Potassium excretion during antinatriuresis: perspective from a distal nephron model

Abstract

Renal excretion of Na⁺ and K⁺ must be regulated independently within the distal nephron, but is complicated by the fact that changing excretion of one solute requires adjustments in the transport of both. It is long known that hypovolemia increases Na⁺ reabsorption while impairing K⁺ excretion, even when distal Na⁺ delivery is little changed. Renewed interest in this micropuncture observation came with identification of the molecular defects underlying familial hyperkalemic hypertension (FHH), which also increases distal Na⁺ reabsorption and impairs K⁺ excretion. In this work, a mathematical model of the distal nephron (Weinstein AM. Am J Physiol Renal Physiol 295: F1353–F1364, 2008), including the distal convoluted tubule (DCT), connecting segment (CNT), and collecting duct (CD), is used to examine renal K⁺ excretion during antinatriuresis. Within the model, Na⁺ avidity is represented as the modulation of DCT NaCl reabsorption, and the K⁺ secretion signal is an aldosterone-like effect on principal cells of the CNT and CD. The first model prediction is that changes in DCT NaCl reabsorption are not mediated by NaCl cotransporter density alone, but require additional adjustments of both peritubular Na-K-ATPase and KCl cotransport. A second observation is that the CNT response to increased DCT Na⁺ reabsorption should not only stabilize CD K⁺ delivery but also compensate for the compromise of K⁺ excretion downstream, as low Na⁺ delivery increases CD K⁺ reabsorption. Such anticipatory regulation is seen with the aldosterone response of hypovolemia, while the FHH phenotype manifests enhanced DCT NaCl transport but a blunted aldosterone effect. The model emphasizes the need for two distinct signals to the distal nephron, regulating Na⁺ excretion and K⁺ excretion, in contrast to a single switch apportioning NaCl reabsorption and Na⁺-for-K⁺ exchange.

Potassium Excretion During Antinatriuresis: Perspective From a Distal Nephron Model

renal potassium excretion is a distal nephron responsibility: under normal circumstances, and through wide variations in dietary potassium, ∼10% of filtered K⁺ is delivered to the distal nephron, where there is substantial and variable secretion by the connecting segment, and subsequent modest reabsorption in collecting ducts (22). K⁺ secretion is Na⁺ dependent, with relatively constant Na⁺ delivery to the distal nephron provided by tubuloglomerular feedback, and regulated excretion achieved by aldosterone-modulation of principal cell transporter density. K⁺ secretion by principal cells involves coordination among the luminal membrane Na⁺ channel (ENaC), the peritubular Na-K-ATPase, and the K⁺ channels of both membranes, and aldosterone impacts all of these pathways (37, 38). With respect to the events underlying the increase in luminal Na⁺ conductance, aldosterone rapidly moves ENaC from cytoplasm to apical cell membrane and, over time, enhances synthesis of α-ENaC (25). An early event following aldosterone administration is induction of the serum- and glucocorticoid-dependent kinase, sgk, which phosphorylates Nedd4-2, and thus inhibits ubiquitin-dependent ENaC retrieval (43). Aldosterone also increases collecting duct Na-K-ATPase activity, and this increase is contingent on the increase in cytosolic Na⁺ (9, 31). Complementing this observation, Na-K-ATPase binding sites vary in parallel with cytosolic Na⁺ concentration, with a steep slope in aldosterone-replete animals and a shallow slope in aldosterone deficiency (4), suggesting an Na-K-ATPase pool, with aldosterone-dependent pool size and Na⁺-dependent transporter insertion. The increase in luminal and peritubular membrane K⁺ conductance after mineralocorticoid parallels that of Na⁺, with a prompt response and an enhanced delayed response (39, 49). Antidiuretic hormone (ADH) is a second hormone whose effect on principal cells is to increase Na⁺ reabsorption and K⁺ secretion. The increase in transepithelial electrical potential difference (PD) is manifest within minutes, due to an ENaC increase (14, 24, 33, 40). Morris and Schafer (27) indicated that altered membrane trafficking was responsible for the cAMP-induced change in ENaC activity, and Snyder et al. (42) delineated the convergence of ADH and aldosterone on Nedd4-2.

Low Na⁺ intake or frank volume depletion poses a physiological challenge to the organism to both intensify renal NaCl reabsorption and maintain adequate distal Na⁺-for-K⁺ exchange. Indeed, the action of aldosterone to achieve either antinatriuresis or kaliuresis has been termed the “aldosterone paradox,” in recognition of an apparent need for further regulatory definition to switch between these two actions of the hormone (1, 18). Interest in K⁺ secretion during reduced Na⁺ delivery has intensified recently, with the recognition of familial hyperkalemic hypertension (FHH) or pseudohypoaldosteronism type 2 (PHA-2) as a disorder in which distal convoluted tubule (DCT) cells increase NaCl reabsorption and in which renal K⁺ excretion is impaired (32). In this condition, mutations of regulatory WNK kinases produce an increase in surface expression of the thiazide-sensitive NaCl cotransporter, and the hypertension and hyperkalemia are eliminated by administration of a thiazide (60, 62). These kinases are also linked to modification of transporters within the connecting segment, specifically principal cell ROMK and tight junction proteins, although there is uncertainty as to the significance of these interactions in the impaired K⁺ transport (26). As in volume depletion, this disorder provides a model in which distal tubule NaCl reabsorption is increased; however, in contrast to volume depletion, aldosterone levels are relatively depressed. It has been hoped that study of the FHH mutations would provide insight into the differential regulation of distal nephron ion transport and insight into the aldosterone paradox (19).

