A mathematical model of rat collecting duct III. Paradigms for distal acidification defects

Alan M. Weinstein

Department of Physiology and Biophysics, Weill Medical College of Cornell University, New York, New York 10021


    ABSTRACT
TOP
ABSTRACT
INTRODUCTION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

The present clinical taxonomy of distal renal tubular acidoses includes "gradient," "secretory," and "voltage" defects. These categories refer to presumed collecting duct defects in which the epithelium may be abnormally permeable and unable to sustain an ion gradient, in which luminal proton ATPases are defective, or in which electrogenic Na+ reabsorption is impaired and luminal electronegativity is reduced. Classification of affected individuals is based on urinary pH and ion concentrations during spontaneous acidosis and during SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion, as well as urinary PCO2 during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. A model of rat CD has been developed that has been used to examine determinants of urinary acidification (Weinstein AM. Am J Physiol Renal Physiol 283: F1252-F1266, 2002) and the interplay of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and PO<UP><SUB>4</SUB><SUP>3−</SUP></UP> loads to generate a disequlibrium pH and equilibrium PCO2. In this paper, pure forms of gradient, voltage, and secretory defects are simulated, with attention to variability in the locus of the defect in the cortical (CCD), outer medullary (OMCD), or inner medullary collecting duct (IMCD). The objective of these calculations is to discover whether the intuitive description of these defects is sustained quantitatively. The most important positive finding is that the locus of the transport defect along the CD plays a critical role in the apparent severity of the lesion, with more proximal defects being less severe and more easily correctable. In particular, model calculations suggest that for gradient or secretory defects to be clinically detectable they need to involve the OMCD and/or IMCD. Additionally, the calculations reveal a possible mechanism for CD K+ wasting, which does not involve failure of H+-K+-ATPase but derives from a paracellular anion leak and thereby a more electronegative lumen. The most important negative finding is the lack of support for the category of renal tubular acidosis associated with a voltage defect. Although CD lesions that present with both K+ and H+ secretory defects suggest mediation by transepithelial electrical potential difference (PD), both PD changes and proton pump PD sensitivity appear too small to account for the observed abnormalities.

distal renal tubular acidosis; renal acid excretion; urinary PCO2


    INTRODUCTION
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ABSTRACT
INTRODUCTION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

DISTAL RENAL TUBULAR ACIDOSIS refers to a group of disorders that manifest failure to achieve an acidic urinary pH (<5.5) despite systemic acidemia. It has long been an objective of workers in the field to develop a taxonomy of these disorders based on the underlying transport defects within the collecting duct (CD). Ideally, these defects were to be revealed through administration of a battery of provocative tests (3, 7, 14, 27). The most widely utilized tests have been SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> administration, with measurement of urinary pH, net acid, and K+ excretion and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> or PO<UP><SUB>4</SUB><SUP>3−</SUP></UP> loading, with measurement of urinary PCO2. From the responses to these tests, some distinct patterns have emerged, namely "gradient," "voltage," or "secretory" defects (14). With a gradient defect, the urine acidifies with infusion of SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>, and PCO2 of alkaline urine increases normally. The CD fails only in circumstances where a tubule-to-blood pH gradient needs to be established, and the presence of an abnormal transepithelial leak pathway is envisioned. With a voltage defect, both K+ and H+ secretion are diminished in acidosis, and there is blunting of the PCO2 response in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. The putative defect is composed of electrogenic Na+ reabsorption, so to the extent that proton secretion depends on a luminal negative PD, it too will be affected. In the secretory defect, urinary acidification cannot be restored by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>, and proton transport into a high-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> urine is markedly decreased. Presumably, the proton pumps themselves are dysfunctional, so that no manipulation of transepithelial driving forces can restore a normal proton secretory rate. Beyond this taxonomy, some have tried to use the pattern of test responses to infer the site, cortical or medullary, of the CD defect (7).

Thus far, all of the discussion of acidification defects has advanced in the absence of model simulations of the proposed pathophysiology. In the foregoing papers, a model of rat CD has been developed that could acidify the urine, and specific attention had been given to the effects of luminal flow on urinary pH and K+ excretion and to simulation of SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion (36). The model CD also produced a high urinary PCO2 in response to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, and specific attention was given to the interplay of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and PO<UP><SUB>4</SUB><SUP>3−</SUP></UP> loads to determine the final urinary PCO2 (37). The program for this paper is to consider three defects, intended to represent pure forms of gradient, voltage, and secretory defects. The gradient defect will be a high-conductance, anion-selective paracellular shunt in one or more CD segments. The voltage defect will be a sharp reduction in luminal membrane Na+ conductance in either cortical (CCD) or inner medullary CD (IMCD), or both. The secretory defect will be a nearly complete reduction in luminal proton pumps in one or more CD segments. For each defect, urinary solute excretion under acidotic conditions, without and with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion, will be examined. Similarly, urinary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading will also be simulated. The objective of these calculations is to discover whether the intuitive description of these defects actually holds up under scrutiny in a model. One important theme that will emerge is that the distal defects (IMCD or full CD) are more severe and less susceptible to correction by solute infusion.


