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(Hypertension. 1996;27:219-227.)
© 1996 American Heart Association, Inc.

Articles

Pathophysiological Consequences of Changes in the Coupling Ratio of Na,K-ATPase for Renal Sodium Reabsorption and Its Implications for Hypertension

David E. Orosz; Ulrich Hopfer

From the Department of Physiology and Biophysics, Case Western Reserve University, School of Medicine, Cleveland, Ohio.

Correspondence to Dr Ulrich Hopfer, Department of Physiology and Biophysics, Case Western Reserve University, School of Medicine, 10900 Euclid Ave, Cleveland, OH 44106-4970. E-mail uxh@po.cwru.edu.

	Abstract

Top Abstract Introduction Methods Results and Discussion References

 
Abstract Recent reports indicate that 1-Na,K-ATPase from Dahl salt-sensitive (DS) rats contains a glutamine for leucine substitution associated with increased Na-K coupling at unchanged maximal velocity. Genetic analyses suggest that 1-Na,K-ATPase is a potential hypertension gene. Therefore, we investigated whether renal Na⁺ metabolism could constitute a pathophysiological link between the molecular/functional change in Na,K-ATPase and hypertension. We simulated the consequences of increased Na-K coupling on overall Na-bicarbonate reabsorption in a proximal tubular transport model that incorporates apical Na-H exchanger and basolateral Na-bicarbonate cotransporter, K⁺ channel, and Na,K-ATPase. As expected, increases in the levels of the former three transport pathways yielded higher Na⁺ reabsorption. In contrast, increases in the maximal velocity of the Na,K-ATPase with a normal 3:2 (Na-K) coupling ratio did not increase Na⁺ reabsorption when apical Na-H exchange activity was limiting overall absorption. However, an increase in the Na-K coupling from 3:2 to 3:1, reported for the mutant 1-Na,K-ATPase in DS rats, was associated with greater Na⁺ reabsorption. This increase is a consequence of lower cytosolic pH and secondary stimulation of the Na-H exchanger at its allosteric H⁺ site. Decreased pH results from activation of Na-bicarbonate cotransport by Na,K-ATPase–dependent membrane hyperpolarization due to greater charge movement in 3:1 Na-K coupling. Thus, an increase in the Na-K coupling ratio results in an altered set point for cellular Na⁺ metabolism, with higher sodium reabsorption at unchanged Na,K-ATPase levels. The simulations thereby lend support for a unifying explanation for the salt sensitivity of DS rats, which has been proposed to stem from a mutation in the 1-Na,K-ATPase.

Key Words: hypertension, genetic • hypertension, essential • kidney • rats, Dahl • Na⁺,K⁺-transporting ATPase • sodium-potassium pump

	Introduction

Top Abstract Introduction Methods Results and Discussion References

 
Salt-sensitive hypertension constitutes a subgroup of essential hypertension characterized by an ability to control or ameliorate blood pressure with a low dietary salt intake or diuretics.¹ This feature points to a nephrogenic origin and, since there is a genetic component to it, a genetic predisposition for increased Na⁺ reabsorption in the kidney. Since pathological reabsorption of Na⁺ by the kidney, regardless of the mechanism, is known to result in hypertension (eg, Liddle's syndrome; see References 2 and 3), a genetic change in the renal set point to elevated Na⁺ reabsorption could provide an etiology for hypertension. However, the underlying cellular and molecular bases responsible for increased Na⁺ reabsorption leading to high blood pressure are unknown in essential hypertension, and hypotheses that have been advanced are controversial. The changes in cellular Na⁺ metabolism associated with human essential hypertension are likely to be slight, as they can be compensated for 3 to 5 decades and only then does hypertension become clinically important.

Genetic animal models for complex traits, such as hypertension, are available. Interestingly, recent evidence supports the concept that a single–amino acid change in the 1 isoform of the Na,K-ATPase might explain why Dahl salt-sensitive (DS) but not Dahl salt-resistant (DR) rats become hypertensive on a high Na⁺ diet.^{4 5 6} Comparison of the 1-Na,K-ATPase cDNA sequences from DS and DR rat kidneys revealed a substitution of a Leu for a Gln at position 276 in the DS rat.⁴ The Leu for Gln mutation in the 1-Na,K-ATPase is associated with an altered transport ratio of Na⁺ to K⁺ when measured in red blood cells.⁵ Canessa et al⁵ observed that Na,K-ATPase levels and Na⁺ transport rates in intact red blood cells were essentially the same in DS and DR rats but the K⁺ transport was reduced in red blood cells from DS rats, suggesting that the Na-K coupling ratio is increased at unchanged Na⁺ transport. Furthermore, a locus for hypertension on chromosome 2 has been recently identified in F₂ populations from DS and Wistar-Kyoto rat crosses as well as from DS and Milan normotensive rat crosses.⁷ Interestingly, the 1-Na,K-ATPase is the closest candidate gene.⁷ The combination of these data support the hypothesis that the 1-Na,K-ATPase is a candidate hypertension gene.

