Sodium and Chloride Transport: Proximal Nephron

Net Fluxes

The filtered load of a solute to the proximal tubule is the product of the single nephron glomerular filtration rate (SNGFR) and the ultrafilterable concentration of the solute. For small nonelectrolyte species the ultrafilterable concentration is that in plasma water. For electrolytes, negatively-charged serum proteins produce a Donnan potential, which acts to decrease ultrafilterable Na ⁺ and increase Cl ⁻ concentration with respect to that of plasma water. In amphibian and mammalian proximal tubules, the net effect of proximal tubule transport is the reabsorption of the luminal solution, resulting in a diminished axial flow rate as one proceeds along the tubules. The systemic infusion of a substance, such as inulin, which is filtered at the glomerulus, not reabsorbed (or secreted) by the proximal tubule, and which may be assayed in aliquots of tubular fluid, permits the calculation of the net volume reabsorption by the tubule from the glomerulus to the point of sampling. Thus, in the rat superficial cortical nephrons, the tubular fluid (TF) inulin concentration at the end of the convoluted proximal tubules is twice that of plasma (P), indicating that half of the filtrate is reabsorbed proximally. In the amphibian, Necturus , the TF/P ratio suggests that about one-third of the filtrate is reabsorbed by the proximal tubule, and in certain fish, the net effect of proximal tubule transport is secretion of fluid into the lumen ; however, in view of translational considerations, only the mammalian kidney is considered in this chapter.

With micropuncture sampling of fluid from the proximal tubule, if a complete collection of tubule fluid is made, then the absolute transport rate by the nephron segment is known and can be expressed as a flux per unit area of epithelium ( Table 33.1 ). Alternatively, one may perfuse dissected segments of tubule to directly establish the epithelial fluxes under well-defined luminal and peritubular conditions. One must then obtain an independent measure of SNGFR to estimate the fractional reabsorption. The advantage of this approach is that proximal nephron segments not accessible to micropuncture may be examined. For the data from the perfused proximal convoluted tubule of the rabbit shown in Table 33.1 , the measured sodium flux, referred to a 5.4 mm segment of tubule, implies sodium reabsorption of 1.2 nEq/min. With a SNGFR of 20 nl/min, the filtered load of sodium is 2.9 nEq/min, so that the fractional reabsorption is predicted to be about 40%. In the instances of successful micropuncture of rabbit proximal tubule, the observed fractional reabsorption of sodium has been 50 and 45%. This type of comparison is particularly important, in that it suggests a reasonably well-maintained transport capacity for tubules examined in vitro . When examined carefully, however, conditions in vitro can produce subtle differences from the tubule in vivo . As might be expected, dissection conditions of isolated rabbit proximal tubules can decrease the peritubular membrane electrical potential and increase cytosolic Na ⁺ concentration; however, they can also engender a peritubular membrane K ⁺ channel, not seen in vivo , and change the Na ⁺ :HCO ₃ ⁻ stoichiometry of the peritubular membrane co-transporter from 3:1 to 2:1.

Unfortunately, attempts to present a concise tabulation of proximal transport ( Table 33.1 ) must be tempered by an appreciation of internephron heterogeneity, and the structural changes along the individual tubule. In broad terms, two nephron populations have been identified: those with superficial cortical glomeruli, whose short loops of Henle turn at the outer–inner medullary border (about ⅔ of rat nephrons); and those with juxtamedullary glomeruli, whose long loops of Henle penetrate the inner medulla to variable extents. In many mammalian species, the juxtamedullary glomeruli are larger and have a greater SNGFR than the mid-cortical or superficial cortical nephrons. In the rat, the filtration rate of juxtamedullary glomeruli has been measured by micropuncture collection of Henle limb fluid, and found to be about 1.5- to 2-fold that of superficial glomeruli. In the rabbit, an indirect technique has given estimates confirming the disparity between superficial and juxtamedullary nephrons (e.g., 43 and 66 nl/min, ; 23 and 29 nl/min ). Comparisons of transport properties of superficial cortical and juxtamedullary proximal tubules are available. Corresponding to the greater SNGFR of the juxtamedullary nephrons, there is a greater overall rate of volume and sodium reabsorption. Perfused tubule data from rabbit has indicated a relative magnitude of juxtamedullary-to-superficial Na ⁺ fluxes from 1.2- to 2-fold larger; the relative magnitude of HCO ₃ ⁻ fluxes is 2-fold larger. Beyond this quantitative distinction, the relative importance of specific transport mechanisms may also differ between the two nephron populations.