    MODEL CALCULATIONS
TOP
ABSTRACT
INTRODUCTION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

In the calculations that follow, model parameters and peritubular conditions are those previously used (36). CD entering solute concentrations for simulation of acidosis ("acid control") have been modified from baseline conditions by HCl titration of luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> from 7.0 to 3.5 mM, keeping total phosphate and ammonia constant (Table 1). To secure maximal acidification of final urine, the input flow rate has also been decreased from 54 to 48 µl/min for all collecting ducts (7.5-6.7 nl/min per CCD). Figures 1 and 2 display the model solution for this acid control condition. Figure 1 displays the tableau of luminal potential difference (PD), volume flow, and concentrations and flows of the nonreacting species, in which the solid curves are those of acidosis, whereas the dotted curves are the baseline curves of model development (36). The obvious changes with acidosis are the decrease in entering volume flow, and the parallel decreases in all of the entering solute flows. In a comparison of the two conditions, there is no important difference in luminal PD along the entire CD. In the CCD and OMCD, there are also no substantive differences in Na+, K+, or Cl- concentration; however, in the IMCD, cation concentrations are lower, whereas Cl- remains little changed from baseline. With reference to Fig. 2, one may see that the depression in IMCD Na+ and K+ concentrations derives from the increase in titratable acid (TA) and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> in this segment. Despite the decrease in flow, there is negligible change in both absolute Na+ reabsorption (2.54 and 2.56 µmol/min under baseline and acidosis, respectively) and K+ reabsorption (1.05 and 1.00 µmol/min under baseline and acidosis, respectively). Nevertheless, luminal K+ concentration remains adequate to sustain H+-K+-ATPase activity. Figure 2 contains the concentrations and flows relevant to the CD acid-base economy, under acid control (solid curves) and baseline conditions (dotted curves). It is apparent that the model CD can acidify the urine, and it achieves nearly complete HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption within the first 2 mm of the IMCD, to a minimal urinary pH of 4.3. Nevertheless, with the smaller delivered loads under acid control, the absolute increase in TA excretion is small, and the absolute increase in NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion is negligible. The noteworthy feature of the acid control simulation is that the low pH of the final urine is achieved early and sustained over distance, so that minor parameter changes will not yield an apparent acidification defect.

                              
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Table 1.   Luminal fluid composition at Initial CD



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Fig. 1.   Electrolyte transport along the model collecing duct (CD) with 3.5 mM HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> in entering fluid and perfusion at 48 µl/min (solid curves), and under control conditions, 7.0 mM HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and perfusion at 54 µl/min (dotted curves). Left: luminal potential difference (PD; mV), and concentrations of Na+, K+, and Cl- (mM; brackets). Right: volume flow within the aggregate of all tubule segments (µl/min) as well as the axial solute flows (µmol/min) within the entire CD. The abcissa is distance along the CD, with x = 0 the initial cortical point, and cortical (CCD), outer medullary (OMCD), and inner medullary CD (IMCD) accounting for 2, 2, and 5 mm of CD length, respectively.



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Fig. 2.   Acid-base transport along the model CD with low-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> perfusate as in Fig. 1 (solid curves) and under control conditions (dotted curves). Left: luminal pH and concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, titratable acid (TA), and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (mM). Right: flows within the aggregate of all CD tubule segments of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (µmol/min), along with their sum-to-net acid flow (TA + NH<UP><SUB>4</SUB><SUP>+</SUP></UP> - HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>).