Although more molecular genetic studies remain to be performed (see "Results and Discussion"), the wider issue raised by the Na,K-ATPase hypothesis in hypertension is how an increased Na-K transport ratio would result in an altered renal set point for increased renal Na⁺ reabsorption. This issue has not been addressed adequately in the literature. The cellular models for renal Na⁺ reabsorption, which describe the behavior of Na⁺ and K⁺ transport, include as an important feature K⁺ cycling at the basolateral plasma membrane; ie, the K⁺ influx through the Na,K-ATPase is balanced in the steady-state by K⁺ efflux through K⁺ channels.⁸ The K⁺ cycling would suggest that changes in Na-K transport ratios at unaltered Na,K-ATPase rates have no consequences for transepithelial Na⁺ pumping rates, ie, for renal Na⁺ reabsorption rates. In other words, changes in the Na-K transport ratio in the mutated 1-Na,K-ATPase may not have any consequences for cellular Na⁺ and K⁺ homeostasis as well as transepithelial Na⁺ transport rates.

As mathematical modeling often provides more precise insights into the consequences of small functional changes in one of the transporters for overall cellular functions, we have explored the effects of changes in the Na-K coupling ratio of the Na,K-ATPase on Na⁺ reabsorption in the proximal tubule. The major type of Na,K-ATPase found in the kidney is the 1 isoform, which is identical to that found in red blood cells,^{9 10} so the same kinetic behavior of the enzyme can be expected in both tissues. The interesting and unexpected finding from the model studies is that an increased Na-K transport ratio predicts increased Na⁺ reabsorption rates in the proximal tubule, and therefore the observed mutation and functional changes in the Na,K-ATPase provide a unifying explanation for increased salt sensitivity of hypertension in DS rats. The reason for initially focusing on the proximal tubule is that the type of hypertension found in DS rats is associated with low renin and aldosterone levels and is not treatable with the distal diuretic amiloride,^{11 12 13} suggesting the involvement of a more proximal nephron segment. As discussed below, the consequences of altered Na-K transport ratios on Na⁺ reabsorption rates may be similar in the proximal tubule and the thick ascending limb of the loop of Henle, although for different molecular reasons, so that either nephron segment could be the dominant site responsible for an altered set point for increased Na⁺ reabsorption in vivo leading to hypertension. The general issues of coupling of electrolyte transport between different transporters in the basolateral plasma membrane and the apical plasma membrane of epithelial cells, which will be discussed below on the basis of proximal tubules, actually have wider applicability; thus, the initial exploration of the consequences of a mutation has provided an opportunity to gain new insights into the importance of different electrolyte transporters for overall transepithelial Na⁺ reabsorption under normal physiological conditions.

	Methods

Top Abstract Introduction Methods Results and Discussion References

 
Overview of Mathematical Model for Proximal Tubular Na-Bicarbonate Reabsorption
The primary purpose of the modeling was to gain insight into the contributions and interactions of different cellular electrolyte transporters to overall salt absorption. This purpose is achieved by leaving out unnecessary transporters and including only the major transport pathways that are recognized to contribute to proximal tubular Na⁺ and bicarbonate reabsorption.¹⁴ This restriction is justified in that the combination of these transporters is sufficient to accomplish Na-bicarbonate reabsorption. The essential transporters included are an Na-H antiporter in the luminal plasma membrane and Na,K-ATPase, Na-bicarbonate cotransporter, and K⁺ conductance in the basolateral plasma membrane. As an optional pathway, a proton leak was added that represents lumped proton/acid influx. It was introduced to test predictions from the mutant Na,K-ATPase under conditions without tight coupling between Na-H antiporter and Na-bicarbonate cotransporter. The model is diagrammed in Fig 1.

View larger version (13K): [in this window] [in a new window]   Figure 1. Diagram shows cellular transporters for Na-bicarbonate reabsorption in the model (based on Emmett et al14 ).

The major considerations in building the model were to describe the kinetics of the individual transporters in terms of the properties known from published studies and then to adjust their maximal velocities (or permeabilities) to achieve realistic intracellular ion concentrations and membrane potential under baseline conditions (see Table 1). The kinetic equations for the individual transporters are described below. Taking the kinetic properties of the transporters, the intracellular ion concentrations, and membrane potential as fixed values as in Table 1, the parameter space of the maximal velocity (or permeability) values has only two residual degrees of freedom, ie, an overall scaling factor that determines the rate of Na⁺ reabsorption and one of the maximal velocity (or permeability) values from the basolateral plasma membrane, eg, the permeability of a proton leak.

View this table: [in this window] [in a new window]   Table 1. Steady-state Values for Selected Model Parameters

The mathematical model was written for the SCoP simulation package (Simulation Resources, Inc), which provides support for compartmentation and kinetics problems. The package was also used to fit the experimental results to formulated transport equations by the principal axis method.¹⁵

The model was validated by three criteria: (1) ability to find self-consistent solutions with realistic intracellular Na⁺, K⁺, and bicarbonate concentrations as well as pH and membrane potential under different conditions (eg, Table 1); (2) ability to mimic intracellular Na⁺ concentration and its time-dependent changes after an acid pulse in monolayers of proximal tubular cells (data not shown); and (3) comparison of predictions from this model under baseline conditions with those of previous proximal tubular models of Verkman and Alpern¹⁶ and Weinstein.¹⁷

Formulation of Mathematical Model of the Proximal Tubule
Flux Equations for Transporters
The model uses a combination of kinetic and phenomenological equations to describe the dependence of solute fluxes on kinetic properties of specific transporters, in a manner similar to that used by Verkman and Alpern¹⁶ and Thomas and Dagher¹⁸ in their proximal tubular models. Positive fluxes are set in the direction from lumen into cell and from cell into plasma (capillary). Membrane potential was referenced to the lumen. Each transport pathway is described below.

