A mathematical model of rat collecting duct II. Effect of buffer delivery on urinary acidification

Alan M. Weinstein

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


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A mathematical model of the rat collecting duct (CD) is used to examine the effect of delivered load of bicarbonate and nonbicarbonate buffer on urinary acidification. Increasing the delivered load of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> produces bicarbonaturia, and, with luminal carbonic anhydrase absent, induces a disequilibrium luminal pH and a postequilibration increase in urinary PCO2. At baseline flows, this disequilibrium disappears when luminal carbonic anhydrase rate coefficients reach 1% of full catalysis. The magnitude of the equilibration PCO2 depends on the product of urinary acid phosphate concentration and the disequilibrium pH. Thus, although increasing phosphate delivery to the CD decreases the disequilibrium pH, the increase in urinary phosphate concentration yields an overall increase in postequilibration PCO2. In simulations of experimental HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading in the rat, model predictions of urinary PCO2 exceed the measured PCO2 of bladder urine. In part, the higher model predictions for urinary PCO2 may reflect higher urinary flow rates and lower urinary phosphate concentrations in the experimental preparations. However, when simulation of CD function during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading acknowledges the high ambient renal medullary PCO2 (5), the predicted urinary PCO2 of the model CD is yet that much greater. This discrepancy cannot be resolved within the model but requires additional experimental data, namely, concomitant determination of urinary buffer concentrations within the tubule fluid sampled for PCO2 and pH. This model should provide a means for simulating formal testing of urinary acidification and thus for examining hypotheses regarding transport defects underlying distal renal tubular acidosis.

disequilibrium pH; urinary PCO2; phosphate; distal renal tubular acidosis


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ESTABLISHING THE MINIMAL URINARY pH during acid challenge and low renal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> delivery is perhaps the most widely used test of urinary acidification. Nevertheless, there has been considerable interest in kidney function during buffer excess, particularly HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> diuresis, as an indicator of collecting duct (CD) acidification. The basic observation is that the PCO2 of an alkaline urine may be several-fold higher than that in arterial blood (16), and this increase in PCO2 is enhanced when urinary phosphate concentrations are high (12, 22). Fundamentally, the PCO2 elevation derives from titration of urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and a delay in dehydration of the resulting H2CO3 until a point along the nephron (or beyond) from which CO2 is not readily absorbed (3). The critical experiment was intravenous administration of carbonic anhydrase and the observation that the presence of this enzyme within the alkaline urine obliterated the PCO2 elevation (15). Subsequent studies have demonstrated that the elevation of urinary PCO2 varies directly with urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration and thus depends in part on an intact mechanism for water abstraction from the CD (2, 17, 21). Clinical interest in urinary PCO2 derives from the observation that patients with primary defects in urinary acidification (10), as well as some with acquired defects (reviewed in Refs. 1 and 3), are also deficient in the capacity to raise urinary PCO2.

Sampling of CD urine, by microcatheterization (9) or by micropuncture (5), has shown that the elevation of PCO2 in bicarbonate diuresis is an intrarenal phenomenon. Looked at more closely, there are two classes of factors at work to elevate urinary PCO2. The first class comprises those local to the collecting duct lumen, which lead to formation of H2CO3 or enhance the delay in its dehydration: 1) luminal proton secretion to establish an acid disequilibrium pH (5), 2) effect of phosphate buffer to decrease H2CO3 concentration and thus (via mass action) slow dehydration, and possibly 3) osmotic concentration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> with resulting generation of CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> plus H2CO3 (13). The second class of factors relates to diffusion trapping of CO2 within the renal medulla. It has been observed that vasa recta PCO2 is comparable to that in the CD (5) and that after administration of carbonic anhydrase to rats, it still takes 1 h for urinary PCO2 to equilibrate with blood PCO2 (8). This means that increases in urinary PCO2 must be understood in part as a consequence of a countercurrent mechanism, presumably with local CD events as the single effect. The CD model in the companion paper (24) has sufficient detail for making predictions regarding the luminal factors that increase urinary PCO2. In particular, the model incorporates the effects of proton secretion, water abstraction, and tubular flow rate to yield a prediction for final urinary PCO2. It permits estimation of the extent to which disequilibrium conditions established within cortical and outer medullary segments can persist through the longer inner medullary collecting duct (IMCD). The model affords predictions of the impact of CD buffer delivery on measures of urinary acidification. Ultimately, the model may give a sense of the reliability of inferences made about the health of the CD from an assessment of urinary PCO2.


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The model of this investigation is identical to that of the companion paper (24), with only variation in CD delivery or carbonic anhydrase activity. In this study, there are supplemental calculations of equilibrium conditions for the luminal fluid at all points along the CD. This includes the concentrations of H2CO3, HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, CO2, and possibly CO<UP><SUB>3</SUB><SUP>2−</SUP></UP>, along with concentrations of phosphate and ammonia species. These equilibrium calculations are undertaken once the full CD model results are obtained along the whole CD. Qualitatively, the equilibration process is illustrated in Fig. 1, in which the three buffers, total CO2, phosphate, and ammonia, are depicted as discrete components. An acid disequilibrium pH (an H2CO3/CO2 ratio greater than the equilibrium ratio of the dehydration reaction) may be the result of either proton addition or water abstraction (with fixed PCO2). Within the bladder, or if tubule fluid is removed within a closed pipette, the H2CO3/CO2 ratio moves to equilibrium. As H2CO3 is dehydrated to CO2, pH alkalinizes and, with alkalinization, protons from phosphate and ammonia titrate HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> to generate new CO2. Throughout this process, there is conservation of total buffer for each component.


