = 0.80). These characteristics mirror those of steady-state (22)Na(+) efflux during electroneutral Na(+)/Na(+) exchange, and follow without additional postulates from the same simple high field access channel model (Gadsby, D.C., R.F. Rakowski, and P. De Weer, 1993. Science. 260:100-103). This model predicts valence z = nlambda, where n (1.33 +/- 0.05) is the Hill coefficient of Na binding, and lambda (0.61 +/- 0.03) is the fraction of the membrane electric field traversed by Na ions reaching their binding site. More elaborate alternative models can accommodate all the steady-state features of the reverse pumping and electroneutral Na(+)/Na(+) exchange modes only with additional assumptions that render them less likely.

Figure 1

Comparison of the shift in holding current (A, single episode) and drop in ⁴²K⁺ efflux (B, average of three) produced by 100 μM H₂DTG in the same axon (25 min between exposures to permit inhibitor washout). (B) Ordinate is scaled to that of A by 2× Faraday's constant; a deflection of similar size produced by H₂DTG in A and B, therefore, signifies that one net charge moves inward per two K ions extruded, as expected for a 2 K⁺/3 Na⁺ pump cycle extruding K⁺ and taking up Na⁺. The longer time scale in B reflects mixing delays in the ⁴²K⁺ collection system. Axon internally dialyzed with Na⁺-free, 160 mM-K (radiolabeled) solution and bathed in 400 mM-Na⁺, K⁺-free artificial seawater. Temperature, 17.9°C.

Figure 2

Changes in holding current (ΔI) produced by 7-min exposures to 10 μM H₂DTG, each followed by a 30-min washout, made in the alphabetical sequence shown. The holding potential was reset during washout, ensuring ≥10 min at each new potential before fresh H₂DTG addition. The ΔI is generally outward, which is consistent with removal of an inwardly directed Na/K pump current; small inward shifts were seen at +30 mV (h and k). The response magnitude at −40 mV declined progressively (a, d, g, and j) during the experiment. Axon perfused with 160 mM-K, Na⁺-free solution and bathed in 400 mM-Na⁺, K⁺-free solution. Temperature, 17.4°C.

Figure 3

Current-voltage relationship of the backward-running Na/K pump constructed from many shifts in holding current (ΔI) produced by 10 μM H₂DTG. (A) H₂DTG-sensitive currents (−ΔI) at various membrane potentials in 14 axons (different symbols); not corrected for rundown. (B) Normalized data. All the data from six axons for which the rundown rate could be established by inter- or extrapolation are plotted relative to measurements at −40 mV. Closed circles are from the axon of Fig. 2. [Na⁺]_o was 400 mM. Temperature range, 17.3–17.6°C.

Figure 4

I-V relationship of the backward-running Na/K pump obtained from the difference between steady-state I-V curves before and during application of 100 μM H₂DTG, with provision for correction for spontaneous baseline drift. (A) A down-up-down voltage staircase, from −30 to −100 mV, then to +20 mV, and back to −30 mV, was applied at 5-min intervals before (a–c) and after (d–f) addition of H₂DTG. (B) Current shifts upon imposition of voltage staircases (partially off-scale in this analogue chart record, but within range of the digital sampling system) or application of H₂DTG. Tic marks are 5 min apart. (C) Steady-state I-V relationships obtained immediately before ([closed circles] b and [open circles] c) and shortly after ([closed squares] d and [open squares] e) application of H₂DTG. The two consecutive I-V relationships in each condition are nearly superimposable, and none of the curves shows significant hysteresis. (D) Difference I-V relationships. Closed circles are point-by-point differences between I-V curves (from panel C) obtained just before (c) and shortly after (d) application of H₂DTG, and represent an approximate (raw) H₂DTG-sensitive I-V plot still uncorrected for any spontaneous baseline drift during the 5-min interval between c and d. Estimates for such drift with time are computed as the difference between successive pairs of I-V curves taken before ([open squares] b and c) and during ([closed squares] d and e) the application of H₂DTG. For clarity, the two additional estimates available for baseline drift correction (a and b and e and f) are not shown. [Na⁺]_o was 400 mM. Temperature, 21.5°C.