Mathematical models of distal nephron segments have been developed and used to analyze tubular K⁺ handling as a function of membrane transporter densities (53, 56), and as a function of delivered load of water and sodium (54, 56). Concatenated as a full distal nephron, the model synthesizes segmental events in the distal tubule and collecting duct to predict whole kidney solute excretion. In its initial development, this model was used to simulate distal K⁺ and acid-base handling during states of excess Na⁺ delivery, namely, diuretic administration (57) and the Bartter's syndromes (58). In the present work, the model will be used to simulate K⁺ handling when the DCT is Na⁺ avid, either in the context of globally enhanced sodium reabsorption (volume depletion), or when the antinatriuresis is limited to the DCT (FHH). The first question addressed is what configuration of DCT transporters can actually yield such increases in DCT NaCl reabsorption, and here it will be demonstrated that both luminal entry and peritubular exit steps must be amplified. We next examine connecting segment (CNT) function to estimate the complementary transporter increases needed to maintain K⁺ secretion when luminal Na⁺ delivery falls. Finally, we append the K⁺-reabsorbing collecting duct to yield predictions for overall K⁺ excretion during perturbations of distal tubule transport. It will be found that with a Na⁺-avid DCT, increased aldosterone is a prerequisite for maintaining K⁺ excretion. Specifically, the same action of aldosterone that produces brisk K⁺ excretion in Na⁺-replete states, buttresses K⁺ excretion in volume depletion; there is little to suggest a paradoxical effect of aldosterone. With the Na⁺-avid DCT of FHH, the blunted aldosterone effect appears sufficient to rationalize impaired K⁺ excretion.

Model Formulation

The distal nephron model used in this work is identical to that used to examine diuretic effects and is illustrated schematically in Fig. 1A (57). Specifically, the distal tubule is composed of a 1-mm DCT and a 2-mm CNT; the collecting duct consists of a 2-mm cortical segment (CCD), a 2-mm outer medullary segment (OMCD), and a 5-mm inner medullary segment (IMCD). To provide estimates of whole kidney function, the full ensemble of tubules is represented: there are 36,000 DCT, which coalesce (constant circumference to cross-section ratio) exponentially within the arcades of the CNT to 7,200 CCD, OMCD, and initial IMCD; the IMCD coalesces exponentially to 112 papillary collecting ducts. Model solutes are Na⁺, K⁺, Cl⁻, HCO₃⁻, H₂CO₃, CO₂, HPO₄²⁻, H₂PO₄⁻, urea, NH₃, NH₄⁺, and H⁺. The baseline parameter sets for each of the tubules have not been changed, and this corresponds to an antidiuretic kidney with ample solute excretion that generally characterizes micropuncture preparations. In particular, the model has not incorporated the recent finding of a Na⁺-dependent chloride-bicarbonate exchanger within luminal membranes of mouse CCD intercalated cells (21). Although this transporter may be active during Na⁺ deprivation, there remains uncertainty regarding the identity of a coordinate peritubular transporter, which could mediate the observed transepithelial Na⁺ flux. DCT entering flow and composition, as well as interstitial solute concentrations in the cortex and medulla, are those used previously, and these are indicated in Table 1. Of note, if the entering fluid flow at 6 nl/mn corresponds to 20% of glomerular filtration rate (GFR), then the entering Na⁺ (65 mM), K⁺ (2.0 mM), and HCO₃⁻ (8.0 mM) correspond to 9.0, 8.0, and 6.4% of filtered loads of these solutes, respectively. There are medullary solute gradients, which include Na⁺ increases from 144 to 284 in outer medulla, and a flat profile in the inner medulla; K⁺ increases from 5 to 10 mM in the outer medulla, increasing to 20 mM by the papillary tip. With regard to this potassium profile, measurements of inner medullary vasa recta K⁺ concentration vary from 2- to 10-fold that of systemic plasma, depending upon the K⁺ load of the animal (6), or on the state of diuresis (28). For the ensemble of tubules, with variable volume flow and variable cross-sectional area, transit time from x₁ to x₂, τ(x₁,x₂), is computed as an integral of luminal area relative to volume flow

$$\tau \left(x_1,x_2\right)={\displaystyle \underset{x_1}{\overset{x_2}{\int }}\frac{A\left(x\right)}{F_{\text{v}}\left(x\right)}\text{d}x}$$ (1)

Fig. 1.

Schematics of model configurations. A: distal nephron, consisting of a 1-mm distal convoluted tubule (DCT), 2-mm connecting tubule (CNT), 2-mm cortical collecting duct (CCD), 2-mm outer medullary collecting duct (OMCD), and 5-mm inner medullary collecting duct (IMCD). Within the CNT, the 36,000 tubules coalesce to form 7,200 CCD. Within the IMCD, tubules coalesce exponentially so that final urine flows through 113 papillary collecting ducts. B: DCT cell showing coupled transport pathways and ion channels within luminal and peritubular membranes. C: principal cell of CNT, CCD, and OMCD.

Table 1.

Luminal and peritubular composition

	Luminal Fluid		Peritubular Interstitium
	Concentration	Delivery, μmol/min	Cortex	OIMJ	Papilla
Na+, mM	65.0	14.04	144	284	284
K+	2.0	0.43	5.0	10.0	20.0
Cl−	56.1	12.12	119.6	266	280.9
HCO3−	8.0	1.73	25	25	25
H2CO3, μM	4.4		4.4	4.4	4.4
CO2	1.5		1.5	1.5	1.5
HPO42−	2.1		2.0	3.0	3.0
H2PO4−	1.9		0.6	0.9	0.9
Total PO4	4.0	0.86	2.6	3.9	3.9
Urea	30	6.48	5	20	500
NH3, μM	15.1		2.9	58	131.4
NH4+	3.2	0.69	0.2	3.9	8.8
pH	6.828		7.323	7.323	7.323
Impermeant	0.0		2.0	2.0	2.0
Osm	169.8		304.9	616	1126

OIMJ, outer-inner medullary junction.