The capacity for volume transport gradually diminishes as one proceeds along the mammalian proximal nephron. This occurs in association with morphologic changes at the electron-microscopic level that have prompted the division of mammalian proximal tubule into three segments ( Figure 33.1 ). The early proximal convoluted tubule, S1, is characterized by tall, densely-packed apical microvilli, numerous mitochondria, and an intricate pattern of folding and interdigitation of the lateral cell membranes. There is a gradual transition to the S2 segment, which comprises the remainder of the proximal convoluted tubule and the very beginning of the proximal straight tubule. Here, there are fewer mitochondria and less amplification of membrane area. Finally, the proximal straight tubule, S3, shows a more cuboidal cell with fewer mitochondria and rare interdigitations. Welling and Welling have compared the cell membrane areas in the S1 and S3 segments of rabbit proximal tubule, and found that for each segment, the apical and basolateral areas are nearly equal. In S1, however, the absorptive area of the cell is increased by membrane folding to 36 cm ² /cm ² epithelium, whereas in S3 this value is 15 cm ² /cm ² epithelium. The transport of solutes and water has been measured in dissected perfused segments of rabbit proximal tubule, and the spontaneous transport rate was substantially less in the proximal straight tubule than in convoluted segments ( Table 33.1 ). In the rat, microperfusion of proximal tubule segments in vivo (with comparable flow rates and luminal fluid composition) has demonstrated a lower volume reabsorption rate for segments more than 1–2 mm from the glomerulus. Serial micropuncture along a single proximal tubule with filtered fluid flowing freely confirmed the sharp decline in reabsorptive flux of volume (sodium) and anions after the first 1–2 mm of tubule ( Figure 33.2 ). Comparison of Na ⁺ transport by perfused proximal straight tubules from superficial and juxtamedullary rabbit nephrons has demonstrated comparable reabsorptive rates. The respective convoluted tubule fluxes are two- and four-fold greater for Na ⁺ , with a similar proportionality for HCO ₃ ⁻ . Proximal convoluted tubule fluxes of glucose may be six-fold greater, and of phosphate three-fold greater than those of proximal straight tubule.

In rat and rabbit kidneys, the Na ⁺ concentration, and hence the total osmolality, remain relatively constant along the proximal tubule. This constancy of tubule fluid osmolality implies “isotonic transport,” and poses a special problem for rationalizing the forces at work in water reabsorption ( vide infra ). The fates of chloride and bicarbonate in the mammalian proximal tubule differ, however, in that the chloride rapidly rises to a level above that of the glomerular filtrate and the bicarbonate falls. This shift in anion composition occurs early in the proximal tubule, that is to say, within the S1 segment. This is referred to as “preferential bicarbonate reabsorption,” and has received much attention as a clue to transport activity at the cellular level. The key features of the compositional changes in tubular fluid during its passage through the mammalian proximal tubule are illustrated in Figure 33.3 . The tubular fluid/plasma (TF/P) concentration ratio of several solutes is plotted as a function of proximal tubular length. TF/P inulin rises to approximately 2.0, indicating water reabsorption. Glucose and amino acids are rapidly reabsorbed so that at 25% proximal tubular length their concentrations decline to some 10% of the filtrate concentration. Preferential bicarbonate reabsorption lowers the bicarbonate concentration of tubular fluid to approximately 5–8 mM. Along the initial portion of the proximal tubule, the chloride concentration is increased by reabsorption of water. In the initial segment, the transepithelial voltage is lumen negative, due to the electrogenic nature of co-transport of sodium with glucose or amino acids. As the concentration of these solutes declines and that of chloride rises, the polarity of the transepithelial electrical potential difference changes to lumen positive values. This voltage is, at least in part, a diffusion potential, generated by the chloride and bicarbonate concentration gradients, and the greater permeability of the tubular wall to chloride than to bicarbonate.