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Fig. 1.   Schematic for the calculation of disequilibrium pH and postequilibration PCO2 of collecting duct (CD) luminal fluid, with the 3 buffers, total CO2, phosphate, and ammonia depicted as discrete components. An acid disequilibrium pH (increase in the H2CO3/CO2 ratio) is obtained by either proton addition or water abstraction with fixed PCO2. In the equilibration phase, there is conservation of total buffer for each component, while protons from phosphate and ammonia titrate HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> to generate new CO2.

To quantify the equilibration process, there are eight reactive species with eight unknown luminal concentrations
C<SUB>M</SUB>(H<SUB>2</SUB>CO<SUB>3</SUB>)  C<SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>)  C<SUB>M</SUB>(CO<SUB>2</SUB>)  C<SUB>M</SUB>(CO<SUP>2−</SUP><SUB>3</SUB>)

C<SUB>M</SUB>(H<SUB>2</SUB>PO<SUP>−</SUP><SUB>4</SUB>)  C<SUB>M</SUB>(HPO<SUP>2−</SUP><SUB>4</SUB>)  C<SUB>M</SUB>(NH<SUP>+</SUP><SUB>4</SUB>)  C<SUB>M</SUB>(NH<SUB>3</SUB>)
Solution of the CD model provides the total buffer concentrations at any point, and these totals are unchanged during equilibration
tC<SUB>M</SUB>(CO<SUB>2</SUB>) = C<SUB>M</SUB>(H<SUB>2</SUB>CO<SUB>3</SUB>) + C<SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>) + C<SUB>M</SUB>(CO<SUB>2</SUB>)

+ C<SUB>M</SUB>(CO<SUP>2−</SUP><SUB>3</SUB>) (1)

tC<SUB>M</SUB>(PO<SUB>4</SUB>) = C<SUB>M</SUB>(H<SUB>2</SUB>PO<SUP>−</SUP><SUB>4</SUB>) + C<SUB>M</SUB>(HPO<SUP>2−</SUP><SUB>4</SUB>)

tC<SUB>M</SUB>(NH<SUB>3</SUB>) = C<SUB>M</SUB>(NH<SUP>+</SUP><SUB>4</SUB>) + C<SUB>M</SUB>(NH<SUB>3</SUB>)
Denote the equilibrium constant for titration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, pKb = 3.57, and for titration of CO<UP><SUB>3</SUB><SUP>2−</SUP></UP>, pKd = 10.1 (13); and corresponding to phosphate and ammonia are pKp = 6.80 and pKn = 9.15. Then, the ratios of base and acid moieties of each buffer pair may be expressed as
<FR><NU>C<SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>)</NU><DE>C<SUB>M</SUB>(H<SUB>2</SUB>CO<SUB>3</SUB>)</DE></FR> = 10<SUP>pH<SUB>M</SUB> − p<IT>K</IT><SUB>b</SUB></SUP>

<FR><NU>C<SUB>M</SUB>(CO<SUP>2−</SUP><SUB>3</SUB>)</NU><DE>C<SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>)</DE></FR> = 10<SUP>pH<SUB>M</SUB> − p<IT>K</IT><SUB>d</SUB></SUP>

<FR><NU>C<SUB>M</SUB>(HPO<SUP>2−</SUP><SUB>4</SUB>)</NU><DE>C<SUB>M</SUB>(H<SUB>2</SUB>PO<SUP>−</SUP><SUB>4</SUB>)</DE></FR> = 10<SUP>pH<SUB>M</SUB> − p<IT>K</IT><SUB>p</SUB></SUP>

<FR><NU>C<SUB>M</SUB>(NH<SUB>3</SUB>)</NU><DE>C<SUB>M</SUB>(NH<SUP>+</SUP><SUB>4</SUB>)</DE></FR> = 10<SUP>pH<SUB>M</SUB> − p<IT>K</IT><SUB>n</SUB></SUP> (2)
This supplies an additional four equations with one new variable, luminal pH. Corresponding to the chemical reaction
H<SUB>2</SUB>CO<SUB>3</SUB> <LIM><OP><ARROW>⇄</ARROW></OP><LL><IT>k</IT><SUB>h</SUB></LL><UL><IT>k</IT><SUB>d</SUB></UL></LIM> H<SUB>2</SUB>O + CO<SUB>2</SUB>
is the equilibrium condition that the H2CO3 concentration is proportional to the dissolved CO2
C<SUB>M</SUB>(H<SUB>2</SUB>CO<SUB>3</SUB>) = <FR><NU><IT>k</IT><SUB>h</SUB></NU><DE><IT>k</IT><SUB>d</SUB></DE></FR> C<SUB>M</SUB>(CO<SUB>2</SUB>) (3)
In the calculations below, kh = 0.145 s-1 and kd = 49.6 s-1, with an equilibrium ratio kh/kd = 2.92 × 10-3.

From the solution of the CD model, one obtains all of the local solute concentrations. For any perturbation of the luminal pH, the three total buffer conservation relationships, plus the four buffer pair equilibria, plus the dissolved H2CO3 equilibrium together provide the eight linear equations that yield the new solute concentrations. Corresponding to a closed system, one then seeks an equilibrium value of the luminal pH that corresponds to proton conservation, or equivalently, conservation of charge in the buffer reactions. Denote by superscript o the (disequilibrium) values of the model variables computed by the CD model. Then, charge conservation may be expressed as
C<SUP>o</SUP><SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>) + 2C<SUP>o</SUP><SUB>M</SUB>(CO<SUP>2−</SUP><SUB>3</SUB>) + C<SUP>o</SUP><SUB>M</SUB>(HPO<SUP>2−</SUP><SUB>4</SUB>) + C<SUP>o</SUP><SUB>M</SUB>(NH<SUB>3</SUB>) (4)

 = C<SUB>M</SUB>(HCO<SUP>−</SUP><SUB>3</SUB>) + 2C<SUB>M</SUB>(CO<SUP>2−</SUP><SUB>3</SUB>) 

+ C<SUB>M</SUB>(HPO<SUP>2−</SUP><SUB>4</SUB>) + C<SUB>M</SUB>(NH<SUB>3</SUB>)
For an initial guess at the disequilibrium pHM, Eq. 4 is evaluated to determine the error in charge conservation, and then Newton iterations are used to refine the guess to a solution. In the calculations below, the solution is also displayed for an "open" system, in which there is no conservation of total CO2 but rather a specified PCO2. In this case, the dissolved CO2 concentration is no longer a variable, and the equation for conservation of total CO2 is eliminated.