Na-H antiporter. The equation for the Na-H antiporter is based on a reaction scheme described by Aronson (see Fig 1 of Reference 19) and is shown in Fig 2. This kinetic model includes competitive interaction between Na⁺ and H⁺ for an external binding site, electroneutral, 1:1 Na-H coupled transport, and regulation by cytosolic protons. Furthermore, this model was selected from among those kinetic models with cytosolic proton regulation because it has the least number of binding sites; ie, this kinetic model does not include a specific, allosteric modifier site for cytosolic protons (for a detailed discussion, see Reference 19). The kinetic equation describing the net turnover (J_NaH) of Na-H exchange was derived with the assumption of rapid equilibrium (reviewed in Reference 20):

View larger version (11K): [in this window] [in a new window]   Figure 2. Diagram shows reaction scheme for the Na-H antiporter from which the kinetic equation was derived (adapted from Reference 19). Details are discussed in "Methods."

(1)

where D=[2·na_o·na_i+2·na_o·h_i+na_i+h_i+2·h_o·na_i+2·h_o ·h_i+h_i·na_i·na_o+h_i·na_i·h_o+(K^H_a·na_o)/K_H+(K^H_a·h_o)/K_H], and na_o=Na_o/K_Na, na_i=Na_i/K_Na, h_o=H_o/K_H, and h_i=H_i/K_H. K_Na, K_H, and K^H_a are dissociation constants for reactions shown in Fig 2; P is the transporter permeability; E_total is the total enzyme (transporter) concentration; and the subscripts "o" and "i" refer to outside (extracellular, apical) and inside (intracellular, cellular), respectively.

Equation 1 was used to fit published steady-state data,^{21 22} and the fits are shown in Fig 3. Activation of the Na⁺ transport rate by intracellular protons and extracellular Na⁺ are described closely by the equation (Fig 3A and 3B). Although the equation does not completely describe the effect of extracellular protons on the Na⁺ transport rate (data not shown), the equation is sufficiently accurate for the simulations presented because the extracellular pH was kept constant. The values of the kinetic parameters for the Na-H antiporter used in the model are given in Table 2. (The kinetic model for the Na-H antiporter was not tested with pre–steady-state data [eg, see Reference 24]. Different kinetic models may be more appropriate to explain published pre–steady-state data.)

View larger version (13K): [in this window] [in a new window]   Figure 3. Line graphs show fits of the kinetic equation for the Na-H exchange to published experimental data, where Na-H turnover (JNa) is activated by intracellular pH (pHi) (A) and extracellular Na+ (Nao) at pHi of 6.6 () and 7.5 () (B). Data in A come from Fig 1 of Aronson et al21 ; data in B were calculated from data in Fig 4 of Aronson et al.22 The curves were drawn from Equation 1, with values of KH, KNa, and KHa as given in Table 2. Goodness-of-fits as described by probability, P,23 were greater than 0.60 for A, greater than 0.40 for B at pHi 6.6, and greater than 0.50 for B at pHi 7.5.

View this table: [in this window] [in a new window]   Table 2. Model Parameters

Na,K-ATPase. The equation used to describe Na⁺ and K⁺ fluxes mediated by the Na,K-ATPase is that used by Latta et al.²⁵ This phenomenological equation is based on the Hill equation²⁶ and is used to describe highly cooperative binding of Na⁺ and K⁺ to separate sites on the pump^{27 28} :

(2)

where J_max is the maximum turnover; K_Na and K_K are apparent K_m values for Na⁺ and K⁺, respectively; Na_c and K_b are the cytosolic [Na⁺] and basal [K⁺], respectively; and n_Na and n_K are the number of Na⁺ or K⁺ ions binding per turnover, respectively. The dependence of J_max on membrane potential in the Na,K-ATPase as demonstrated by Gadsby et al²⁹ was also included in the model. An empirical function was used to relate J_max to J_max(=0) and membrane potential (), which accurately described (P>0.95) the data from Fig 2 of Gadsby et al²⁹ between -150 and 0 mV. (The potential dependence of J_max for the Na,K-ATPase was described by the following empirical equation: J_max=J_max[=0]·cos[0.277·U], where U is the reduced membrane potential expressed as ·F/[R·T]. F, R, and T are the Faraday constant, gas constant, and absolute temperature, respectively. At -70 mV, the change in J_max with potential is less than 1%/mV.)