Transport Forces

To attribute mechanisms to epithelial transport, fluxes must be resolved in terms of responsible driving forces, specifically hydrostatic or osmotic pressure, solute concentration gradients, electrical potential or metabolic energy. The transepithelial volume flow, J _v (ml/s·cm ² epithelium), is a function of hydrostatic and osmotic driving forces:

Here the water permeability of the epithelium is represented either by the coefficient L _p (ml/s·cm ² ·mmHg), by RTL _p (ml/s·cm ² ·Osm) or by P _f (cm/s), where RT is the product of the gas constant and absolute temperature (1.93×10 ⁴ mmHg/Osm at 37°C), and ${\overline{v}}_w$ is the partial molar volume of water (0.018 ml/mmol). In Eq. (33.1) the osmotic effect of any species is incorporated in the reflection coefficient, σ _i , (0.0≤ σ _i ≤1.0). For σ _i =1.0, the species exerts a full osmotic effect, and the epithelium is an ideal semipermeable membrane. When σ _i =0.0, the species exerts no osmotic force. To determine the reflection coefficient for a specific solute, the change in the transepithelial volume flow produced by a transepithelial concentration gradient, Δ c _i , is compared to the volume flow produced by an equal concentration gradient of an impermeant species. The ratio of these two volume flows is just the reflection coefficient, σ _i .

To represent solute transport, J _i (mmol/s·cm ² ), the epithelial flux equation is of the form:

in which the first term is a convective flux in which a mean concentration appears:

in which c _i (l) and c _i (p) designate luminal and plasma concentrations. It is a consequence of thermodynamic theory (Onsager symmetry) that the reflection coefficient, σ _i , from Eq. (33.1) also appears in Eq. (33.2) for convective solute drag. This formalizes the intuitive notion that the smaller solutes, which are least osmotically effective, are more likely to be entrained in the volume flow. The second term in Eq. (33.2) represents electrodiffusive solute flux, namely the flux of solute i as a function of the electrochemical potential differences, $\Delta {\overline{\mu }}_j^c$ , of all of the solutes under consideration. Expansion of this potential is shown in the right-most expression, in which RT is the product of gas constant and absolute temperature (2.57 J/mmol at 37°C), z _i is the valence of solute j, F is the Faraday (96.5 C/mEq), and Δψ is the electrical potential difference across the epithelium. It is also a consequence of Onsager symmetry that the coefficients L _ij = L _ji (mmol ² /J·s cm ² ). When the coefficient L _ij is positive (for i≠j), then a reabsorptive driving force on solute i will also promote reabsorption of solute j, so that this coefficient may be considered to represent co-transport of the two solutes. Such co-transport obviously arises when a common carrier transports the two species, but may also occur as a result of intraepithelial convective flows.

Some of the most precise experimental measurements that can be made are those of electrical potentials and currents. In the absence of solute-solute interaction, the transepithelial solute flux is written:

where ${\mathrm{RTL}}_{\mathrm{ii}}/{\overline{c}}_i=P_i$ (cm/s) is the conventional solute permeability. Equation (33.3) has generally been the starting point for the application of electrophysiology to characterize proximal tubule. For example, if luminal and peritubular solutions have equal ionic concentrations (Δ c _i =0), and there is zero volume flow, then application of an electrical potential difference (Δψ) produces a change in ionic current:

in which g _i (S/cm ² ) is the partial ionic conductance of species i. The total epithelial electrical conductance, g =Σ g _i , or the epithelial electrical resistance, R=1/g, thus provides a measure of the sum of the ionic permeabilities. When the luminal and peritubular solutions are unequal, the open-circuit potential, in the absence of net transepithelial volume flow ( J _v =0), gives useful information about the relative ionic permeabilities. In this case, the sum of all ionic currents is zero (0=Σ I _i ), so that the transepithelial electrical potential is:

If, for example, the only concentration differences across the epithelium are equal and opposite anion gradients (such as chloride and bicarbonate), Eq. 33.5 ) shows that the difference in ionic conductances determines the magnitude of the transepithelial “diffusion potential.”