The calculations of this work involve variations of transporter densities within the distal tubule and collecting duct. The configuration of transporters in the DCT and CNT are those used previously (55, 56), and are displayed Fig. 1, B and C. Microperfusion of early and late distal tubule has indicated that Na⁺ reabsorption rates are comparable for these two segments (see data summary in the appendix of Ref. 54), which is reflected in similar DCT and CNT Na⁺ transport rates at model baseline conditions. Within the DCT, the luminal entry pathways are the NaCl cotransporter (NCC) and the Na⁺/H⁺ exchanger (NHE2), and microperfusion of early DCT has indicated a proton secretory rate about half that of total Na⁺ reabsorption. Within the DCT peritubular membrane, Na⁺ exit is via the Na-K-ATPase, which mandates substantial cellular uptake of K⁺; the two pathways for Cl⁻ exit are a KCl cotransporter (KCC) and a Cl⁻ channel, with KCC the dominant flux. The connecting segment is composed of principal cells and α-and β-intercalated cells. Only the principal cell is shown, with luminal conductances for Na⁺ (ENaC) and K⁺ (ROMK), and the model provides only for an aggregate luminal K⁺ conductance, not representing insertion of different K⁺ channel types. In the model CNT at baseline, the bulk of Na⁺ reabsorption is balanced by the sum of K⁺ secretion plus H⁺ secretion via α-cell H⁺-ATPase; the smaller reabsorptive Cl⁻ flux is via the β-cell luminal Cl⁻/HCO₃⁻ exchanger (pendrin) or tight-junctional electrodiffusion. In the model calculations that examine only CNT function, this segment is configured as a single 1-mm unbranched tubule, with the same cells and the same luminal surface area and volume, as the 2-mm segment of the full model. Of note, the model CCD has the same cells as the CNT, with transport rates that are scaled down; the OMCD has only principal cells and α-intercalated cells.

Model Calculations

Representing Na⁺ conservation by the DCT.

Central to all of the model simulations of volume depletion are increases in DCT Na⁺ reabsorption. In microperfused early distal tubule, both Na⁺ reabsorption and proton secretion are increased by angiotensin II, while in late distal tubule, only Na⁺ flux is increased (48). Angiotensin was found to induce NCC trafficking to the luminal membrane of the DCT (36), and indeed, angiotensin and aldosterone can each provoke increases in plasma membrane abundance of NCC (46). Configuring the model transporters to represent an increase in DCT Na⁺ reabsorption requires a number of choices. The calculations of Fig. 2 were obtained using the epithelial model of the DCT (55), in which the density of luminal membrane NCC is varied; luminal and peritubular conditions are early DCT and renal cortex (Table 1). The left panes display solute fluxes through NCC, NHE2, KCC, and the Na-K-ATPase (1 nmol·s⁻¹·cm⁻² corresponds to 28 pmol·min⁻¹·mm⁻¹ for a 15-μm tubule diameter), and the right panes are DCT cell volume and cytosolic concentrations of Na⁺, Cl⁻, and HCO₃⁻. When only NCC density is increased (dotted curves), the model predicts an increase in NCC flux, and secondary increases in cell Na⁺ and Cl⁻; consequent to an increase in the cell Na⁺ concentration is an increase in Na⁺ exit via Na-K-ATPase and a decrease in entry via NHE2. With the decrease in Na⁺/H⁺ exchange (both luminal and peritubular), there is a decrease in cell HCO₃⁻; the net effect on cell volume is a surprising constancy. An important observation is that the magnitudes of the flux changes are relatively small (Table 2). For example, with a doubling of NCC density over control, NCC flux increases from 3.3 to 4.8 nmol·s⁻¹·cm⁻², while NHE2 flux decreases from 4.4 to 3.9 nmol·s⁻¹·cm⁻², so that there is a net increase of only 13% in luminal membrane Na⁺ transport.

Fig. 2.

Impact of NaCl cotransporter (NCC) density on DCT fluxes and composition. Calculations utilize the epithelial model of DCT (55); luminal and peritubular conditions are early DCT and renal cortex (Table 1). NCC density is varied, and its value, relative to baseline, appears on the abcissa. The left panes display solute fluxes through NCC, Na⁺/H⁺ exchanger (NHE2), KCl cotransporter (KCC), and the Na-K-ATPase, and the right panes are DCT cell volume and cytosolic concentrations of Na⁺, Cl⁻, and HCO₃⁻. Dotted curves derive from an isolated change in NCC density. For the solid curves, when the fractional NCC density relative to baseline is ρ_DCT, Na-K-ATPase density and KCC density are both 0.5·ρ_DCT.

Table 2.

DCT fluxes and composition with variation in transporter density

	Transporter Fluxes, nmol · s−1 · cm−2				Cell Volume, ml × 104	Cytosolic Concentration, mM
NCC scale	NCC	NHE2	KCC	Na-K-ATPase (Na+)		[Na+]	[Cl−]	[HCO3−]
NCC
0.1	0.62	5.34	4.84	8.82	6.45	12.54	12.94	27.09
0.5	2.18	4.81	5.47	9.74	6.38	14.34	15.96	25.38
1	3.34	4.41	5.92	10.42	6.36	15.85	18.57	24.07
2	4.80	3.90	6.46	11.26	6.37	17.96	22.27	22.43
3	5.76	3.56	6.79	11.81	6.40	19.52	25.00	21.33
NCC+Na-K-ATPase
0.1	0.36	4.34	4.02	7.12	5.46	22.97	11.64	17.78
0.5	1.78	4.40	4.97	8.74	5.84	18.93	14.56	20.85
1	3.34	4.41	5.92	10.42	6.36	15.85	18.57	24.07
2	5.89	4.33	7.33	13.02	7.60	12.38	26.94	29.26
3	7.92	4.23	8.35	15.02	9.22	10.44	35.43	33.39
NCC+Na-K-ATPase+KCC
0.1	0.29	3.86	3.06	6.60	6.14	19.68	17.07	20.76
0.5	1.59	4.16	4.32	8.32	6.29	17.34	17.73	22.70
1	3.34	4.41	5.92	10.42	6.36	15.85	18.57	24.07
2	6.91	4.77	9.12	14.50	6.34	14.42	19.85	25.38
3	10.47	5.08	12.29	18.51	6.22	13.75	20.62	25.85
NCC+Na-K-ATPase+KCC+NHE2
0.1	0.41	2.63	2.84	5.92	5.71	16.02	15.26	14.23
0.5	1.69	3.8	4.28	8.15	6.15	16.68	17.49	20.66
1	3.34	4.41	5.92	10.42	6.36	15.85	18.57	24.07
2	6.74	5.19	9.15	14.68	6.52	14.72	19.88	27.77
3	10.19	5.77	12.33	18.81	6.51	14.12	20.61	29.79

