The Post-Albers reaction scheme of the Na+,K+-ATPase has been remarkably successful, for over a quarter-century, in explaining the biochemical behavior of the isolated enzyme, and is still the backbone of current biophysical models for the various transport modes (electrogenic Na/K exchange; electroneutral and electrogenic Na/Na exchanges; K/K exchange, etc.) of the sodium pump. Because of its unique ability to accommodate such a vast array of observations, any shortcomings or ambiguities of the model are viewed with justified concern by some, or expediently ignored by others. An article by Suzuki and Post (1997) in this issue of The Journal of General Physiology brings a measure of clarity to some such problems and thus reaffirms the model's power and also makes a case for greater precision (or less ambiguity) in nomenclature when the model is extended beyond its original purview to include sidedness, occluded forms, and occupancy by specific ions or ligands. A second article in this issue of the Journal, by Nørby and Esmann (1997) brings clarity to a different issue that arises from the simple fact that the isolated Na+,K+-ATPase can be, and has been, studied in a bewildering array of conditions and solutions of various compositions and ionic strengths. These authors systematically separate solution effects into electrostatic (ionic strength) and specific components and show how the former can be exploited to estimate the local charge on the site where ADP, eosin, and presumably ATP, interact with the enzyme.

The Post-Albers model for the Na+,K+-ATPase (Albers, 1967; Post et al., 1969) was designed to accommodate the observed kinetics of enzyme phosphorylation and dephosphorylation catalyzed by Na+ and K+, respectively. According to the model, the enzyme is phosphorylated by ATP (in the presence of Na+ and Mg2+) in one conformation yielding a high-energy intermediate E1P capable of phosphorylating ADP, and then undergoes a conformational change to a low-energy (ADP-resistant) E2P form that is rapidly dephosphorylated in the presence of K+. The obvious corollary, that all phosphorylated enzyme must be either E1P or E2P, has often been challenged experimentally (Kuriki and Racker, 1976; Klodos et al., 1981; Yoda and Yoda, 1982; Nørby et al., 1983; Lee and Fortes, 1985). Sequential three-pool models were therefore proposed, some very detailed (Nørby et al., 1983), in which a fraction of the phosphorylated enzyme is sensitive to either ADP or K+. A three-pool sequential model, however, was found inadequate in presteady-state phosphorylation experiments by Froehlich and Fendler (1991) which led these authors to suggest a parallel two-pool scheme.

Suzuki and Post (1997) retrace the steps of Post et al. (1969) but with optimized electrolyte solutions, more data points, and greater accuracy. The experiment is simple in principle. Enzyme is briefly exposed to labeled ATP in the presence of Na+ and Mg2+. At time zero further phosphorylation is stopped with chelator and/or excess cold ATP, after which the decay of phosphoenzyme is followed (the “chase”). Even without ADP or K+ present (blank chase), phosphoenzyme is lost by spontaneous hydrolysis. With ADP in the chase, there is a time-unresolved (“instantaneous”) drop representing the ADP-sensitive species, followed by further slow spontaneous loss. Back-extrapolation to time zero gives an estimate of ADP-resistant phosphoenzyme. An analogous chase with K yields the K+-resistant phosphoenzyme. The two phosphoenzyme species add up to 100%. So where is the problem? A true two-pool system would yield single-exponential decays (straight semilog plots) for each (ADP or K+) resistant species following the instantaneous loss of the sensitive species. An experimental fit of such a model requires five independent parameters: one hydrolysis rate constant for each pool; exchange rate constants between the pools; and the initial pool size ratio. The data clearly do not follow straight semilog plots, and attempts to fit straight lines to the data would have yielded erroneous zero-time intercepts. Suzuki and Post resolve this issue by assuming two noncommunicating two-pool pathways. As expected, additional adjustable parameters were needed to fit the data: one giving the relative size of the parallel pathways and, remarkably, only one additional factor giving the speeds of all four rate constants in one pathway relative to that of their counterpart in the other. (In the worst—hopeless?—case, four separate additional rate constants might have been needed.) The (about fivefold) slower pathway was found to represent 10–20% of the total. Why the enzyme should be present in slow and fast forms remains an intriguing physiological question (Post and Klodos, 1996).

Careful analysis of the effects of [Na+] on the parameters of their model leads Suzuki and Post to two additional conclusions of great interest to kinetic modelers of the sodium pump. First, the rates of interconversion between E1P and E2P are little affected by [Na+], which must mean that the affinities of the two forms for Na+ are comparable, as proposed already by Pedemonte (1988). Second, taking advantage of their earlier observation that chaotropic ions favor the E1P conformation, they study the transphosphorylation equilibrium:

\begin{equation*}{\mathit{K}}_{int}=ADP{\cdot}E_{1}P/ATP{\cdot}E_{1},\end{equation*}

and show that it varies linearly with 1/[Na+], i.e., a tenfold drop for a tenfold increase in [Na+]. This suggests a reaction that is monomolecular, and low-affinity, with respect to Na+:

\begin{equation*}{\mathit{K}}={\mathit{K}}_{int}(1+{\mathit{K}}_{Na}/[Na^{+}]).\end{equation*}

Since the transphosphorylation reaction itself, ATP· E1 ADP·E1P, likely involves only the Na3 forms, the low-affinity monomolecular reaction is undoubtedly:

\begin{equation*}Na^{+}\;+\;ADP\;{\cdot}\;E_{1}P\;{\cdot}\;Na_{2}\;\;ADP\;{\cdot}\;E_{1}P\;{\cdot}\;Na_{3}.\end{equation*}

The paper by Nørby and Esmann (1997) presents a unifying analysis of a variety of “salt effects” on the equilibrium binding of ADP and eosin, whose apparent affinity can vary dramatically depending on the assay medium's anion species and concentration. Using a simple point-charge model and Debye-Hückel limiting law, these authors could fit the data in NaCl and Na2SO4 media very well assuming a +1 charge at the binding site. Additional binding affinity reductions in nitrate were shown to reflect competitive binding by NO3 (Kd ≃ 32 mM) whereas those in thiocyanate and per-chlorate were ascribed to specific effects of these anions.

To analyze solution effects on the kinetics of ATP or p-nitrophenylphosphate hydrolysis, Nørby and Esmann develop an imaginative approach where Vmax/Km, shown to depend solely on the formation of the transition-state complex, is plotted against ionic strength. Again using the Debye-Hückel limiting law, a point charge of +1 at the binding site for p-nitrophenylphosphate is inferred, and of near zero for the (low-affinity) ATP binding site, in “pure” ionic strength media such as chloride or sulfate.

Individually and together, the new findings presented in this issue bring some order to much of the scattered information concerning the kinetic properties of the sodium pump. If not exactly simple, sodium pump kinetics need perhaps not be as complex as once feared.

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