Figure 5

Control experiments. (A) Lack of effect of DMSO. Difference currents shown obtained by subtracting I-V data in the presence of 0.1% DMSO from data obtained before its application. The axon previously had been exposed to 100 μM ouabain. (B) Lack of effect of H₂DTG on membrane current in an axon already exposed to 100 μM ouabain. The difference currents shown were obtained by subtracting data collected during exposure to 100 μM H₂DTG from data before its application. No correction for baseline drift, which was imperceptible in these axons, was applied in A or B; the raw difference records are shown. (C) K⁺-sensitive current not blocked by 50 mM internal PPTEA and 1 mM external DAP. An estimate of the maximum error that could result from local [K⁺]_o changes on stopping the Na/K pump is obtained by making deliberate [K⁺]_o changes in the presence of 100 μM ouabain. The I-V data obtained in K⁺-free solution were subtracted from those obtained in the presence of 10 mM K⁺ and corrected for baseline drift. The average values ± SEM (seven measurements on three axons) of the residual K⁺-sensitive current are shown. Temperature (all three axons), 17.8°C.

Figure 6

I-V relationship of the backward-running Na/K pump obtained by H₂DTG or ouabain addition. (A) Solid symbols represent the mean value of H₂DTG-sensitive current (uncorrected for drift) obtained from seven measurements on four axons. The open symbols represent the mean I-V drift that occurred during the same interval of time (∼5 min) that was needed to record the H₂DTG difference I-V data. (B) Closed symbols represent the mean value of ouabain-sensitive current obtained from four axons. Open symbols represent the mean I-V drift occurring during a time interval similar to that required to record the ouabain difference I-V data. (C) Comparison of H₂DTG- and ouabain-sensitive current in a single axon. Closed symbols plot the (100 μM) H₂DTG difference I-V relationship corrected for baseline drift. After a 45-min washout, the procedure was repeated with 100 μM ouabain. Open symbols plot the ouabain difference I-V relationship corrected for baseline drift. In both instances, the baseline drift corrections were smaller than the size of the symbols used in the graph. The voltage ranged from −95 to +35 mV in H₂DTG, but from −80 to +20 mV in ouabain because the intervening increase in leak conductance limited the useful range of membrane voltages. Temperature: (A) 17.8–17.9°C; (B) 17.4–17.8°C; (C) 17.8°C.

Figure 7

Identical shifts of the normalized I-V relationship of the backward-running Na/K pump produced by doubling of [Na⁺]_o. (A) Mean values of normalized H₂DTG-sensitive current measured in solutions of normal tonicity at 200 (open circles) and 400 mM (closed circles) Na⁺ _o. The midpoint voltages are −53 and −24 mV, respectively. The number of I-V curves/axons examined for each data set was 5/3 and 9/4, respectively. (B) Mean values of normalized H₂DTG-sensitive current measured in hypertonic seawater containing 200 mM (open circles), 400 mM (closed circles), or 800 mM (open squares) Na⁺ _o. The midpoint voltages are −70, −41, and −12 mV, respectively. The number of I-V curves/axons examined for each data set was 3/3, 12/8, and 10/6, respectively. All five Boltzmann functions I_pump(norm) = −1/(1 + exp[(V_m -- V–)zF/RT]) are identical in shape with apparent valence z = 0.80 and midpoint voltages –V as stated. Hypertonicity alone causes a 17-mV leftward shift. The relationship between apparent valence and the shift produced by doubling [Na⁺]_o is discussed in the text.

Figure 8

Albers-Post kinetic scheme for the sodium pump. Cycle steps are grouped into four ion occlusion or deocclusion reactions: (1) binding and occlusion of three intracellular Na ions, and concomitant phosphorylation of E₁ and release of ADP, with lumped rate coefficients k₁ and k₋₁; (2) deocclusion of 3 Na ions to the outside as E₁-P undergoes a conformational change to E₂-P, with lumped rate coefficients k₂ and k₋₂; (3) binding and occlusion of two extracellular K ions, and concomitant dephosphorylation of E₂, with lumped rate coefficients k₃ and k₋₃; and (4) deocclusion of K⁺ as E₂ is converted back to E₁ in a process accelerated by ATP, with lumped rate coefficients k₄ and k₋₄.

Figure 9

Reduced kinetic schemes, derived from that in Fig. 8, for two specific modes of operation of the pump. (A) Pseudo-4-state model for Na/Na^* (isotopic) exchange. Note that identical rate coefficients appear in both hemicycles. (B) Pseudo-4-state model for reverse pumping. Note by comparison with Fig. 8 that the pseudo-first-order rate coefficients k₁ and k₃ have been dropped since [Na⁺]_i and [K⁺]_o were nominally zero in the experiments. Note also that k₂ and k₋₂ in the top hemicycle are identical to those in A. (C) Pseudo-2-state model for Na/Na^* exchange, derived from A by lumping all reaction steps but Na⁺ deocclusion/reocclusion. (D) Pseudo-2-state model for reverse pumping, derived from B by lumping all reaction steps but Na⁺ deocclusion/reocclusion.