NCC, NaCl cotransporter; NHE2, Na/H exchanger; KCC, KCl cotransporter.

A key observation from proximal tubule models is that to achieve substantial perturbations in flux, there need to be coordinated changes in luminal and peritubular transporter density (59). Table 2 displays results from a calculation in which both NCC and Na-K-ATPase are varied, and the fractional change in Na-K-ATPase density is 50% that of the change in NCC density. Compared with solitary NCC perturbation, an increase in NCC now produces a greater increase in NCC flux and cell Cl⁻, but cytosolic Na⁺ decreases, due to the Na-K-ATPase. By virtue of the peritubular Cl⁻/HCO₃⁻ exchanger, the increase in cell Cl⁻ increases cytosolic HCO₃⁻, which blunts any increase in NHE2 flux. Cell volume increases with increasing fluxes. Specifically, a doubling of NCC and a 50% increase in Na-K-ATPase produce a 33% increase in luminal membrane Na⁺ transport, and a 20% increase in cell volume. In this configuration, when luminal fluxes are asked to increase by 60% (3-fold NCC increase), cell volume increases by 45%. If one now introduces concomitant increases in KCC, with NCC and Na-K-ATPase, this blunts the increase in cell Cl⁻, and as a consequence, increases NCC transport and eliminates the change in cell volume. This is depicted as solid curves in Fig. 2, in which the fractional changes in KCC density are equal to those of the Na-K-ATPase (i.e., 50% of the change in NCC). Here, the stable cytosolic Cl⁻ produces a stable cell HCO₃⁻, so that any decrease in cell Na⁺ enhances NHE2 flux. With a doubling of NCC, NCC flux more than doubles and overall luminal Na⁺ transport increases by 52%, with no increase in cell volume; proton secretion increases by 8%. It is this configuration of transporters (doubling of NCC and 50% increase in both KCC and the Na-K-ATPase) that will be adopted in the subsequent tubule simulations, to represent the impact of angiotensin II on the DCT. Of note, Table 2 contains the results of calculations in which both fractional changes in NCC and NHE2 density vary equally (along with 50% changes in KCC and Na-K-ATPase). This provides no additional increase in overall luminal Na⁺ flux, and only a 17% increase in luminal proton secretion, with a doubling of NHE2. It seems likely that, as in the proximal tubule, some coordinated variation in peritubular base exit, in parallel with changes in NHE density, must be present to achieve robust variation in luminal proton secretion, but this has not been explored further.

CNT compensation for diminished Na⁺ delivery.

K⁺ secretion by the CNT varies directly with Na⁺ delivery from the DCT, whether achieved by increases in luminal Na⁺ concentration or luminal flow rate (56). Figure 3 displays the response of a 1-mm CNT segment, perfused at 6 nl/min, in which entering luminal NaCl is varied, with Na⁺ ranging from 20 to 100 mM (and Cl⁻ ranging from 11 to 91 mM). In the panes on the left, Na⁺ and Cl⁻ fluxes vary over the whole range of NaCl perfusion concentrations, while K⁺ secretion is sensitive to luminal NaCl when concentrations are below baseline (65 mM); there is little change in mean luminal PD. The fraction of Na⁺ reabsorption that is balanced by K⁺ secretion decreases from 65% at low luminal Na⁺ to 48% at high luminal Na⁺. At the lowest luminal Na⁺, there is zero net Cl⁻ reabsorption, so that the remaining Na⁺ reabsorption is balanced largely by HCO₃⁻ reabsorption, ultimately the result of α-cell proton secretion. Thus, when entering luminal NaCl is low, the model CNT predicts an increase in net acid secretion. This complements the situation in the DCT, in which there is a predicted decrease in Na⁺-dependent proton secretion via NHE2, so that overall distal tubule acid excretion is relatively insensitive to delivered Na⁺ (see Figs. 4 and 5 in Ref. 57).

Fig. 3.

CNT solute transport as a function of entering Na⁺ concentration. Calculations utilize the model of a 1-mm CNT segment, perfused at 6 nl/min (56); luminal and peritubular conditions are early DCT and renal cortex (Table 1). Entering luminal NaCl is varied, with Na⁺ ranging from 20 to 100 mM (displayed on the abcissa), and Cl⁻ ranging from 11 to 91 mM. Top left pane shows reabsorption of Na⁺ and Cl⁻ and secretion of K⁺; on the top right are reabsorption of HCO₃⁻ and NH₄⁺ and secretion of titratable acid. Net acid secretion is the composite of HCO₃⁻ reabsorption plus titratable acid (TA) secretion, less NH₄⁺ reabsorption. In the bottom panes, transepithelial electrical potential (PD) and lumen pH are averaged over the tubule length.

Fig. 4.