There are a number of possible parameter selections that might represent a gradient acidification defect in this CD model. If one considers amphotericin toxicity as the paradigm for such defects, then studies in lipid bilayers suggest that the drug could be an anion-selective channel within cell membranes (9, 17). However, on the basis of studies of turtle urinary bladder, Steinmetz and co-workers (18, 30) concluded that amphotericin provided a large conductance pathway for H+ and K+ through luminal membranes. With respect to the kidney, amphotericin can induce nonselective anion-conducting channels in isolated proximal tubule brush-border membranes (28). However, amphotericin toxicity does not appear to have been studied in any perfused tubule preparation, so there are no data identifying affected segments or the transport abnormalities. From the perspective of the model, the simple inclusion of a large H+- and K+-conductive pore within the luminal membrane of OMCD cells does not produce an acidification defect. Thus absent the ability to simulate amphotericin with any degree of confidence, a pure gradient defect will be considered in which only tight junctional Cl- and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> permeabilities are both increased from control by approximately a factor of 30. The increase in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> permeability creates a tubule segment that cannot sustain a transepithelial HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> gradient, and the parallel increase in Cl- permeability was included simply because it seems most likely that a paracellular pathway with a high HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> permeability would conduct both species. Three such defects will be considered, in which junctional anion conductance is increased solely in the CCD, OMCD, or IMCD.

In Figs. 3-5, the three leaky junctions are examined under acid control conditions or when 60 mM luminal Cl- has been replaced by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> (Table 1). Figure 3 is a tableau of bar graphs in which the abcissa references one of seven simulations: acid control perfusion with control parameters, acid control perfusion with the three gradient defects, or the gradient defects with an attempt at SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> correction; the panels display electrical PD, and solute concentrations and flows at the CD terminus. Figure 4 displays the axial profiles of luminal PD, K+ concentration, and flow for each of the leaky tight junctions. In Fig. 3, it may be seen that when the abnormality is in the CCD, there is a 55% decrease in Na+ excretion and nearly absent K+ excretion (87% decrease). This derives from the paracellular Cl- shunt of the principal cell Na+ current, producing a 20-mV depolarization within the CCD (Fig. 4). The impact of the IMCD defect is smaller but parallels that of the Na+-reabsorbing CCD, with a decrease in Na+ and K+ excretion of 18 and 27%, respectively. With reference to Fig. 4, the IMCD effect is more complex than in the CCD: early in the IMCD, the leaky junctions short circuit the transport potential, thus depolarizing the epithelium and enhancing K+ reabsorption; late in the IMCD, the PD is hyperpolarized, consistent with an accentuated Cl- diffusion potential that enhances K+ excretion. Because the IMCD coalesces and the bulk of luminal area is early, the net effect is the small decrease in K+ excretion. The OMCD defect imposes increases in both Na+ and K+ excretion (28 and 27%, respectively), due to a luminal negative PD generated by blood-to-lumen anion gradients (Fig. 4). With this observation, the model CD offers a possible mechanism for an acidification defect accompanied by renal K+ wasting that does not involve an associated defect in K+ reabsorption via the H+-K+-ATPase. With CCD and IMCD defects, there are increases in Cl- reabsorption, whereas with the leaky OMCD, urinary Cl- increases. Regardless of the defect, however, it appears that the hyperpolarization of SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> administration is a strong perturbation that provides nearly identical cation excretion and urinary flow rate (Fig. 3).


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Fig. 3.   Urinary composition and flows under acid perfusion, with tight junctions leaky to anions. Gradient defects are simulated by increasing tight junctional anion permeability to both Cl- and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> by a factor of 30, in the CCD, OMCD, or IMCD. In each bar graph, the abcissa references 1 of 7 simulations: acid control perfusion with control parameters (Con), acid control perfusion with the 3 gradient defects, or the gradient defects when 60 mM luminal Cl- has been replaced by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> (Table 1). The panels display electrical PD and solute concentrations and flows at the CD terminus.



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Fig. 4.   K+ handling by the CD with tight junctional (TJ) anion leaks. The 3 tiers correspond to the simulations of Fig. 3, in which the paracellular Cl- and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> permeabilities of CCD, OMCD, or IMCD have been increased by a factor of 30 over control. For each parameter set, the panels display luminal PD, K+ concentration, and axial K+ flow as a function of distance along the CD. In each panel, the dotted curve corresponds to the control parameters (Fig. 1).