Table 33.2 is a compilation of the permeability properties of the proximal tubules of rat and rabbit. Again, the inclination to present such tabulation must be tempered by acknowledgement of variation of the permeabilities along the nephron, and of differences between superficial and juxtamedullary nephrons. With respect to water permeability, it has been suggested that there is a decline in L _p from the S1 to the S2 segment of the rat tubule. Nevertheless, the water permeability remains at least as large in the straight segment as in the convoluted segment. With respect to solute permeabilities, an increase in the electrical conductance of the rat proximal tubule has been observed as one moves from the earliest to the latest accessible segments. Experiments in perfused rabbit tubules suggest that the increase in total conductance is due to an increase in the chloride permeability. Comparison of tubule permeabilities indicates that juxtamedullary proximal convoluted tubules and proximal straight tubules are more cation selective than the superficial proximal tubule segments. Comparison of permeabilities of K ⁺ and of Cl ⁻ , between rabbit juxtamedullary and superficial proximal straight tubules suggests that the increase in cation selectivity derives from an absolute increase in juxtamedullary nephron cation permeability, with little difference in anion permeability.

There is no doubt that proximal tubule metabolism is required for transport to proceed at its normal rate. In the absence of ionic concentration gradients across the epithelium, reabsorption still proceeds and cooling or poisoning with metabolic inhibitors abolishes transport. A generally accepted treatment of active transport by the proximal tubule has been that of Frömter in which Eq. (33.2) is extended by inclusion of a term for metabolically driven transport, $J_i^a$ :

or in the absence of coupled fluxes

It may also occur that water flux is linked to metabolic reactions in a way that reabsorption proceeds in the absence of transepithelial driving forces. This flux, $J_v^a$ , has been termed “active water transport,” and, by analogy with Eq. (33.6) , Eq. (33.1) for transepithelial volume flow has been written :

A derivation of $J_v^a$ from considerations of the internal structure of the tubule epithelium will be indicated in the section on the paracellular pathway.

Cytosolic Concentrations

In the foregoing, proximal tubule transport has been treated from the perspective of the epithelium as a homogeneous entity, with reflection coefficients and permeabilities inferred from the transepithelial fluxes produced by changes in luminal and peritubular solutions. Over the last decades, however, a more microscopic view of proximal tubule transport has evolved. Crucial to this perspective were the observations that the intercellular tight junctions could serve as a low resistance route for transepithelial ion permeation. This defines a “paracellular pathway” for fluxes, across the tight junction, into the lateral intercellular space, and out across the basement membrane to the peritubular capillaries. The “transcellular pathway” enters the cell cytosol via the luminal membrane and exits across the basal cell surface or across the lateral cell membrane into the lateral intercellular space. To discern solute transport across individual cell membranes, one must be able to monitor changes in intracellular concentrations. Historically, the first estimates of cell ion content derived from chemical analysis of tissue. Difficulties with this method include the inaccuracy associated with the subtraction of the extracellular contribution to the total, as well as the limitation of examining the concentration at only a single point in time. An additional concern arises when one tries to estimate transmembrane chemical potential differences, if some of the cell ion content is bound or sequestered, and thus not available to the “transport pool.” Somewhat akin to the chemical assay has been the application of the electron probe to determine cell solutes. With the small beam of this technique, true intracellular sampling can be ensured, although the estimate of cell water is indirect and an important source of uncertainty. Nuclear magnetic resonance (NMR) spectroscopy has been used as a non-destructive method for measuring intracellular sodium of proximal tubules in suspension. Unfortunately, only a portion of the cell sodium is “visible” by NMR, and additional steps must be taken to estimate the total pool. One fruitful technique for probing the cell interior has been the use of microelectrodes capable of penetrating the cell membrane, presumably without destroying the functional integrity of the cell. The electrodes may record the electrical potential of the cytosol or, when fashioned with a substance that reacts selectively with an ion, the cytosolic electrochemical potential of the selected ion species. Although technically challenging, these measurements provide precisely the information necessary for establishing the driving forces for ionic fluxes. Subsequently, ion-sensitive fluorescent dyes were developed, and these could be loaded into proximal tubule cells and used to monitor continuous changes in pH, calcium or chloride.