CNT solute transport as a function of entering Na⁺ concentration while maintaining constant K⁺ secretion. Calculations use the CNT model and bath conditions in Fig. 3, with the exception that the transporter densities of both ENaC and Na-K-ATPase in principal cell membranes are scaled relative to their baseline values by a common factor, ρ_PC. This scaling factor is determined from the iterative solution of the CNT model, so that overall K⁺ secretion is maintained at its baseline value. Solute fluxes and lumen conditions are displayed as in Fig. 3.

Fig. 5.

For the calculations of Fig. 4, the common scaling factor for both luminal membrane Na⁺ channel (ENaC) and Na-K-ATPase, ρ_PC, is displayed as a function of entering luminal Na⁺ concentration.

In light of the response of the CNT to changes in Na⁺ delivery, a natural problem is to define the ability to adjust CNT principal cell transport to compensate for changes in entering Na⁺, i.e., to stabilize K⁺ secretion by changing Na⁺ reabsorption. Acknowledging that aldosterone impacts both ENaC and the Na-K-ATPase, and that coordinated increases in these two principal cell transporters are more effective than changes in ENaC alone in modulating K⁺ secretion (53), the problem may be posed as identifying the factor, ρ_PC, by which the density of these two transporters needs to be scaled in response to entering Na⁺ concentration. The solution to that problem is obtained as an iterative solution of the CNT tubule model, and is displayed in Figs. 4 and 5. Figure 4 has a tableau similar to Fig. 3, which includes solute fluxes as a function of entering Na⁺ concentration, and the constancy of the secretory K⁺ flux verifies the desired result. In Fig. 5, the scaling factor, ρ_PC, is displayed, showing little change at high Na⁺ concentrations, but a near doubling at low Na⁺. Of note, this scaling factor corresponds to transporter density, but the luminal membrane Na⁺ permeability, H_M(Na,x), itself depends upon both luminal and cytosolic Na⁺ concentrations, C_M(Na,x) and C_I(Na,x), as functions of distance, x, along the tubule

$$H_{\text{M}}\left(\text{Na},x\right)={\rho }_{\text{PC}}·H_{\text{M}0}·\left(5/3\right)·\frac{\left[1-{\text{C}}_{\text{I}}\left(\text{Na},x\right)/50.\right]}{\left[1+{\text{C}}_{\text{M}}\left(\text{Na},x\right)/30.\right]}$$ (2)

This formula had been developed to represent intrinsic cellular mechanisms that stabilize Na⁺ transport, as the channel permeability increases in response to decreases in either luminal or cytosolic Na⁺ concentrations (mM) (44). Comparing Figs. 3 and 4, the stabilization of luminal K⁺ secretion is achieved with a stabilization of Na⁺ reabsorption. Specifically, at low entering Na⁺, increases in ENaC and Na-K-ATPase increase Na⁺ reabsorption and luminal negativity, and this increases both K⁺ secretion and net acid secretion.

Concatenating DCT and CNT segments.

The considerations thus far have provided a model DCT which can represent either baseline or increased Na⁺ reabsorption, and a CNT with baseline, high, or low aldosterone effect, yielding in all, six possible states for a distal tubule comprised of the DCT and CNT in series. Of particular interest, is the condition of increased Na⁺ flux in both segments, as in the high angiotensin and high aldosterone of volume depletion, and the condition of increased DCT flux, but low or normal aldosterone, as in FHH. Predicted flows of Na⁺ and K⁺ for each of the six states are shown in Fig. 6 and displayed in Table 3. For each pane, the abcissa is the distance along the distal tubule; on the left are Na⁺ flows, and on the right K⁺ flows for a single tubule (pmol/min). Each curve is marked with parameter sets for the DCT and CNT: DCT parameters are either baseline or aII (a doubling of NCC and 50% increases in Na-K-ATPase and KCC); CNT parameters are baseline, high, or low aldosterone (transporter density, ρ_PC, for ENaC and Na-K-ATPase of 1.0, 2.0, or 0.5). With reference to Table 3, when both segments are at baseline, Na⁺ reabsorption is 155 pmol/min in the DCT and 108 pmol/min in the CNT, and in the top left pane of Fig. 6, it is difficult to discern a change in the slope of Na⁺ flow at the junction of the two segments; overall, about two-thirds of entering Na⁺ is reabsorbed by this distal tubule. K⁺ entry is 12 pmol/min, and at baseline, about half of CNT Na⁺ reabsorption is matched by K⁺ secretion, so that end-CNT K⁺ flow is 73 pmol/min. The aII parameters for the DCT provide a steeper slope of Na⁺ flow, so that CNT Na⁺ delivery decreases by 40%; under baseline aldosterone, this reduces CNT Na⁺ reabsorption by 28% and reduces CNT K⁺ secretion by 24%. For the condition corresponding to volume depletion (aII+Aldo), overall distal tubule Na⁺ reabsorption is 95% of delivered load, but exiting K⁺ flow has been preserved (actually 13% above baseline). The rationale for securing model CNT K⁺ secretion greater than baseline will become clear when K⁺ transport in the collecting duct is considered. When aldosterone is depressed, the impact on distal K⁺ delivery is approximately a 40% reduction, for either DCT parameter set.

Fig. 6.

Flow profiles along distal tubule under hormonal influence. Calculations use the concatenated DCT (1 mm) and CNT (1 mm) tubule models (56), perfused at 6 nl/min, with the perfusate and bath composition as in Table 1. The abscissa is distance along the tubule; panes on the left and right show the axial flows of Na⁺ and K⁺ (pmol/min). Each curve is labeled according to the scaling of DCT/CNT transporter densities, ρ_DCT/ρ_PC. DCT parameters are either baseline or aII (a doubling of NCC and 50% increases in Na-K-ATPase and KCC); CNT parameters are baseline, high (+aldo), or low (−aldo) aldosterone (fractional transporter density, ρ _PC, for ENaC and Na-K-ATPase of 1.0, 2.0, or 0.5).