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Bicarbonate loading can be simulated either with addition of NaHCO3 or with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-for-Cl- substitution in the entering luminal fluid. The latter is simpler in that it avoids a superimposed natriuresis, augmenting what is already a generous CD Na+ delivery. The solid curves in Figs. 2-4 display the results of a simulation in which 25 mM of luminal Cl- has been replaced by HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, so that entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration is 32 mM. Figure 2 is a tableau of nonreacting species, with luminal PD and solute concentrations on the left, and volume and solute flows for the ensemble of all collecting ducts on the right. The dotted curves are the solution of the model equations for the control simulation, in which luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> is 7 mM. The abcissa for each panel is distance along the 9-mm CD. In this simulation, the transit times for the cortical CD (CCD), outer medullary CD (OMCD), and IMCD are 10.5, 23.0, and 31.6 s, respectively. Compared with control, the most obvious change is the decrease in luminal Cl- at CD entry, which propagates through the CCD and OMCD, and is amplified in the IMCD. There is a small luminal hyperpolarization, but little difference in volume or urea flows. Both Na+ and K+ concentrations appear to be increased over control, and with reference to Table 1, the increase in urinary excretion rates are, respectively, 20 and 50%. Figure 2 suggests that the increase in K+ excretion derives largely from decreased reabsorption within the IMCD. Examination of the detailed model output provides the rationalization. At the midpoint of the IMCD under control conditions, luminal and cytosolic HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations are 6.3 and 18 mM, respectively, and cellular proton secretion is 0.75 nmol · s-1 · cm-2, with 90% through the H-K-ATPase. During HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, luminal and cytosolic HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations are 80 and 24 mM, respectively, with proton flux increased to 0.84 nmol · s-1 · cm-2 but only 48% via the H-K-ATPase. These differences reflect the different pH sensitivities of the two luminal proton pumps (23).


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Fig. 2.   Electrolyte transport along the model CD with 25 mM HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> for Cl- replacement (solid curves) and under control conditions (dotted curves). Left: luminal potential difference (PD; mV) and the luminal concentrations of Na+, K+, Cl-, and urea (mM). 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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Table 1.   CD tubule input flows, reabsorptive fluxes, and excretion

In Fig. 3, luminal pH is displayed along with the components of net acid excretion in both HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading and control. With HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> delivery 4.5-fold greater than control, HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption increased by more than a factor of 3 (Table 1). Despite increased reabsorption, urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration rose with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading, and this high urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> is similar to values obtained in experimental studies in rats (e.g., Ref. 5). Figure 3 also shows that virtually all of the change in net acid flow derives from the change in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> flow, with only trivial changes in titratable acid (TA) or NH<UP><SUB>4</SUB><SUP>+</SUP></UP> along the CD. Despite the increase in luminal HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, the pH along the CD actually decreases to 7.06, due to the development of a disequilibrium pH. The impact of delayed dehydration of H2CO3 is explored in more detail in Fig. 4 and Table 2. In the top left of Fig. 4, the net flux through the dehydration reaction is plotted at each point along the CD. A maximal value occurs within the OMCD, ~0.2 µmol · min-1 · mm-1 for all 7,200 tubules, or 28 pmol · mm-1 · min-1 · tubule-1. This may be related to the local proton secretory rate of ~0.6 nmol · s-1 · cm-2, equivalently 34 pmol · mm-1 · min-1 for an OMCD of 30 µm diameter. In the bottom left panel of Fig. 4, the curves in the top left panel have been integrated numerically to yield the net generation of CO2 along the CD. The end-luminal value, ~0.9 µmol/min, is slightly less than net CD HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption, 1.15 µmol/min (Table 2), reflecting the presence of other pathways for direct HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption, which do not involve titration to CO2.


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Fig. 3.   Acid-base transport along the model CD with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading as in Fig. 2 (solid curves) and under control conditions (dotted curves). Left: luminal pH and the 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>).



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Fig. 4.   CO2 generation along the CD with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading as in Fig. 2 (solid curves) and under control conditions (dotted curves). Top left: rate of CO2 formation via the dehydration of luminal H2CO3. Bottom left: integral of this rate along the CD. Top right: luminal disequilibrium pH on the assumption of either a perfectly closed sampling system or else complete equilibration with an ambient PCO2 of 50 mmHg. Bottom right: equilibrium PCO2 of luminal fluid, with and without scaling for local osmolality.


                              
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Table 2.   Equilibration of end-luminal CD fluid for closed systems or fixed PCO2