Figure 5 displays the data relevant to acid excretion by the model CD: end-luminal pH and concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (left) and urinary excretion of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, and net acid (right). These data, along with K+ excretion, are also summarized in Table 2. All three leaky junctions lead to an acidification defect, in the sense that all of the urinary pH values in acidosis are well above that in control, and all of the values for net acid excretion are diminished. Nevertheless, the CCD defect appears to be mild and might not even be discerned if the diagnostic threshold were a urinary pH >5.5. With the CCD defect, urinary TA and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> concentrations are higher than in control, but urinary excretion is diminished as a result of decreased urinary flow. Both OMCD and IMCD defects are severe, with urinary pH values near 6.4 and net acid excretion ~60% of the control CD. Nevertheless, these two defects may behave differently with respect to their response to SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion. With the leaky OMCD, SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> brought the urinary pH to 5.3, below the diagnostic threshold, and thus "corrected" the acidification defect. With the leaky IMCD, urinary pH with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> fell to only 5.7, suggesting that with the most distal defect there was just not the opportunity to correct the HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> leak. Thus with similar transport defects, namely, high tight junctional anion permeability, the CCD lesion might be inapparent, the OMCD lesion severe but correctable, and the IMCD lesion not correctable.


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Fig. 5.   Urinary composition and flows under acid perfusion, with tight junctions leaky to anions. Using the parameters and perfusion conditions of Fig. 3, the panels display end-luminal pH and concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (left) and urinary excretion of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, and net acid (right).


                              
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Table 2.   CD function in acidosis

HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading with these gradient defects has been simulated using the high-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> perfusion solution of the previous paper (37), and its composition and flow rate are specified in Table 1. Figure 6 shows the results of these calculations, specifically, end-luminal pH and its disequilibrium value, end-luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration and flow, total CD CO2 generation, and the end-luminal equilibrium PCO2. Some of these quantities are also indicated in Table 3. The most prominent feature of these simulations is that with each anion leak, there is a substantial and nearly identical decrease in urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> excretion, due to paracellular flux of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> from the lumen. That this reflects HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> leak is seen by noting that despite the leaky junctions, the changes in luminal titration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>("CO2 generation") are quite a bit smaller than the steep decreases in luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> flow. With each of the defects, there is a substantial decrease in the disequilibrium pH, reflecting the decrease in luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration. In a comparison of the CCD defect with control, there is a decrease in urinary flow rate (a 48% decrease in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration compared with a 67% reduction in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> flow) and thus a commensurate increase in urinary phosphate concentration. This increase in phosphate buffer concentration contributes to both the decrease in disequilibrium pH and the maintenance of the near-identical value of the equilibrium PCO2 (37). With the OMCD and IMCD lesions, urinary volume flows are little different from control, so that phosphate concentrations are comparable, and the decline in disequilibrium pH is reflected in the decline in the equilibrium PCO2 predicted for these lesions. Nevertheless, the equilibrium PCO2 for both OMCD and IMCD defects are still substantially (104 and 83 mmHg, respectively) greater than the ambient PCO2.


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Fig. 6.   Urinary composition and flows under HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, with tight junctions leaky to anions. Using the parameters of Fig. 3, HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading with these gradient defects has been simulated using a perfusion solution in which HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration is 32 mM, obtained by Cl- replacement, and entering at 54 µl/min. The panels display end-luminal pH and its disequilibrium value, end-luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration and flow, total CD CO2 generation, and the end-luminal equilibrium PCO2. Calculation of the disequilibrium pH (and equilibrium PCO2) assumes a system with no CO2 escape.


                              
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Table 3.   CD response to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading

With respect to choices for simulating secretory acidification defects, a number of possibilities derive from the fact that both H+-ATPase and H+-K+-ATPase have been identified along the entire rat CD and that the integrity of the peritubular HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> exit pathways may also impact on luminal proton secretion. In the prior OMCD model (34), it had been observed that not only abundance of luminal proton pumps but also the activity of the peritubular Cl-/HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> exchanger and peritubular Cl- (and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>) conductance could modulate proton secretion. In the present work, three segmental secretory defects are examined, namely, 99% reductions in the abundance of both luminal proton ATPases in the CCD, OMCD, and IMCD. Input conditions for acidosis and SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> correction are the same as those used to investigate the gradient defects (Table 1). Figures 7 and 8 contain the results of those simulations, with tableaux of end-luminal concentrations and flows. The panels in Fig. 7 indicate that with each of the three secretory defects, there is little change in urinary flow rate or Na+ excretion. K+ excretion, however, varies substantially with the site of the lesion: with CCD pump defects, K+ excretion is identical to control; with OMCD defects, K+ excretion is 60% greater than control; and without IMCD pumps, K+ excretion is more than double control (Table 2). Infusion of SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> hyperpolarizes the CD and increases volume, Na+, and K+ excretion nearly equally in all of the defects. With respect to K+ excretion during SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion, the absolute differences among the three lesions are maintained, but they become small relative to total urinary K+ delivery.