Another commonly used equation for describing Na⁺ and K⁺ fluxes mediated by the Na,K-ATPase is the Garay and Garrahan equation.³⁰ This equation assumes noncooperative binding of Na⁺ and K⁺ to separate sites on the Na,K-ATPase. The Hill equation was chosen over the Garay and Garrahan equation for two reasons: (1) The data of Canessa et al⁵ from DR and DS rats could be fitted significantly better to the Hill equation (Fig 4), and (2) the Hill equation better describes data on electrical flux generated by the Na,K-ATPase (S.A. Lewis, personal communication, 1995).

View larger version (14K): [in this window] [in a new window]   Figure 4. Line graph shows fits of the Hill equation (Equation 2) for Na,K-ATPase to published experimental data obtained in red blood cells from Dahl salt-resistant () and salt-sensitive () rats (Fig 7 of Reference 5). The rate of K+ influx mediated by the Na,K-ATPase is activated by extracellular K+ concentration ([K+]ext). The curves represent the best simultaneous fit of data from each rat strain, when nK=2 for DR rat data and nK=1 for DS rat data. The probability, P,23 was greater than 0.99 for each data set.

It is important to realize that the apparent Michaelis constant for Na⁺, K_Na, is a function of cellular K⁺ concentration, and likewise that for K⁺, K_K, is a function of extracellular Na⁺ concentration. This is evident from the Albers-Post reaction scheme for the Na,K-ATPase, where the binding of Na⁺ and K⁺ is competitive at internal and external sites.^{30 31} The values of K_Na and K_K used in the model come from fits of the data of Canessa et al⁵ and are given in Table 2.

Na-bicarbonate cotransporter. The equation used to describe the Na-bicarbonate cotransporter is that used by Verkman and Alpern.¹⁶ This kinetic-phenomenological hybrid equation closely describes published Na⁺ saturation data (P>0.99 to data from Fig 5 of Reference 32); this equation further fits published bicarbonate concentration data in the range of interest for the simulations described in this article, ie, between 5 and 40 mmol/L bicarbonate (P>0.95 to data from Fig 6 of Reference 33). This equation derived by Verkman and Alpern incorporates the dependence of turnover on Na-bicarbonate stoichiometry and Goldman-type dependence on membrane potential. The values of constants for the Na-bicarbonate cotransporter used in the model are shown in Table 2.

View larger version (15K): [in this window] [in a new window]   Figure 5. Line graphs show effect of an increase in Na-K coupling ratio of the Na,K-ATPase from 3:2 to 3:1 on intracellular pH (pHc) (A), intracellular [Na+] ([Na+]c) (B), intracellular [K+] ([K+]c) (C), basolateral membrane potential (Ebl) (D), and transporter-mediated Na+-transport rates (Na+ Turnover) (E). Na+ transport rates for the different transporters are expressed as rates relative to rates when the Na,K-ATPase coupling ratio is 3:2 (Na-K). Na-BiC indicates Na-bicarbonate cotransporter; Na/H, Na-H antiporter; and Na/K, Na,K-ATPase.

View larger version (20K): [in this window] [in a new window]   Figure 6. Line graph shows dependence of Na+ reabsorption rates on the Jmax for 3Na,2K-ATPase, 3Na,1K-ATPase, and 3Na,1K,1H-ATPase. Jmax values of the Na,K-ATPase and Na+ reabsorption rates are expressed as the fraction of the respective values at steady state under normal 3:2 Na-K coupling as given in Tables 1 and 2.

K⁺ and H⁺ channels. The passive K⁺ and H⁺ fluxes across the basolateral membrane are described by the Goldman-Hodgkin-Katz equation (reviewed in Reference 20). The K⁺ flux is necessary to achieve electroneutrality and appropriate cytosolic K⁺ concentration (Fig 1). The proton permeability is optional but allows introduction of dissipative proton fluxes. The permeability coefficients, P_K and P_H for the K⁺ and H⁺ fluxes, respectively, are given in Table 2 for the simulation conditions used in Figs 5 and 6.

Volume Flux
The model used for the simulations in this article included no volume flux; thus, the cellular volume remains constant (at 1.0 µL/cm²). This assumption was also made by Verkman and Alpern,¹⁶ who demonstrated that the inclusion of volume flux did not have a significant effect on their simulation results. The present model has only a maximum osmolarity change of 7 mmol/L under the most extreme conditions, which would not result in a significant volume change in the model (<3%).

Buffer Capacity
The total cytosolic buffer capacity in the model cell is composed of the impermeant cellular buffers and bicarbonate. The theoretical expression for impermeant buffer capacity (ß_cell) is derived directly from the Henderson-Hasselbalch equation (reviewed in Reference 33). This buffer capacity in our model is represented as a lumped two-buffer system, and since buffer capacity is additive, the cellular buffer capacity expression takes the following form:

(3)

where K_c,A and K_c,B are apparent cellular buffer association constants, and [Cell Buffer A] and [Cell Buffer B] are apparent cellular buffer concentrations representing all impermeant cellular buffers.³³ Parameters for the cellular buffer capacity used in the model were determined from experiments with cells from an early proximal tubular cell line (SKPT cell line) derived from spontaneously hypertensive rats^{34 35} (reviewed in Reference 36) loaded with the pH-sensitive fluorescent dye 2',7'-bis(2-carboxyethyl)-5(6)-carboxyfluorescein (BCECF) and performed as described in Boyarsky et al³⁷ (unpublished data, 1994). The experimentally determined values used in the above equation for the model cell were pK_c,A of 5.4, pK_c,B of 8.3, [Cell Buffer A] of 100 mmol/L, and [Cell Buffer B] of 27 mmol/L.