The top right panel in Fig. 4 displays the disequilibrium pH along the CD, on the assumption of either a fully closed system or a fully open system with equilibration to a PCO2 of 50 mmHg. For the closed system, the maximal disequilibrium pH is -0.26, which occurs early in the OMCD; end-urinary disequilibrium pH is -0.17. The interpretation of these disequilibrium values is not totally straightforward. As indicated above, the proton secretory rates within the OMCD and IMCD are ~0.6 and 0.8 nmol · s-1 · cm-2, apparently at odds with the relative magnitudes of the disequilibrium pH. What must also be considered, however, is that in the transition from the OMCD to IMCD, the concentration of urinary phosphate has increased several-fold (Fig. 3), so that the decline in disequilibrium pH must be referred to this increase in urinary buffer. The effect of phosphate delivery will be given more attention in calculations below. The bottom right panel in Fig. 4 shows the equilibrium PCO2 for the closed system, which rises monotonically along the CD to 200 mmHg by tubule end. The components of end-luminal equilibration (corresponding to each of the variables in Eqs. 1-4) are displayed in Table 2, and the top section of the table shows the numerical results corresponding to the data in Fig. 4. The end-luminal fluid shows pH of 7.064, HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> of 85.9 mM, and CO2 = 1.6 mM. With equilibration, there is titration of 4.45 mM HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> by acid phosphate to form a nearly equal amount of dissolved CO2; this corresponds to an increase in PCO2 of 148 mmHg. The contribution from the ammonia buffer is negligible. The calculations in Figs. 2-4 have been repeated with the inclusion of luminal CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> (with the model formulation indicated in the companion paper) (24). The results of these calculations are displayed in the middle section of Table 2, and there are no significant differences between the two models, in terms of either disequilibrium pH or PCO2. The contribution of CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> remains trivial, essentially due to the high PCO2 of the closed system. Finally, the bottom right panel in Fig. 4 includes an attempt to factor out the osmotic impact on the equilibrium PCO2, in the curve that has been scaled for osmolality. The rationale for this curve is that even if there were 0 proton secretion along the CD, water abstraction would elevate all CD solutes, with the exception of dissolved CO2. Whether this scaling to an isotonic urine might provide additional sensitivity to detect proton secretory defects remains to be determined.

To generate Figs. 5 and 6, the delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration has been varied over the range 5-45 mM (in steps of 2 mM) via Cl--for-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> substitution. Figure 5 shows the urinary output, along with the delivery and excretion of the important solutes. In this range of delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, no diuresis is produced, nor is there significant change in flows of urea or Na+. With respect to K+, the effect of high HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> is a near doubling of K+ excretion, compared with that at the most acidic urine, again due to the shift in proton flux from the H-K-ATPase to the H+-ATPase. With increasing HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> delivery, there is an increase in both excretion and in the difference between delivery and excretion (i.e., an increase in CD HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption). The increase in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> is acompanied by a sharp decline in urinary NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, reflecting the increased concentration of NH3 in progressively alkaline urine. The urinary CO2 data for these simulations have been summarized in Fig. 6, in which the bottom panel documents the increase in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> consumption. The panels show urinary pH increasing from 5.82 to 7.21, urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration increasing from 1.9 to 128 mM, and the disequilibrium pH for a closed system increasing from -0.05 to -0.21, all progressively over the range of delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>. Nevertheless, the equilibrium PCO2 clearly plateaus. Indeed, above a delivered concentration of 25 mM, the equilibrium PCO2 values are all within 2% and show a maximum value at the delivered concentration, 33 mM. As indicated with the analysis of Table 2, the magnitude of the disequilibrium CO2 reflects both the concentration of acid phosphate plus the magnitude of disequilibrium pH. With progressively alkaline urine, the H2PO4 concentration is decreasing while the disequilibrium pH is increasing, setting the stage for nearly constant CO2 generation. Repetition of these calculations with luminal NaHCO3 addition (rather than Cl- substitution) adds relatively little to this discussion. The results are those expected from the preceding considerations of natriuresis (24): an increase in urinary flow and in the excretion of urea, K+, NH<UP><SUB>4</SUB><SUP>+</SUP></UP>, and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>. The CO2 data for these simulations look similar to the curves in Fig. 6, including the plateau of the equilibrium CO2.


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Fig. 5.   CD excretion as a function of entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-for- Cl- replacement. Entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration has been varied from 5 to 45 mM, and corresponding to each of 21 abcissa points is a solution of the full CD model. The panels display the single-kidney urine output (µl/min) and the delivery (x = 0) and excretion (x = 9 mm) of Na+, K+, urea, and the components of net acid flow.



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Fig. 6.   Urinary acid-base parameters as a function of entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-for- Cl-replacement as in Fig. 5. Left: end-luminal pH and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> before equilibration, respectively. Top right: end-luminal disequilibrium pH for either a perfectly closed system or one completely equilibrated with an ambient PCO2 of 50 mmHg. Bottom right: equilibrium PCO2 of luminal fluid with and without scaling for urinary osmolality. Bottom: total CO2 generation along the CD.

The effect of isolated variation in phosphate delivery to the CD is examined in Figs. 7 and 8, in which the abcissa is luminal total phosphate concentration over the range 0.8-24.8 mM. In these simulations, entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration = 7 mM, as in control conditions, and the phosphate is varied as a substitution for Cl-. The excretion profiles in Fig. 7 indicate that changing phosphate delivery has only a small effect on luminal flow and on excretion of urea or Na+. There is a 60% increase in K+ excretion over the full range of phosphate delivery, but the absolute rate of K+ excretion remains small. The major impact of phosphate delivery is the increase in net acid excretion due to the increase in TA. With the additional urinary buffer, HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption is blunted, and urinary excretion increases. By itself, the flow increase would increase NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion, and, by itself, the increase in urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> would decrease NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion. Thus the net effect of phosphate delivery is to leave NH<UP><SUB>4</SUB><SUP>+</SUP></UP> excretion unchanged. The urinary CO2 data for these calculations are summarized in Fig. 8. The bottom and left panels indicate in more detail the effect of increasing phosphate delivery to decrease HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration, increase its end-luminal concentration, and alkalinize the urine. The top right panel displays the disequilibrium pH of the final urine for a closed system, and one equilibrated to the ambient PCO2. Figure 8 shows that above the lowest delivery rates, increasing phosphate buffer decreases the disequilibrium pH. At the very lowest phosphate delivery, urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> is exhausted, so the disequilibrium pH also collapses. Overall, the effect of increasing phosphate delivery is to increase the disequilibrium PCO2. This occurs despite the fact that progressive urinary alkalinization acts to decrease the relative abundance of acid phosphate; also, the decline in disequilibrium pH diminishes the fraction of this acid phosphate that titrates HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>. The effect of phosphate delivery in an alkaline urine is shown in Table 1, in the simulation in which entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and entering phosphate are 32 mM, both as Cl- substitutions. In this case, there is little impact on HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption, and only an increase in net acid excretion with the increase in TA. By replacing much of the available Cl-, the additional phosphate does act as a nonreabsorbable ion and enhances urinary flow plus excretion of urea, Na+, and K+.