Despite the technical difficulty of studying the small cells of mammalian proximal tubules, a reasonably complete picture of the intracellular milieu is available ( Table 33.3 ). In the rat, the intracellular potential has been found to be −76 mV. Good agreement has been reported for the cell sodium concentration estimated electrophysiologically (17.5 mmol/l) and with the electron probe (20.3 mmol/l). Potassium is actively accumulated above its electrochemical equilibrium. Although an early investigation suggested passive distribution of chloride across the proximal tubule, subsequent work established cellular chloride uptake against a potential gradient. The mechanism underlying this elevation of cytosolic chloride will be considered below. At this point, it suffices to acknowledge that the potential hill for chloride is linked via several anion exchangers to the bicarbonate potential. In turn, the elevation of cytosolic bicarbonate is regulated and maintained well above the equilibrium value (1.4 mmol/L) by a number of transport processes, including Na ⁺ /H ⁺ exchange and metabolically driven proton extrusion from the cell (H ⁺ -ATPase).

It has also been possible to impale cells of the isolated perfused rabbit proximal tubule. The intracellular potentials of the proximal convoluted and proximal straight tubules were first found to be −51 and −47 mV respectively, and subsequent determinations have been confirmatory (−50 mV ; −61 mV, ). In the proximal straight tubule, the cell potassium activity is higher than its electrical equilibrium. Both the cell potassium activity and the cell potential fall (depolarize) with ouabain-inhibition of the peritubular Na ⁺ , K ⁺ -ATPase. As in the rat, the chloride activity is elevated above equilibrium, and there is good agreement between the electrophysiologic determination (18 mmol/L) and that found using a fluorescent dye (21 mmol/L). The intracellular pH of rabbit proximal tubules in suspension was first investigated using a radiolabeled weak organic acid. Under control conditions, the cells were found to be alkaline, 7.51, becoming acid with the application of ouabain, 7.42. Subsequent determinations have revealed the pH to be lower (7.22, ), and thus more akin to that found in the rat proximal tubule.

Luminal Membrane

Sodium/Proton Exchange

From a quantitative perspective, the most important sodium flux across the luminal cell membrane is the Na ⁺ /H ⁺ counter-transporter. The Na ⁺ /H ⁺ exchanger was securely established by Murer et al., using a suspension of vesicles composed predominately of luminal membrane. Their basic observation was that a sodium concentration gradient from suspension medium to vesicle interior resulted in acidification of the medium. This effect required the presence of intact vesicles, but was undisturbed when electrical potential differences between the vesicle interior and the medium were eliminated. Further, a suspension medium alkaline, with respect to vesicle interior, stimulated sodium uptake by the vesicles. These results were confirmed in rabbit proximal tubule vesicles by Kinsella and Aronson ( Figure 33.4 ) , who further demonstrated alkalinization of the vesicle interior by the inwardly directed sodium gradient. This countertransport is reversibly inhibited by amiloride, and proceeds with a Na ⁺ :H ⁺ stoichiometry of 1:1. Following those early observations, kinetics of the proximal tubule luminal membrane Na ⁺ /H ⁺ antiporter were studied intensively. Vesicle preparations revealed a transport site that bound a single Na ⁺ with an affinity roughly one-tenth that of the external Na ⁺ concentration, and with competitive binding by H ⁺ or NH ₄ ⁺ . Studies of the antiporter at lower temperatures indicated that Na ⁺ uptake and H ⁺ extrusion occurred in a sequential (“ping-pong”) fashion, with H ⁺ transport likely to be the rate-limiting step. The effect of intracellular pH is more complex, with cytosolic alkalosis shutting off Na ⁺ /H ⁺ exchange more sharply than a simple substrate depletion effect. Cytosolic pH appears to have little impact on the Na ⁺ affinity of the antiporter, but rather modifies the turnover rate. With respect to the kinetic properties of this transporter, the information gained from renal brush border membrane vesicles has generally received confirmation in studies of isolated proximal tubule cell suspensions, and in vesicles prepared from established cell lines or from primary culture of proximal tubule cells.