Table 3.

Impact of parameter variation on distal tubule Na⁺ and K⁺ transport

Baseline DCT
	Enter-Na	DCT-JNa	CNT-JNa	Exit-Na	Enter-K	DCT-JK	CNT-JK	Exit-K
Base	390.00	155.28	107.64	127.08	12.00	−10.26	−50.70	72.96
+Aldo	390.00	155.28	173.88	60.84	12.00	−10.26	−93.96	116.22
−Aldo	390.00	155.28	54.42	180.30	12.00	−10.26	−20.70	42.96
+ROMK	390.00	155.28	112.86	121.86	12.00	−10.26	−58.38	80.64
−ROMK	390.00	155.28	99.78	134.94	12.00	−10.26	−39.30	61.56
−GKPS	390.00	155.28	107.94	126.78	12.00	−10.26	−57.78	80.04
TJCl	390.00	155.28	112.68	122.04	12.00	−10.26	−45.78	68.04
+pendrin	390.00	155.28	107.94	126.78	12.00	−10.26	−50.40	72.66

Stimulated DCT (aII)
	Enter-Na	DCT-JNa	CNT-JNa	Exit-Na	Enter-K	DCT-JK	CNT-JK	Exit-K
Base	390.00	251.58	78.48	59.94	12.00	−7.44	−38.52	57.96
+Aldo	390.00	251.58	117.48	20.94	12.00	−7.44	−63.06	82.50
−Aldo	390.00	251.58	37.56	100.86	12.00	−7.44	−15.78	35.22
+ROMK	390.00	251.58	81.12	57.30	12.00	−7.44	−43.02	62.46
−ROMK	390.00	251.58	73.86	64.56	12.00	−7.44	−31.14	50.58
−GKPS	390.00	251.58	78.72	59.70	12.00	−7.44	−44.64	64.08
TJCl	390.00	251.58	79.32	59.10	12.00	−7.44	−36.90	56.34
+pendrin	390.00	251.58	78.78	59.64	12.00	−7.44	−38.16	57.60

J_Na and J_K, reabsorptive fluxes (pmol/min). Key to parameter variations: stimulated distal convoluted tubule (DCT), NCC increased by 100%, Na-K-ATPase increased by 50%, and KCC increased by 50% over baseline; TJCL, tight junction Cl⁻ and HCO₃⁻ permeabilities doubled; ±Aldo, connecting tubule (CNT) principal cell epithelial Na channel (ENaC) and Na-K-ATPase increased by 100% or decreased by 50%; ± ROMK, CNT principal cell ROMK increased by 100% or decreased by 50%; −GKPS, CNT principal cell peritubular K⁺ permeability decreased by 50%; + pendrin, CNT β-cell pendrin increased by 100%.

Table 3 examines variations of other CNT transporters, which have been linked either to volume depletion or to FHH. WNK kinases have been associated with ROMK function, but the physiological significance is uncertain. From the perspective of the model CNT, changes in luminal membrane K⁺ permeability affect the rate of K⁺ secretion when luminal K⁺ is low, but have little impact on the equilibrium K⁺ concentration (i.e., the lumen concentration at which K⁺ flux is zero); it is peritubular K⁺ permeability that determines the maximum luminal K⁺ concentration. In Table 3, the model distal tubule has been solved with luminal membrane K⁺ permeability in CNT principal cells increased or decreased by a factor of 2.0 or 0.5 (labeled +ROMK or −ROMK, respectively). The results show changes in end-tubule K⁺ delivery of +10% and −16% under baseline DCT parameters, and +8% and −13% during high DCT Na⁺ reabsorption. When peritubular K⁺ permeability is decreased by a factor of 0.5, the impact on end-CNT K⁺ flow is +10% for either DCT parameter set. All of these perturbations seem relatively inconsequential, and are not explored further. In view of the tight junctional association of WNK-4, specifically the report of a factor of 2.0 increase in paracellular Cl⁻ permeability in a WNK-4-transfected epithelium (61), model CNT tight junction Cl⁻ and HCO₃⁻ permeabilities were doubled for either DCT parameter sets (with normal aldosterone parameters in the CNT); the resulting perturbations of Na⁺ and K⁺ flux were small. In view of the effect of angiotensin II to increase pendrin-mediated Cl⁻ transport in CCD (29), pendrin density and the density of the peritubular Cl⁻ channel were doubled in tandem, but the model fluxes of Na⁺ and K⁺ showed little impact. Of note, in the experiments of Pech et al. (29), luminal Cl⁻ (∼127 mM) was substantially higher than the concentrations in these simulations. In sum, although aldosterone and angiotensin may have a number of transport targets in each of the cells comprising the CNT, for the purpose of K⁺ secretion, it appears that their impact on ENaC and Na-K-ATPase are the most important.

Appending the collecting duct for a full distal nephron model.