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Fig. 7.   CD excretion as a function of entering phosphate during phosphate-for- Cl- replacement. Entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration is 7 mM, and entering total phosphate is varied from 0.8 to 24.8 mM. Corresponding to each of 25 abcissa points is a solution of the full CD model. Shown are single-kidney urine output (µl/min) and the delivery (x = 0) and excretion (x = 9 mm) of Na+, K+, urea, and the components of net acid flow.



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Fig. 8.   Urinary acid-base parameters as a function of entering phosphate during phosphate-for- Cl- replacement as in Fig. 7. Left: end-luminal pH and HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> before equilibration, respectively. Top right: end-luminal disequilibrium pH for either a perfectly closed system or one completely equilibrated with an ambient PCO2 of 50 mmHg. Bottom right: equilibrium PCO2 of luminal fluid with and without scaling for urinary osmolality. Bottom: total CO2 generation along the CD.

The interplay of luminal buffers in establishing the disequilibrium pH and PCO2 of the final urine is examined systematically in Fig. 9. The abcissa of each panel is a range of total phosphate concentrations in delivered fluid, from 0.8 to 24.8 mM, and the ordinate of each panel is a range of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations in delivered fluid, from 5 to 45 mM. Division of the abcissa into 24 subunits (25 phosphate concentrations) and division of the ordinate into 20 subunits (21 HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations) defines a grid of 525 CD model calculations. In each calculation, constancy of entering anions is achieved by adjusting the Cl- concentration, and thus a final urinary PCO2 and disequilibrium pH is determined for each grid point. The top panel shows level curves of constant PCO2 on the PO4-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> grid, determined by linear interpolation among the grid points. It is clear that the highest PCO2 values are obtained when both buffers are increased nearly proportionally and that when only one buffer is increased, a plateau is quickly reached. For each of these calculations, the interstitial PCO2 is 50 mmHg, so that the urine - blood PCO2 difference is just that fixed offset. The bottom panel displays the level curves for disequilibrium pH. It is apparent that at each entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> level, increasing the delivered phosphate depresses the disequilibrium pH. Conversely, at each entering phosphate concentration, increasing the delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> increases the disequilibrium pH, and this effect is most pronounced at the lower phosphate concentrations. Finally, in regions of buffer abundance, the level curves are linear, suggesting that the disequilibrium pH depends on the concentration ratio of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and phosphate.


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Fig. 9.   Relationship between entering phosphate and entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations on determining final urinary disequilibrium pH and PCO2. For each panel, the abcissa is entering phosphate, and the ordinate is HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> (mM). Corresponding to a grid determined by 25 abcissa points and 21 ordinate points are solutions of the CD model for all 525 grid points. Top: plot with level curves corresponding to loci of constant urinary (end-luminal) postequilibration PCO2 from 80 to 240 mmHg. Bottom: loci of constant end-luminal disequilibrium pH.

Experimental observation in the rat requires that the rate coefficients for the dehydration/hydration of H2CO3/ CO2 within the CD lumen be taken at values consistent with complete absence of carbonic anhydrase. To assess the sensitivity of the model results to this assumption, the calculations in Figs. 2-4 (entering HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> = 32 mM) have been repeated over a range of rate coefficients, from complete absence to full catalysis (10,000-fold increase). With a variation in catalysis, the changes in urinary flow or excretion of urea, Na+, and K+ are all minor. Table 1 contains a summary of these values for full catalysis, which may be compared with the 0-catalysis condition. Figure 10 displays the CO2 data for these simulations, in which the abcissa is the log (base 10) of the ratio of the rate coefficients to the uncatalyzed value. It is clear that as the rate coefficients increase, the disequilibrium pH falls to 0, and PCO2 approaches the ambient value. As catalysis increases, CO2 titration increases by ~60%, from 0.93 to 1.47 µmol/min, which may be compared with the delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> load, 1.73 µmol/min. From the perspective of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> excretion, full catalysis decreases this by two-thirds (Table 1). Thus Fig. 10 shows a decline in urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration from 85 to 37 mM over the range of catalysis. Nevertheless, the urinary pH is predicted to increase from 7.06 to 7.46 due to the fall in the luminal concentration of H2CO3 (not shown). What Fig. 10 offers, beyond the data of Table 1, is the demonstration that virtually all of the changes in urinary composition with catalysis are complete when the rate coefficients are just 1% of full catalysis, and most of this occurs within 0.1%. The urinary flow rates of these simulations are relatively low (0.16 ml/day), consistent with the assumed antidiuretic conditions. More rapid urinary flows would be expected to require higher rate coefficients and thus shift the curves of Fig. 10 to the right.


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Fig. 10.   Urinary acid-base parameters as a function of the rate coefficient for dehydration of urinary H2CO3. The delivered solution is the high-HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> solution used in the calculations of Figs. 2-4. Both luminal rate coefficients, for H2CO3 dehydration and CO2 hydration, have been scaled by the same factor, from 1 (for no catalysis) up to 10,000 (for full carbonic anhydrase activity; CA), and the logarithm of this scaling constitutes the abcissa. The tableau of panels are those in Figs. 6 and 8.