The integral of the sums of buffer capacities for each buffer in the cell gives the amount of acid necessary to change the pH from the initial pH (pH_i) to the final pH (pH_t):

(4)

The theoretical buffer capacity of bicarbonate, ß_bicarb, is equal to d[HCO₃]/dpH and is also calculated from the Henderson-Hasselbalch equation.³³ The inclusion of this buffer system effectively allows for experimental acid-load protocol to be simulated.

Solution of Model Equations
So that the model was more widely applicable, the equations were set up for solutions under short-circuit current conditions; ie, electroneutrality is maintained and the net current across the apical plasma membrane equals the current across the basolateral plasma membrane in the absence of transepithelial electrical and chemical gradients. However, in the particular case of the proximal tubular model in Fig 1 with leaky "tight" junctions (assumption in the model about 0.1 S/cm²) and no electrogenic transport processes in the luminal plasma membrane, there is no short-circuit current, the membrane potentials are identical across the luminal and basolateral plasma membranes, and the short-circuit condition narrows down to no net charge transport across the basolateral plasma membrane.

The model was designed to compute a numerical solution for very small time steps, with a flow similar to those already published.^{16 25} Briefly, the flow of the model is as follows: Step 1, determine initial conditions; step 2, solve for membrane potential; step 3, compute all ion fluxes; step 4, integrate fluxes from t to t+t and compute new pH_c, solute concentrations; and step 5, repeat cycle from step 2 as long as t<t_final.

It is important to note that the program finds unique values of J_max for the transporters and K⁺ permeability for desired steady-state solutions of overall Na⁺ reabsorption rate and intracellular ion concentrations, pH, and membrane potential. These values also depend on the desired leak proton conductance. The cellular concentrations of Na⁺, K⁺, and bicarbonate as well as pH and membrane potential come from values used by Weinstein³⁸ for rat cells. Luminal and basolateral compartment solute concentrations come from values typically used in experimental protocols. The actual program solution of these values for the initial, ie, baseline, condition is listed in Table 1, together with the rates of Na⁺ reabsorption (proton secretion) and K⁺ cycling. The time constant () for cellular Na⁺ turnover is about 1.6 second. The steady-state fluxes are in reasonable agreement with values reported by Verkman and Alpern¹⁶ and Weinstein^{17 38} for their proximal tubular cell models.

The executable version for DOS-based machines of this mathematical model is available from the authors to any interested reader.

Statistics
The goodness-of-fits of the model equations to experimental or published results were assessed by determining the probability value (P) from the reduced ² as described by Bevington.²³

	Results and Discussion

Top Abstract Introduction Methods Results and Discussion References

 
One of the important features of proximal tubular Na⁺ reabsorption is the strong dependence of the luminal Na-H exchanger on intracellular pH.^{19 21} This feature provides for a tight coupling between Na⁺ influx into the cell at the luminal plasma membrane and Na⁺ and bicarbonate efflux at the basolateral plasma membrane. Moreover, because all electrogenic fluxes at the basolateral plasma membrane are coupled by virtue of the membrane potential, Na-bicarbonate cotransport is coupled to the other major transporters at the basolateral plasma membrane, ie, Na,K-ATPase and K⁺ conductance. The net effect is a strong coupling of Na⁺ influx at the luminal plasma membrane with Na⁺ efflux at the basolateral plasma membrane. Because of this coupling, changes in either basolateral or luminal transporters could result in changes in transepithelial Na⁺ fluxes. Thus, the cellular physiology of proximal tubular Na⁺ reabsorption is very different from that in the distal tubule, where the rate-limiting step has clearly been identified at the amiloride-sensitive Na⁺ conductance at the luminal plasma membrane¹³ and excess Na,K-ATPase is maintained by the distal epithelial cell to transport out any Na⁺ that may enter the cell.¹³ This picture of a distal tubular epithelial cell ready to acutely reabsorb Na⁺ makes sense because the distal tubule is involved in the final regulation of Na⁺ reabsorption, where the amount of Na⁺ reabsorbed and thus the overall energy expenditures are small compared with those in proximal segments. In contrast, the picture emerging for proximal tubular Na⁺ reabsorption is that of tight coupling between Na⁺ transport at the luminal and basolateral plasma membranes, consistent with neither plasma membrane being uniquely rate limiting under normal conditions of high Na⁺ reabsorption rates. Furthermore, the overall stoichiometry of Na⁺ transported through the cell per ATP hydrolyzed is greater than the 3:1 stoichiometry of the enzyme, as indicated in Fig 1. In other words, the sum of membrane transporters in the proximal tubule delivers a more efficient use of metabolic energy, partly because of the tight coupling between luminal and basolateral plasma membranes. As the proximal tubule provides more than 80% of renal Na⁺ reabsorption, energetic considerations may have played a role in the evolution of the cellular mechanisms present in today's metanephric kidneys. A similar situation with respect to efficiency of the energy use is found in the cellular mechanism for NaCl secretion in salivary acini, where six Na⁺ ions are secreted per ATP hydrolyzed.³⁹