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Fig. 7.   Urinary composition and flows under acid perfusion, with defective proton secretion. Three segmental secretory defects are examined: 99% reductions in the abundance of both luminal H+-ATPase and H+-K+-ATPase in the CCD, OMCD, and IMCD. Input conditions for the acidosis and for SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> correction are the same as those used for the gradient defects (Fig. 3). The panels display electrical PD and solute concentrations and flows at the CD terminus.



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Fig. 8.   Urinary composition and flows under acid perfusion, with defective proton secretion. Using the parameters and perfusion conditions of Fig. 7, the panels display end-luminal pH and concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (left) and urinary excretion of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, and net acid (right).

Of the three secretory defects, only the OMCD and IMCD lesions yield an acidification defect discernible from the final urinary composition. While the CCD defect yields a urinary pH greater than control, it is well below any standard diagnostic threshold, and there is a negligible difference in TA and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion (Fig. 8 and Table 2). Both the OMCD and IMCD defects are severe, with high urinary pH and net acid excretion rates 40 and 50% below control, respectively. Of interest, the OMCD pump lesion produces a greater reduction in urinary NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion than the IMCD defect. This reflects the fact that in the model CD, there is NH<UP><SUB>4</SUB><SUP>+</SUP></UP> secretion that occurs mainly in the OMCD (Fig. 2). Attempts to correct either OMCD or IMCD secretory defects with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion fail to lower urinary pH even close to the diagnostic threshold of 5.5, with the more distal lesion the more refractory to correction.

The response of the CD with a secretory defect to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading is examined in Fig. 9 and Table 3. In addition to the three segmental defects, the calculations include the case in which all three segmental defects are in place simultaneously and also the case in which this totally defective CD is undergoing water diuresis. (Luminal membrane water permeability for CCD, OMCD, and IMCD principal cells is decreased by a factor of 30 from control.) The first observation from these calculations is that with absent proton secretion from the CCD, OMCD, and IMCD, luminal CO2 titration decreases by 0.13, 0.35, and 0.21 µmol/min, or by 14, 38, and 23%, respectively. This yields a measure of the overall importance of each segment to proton secretion along this CD. When all of the segments are simultaneously defective, CO2 titration is reduced by 0.74 µmol/min, or 80%. This is slightly larger than sum of the three individual defects, 0.69 µmol/min (74%), and due to the fact that, with an isolated proximal defect, more distal segments may increase proton secretion. The prediction that with nearly complete proton pump inhibition there may still be titration of 20% of the delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> derives from the assumption of antidiuresis in these simulations. With water abstraction from luminal fluid, there is a concentration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and phosphate at a constant PCO2. As examined in detail in the companion paper (37), this urinary alkalinization yields an acid disequilibrium pH and titration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> by H2PO4. Indeed, with water diuresis and global CD secretory defects, CO2 titration falls further to 7.5% of control. Figure 9 (and Table 3) display the disequilibrium pH in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading for each of the secretory defects. With either CCD or OMCD proton pumps missing, there is no decrease (and actually a small increase) in the end-luminal disequilibrium pH, and this derives from intact acidification within the IMCD. However, when IMCD proton secretion is defective, the disequilibrium pH does collapse and is sustained only by the osmotic effect. These observations provide the rationalization for the predicted changes in urinary equilibrium PCO2. In the case of either CCD or OMCD defects, equilibrium PCO2 is normal; with IMCD or full CD secretory failure, the equilibrium PCO2 falls by ~100 mmHg. In the absence of antidiuresis, the equilibrium PCO2 with defective CD proton secretion is only 4 mmHg greater than the ambient value.


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Fig. 9.   Urinary composition and flows under HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, with defective proton secretion. Labels on the abcissa refer to the segmental defects of Fig. 7, plus one in which all proton secretory defects are present simultaneously (CD), and one in which all defects are present and principal cell luminal membrane water permeability is 1/30 of control in all segments [CD-antidiuretic hormone (ADH)]. The perfusion solution is that of Fig. 6, in which HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration is 32 mM, entering at 54 µl/min. The panels display end-luminal pH and its disequilibrium value, end-luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration and flow, total CD CO2 generation, and end-luminal equilibrium PCO2. Calculation of the disequilibrium pH (and equilibrium PCO2) assumes a system with no CO2 escape.