Finally, in view of the observation that during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading the ambient medullary PCO2 is well above that in arterial blood (5), the model CD should be examined in those circumstances. In the calculations in Figs. 11 and 12, we set the following interstitial PCO2: ambient PCO2 in the cortex remains at 50 mmHg but increases linearly through the outer medulla to 100 mmHg at the outer-inner medullary junction, then further increases linearly in the IMCD to 200 mmHg at the papillary tip. The impact on urinary flow rate and urea and Na+ excretion is relatively minor and is indicated in Table 1. The effect on K+ is more significant, with an 18% increase in reabsorption that translates into a 46% decrease in K+ excretion. This is due to increased IMCD proton secretion in response to cytosolic acidosis, specifically an increase in flux through the H-K-ATPase. With the higher PCO2, IMCD total and H-K-ATPase proton secretion are ~1.20 and 0.85 nmol · s-1 · cm-2, respectively, which may be compared with 0.84 and 0.40 nmol · s-1 · cm-2 under the conditions in Figs. 2-4. Flux through the model H+-ATPase is sensitive only to pH differences across the luminal membrane and is thus unchanged by the change in PCO2, whereas the model H-K-ATPase is preferentially activated by changes in cytosolic pH (23). Figure 11 displays the tableau of acid-base fluxes along the CD in the high PCO2 condition (solid curves), with the lower PCO2 calculations (Fig. 3) reproduced as dotted curves. Under high PCO2, there is a depression in luminal pH and enhanced HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> reabsorption and TA generation. The effect on net acid excretion is blunted by the decrease in NH<UP><SUB>4</SUB><SUP>+</SUP></UP> trapping. In Fig. 12, the enhanced generation of CO2, beginning in the OMCD, is apparent. It is also clear from the bottom right panel that the equilibrium PCO2 of the closed system is quite a bit higher with the high ambient PCO2, in fact nearly additive with the PCO2 increase. However, the top right panel in Fig. 12 shows that that the disequilibrium pH for the closed system is similar to that with the lower ambient PCO2, and this occurs despite the fact that luminal proton secretion is 50% higher with the high PCO2. The explanation can be gleaned from the data in the bottom section of Table 2. At the higher CO2 concentration, the equilibrium H2CO3 concentration is also increased. Because comparable disequilibrium pH corresponds to the same ratio of H2CO3 concentrations (disequilibrium to equilibrium), a higher ambient PCO2 will necessitate a higher disequilibrium H2CO3. This will drive H2CO3 dehydration more rapidly and thus require a higher rate of luminal proton secretion to generate this disequilibrium pH. Thus in a truly closed system, the predicted equilibrium PCO2 is quite a bit higher than any value measured in urine or by micropuncture.


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Fig. 11.   Acid-base transport along the model CD with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading and high ambient PCO2. Cortical PCO2 remains at 50 mmHg but increases linearly through the OMCD to reach 100 mmHg by the outer-inner medullary junction (OIMJ), and there is a further linear increase to 200 mmHg by the papillary tip (solid curves). The abcissa is length along the CD, and the tableau of panels is that in Fig. 3. Dotted curves correspond to the uniform PCO2 (50 mmHg) used in the calculations of Fig. 3.



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Fig. 12.   CO2 generation along the CD with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading and high ambient PCO2 (Fig. 11). The abcissa is length along the CD, and the tableau of panels is that in Fig. 4. Dotted curves correspond to the uniform PCO2 (50 mmHg) used in the calculations of Fig. 4.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
MODEL FORMULATION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

This has been the first effort to explore determinants of urinary PCO2 using a mathematical model of the CD. The first model of disequilibrium conditions developing along a kidney tubule was that of Star et al. (20). This was a simpler CCD model, without cellular structure or nonreactive solutes, but one that included the important buffers and sufficient kinetics to predict the axial evolution of a disequilibrium pH. In their simulations of experiments in vitro, no attention was directed to osmotic effects or the generation of a disequilibrium PCO2. The paper of Berliner and DuBose (3), however, focused squarely on both disequilibrium pH and CO2 generation in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-rich urine. The calculations in that work were from the perspective of solution chemistry in a well-mixed beaker, but they were sufficient to identify the critical kinetic factors. The key step to developing the disequilibrium pH is luminal proton addition, with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration. Berliner and DuBose emphasized that the dehydration coefficient for H2CO3 is relatively large and that in the absence of nonbicarbonate buffer, the disequilibrium pH would be substantial and dehydration would be rapid. With high phosphate concentrations, accumulation of H2CO3 is diminished, and thus, from mass action considerations, equilibration is slowed. They also examined the effect of water abstraction (with fixed ambient PCO2) to concentrate urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and H2CO3 and, consequently, generate an acid disequilibrium. Again in this circumstance, substantial phosphate buffering would delay dehydration of H2CO3. Berliner and DuBose considered CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> generation as a proton source, recognizing that this reaction would be immediate and, compared with phosphate buffering, relatively minor.

With respect to assessing whether kinetic coefficients are large or small, or whether processes are rapid or slow, the relevant frame of reference is the timing of events within the collecting duct. In particular, this means considering the rate of H2CO3 dehydration in relation to the rate of proton secretion and in relation to the rate of water abstraction, and within the time period of fluid transit through the CD. Because this is sufficiently complex, it is difficult to do outside the framework of a CD model. Nevertheless, some crude estimates can be made. The first important rate is that of dehydration of H2CO3. With regard to Table 2, 10 µM might be considered a representative disequilibrium H2CO3 concentration, so that for a dehydration rate coefficient of 50 s-1, one would expect a CO2 generation rate of 0.5 mM/s. The proton secretory rate for the model IMCD with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading is ~1 nmol · s-1 · cm-2. For a cylindrical tubule of 30-µm diameter, this rate is ~1 pmol · s-1 · mm-1, and the tubule volume is 0.7 nl/mm, so this rate of proton secretion corresponds to a titration of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> of 1.4 mM/s. Finally, over the length of the inner medulla, water abstraction produces a near doubling of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>. By itself, this would yield a disequilibrium pH of 0.3. If one started with 45 mM total phosphate at a pH of 7.1 (HPO<UP><SUB>4</SUB><SUP>2−</SUP></UP>/H2PO<UP><SUB>4</SUB><SUP>−</SUP></UP> = 30:15), then a shift of 0.3 pH units to 7.4 corresponds to deprotonation of 6 mM H2PO<UP><SUB>4</SUB><SUP>−</SUP></UP> (HPO<UP><SUB>4</SUB><SUP>2−</SUP></UP>/H2PO<UP><SUB>4</SUB><SUP>−</SUP></UP> = 36:9). In this model, the tubular fluid spends ~30 s in the IMCD, so that the corresponding rate of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration is 0.2 mM/s. From these considerations, the proton secretory rate is clearly the dominant factor in generating and maintaining the disequilibrium. Indeed, with regard to Fig. 4, the disequilibrium PCO2 increases along the IMCD, consistent with a rate of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration greater than H2CO3 dehydration. The osmotic effect is small but nontrivial.