Given the model in Fig 1, it is immediately obvious that increases in luminal Na-H exchange activity and Na-bicarbonate cotransporter activity are associated with increased Na⁺ reabsorption (see also below). The effects of changes in the coupling ratio of Na,K-ATPase are less clear. The modeling allows thought experiments to be carried out with an acute change in the ratio of Na⁺ and K⁺ transported by the Na,K-ATPase at identical J_max values. When this is done in the context of the proximal tubular Na-bicarbonate reabsorption mechanism, one finds that an increase in the Na-K ratio from 3:2 to 3:1 increases the rate of active Na⁺ reabsorption by the cell; ie, the Na⁺ load on the cell increases and more Na⁺ is transported (Fig 5). A close inspection of the time course in Fig 5 reveals that the sequence of activation is as follows: (1) The increased Na-K transport ratio of the Na,K-ATPase is associated with an increase in net charge transport and hence increased potential at the basolateral plasma membrane (Fig 5D); (2) the increased membrane potential drives a higher Na-bicarbonate efflux through the cotransporter (Fig 5E), which decreases cytosolic pH (Fig 5A); and (3) the decreased pH in turn activates the Na-H influx via the proton allosteric site (Fig 5E). (The change in Na-K coupling stoichiometry is associated with an initial drop in Na,K-ATPase activity [Fig 5E]. This drop in activity is a result of an increase in the value of the term [1+(K_K/K_b)^nK] in Equation 2 when n_K decreases from 2 to 1 and is not a result of a change in membrane potential on the Na,K-ATPase. This decreased activity between Na,K-ATPase with different Na-K coupling ratios is supported by published results of Canessa et al⁵ [also see Fig 4].) Interestingly, given the experimental data for pH sensitivity of the Na-H antiporter²¹ (also see Fig 2), Na⁺ transport rates in proximal tubular cells, and initial intracellular pH, a decrease of the intracellular pH of only 0.1 pH unit is associated with an approximate 10% increase in Na⁺ influx. Given the large amount of daily Na⁺ normally reabsorbed by the proximal tubule (80%), a 10% increase constitutes a large load on body Na⁺ homeostasis. Cellular pH changes with magnitudes of 0.1 unit are experimentally difficult to measure with certainty, given the background of other processes that regulate cytosolic pH, and would show up as background "noise" when comparing cells from genetically hypertensive versus normotensive individuals. Nevertheless, several studies have demonstrated lower intracellular pH values in cells from hypertensive animals and humans compared with normotensives,^{40 41} concordant with the predictions of the model. Similarly, the associated membrane potential changes are also small (4 mV hyperpolarization; see Fig 5D). This change would be easy to detect in acute experiments—ie, if the Na-K transport ratio of the Na,K-ATPase could be acutely altered—but is likely to be difficult to detect when cells with normal and mutant Na,K-ATPase molecules are being compared because of other processes that influence the membrane potential.

One would expect that the changes caused by the mutated Na,K-ATPase depend on which membrane is rate limiting for overall Na⁺ reabsorption. Fig 6 illustrates the model predictions for the dependence of proximal tubular Na⁺ reabsorption on Na,K-ATPase over a wide range of activity. As long as Na,K-ATPase activity is rate limiting, overall Na⁺ absorption is directly proportional to ATPase activity; at higher Na,K-ATPase activity, as apical Na⁺ influx becomes rate limiting, Na⁺ reabsorption becomes independent of small changes in Na,K-ATPase levels. Interestingly, the relationship between overall Na⁺ reabsorption rates and Na,K-ATPase activity in the proximal tubule goes through a maximum, with very high activity of the Na,K-ATPase becoming inhibitory (about 6% decrease for a twofold increase in enzyme level). This inhibition results from lowered intracellular Na⁺ concentrations and thereby decreased Na-bicarbonate fluxes, which in turn leave the cytosolic pH at higher values and thereby provide less allosteric activation of Na⁺ influx via the Na-H exchanger. Fig 6 also demonstrates that the above-discussed increase in overall Na⁺ reabsorption with a coupling ratio of 3:1 (Na-K) persists over a wide range of Na,K-ATPase activity. In addition, the increased coupling ratio is associated at the lower Na,K-ATPase levels with a right shift in the curve for the Na⁺ reabsorption rate versus Na,K-ATPase activity. This altered activity-response curve suggests that normal homeostatic regulatory mechanisms (hormonal and nervous regulation of body Na⁺ homeostasis) may not be optimally suited to regulate this mutant Na,K-ATPase.