In mammalian proximal tubule, comparison of brush border and basolateral membrane vesicle showed that the Na ⁺ /H ⁺ exchanger is primarily within the luminal cell membrane. In the intact tubule, Schwartz presented evidence for the direct coupling of Na ⁺ and H ⁺ fluxes, showing that ouabain inhibition of the peritubular Na,K-ATPase, presumably raising cell sodium concentration, could run the luminal Na ⁺ /H ⁺ exchanger in reverse. Examination of vesicles from cortical and outer medullary regions of the kidney indicated that the Na ⁺ /H ⁺ exchanger is present along both convoluted and straight segments of proximal tubule. More direct evidence for the presence of the luminal membrane Na ⁺ /H ⁺ exchanger in the S3 segment was offered by Kurtz. Using tubules whose cells had been loaded with the pH-sensitive fluorescent dye, BCECF, he found acidification of the cell interior with removal of luminal sodium. Nevertheless, the vesicle studies indicated that the maximal Na ⁺ /H ⁺ exchange rate was lower in the outer medullary population, suggesting a lower density of the transporter in straight proximal tubules. This also received confirmation by Baum, who perfused both convoluted and straight proximal tubules with BCECF-loaded cells. Comparing the impact of changes in luminal sodium on intracellular pH, he concluded that, relative to the convoluted segment, the straight tubule had a 30% capacity for Na ⁺ /H ⁺ exchange.

In the molecular era, the Na ⁺ /H ⁺ exchangers came to be recognized as a family of transport proteins, NHE-, with the luminal membrane exchanger of proximal tubule identified as NHE3 (SLC9A3). The gene for NHE3 was cloned and sequenced, and the product identified immunocytochemically in the brush border membrane. Kinetic studies of the NHE3 in expression systems generally confirmed the properties noted a decade earlier in the membrane preparations. With respect to the Na ⁺ /H ⁺ exchange activity of the peritubular membrane, the NHE1 isoform was identified in basolateral membrane vesicles and in immunohistochemical staining of rabbit proximal tubule. Failure to detect NHE3 protein in proximal straight tubule prompted speculation that another NHE isoform may be operative in this segment. More generally, even in tubule segments in which NHE3 was abundant, the magnitude of the Na ⁺ /H ⁺ flux that actually traversed this isoform was uncertain. Based on the observation that the inhibitor profile of rat brush border vesicle Na ⁺ /H ⁺ exchange was identical to the inhibitor profile of NHE3 in expression systems, it was concluded that NHE3 was the sole exchanger within the luminal cell membrane. That view was quickly amended with the development of the NHE3 knockout mouse, in which proximal microperfusion revealed rates for Na ⁺ and HCO ₃ ⁻ reabsorption of 25% and 40% compared with wild-type. In subsequent in vivo microperfusion studies, residual Na ⁺ reabsorption was found to be slightly greater, 60% and 45%. When the proximal tubules from knockout mice were dissected, loaded with BCECF, and perfused in vitro , the magnitude of luminal Na ⁺ /H ⁺ exchange could be assessed as the change in intracellular pH in response to restoration of luminal Na ⁺ . In those experiments, the Na ⁺ -dependent proton secretion in knockout tubules was about 50% of the wild-type, and completely inhibitable by amiloride. The magnitude of NHE3 flux was also assessed in rat proximal tubules perfused in vivo , in which a specific NHE3 inhibitor reduced Na ⁺ reabsorption by 30% and 40%. These values are likely to be underestimates of the NHE3 flux, in view of the fact that amiloride inhibition was only 50%. In sum, it seems safe to attribute about half of the luminal membrane Na ⁺ /H ⁺ exchange to NHE3. With respect to the molecular identity of the residual transport, both NHE2 knockout and specific inhibitor studies have eliminated NHE2 as a candidate. Goyal and co-workers identified NHE8, within kidney cortex and expressed on proximal tubule brush border. Its quantitative role in luminal Na ⁺ /H ⁺ exchange remains to be defined.