Despite the complexity of the system, certain qualitative aspects of the buffer effects on disequilibrium pH and PCO2 emerge (Fig. 9). With increasing phosphate buffer, the disequilibrium pH is blunted, and with increasing HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> it is enhanced. Although the disequilibrium pH predicted by this model is less than that observed in the rat IMCD (5), Fig. 9 indicates that in this pH neighborhood small decreases in entering phosphate, combined with an increase in delivered HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration, could reproduce the experimental finding. Furthermore, with reference to Figs. 4 and 6, the disequilibrium pH determination is clearly sensitive to small losses of dissolved CO2 during the experimental protocol. The disequilibrium PCO2 depends on the product of end-luminal H2PO<UP><SUB>4</SUB><SUP>−</SUP></UP> concentration and the disequilibrium pH. Increasing either buffer alone had a smaller impact on the disequilibrium PCO2 than when both buffers increase in proportion. In this model, there was no significant impact of the ampholyte property of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>, namely, generation of CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> and H2CO3. In large measure, this derived from the fact that with end-luminal equilibration in a closed system, the resulting PCO2 increase kept the tubule fluid relatively acid, with virtually no generation of CO<UP><SUB>3</SUB><SUP>2−</SUP></UP>. Even when the system was open and the urine alkalinized, there was a concomitantly larger contribution (to HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> titration) from the phosphate buffer, so that the CO<UP><SUB>3</SUB><SUP>2−</SUP></UP> effect remained insignificant (Table 2).

The most disturbing feature of these model simulations is the predicted magnitude of the equilibrium PCO2 within a truly closed system. In the calculations of Figs. 2-4, the predicted urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentration was 86 mM, total phosphate was 53 mM, and equilibrium pH and PCO2 were 7.23 and 202 mmHg, respectively. For comparison, Table 3 includes data from a number of HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-loading studies in rats. For all of these studies, the emphasis had been on urinary PCO2, so that only two (18, 19) had included measurements of urinary phosphate concentrations. Although some studies did not record urinary flow, all indicated the steady-state infusion rate of their HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> solution, and this should be a good approximation of urinary flow. While the model CD generally matches the urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> concentrations, it is clear that the model equilibrium pH is lower and the equilibrium PCO2 is higher than measured values. To some extent, this may be explained by the fact that the model has assumed a moderately antidiuretic rat kidney, with a final urinary osmolality of 945 mosmol/kgH2O and thus a higher concentration of urinary phosphate. Indeed, Arruda et al. (Fig. 2 in Ref. 2) demonstrated an inverse relationship between urinary flow rate and urinary PCO2. Consistent with those findings are the observations of DuBose et al. (5, 6), who worked with much lower infusion rates and found much higher urinary PCO2. Nevertheless, when the data of Arruda et al. (2) are examined in the range of urinary flow rates comparable to those of the model CD (~1.4% of glomerular filtration rate), they found urinary PCO2 to be only ~50 mmHg higher than plasma PCO2 (35 mmHg). The model CD can be used to estimate the impact of increasing urinary flow. This has been done in Table 3 by increasing the delivery of the HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-rich perfusate by a factor of three. This leads to a 10-fold increase in urinary flow, a 60% decrease in urinary phosphate, and a 30% decrease in the equilibrium PCO2. The urinary flow and buffer concentrations are now closer to some of the published studies, but urinary PCO2 remains twofold greater.

                              
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Table 3.   Urine composition in HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-loaded rats

The model estimate of equilibrium PCO2 is considerably more discrepant with data if one tries to accommodate the observation that ambient medullary PCO2 is higher than arterial blood PCO2 and is in fact relatively close to the values reported for bladder urine (5, 9). When ambient PCO2 is increased in the model CD (Figs. 11 and 12), the predicted disequilibrium PCO2 is nearly additive with the increment. This places the predicted urinary PCO2 well beyond reported values. Indeed, in the study by DuBose (5), the difference in PCO2 between IMCD fluid and bladder urine during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> infusion was only 14 mmHg. Concern regarding CO2 escape from the renal collecting system does not appear to have received extensive experimental investigation. Kennedy et al. (12) acknowledged that they had undertaken a comparison of ureteral and bladder urinary CO2 but indicated only that renal pelvic urine showed "the same general relationship" to arterial PCO2 as did bladder samples. Estimating the increase in ambient medullary PCO2 with HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading is beyond the scope of this model, although this study can offer something to the discussion of the "single effect" of medullary CO2 generation. With regard to Fig. 4, it is clear that the preponderance of CO2 generation occurs in the OMCD or near the outer-inner medullary junction. This CO2 will diffuse into descending vasa recta, be carried toward the papilla, and become trapped within inner medulla. A simple analytic model of vasa recta flow predicts that OMCD CO2 generation can yield a substantial increase in papillary PCO2 even in the absence of IMCD CO2 generation.