The last category of abnormal acidification is that which follows from defective electrogenic Na+ reabsorption. It has been assumed that the intermediate abnormality in this defect is the failure to hyperpolarize the CD lumen and thus drive electrogenic proton secretion or HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption. Thus this has been termed a voltage defect in acidification, and the prototype is the application of amiloride. To simulate this defect in the CCD, the principal cell luminal membrane Na+ channel has had its permeability reduced to 5% of control; to simulate this defect in the IMCD, the luminal membrane cation channel (equally permeable to both Na+ and K+) has had its permeability reduced to 5% of control. Figures 10 and 11 and Table 2 display CD function in acidosis, with either segmental defect or with a global lesion comprising both CCD and IMCD defects. Figure 10 contains the bar graphs of end-luminal PD, urinary flow, and end-luminal concentration and flows of the nonreacting solutes. As expected, the defective cation channel in the IMCD produces a depolarization of end-luminal PD. For either segment, the channel defect is mildly natriuretic with the CCD and IMCD lesions enhancing Na+ excretion by 42 and 29%, respectively. Both segments together produce a 75% increase, with total Na+ excretion corresponding to 42% of delivery to the CD. The most profound impact of these lesions is on K+ excretion. With the CCD lesion alone, urinary K+ is one-third of control, and with both CCD and IMCD defects, the urine is essentially K+ free (Table 2). With reference to Fig. 10, infusion of SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> is clearly effective in hyperpolarizing luminal PD and in restoring K+ excretion.


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Fig. 10.   Urinary composition and flows under acid perfusion, with defective cation channels. Two segmental and one global defect are examined: 95% reduction in CCD principal cell luminal membrane Na+ permeability, 95% reduction in IMCD luminal membrane cation (Na+ and K+) permeability (IM), and the combination of these 2 (CD). Input conditions for the acidosis and for SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> correction are the same as those used for the gradient defects (Fig. 3). The panels display electrical PD and solute concentrations and flows at the CD terminus.



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Fig. 11.   Urinary composition and flows under acid perfusion, with defective cation channels. Using the parameters and perfusion conditions of Fig. 10, the panels display end-luminal pH and concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, and NH<UP><SUB>4</SUB><SUP>+</SUP></UP> (left) and urinary excretion of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, TA, NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, and net acid (right).

Figure 11 and Table 2 indicate that of the three tubules, only the combined CCD and IMCD cation channel defects produce a mild renal tubular acidosis, with a urinary pH of 5.9. The nature of this defect, however, has little to do with the altered luminal PD, but rather the absence of urinary K+ acts to shut off proton secretion by the H+-K+-ATPase. With this combined defect, net acid excretion is barely abnormal (decreased by 8%), because the bulk of ammonia addition occurs in the unaffected OMCD (Fig. 2) and the H+-ATPase is still functional. With both CCD and IMCD defects, urinary acidification is restored (pH = 4.6) with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion, in parallel with the delivery of K+ to the IMCD. Despite the voltage defects, urinary acidification with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading is entirely normal, with no significant differences from control in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration, disequilibrium pH, or equilibrium PCO2. The end-luminal PD under these circumstances, for the combined CCD and IMCD defects is -7 mV, which may be compared with the end-luminal PD of the control tubule of -17 mV. This 10-mV difference is of minor impact on H+ secretion via the H+-ATPase, in view of the fact that this proton pump can transport protons against a full 180-mV electrochemical potential (1). With respect to the CD response to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>loading, Fig. 12 and Table 3 indicate that the absence of functional Na+ channels in either the CCD, IMCD, or both has no significant impact on luminal pH or CO2 concentrations, or their changes after equilibration. In the taxonomy of renal tubular acidosis by Arruda and Kurtzman (3), the high urinary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading is compromised with the voltage-dependent defect but may be corrected (e.g., lithium) or may not be corrected (e.g., amiloride) during phosphate loading. In this model CD, because the voltage-dependent defect shows no compromise of urinary PCO2, further testing with phosphate is not undertaken.


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Fig. 12.   Urinary composition and flows under HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, with defective cation channels. Model calculations use the transport defects in Fig. 10 under perfusion conditions in Fig. 6, in which HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration is 32 mM, entering at 54 µl/min. The panels display end-luminal pH and its disequilibrium value, end-luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration and flow, total CD CO2 generation, and the end-luminal equilibrium PCO2. Calculation of the the disequilibrium pH (and equilibrium PCO2) assumes a system with no CO2 escape.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