Regarding the functional importance of the luminal membrane Na ⁺ /H ⁺ exchanger in the proximal nephron, two caveats are in order. It is important to distinguish total HCO ₃ ⁻ reabsorption from the Na ⁺ -dependent portion of HCO ₃ ⁻ reabsorption. The luminal membrane contains an H ⁺ -ATPase, and amiloride block of the Na ⁺ /H ⁺ transporter has been used to identify a significant component of proton secretion via the H ⁺ -ATPase. The second caveat is that total Na ⁺ -dependent proton secretion may be considerably greater than tubular HCO ₃ ⁻ reabsorption. Preisig and Rector microperfused rat proximal convoluted with a late proximal solution, low in bicarbonate and high in chloride. In this situation, where net bicarbonate absorption was virtually absent, amiloride still inhibited 44% of NaCl reabsorption. These findings were taken as evidence for the importance of parallel pathways through the luminal membrane for Na ⁺ (via the Na ⁺ /H ⁺ exchanger) and for Cl ⁻ (via a Cl ⁻ base exchanger) in the net reabsorption of NaCl. The implication of such a scheme is that the net flux of Na ⁺ across the Na ⁺ /H ⁺ transporter can well exceed the total reabsorptive bicarbonate flux. The first mathematical model of NHE3 was based on a scheme of Na ⁺ -binding, translocation, and release, H ⁺ -binding, translocation, and release, and also included competing NH ₄ ⁺ -binding, translocation, and release. In this model, all binding was assumed to be rapid (equilibrium), and affinity coefficients were assumed to be symmetric with respect to internal and external faces of the transporter. With one additional assumption, namely the inclusion of an internal modifier site which enhances translocation in response to cytosolic acidification, the kinetic behavior described in vesicle studies could be represented. When this simulation of NHE3 was incorporated into a mathematical model of rat proximal tubule, Na ⁺ /H ⁺ exchange functioned directly to reabsorb luminal NaHCO ₃ , and in parallel with a luminal membrane Cl ⁻ /base exchanger, yielded net NaCl reabsorption. An additional prediction of this kinetic model was that Na ⁺ /NH ₄ ⁺ exchange via NHE3 is the most important mechanism for ammonia secretion by proximal tubule. This comported with conclusions from tubules in vitro , that ammonia secretion from cellular ammoniagenesis could be blocked by inhibition of NHE3. Both experiment and model cast doubt on an earlier scheme of diffusive NH ₃ secretion and trapping in acidic luminal fluid. With respect to NHE function, more sensitive experimental techniques have revealed non-linearities. Fuster et al. used a pH-sensitive electrode to determine bath pH gradient in the immediate neighborhood of proton-transporting cells; from the gradient magnitude and the cell shape, they calculated the transmembrane proton flux. When this methodology was applied to cells expressing NHE1 (and to a lesser extent NHE3), it was found that NHE turnover rate as a function of external Na ⁺ became sigmoidal. Their observations were consistent with NHE schemes in which two “monomers” functioned cooperatively to yield a functional transport stoichiometry of 2Na ⁺ for 2H ⁺ . The study demonstrated the power of an electrophysiological technique to examine an electroneutral transporter; whether the observations have a physiologic correlate in kidney tubule function, remains uncertain.