The impact of distal tubule transport on renal K⁺ excretion requires an estimate of collecting duct K⁺ transport, since this is a site for K⁺ reabsorption (22). In a mathematical model of the collecting duct, this reabsorptive flux is enhanced by osmotic water extraction, which elevates luminal K⁺ concentration, thus establishing a favorable gradient from lumen to blood. When luminal Na⁺ concentration entering the CCD is diminished, flow along the entire collecting duct becomes more sluggish, transit time increases, and K⁺ reabsorption is augmented; overall, fractional K⁺ reabsorption within the collecting duct increases (54).¹ The calculations of Figs. 7 and 8 utilize the full distal nephron model (Fig. 1A) to examine the impact of hypovolemia on Na⁺ and K⁺ excretion; numerical data are displayed in Table 4. In these simulations, scaling of principal cell transporters in the CCD and OMCD parallels the variation of CNT ENaC and Na-K-ATPase. In Fig. 7, the abcissa is the distance along the nephron, and the top and bottom panes show axial flows of Na⁺ and K⁺ for the baseline parameters, for the isolated increase in DCT Na⁺ transport, and for combined angiotensin and high aldosterone parameters. The effect on Na⁺ flows is straightforward, with delivered Na⁺ of 14 μmol/min, and excreted Na⁺ of 2.5, 0.77, and 0.25 μmol/min for the three parameter sets (18, 5.5, and 1.8% of delivered load, respectively). Estimated transit times are 56, 112, and 148 s. The isolated increase in DCT Na⁺ reabsorption diminishes CNT K⁺ secretion and cuts K⁺ excretion by 60%. Superimposing high aldosterone in CNT, CCD, and OMCD, there is an increase in K⁺ flow in these segments to values above baseline, but these fall substantially in IMCD, so that K⁺ excretion is not much improved. Figure 8 provides an accounting of Na⁺ and K⁺ fluxes by tubule segment: the first set of bars is delivery of Na⁺ and K⁺ to the DCT (μmol/min), the next five sets show reabsorption (negative) or secretion (positive) for each nephron segment, and the final set is the summation to obtain renal excretion of Na⁺ and K⁺. (In essence, Fig. 8 displays the derivatives of the curves in Fig. 7, which are not easily appreciated from an inspection of Fig. 7). In the baseline case, fractional delivery of Na⁺ and K⁺ (presuming a GFR of 1 ml/min) are both ∼10% of filtered load; CNT augments the K⁺ flow with an additional 40% of filtered load, and fractional excretion of K⁺ is 20% of filtered load. In this figure, it is apparent that by itself, the angiotensin II parameter set for the DCT impacts CNT K⁺ excretion, but has little effect on collecting duct K⁺ transport.

Fig. 7.

Impact of increased DCT NaCl reabsorption on distal flows. Calculations use the distal nephron model, whose configuration is shown in Fig. 1A (57); perfusion rate is 6 nl/min, with perfusate and interstitial composition as in Table 1. The abcissa is distance along the nephron; top and bottom panes show axial flows of Na⁺ and K⁺ along the full ensemble of tubules (μmol/min), respectively. Each curve is labeled according to the scaling of DCT and principal cell transporter densities ρ_DCT/ρ_PC: DCT parameters are either baseline or aII (a doubling of NCC and 50% increases in Na-K-ATPase and KCC); principal cell parameters are baseline or high aldosterone (+aldo), in which the fractional transporter density, ρ_PC, for ENaC and Na-K-ATPase is 1.0 or 2.0, for all principal cells of the CNT, CCD, and OMCD.

Fig. 8.

Impact of increased DCT NaCl reabsorption on distal flows. For the calculations of Fig. 7, segmental modifications to Na⁺ and K⁺ flows are displayed. In top and bottom panes, the first set of bars is delivery of Na⁺ and K⁺ to DCT (μmol/min), the next 5 sets show reabsorption (negative) or secretion (positive) for each nephron segment, and the final set is the summation to obtain renal excretion of Na⁺ and K⁺. Open bars correspond to baseline transport parameters; middle bars (labeled “\”) are obtained from calculations with an isolated increase in DCT NaCl transport (curves aII in Fig. 7); right bars (labeled “/”) are obtained from calculations with increased DCT and principal cell transporter density (curves aII/+aldo in Fig. 7). Numerical data for the bars appear in Table 4.

Table 4.

Distal nephron solute transport under antinatriuresis and diuresis

	Delivery, μmol/min	Reabsorption						Excretion, μmol/min
		DCT	CNT	CCD	OMCD	IMCD	Total
Base/Base
Na+	14.040	5.624	3.629	0.217	−0.176	2.212	11.510	2.534
K+	0.432	−0.371	−1.898	0.173	0.875	0.623	−0.598	1.030
Cl−	12.120	4.099	1.600	0.476	0.448	2.512	9.135	2.983
HCO3−	1.728	0.935	0.153	0.139	0.178	0.238	1.643	0.085
aII/Base
Na+	14.040	9.094	2.613	0.032	−0.381	1.912	13.270	0.770
K+	0.432	−0.269	−1.486	0.235	0.908	0.654	0.042	0.390
Cl−	12.120	7.785	0.850	0.338	0.273	2.208	11.450	0.666
HCO3−	1.728	0.856	0.318	0.177	0.199	0.170	1.719	0.009
aII/+Aldo
Na+	14.040	9.094	4.076	−0.022	−0.425	1.065	13.790	0.253
K+	0.432	−0.269	−2.435	0.358	1.192	1.128	−0.025	0.457
Cl−	12.120	7.785	1.201	0.405	0.496	1.888	11.780	0.343
HCO3−	1.728	0.856	0.426	0.160	0.187	0.099	1.727	0.001
aII/−Aldo
Na+	14.040	9.094	1.159	−0.032	−0.331	2.410	12.300	1.740
K+	0.432	−0.269	−0.641	0.163	0.571	0.343	0.166	0.266
Cl−	12.120	7.785	0.428	0.215	0.006	2.356	10.790	1.328
HCO3−	1.728	0.856	0.194	0.181	0.199	0.255	1.684	0.044
aII/−Aldo/+NaCl (10 mM)
Na+	16.200	9.464	1.508	0.035	−0.251	2.514	13.270	2.930
K+	0.432	−0.278	−0.773	0.143	0.562	0.345	−0.001	0.433
Cl−	14.280	8.012	0.769	0.276	0.087	2.490	11.630	2.644
HCO3−	1.728	0.944	0.071	0.155	0.182	0.270	1.622	0.106
aII/−Aldo/+Na2SO4 (10 mM)
Na+	16.200	9.127	1.204	−0.103	−0.550	1.688	11.370	4.834
K+	0.432	−0.318	−0.997	0.091	0.531	0.292	−0.400	0.832
Cl−	9.959	7.562	0.078	0.065	−0.263	1.587	9.029	0.930
HCO3−	1.728	0.991	0.220	0.129	0.139	0.196	1.675	0.053

CCD, cortical collecting duct; OMCD, outer medullary collecting duct; IMCD, inner medullary collecting duct.