The assumption made in the simulations in Fig 5 and Table 2 is that K⁺ is not replaced by another cation when the Na-K coupling ratio increases from 3:2 to 3:1 in the Na,K-ATPase. However, that assumption has not been proved. It is possible that protons take the place of K⁺. Because fluxes of protons are difficult to measure by chemical methods, experimental data are lacking about any such replacement. If the transport ratio becomes 3:1:1 (Na-K-H) in the Na,K-ATPase, the Na⁺ reabsorption rate is further shifted to the right and up; ie, Na⁺ reabsorption rates are very sensitive to Na,K-ATPase when the Na,K-ATPase is rate limiting but are increased when the apical Na-H exchanger determines the rate. Fig 6 compares the model predictions for changes in Na⁺ reabsorption depending on the coupling ratio of Na,K-ATPase (3:2 Na-K versus 3:1 Na-K versus 3:1:1 Na-K-H).

It is noteworthy that the effects of the mutation in Na,K-ATPase on overall Na⁺ reabsorption and intracellular ion concentrations are independent of the level of assumed proton leak. With the proton leak set to zero, a stoichiometry increase from 3:2 to 3:1 gives similar or more pronounced changes in the cellular parameters as illustrated in Figs 5 and 6 for a high proton leak (data not shown). Furthermore, a stoichiometry increase of Na,K-ATPase also leads to increased overall Na⁺ reabsorption when a noncooperative (Garay and Garrahan) model is assumed, although in this case the intracellular ion concentration changes are different from those predicted by the cooperative (Hill) model (data not shown).

As explained in the modeling considerations, all electrogenic processes at the basolateral plasma membrane are coupled by virtue of the membrane potential. The increase in the Na-K coupling ratio from 3:2 to 3:1 predicts increased Na⁺ reabsorption, provided that the kinetic parameters of the Na-bicarbonate cotransporter as well as K⁺ conductance are unchanged. In other words, the other basolateral players that can influence Na⁺ reabsorption are the K⁺ conductance and Na-bicarbonate cotransporter. For example, an increase in K⁺ conductance (P_K increased by about threefold) at a normal 3:2 coupling ratio of the Na,K-ATPase can also achieve an increase in membrane potential, Na-bicarbonate cotransporter turnover, and Na⁺ reabsorption in a manner similar to that discussed above for an increase in coupling ratio of the Na,K-ATPase (Table 3). The simulations are interesting as they predict that the increased coupling ratio of Na,K-ATPase and an increased K⁺ conductance have additional similar consequences in terms of cytosolic pH and Na⁺ and K⁺ concentrations; the major differences are in terms of the rate of K⁺ cycling at the basolateral plasma membrane and magnitude of the K⁺ conductance.

View this table: [in this window] [in a new window]   Table 3. Comparison of Different Mechanisms for Increasing Na+ Reabsorption

For comparison, it is interesting to evaluate what increases in the maximal velocity of the Na-H exchanger and the Na-bicarbonate cotransporter are necessary to achieve similar increases in overall Na⁺ reabsorption. The results for an 8% increase in Na⁺ reabsorption (same increase as observed with a change of the Na-K coupling ratio in the Na,K-ATPase from 3:2 to 3:1) are shown in Table 3. Interestingly, the activity of the Na-H exchanger would have to increase only 14% and the Na-bicarbonate cotransporter by 30% compared with a necessary threefold increase in K⁺ conductance to achieve the same overall Na⁺ transport effect. It is remarkable that changes in all four transporters are associated with only small changes in the cytosolic concentration of Na⁺ and K⁺ as well as pH. This prediction is a result of relatively tight coupling of luminal Na⁺ influx with basolateral Na⁺ efflux. The cellular parameters that can be used to distinguish which of the transporters is altered and responsible for overall increased transport are changes in cytosolic pH and changes in the ratio of the basolateral membrane potential to the Nernst potential for K⁺ (E_bl/E_K). Cytosolic pH increases with an increase in Na-H exchange activity; cytosolic pH decreases with an increase in Na-bicarbonate cotransport activity or in K⁺ conductance or when the coupling ratio of Na-K is increased in the Na,K-ATPase (Table 3). The ratio of actual basolateral membrane potential (E_bl) to the Nernst potential for K⁺ (E_K) reflects the ratio of conductance for ions other than K⁺ to that of K⁺ conductance. An increase in E_bl/E_K is associated with an increase in K⁺ conductance or Na-K coupling in the Na,K-ATPase (Table 3).

Salt-sensitive, essential hypertension is thought to result from a lowering of the threshold for Na⁺ intake at which Na⁺ homeostasis can be maintained by the kidney without an increase in blood pressure. Any gene that increases renal Na⁺ reabsorption could therefore be a "hypertension" gene. However, essential hypertension is a relatively mild disease in that it takes decades to become clinically overt in humans. The late onset of high blood pressure would indicate that increased salt reabsorption by any particular nephron segment can be compensated within the kidney early in life. The proximal tubule is a major site for Na⁺ reabsorption and a target for many nervous and hormonal regulatory mechanisms and, in addition, increased proximal Na⁺ reabsorption could be balanced by compensatory changes in distal segments. Therefore, a proximal tubular site for a "hypertension" gene would seem consistent with the observed phenotype of salt-sensitive, late onset, high blood pressure. Experimental support for this concept comes from measurements of Na-H exchange activity in proximal tubular brush border membranes from DR and DS rats under a low and high Na⁺ dietary load.⁴² Lewis and Warnock⁴² report that increased dietary Na⁺ in DR rats results in a decreased V_max of Na-H exchange activity and that this activity is already maximally downregulated in DS rats under a normal Na⁺ load that cannot be further lowered under a high dietary Na⁺ intake. These results are consistent with our modeling studies extrapolating the findings for red blood cell Na,K-ATPase to Na⁺ reabsorption in the proximal tubule. They also point out the complexities due to adaptations in vivo with both short-term regulation by intracellular messenger systems and long-term regulation by induction or repression of transporter gene expression.