The objective of these calculations was to visit the taxonomy of distal renal tubular acidoses from the perspective of a model CD. The classification scheme recognizes "gradient defects," in which proton secretion is intact but the epithelium is leaky; "secretory defects," in which the proton pumps are defective; and "voltage defects," in which failure of electrogenic Na+ reabsorption induces an acidification defect. This taxonomy had been developed intuitively from a substantial body of experimental data with intact kidneys, but it has remained inferential, with limited support from micropuncture or microperfusion studies. The premise of this work is that if the postulated defects are operative in vivo, then they should produce acidification defects in the model CD, with the expected responses to provocative testing. It should be acknowledged that this task is much simpler than the reverse problem of starting with a set of test results and then trying to infer the transport defect. The major assumptions of this work are that the model CD captures the key features of the segmental physiology and that the simulations with specified peritubular conditions are applicable to the tubule in vivo. Obviously, every effort has been made to develop reliable segmental models (32, 33, 34, 35). The first of the two companion papers described the synthesis of these segmental models into a full CD and its ability to excrete an acidic urine (36). It had been known from the IMCD model that maximal acidification required fully functional H+-K+-ATPase, and thus required adequate K+ delivery to the IMCD (33). In the full CD model, obtaining a minimal urinary pH also depended on limiting buffer delivery to the CD. Thus in the simulations here, urinary flow rates are lower than the typical infusion rates in whole animal studies, and CCD entering concentrations included low HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and high K+. The second of the two companion papers examined the response of the model CD during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading and specifically its ability to generate a high equilibrium PCO2 (37). The magnitude of the PCO2 was found to depend on the acid disequilibrium pH, along with the end-luminal concentrations of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and H2PO4.

There has been general agreement that amphotericin toxicity could be considered the prototype of a gradient defect. Data from several studies have been summarized in Table 4 and indicate that amphotericin can induce a relatively high urinary pH despite systemic acidosis, with correction of the pH by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion. With HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, the animals are fully capable of generating a high equilibrium PCO2. Isolated tubule segments from amphotericin-treated animals have not been studied in vitro, so the precise defect in rats remains unknown. On the basis of experiments in turtle urinary bladder, it had been suspected that the defect of amphotericin was a luminal membrane channel permeable to H+ and K+ (18, 30). Such a defect had the intuitive appeal of providing an explanation for the renal K+ wasting and hypokalemia associated with amphotericin (21). In the model CD, an isolated OMCD luminal membrane cation channel, permeable to K+ and H+, did not yield a simulated acidification defect, and this was not explored extensively. More recently, the membrane pathway induced by amphotericin has been recognized to shift from a selective cation channel to a nonselective anion-conducting pore, as drug level and time of incubation increase, due to interaction with membrane lipid (10). In the absence of experimental guidance regarding luminal and peritubular membrane effects of amphotericin along the CD, the simplest example of a true gradient defect was created by introducing high tight junctional HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> (and Cl-) permeabilities in the CCD, OMCD, or IMCD. The notable finding of these simulations was that the OMCD anion leak produced acidification failure, which was correctable with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>, and a relatively normal increase in urinary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. With leaky CCD junctions, urinary acidification was negligibly impaired; with a leaky IMCD, the defect was too late along the tubule to be corrected by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>. One unexpected finding of these simulations was that with the OMCD anion leak, diffusion potentials rendered the lumen more electronegative than control and thus enhanced urinary K+ excretion. Thus one might achieve compatibility with the observed hypokalemia of amphotericin treatment despite the absence of any new leak pathway for K+.

                              
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Table 4.   Experimental models of renal tubular acidosis

While it is likely that many patients with distal renal tubular acidosis have a secretory defect (8), a satisfactory animal model is not available for comparison with model calculations. For such a secretory model, consideration has been given to vanadate intoxication, which produces acidification failure with hypokalemia, in association with profound inhibition of CD H+-K+-ATPase (12). However, the response of these animals to SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion or HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading was not determined. At one time, the acidification defect that follows transient ureteral obstruction had been considered exemplary of a secretory defect (3). Representative findings appear in Table 4, where one sees acidification failure that does not correct with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> and a distinctly low urinary PCO2 during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. Nevertheless, subsequent reviews have been more likely to categorize the postobstructed kidney as a voltage defect, perhaps in view of the prominent K+ retention (14, 27). The finding in the model CD is that with isolated CCD proton pump absence, more distal segments compensate fully, and no acidification defect is perceived. When proton pumps are absent from the OMCD, there is acidification failure that is not correctable with SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>, but because of the intact IMCD, there is a completely normal PCO2 response to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. When IMCD pumps are missing, the acidification defect is compatible with the pattern observed in the obstructed kidney. Indeed, when ATPase activities have been examined in isolated tubule segments from obstructed kidneys, the observations included near obliteration of both H+-ATPase and H+-K+-ATPase activities from medullary collecting ducts (16, 26). An additional observation in the model CD was the impact of water diuresis to further blunt the increase in urinary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. This is also coherent with findings in the obstructed kidney, in which tubular resistance to ADH is expected. One aspect of the model CD that is not compatible with obstruction is the prediction of prominent urinary K+ wasting, due to the absence of IMCD H+-K+-ATPase. In this regard, Sabatini and co-workers (16, 26) have shown that in the postobstructed kidney, there is a sharp decrease in CCD Na+-K+-ATPase and an increase in CCD H+-K+-ATPase, additional enzyme defects that sharply decrease CD K+ secretion. Furthermore, a study in humans with hyperkalemic distal renal tubular acidosis (most of whom were postobstructive), demonstrated that amiloride and bumetanide could still modulate K+ excretion comparably to control subjects (29). Thus the postobstructed kidney exhibits secretory defects of both protons and K+, although it is not clear that transepithelial voltage per se is critical to this pathophysiology.