In summary, this model has provided a means for simulating CD function during HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> loading. In the rat, with absent luminal carbonic anhydrase, the model yields predictions for the luminal disequilibrium pH and the equilibrium increment in urinary PCO2. From the rate of luminal proton secretion and the transit time of tubular fluid within the CD, the kinetic coefficient for the dehydration of H2CO3 must be within 1% of its uncatalyzed value to obtain significant end-tubule disequilibrium. The concentrations of urinary HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> and phosphate are critical to the magnitude of disequilibrium pH and equilibrium PCO2, so the antidiuretic state of the animal is a major factor in these calculations. The disequilibrium pH increases with either increased HCO<UP><SUB>3</SUB><SUP>−</SUP></UP> or decreased phosphate; the increment in equilibrium PCO2 increases with increases in either species. A prediction of this model is that in a truly closed system, the disequilibrium pH should be slightly lower than the reported value and that the urinary equilibrium PCO2 for HCO<UP><SUB>3</SUB><SUP>−</SUP></UP>-loaded rats should be substantially higher than reported values. Certainly, a CO2 "leak" during experimental determinations would be compatible with both discrepancies, but in view of the experimental care exercised, other explanations may need to be sought. Specifically, the first item of investigation should be concomitant determination of urinary buffer concentrations within the tubular fluid sampled for PCO2 and pH. This model should provide a means for exploring the impact of proposed transport defects during formal testing of urinary acidification.


    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.00163.2002

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


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
MODEL FORMULATION
MODEL CALCULATIONS
DISCUSSION
REFERENCES

1.   Arruda, JAL, and Kurtzman NA. Mechanisms and classification of deranged distal urinary acidification. Am J Physiol Renal Fluid Electrolyte Physiol 239: F515-F523, 1980[Abstract/Free Full Text].

2.   Arruda, JAL, Nascimento L, Mehta PK, Rademacher DR, Sehy JT, Westenfelder C, and Kurtzman NA. The critical importance of urinary concentrating ability in the generation of urinary carbon dioxide tension. J Clin Invest 60: 922-935, 1977[ISI][Medline].

3.   Berliner, RW, and DuBose TD, Jr. Carbon dioxide tension of alkaline urine. In: The Kidney: Physiology and Pathophysiology, edited by Seldin DW, and Giebisch G.. New York: Raven, 1992, chapt. 77, p. 2681-2693.

4.   DiTella, PJ, Sodhi B, McCreary J, Arruda JAL, and Kurtzman NA. Mechanism of the metabolic acidosis of selective mineralocorticoid deficiency. Kidney Int 14: 466-477, 1978[ISI][Medline].

5.   DuBose, TD, Jr. Hydrogen ion secretion by the collecting duct as a determinant of the urine to blood PCO2 gradient in alkaline urine. J Clin Invest 69: 145-156, 1982[ISI][Medline].

6.   DuBose, TD, Jr, and Caflisch CR. Validation of the difference in urine and blood carbon dioxide tension during bicarbonate loading as an index of distal nephron acidification in experimental models of distal renal tubular acidosis. J Clin Invest 75: 1116-1123, 1985[ISI][Medline].

7.   Garg, LC. Lack of effect of amphotericin-B on urine-blood PCO2 gradient in spite of urinary acidification defect. Pflügers Arch 381: 137-142, 1979[ISI][Medline].

8.   Giammarco, RA, Goldstein MB, Halperin ML, and Stinebaugh BJ. The effect of hyperventilation on distal nephron hydrogen ion secretion. J Clin Invest 58: 77-82, 1976[ISI][Medline].

9.   Graber, ML, Bengele HH, and Alexander EA. Elevated urinary PCO2 in the rat: an intrarenal event. Kidney Int 21: 795-799, 1982[ISI][Medline].

10.   Halperin, ML, Goldstein MB, Haig A, Johnson MD, and Stinebaugh BJ. Studies on the pathogenesis of type I. (distal) renal tubular acidosis as revealed by the urinary PCO2 tensions. J Clin Invest 53: 669-677, 1974[ISI][Medline].

11.   Julka, NK, Arruda JAL, and Kurtzman NA. The mechanism of amphotericin-induced distal acidification defect in rats. Clin Sci (Colch) 56: 555-562, 1979[ISI][Medline].

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13.   Maren, TH. Carbon dioxide equilibria in the kidney: the problems of elevated carbon dioxide tension, delayed dehydration, and disequilibrium pH. Kidney Int 14: 395-405, 1978[ISI][Medline].

14.   Mehta, PK, Sodhi B, Arruda JAL, and Kurtzman NA. Interaction of amiloride and lithium on distal urinary acidification. J Lab Clin Med 93: 983-994, 1979[ISI][Medline].

15.   Ochwadt, BK, and Pitts RF. Effects of intravenous infusions of carbonic anhydrase on carbon dioxide tension of alkaline urine. Am J Physiol 185: 426-429, 1956[Abstract/Free Full Text].

16.   Pitts, RF, and Lotspeich WD. Bicarbonate and the renal regulation of acid base balance. Am J Physiol 147: 138-154, 1946[Free Full Text].

17.   Reid, EL, and Hills AG. Diffusion of carbon dioxide out of the distal nephron in man during antidiuresis. Clin Sci (Colch) 28: 15-28, 1965[ISI].

18.   Roscoe, JM, Goldstein MB, Halperin ML, Schloeder FX, and Stinebaugh BJ. Effect of amphotericin B on urine acidification in rats: implications for the pathogenesis of distal renal tubular acidosis. J Lab Clin Med 89: 463-470, 1977[ISI][Medline].

19.   Roscoe, JM, Goldstein MB, Halperin ML, Wilson DR, and Stinebaugh BJ. Lithium-induced impairment of urine acidification. Kidney Int 9: 344-350, 1976[ISI][Medline].

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