Attempts have been made to confirm the findings of Herrera and Ruiz-Opazo⁴ and Canessa et al⁵ on molecular and functional levels. Results by Simonet et al⁴³ appeared to refute the discovery reported by Herrera and Ruiz-Opazo.⁴ Ruiz-Opazo et al⁴⁴ have since provided evidence that the lack of confirmation of the change in the cDNA in DS rats may be a result of a technical artifact or a nondetected strain contamination. The contradictions in the functional assays^{5 45} may be related to the subtlety of the change in the structure of Na,K-ATPase. The amino acid change at position 276 from a Gln to a Leu in the 1-Na,K-ATPase from DS rat is in the region associated with a domain that shows an Na⁺-sensitive conformation.^{4 46} It is conceivable that the 1-Na,K-ATPase from DS rats behaves differently in an intact cell at physiological membrane potentials and field strengths of greater than 10 000 V/cm than in a test tube with broken cell membranes and zero membrane potential. Leucine is less polar than glutamine and has a different dipole moment, suggesting that the spatial orientation of Leu at position 276 in the mutated Na,K-ATPase is less sensitive to membrane potential. If the amino acid at position 276 is exposed to membrane potential, a different three-dimensional structure could be present in the mutant compared with the normal protein under physiological conditions. Canessa et al⁵ observed differences between DS and DR rats measuring the ATPase-dependent (actually, ouabain-inhibitable) Na⁺ and K⁺ fluxes in intact red blood cells, while Nishi and colleagues⁴⁵ measured kinetic parameters of Na,K-ATPase in isolated renal membranes and observed no differences between DS and DR rats. Interestingly, however, the latter research group found a change in the Michaelis constant for activation of Na⁺ transport by extracellular K⁺ when they used intact epithelial cells.⁴⁵

Although the mechanistic and genetic roles of the Leu for Gln substitution at position 276 in the 1-Na,K-ATPase of DS rat in salt-sensitive hypertension remain to be elucidated in a polygenic pathophysiological context, our modeling studies provide a pathophysiological mechanism whereby this defect results in increased Na⁺ load on proximal tubular epithelial cells. In the intact animal, this increased Na⁺ load would be manifest as a reduced ability to effect natriuresis by downregulating renal Na⁺ reabsorption. The predicted changes in the cellular concentration of Na⁺ and K⁺, cytosolic pH, or membrane potential would be minor and well within the "noise" in population studies. For cells that have only low levels of the 1-Na,K-ATPase isoform for housekeeping functions (eg, red blood cells), the expected changes in cellular ion concentrations or membrane potential due to a mutated Na,K-ATPase would be even lower. Thus, most cells would be expected not to exhibit significant changes in cellular functions in vivo. In other words, the modeling predicts that the mutation in the 1-Na,K-ATPase resulting in an altered coupling ratio would predominantly affect epithelia that are involved in high rates of Na⁺ absorption and thus have high turnovers of the Na,K-ATPase and, in addition, exhibit coupling between basolateral Na,K-ATPase and luminal Na⁺ entry.

A case can be made that the situation in the thick ascending limb of the loop of Henle is similar to that in the proximal tubule, even though the transporters involved in Na⁺ reabsorption are very different. In this segment, Na⁺ entry at the luminal pole depends on a loop-diuretic–sensitive Na,K,2Cl-cotransporter.⁴⁷ This transporter is activated by lower cytoplasmic Cl^- concentrations.⁴⁷ Therefore, any mechanism that would lower cytosolic Cl^- concentrations would result in increased Na⁺ reabsorption, particularly as in the long term sufficient high Na,K-ATPase levels are induced to handle the load. Steady-state Cl^- levels in cells from the thick ascending limb of the loop of Henle are determined by the influx rate through the luminal cotransporter and basolateral efflux through Cl^- channels. The Cl^- efflux and thus the cytoplasmic Cl^- levels would be expected to be influenced by changes in the coupling ratio of Na,K-ATPase and thus changes in the electrical charge flux provided by this enzyme. In agreement with this prediction, increased NaCl reabsorption in the thick ascending limb of the loop of Henle has been measured in DS rats by Roman and Kaldunski.⁴⁸

	Acknowledgments

 
This project was supported by the National Institutes of Health (HL-50173 and CA-43703). Dr Orosz was supported by a fellowship awarded by the American Heart Association, Northeast Ohio Affiliate. The authors wish to recognize Dr Victoria Herrera for her stimulating discussions and her critical reading of this manuscript.

Received June 5, 1995; first decision July 6, 1995; accepted October 25, 1995.

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