Both amiloride administration and lithium toxicity have been used as illustrative of a voltage-dependent acidification defect. In the open-circuited turtle bladder, luminal application of lithium reduced Na+ reabsorption, transepithelial PD, and proton secretion (2). In the short-circuited preparation, lithium had no effect on proton secretion, and in particular, when epithelial PD was held at the control value, proton secretion proceeded at control rates. In vivo, both lithium and amiloride result in a high urinary pH during acidosis, as well as abnormally low urinary PCO2 during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading; with lithium, but not with amiloride, urinary acidification can be restored by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP> infusion (Table 4). The lithium-induced acidification defect was localized to the CD via micropuncture (6). In the model CD, the voltage defect was simulated with 95% reductions in luminal Na+ permeability either in the CCD or IMCD or both. With the defects in both segments, there was natriuresis and nearly complete elimination of K+ from the urine. This combined defect did produce acidification failure, but this was due to lack of K+ availability to the H+-K+-ATPase and not to the minor depolarization of luminal PD. In contrast to experimental observation with amiloride, the model CD with the voltage defect showed no depression of urinary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, and the acidification defect in acidosis was completely correctable by SO<UP><SUB>4</SUB><SUP>2−</SUP></UP>. In this regard, examination of CD ATPases during lithium and amiloride administration have shown pronounced depression of both cortical and medullary H+-ATPase activity (11), and with lithium, additional depression of CCD H+-K+-ATPase (16). Thus model calculations do not support acidification failure mediated by a voltage, and the prototypes for this defect have additional associated enzyme defects. One must consider the possibility that the pathophysiology defined in the turtle bladder for the lithium effect may not be applicable to the kidney tubule.

In summary, the most important positive finding from this modeling effort has been that the locus of the transport defect along the CD plays a critical role in the apparent severity of the lesion, with more proximal defects being less severe and more easily correctable. In particular, model calculations suggest that for gradient or secretory defects to be clinically detectable they need to involve the OMCD and/or IMCD. Additionally, the calculations have revealed a possible pathophysiology for CD K+ wasting, which does not involve failure of H+-K+-ATPase but that derives from a paracellular anion leak and thereby a more electronegative lumen. The most important negative finding in this study is the inability to support the category of renal tubular acidosis associated with a voltage defect. Certainly, CD lesions that present with both K+ secretory defects and H+ secretory defects suggest transepithelial electrical potential as a common intermediate. However, no prior model of CD function has supported this construct, nor can this one. Finally, from an overall perspective, the CD complexity, which is apparent in the calculations of this paper, does not encourage undertaking the inverse problem: to define a set of clinical tests that can pinpoint a CD transport defect. Alternatively, modern investigations of renal tubular acidosis have focused attention on genetic defects in specific transporters (8). These studies have already provoked questions as to whether a specific transport defect can, in isolation, account for the full phenotype of the acidosis or whether one bad transporter is bringing down others within the cell (13). Such questions fall easily within the scope of a mathematical model of the CD.


    ACKNOWLEDGEMENTS

This investigation was supported by Public Health Service Grant 1-R01-DK-29857 from the National Institute of Arthritis, Diabetes, and Digestive and Kidney Diseases.


    FOOTNOTES

Address for reprint requests and other correspondence: A. M. Weinstein, Dept. of Physiology and Biophysics, Weill Medical College of Cornell University, 1300 York Ave., New York, NY 10021 (E-mail: alan{at}nephron.med.cornell.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

August 6, 2002;10.1152/ajprenal.00164.2002

Received 29 April 2002; accepted in final form 25 July 2002.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

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