The calculations of Figs. 9 and 10 relate to FHH, with increased DCT Na⁺ transport and low principal cell ENaC and Na-K-ATPase (numerical data in Table 4). For this parameter configuration, in each of the simulations there is almost no net Na⁺ reabsorption in the CNT, CCD, and OMCD. When entering Na⁺ flow is 14 μmol/min (as in Fig. 7), Na⁺ excretion is 1.7 μmol/min, or ∼68% of that with baseline parameters; K⁺ excretion is ∼25% of baseline. Although this calculation uses the baseline conditions of Fig. 7 to facilitate comparison, this choice of entering flows fails to take cognizance of the fact that Na⁺ excretion is set by dietary Na⁺ intake, so that a more relevant comparison for FHH simulation would be to match Na⁺ excretion to that of the baseline case. This was achieved by increasing entering DCT NaCl concentration by 10 mM (entering Na⁺ = 75 mM), and for this condition Na⁺ excretion increases to 2.9 μmol/min and K⁺ excretion is 0.43 μmol/min, ∼40% that of baseline. When the entering solute contains an additional 10 mM Na₂SO₄ (entering Na⁺ = 75 mM, with 20 mM Cl⁻ replaced by SO₄²⁻), the K⁺ excretion increases to 82% of baseline. This simulation appears to capture the ability to use sulfate infusion to rescue renal K⁺ excretion in patients with FHH. With reference to Fig. 10, the locus of this restored K⁺ excretion appears to be largely the CNT, although collecting duct K⁺ reabsorption is blunted in each segment. For the simulations of Figs. 7–10, Table 5 displays luminal conditions along the CNT and the K⁺ fluxes across tight junctions and principal cell luminal membranes. With luminal SO₄, there is a sharp drop in luminal Cl⁻, so that a Cl⁻ diffusion potential hyperpolarizes the lumen and enhances K⁺ secretion. A key observation is that under all conditions, the transcellular K⁺ flux is at least an order of magnitude greater than the paracellular flux, and that along most of the CNT the paracellular K⁺ flux is reabsorptive. In particular, this calculation suggests sulfate rescue of K⁺ excretion relies upon an intact principal cell pathway for K⁺ secretion.

Fig. 9.

Impact of increased DCT NaCl reabsorption with diminished principal cell transport on distal flows. Calculations and display are as in Fig. 7. For each curve, DCT uses the aII parameter set (doubling of NCC and 50% increases in Na-K-ATPase and KCC); principal cell parameters are low aldosterone (−aldo), in which the fractional transporter density, ρ_PC, for ENaC and Na-K-ATPase is 0.5, for all principal cells of the CNT, CCD, and OMCD. For the curves labeled aII/−aldo, perfusion and interstitial conditions are as in Table 1; for the curves labeled +NaCl, luminal Na⁺ and Cl⁻ have been increased to 75.0 and 56.1 mM; for the curves labeled +Na₂SO₄, luminal Na⁺ is 75.0 mM, Cl⁻ is 46.1 mM, and a 10.0 mM impermeant has been added to the entering luminal solution.

Fig. 10.

Impact of increased DCT NaCl reabsorption with diminished principal cell transport on distal flows. For the calculations of Fig. 9, segmental modifications to Na⁺ and K⁺ flows are displayed, as in Fig. 8. Open bars correspond to aII/−aldo parameters for the entering solution as in Table 1; middle bars (labeled “\”) are obtained from calculations with increased entering NaCl; and right bars (labeled “/”) are obtained from calculations with entering Na₂SO₄. Numerical data for the bars appear in Table 4.

Table 5.

CNT PD, concentrations, and K⁺ fluxes in antinatriuresis and diuresis

Distance, cm	VM, mV	CM(Na), mM	CM(K), mM	CM(Cl), mM	CM(SO4), mM	FIM(K), nmol · s−1cm · −2	FEM (K), nmol · s−1cm · −2
Base/Base
0.0	−27.6	43.3	4.1	41.2	0.0	−2.964	−0.053
0.1	−37.7	52.2	21.9	64.0	0.0	−1.557	0.015
0.2	−39.6	53.7	30.3	72.0	0.0	−0.910	0.046
aII/Base
0.0	−23.8	25.8	3.7	22.6	0.0	−2.607	−0.051
0.1	−37.5	34.1	23.4	44.5	0.0	−1.195	0.022
0.2	−40.3	36.3	34.0	54.2	0.0	−0.462	0.059
aII/+Aldo
0.0	−39.3	25.8	3.7	22.6	0.0	−4.446	−0.068
0.1	−46.8	18.6	35.2	42.3	0.0	−1.540	0.036
0.2	−47.2	14.2	51.3	51.2	0.0	−0.075	0.094
aII/−Aldo
0.0	−12.3	25.8	3.7	22.6	0.0	−1.505	−0.034
0.1	−25.9	46.1	15.0	46.8	0.0	−0.673	0.015
0.2	−28.3	56.2	19.9	57.9	0.0	−0.267	0.037
aII/−Aldo/+NaCl (10 mM)
0.0	−14.0	34.8	3.7	32.3	0.0	−1.646	−0.037
0.1	−25.4	55.7	14.1	57.7	0.0	−0.785	0.011
0.2	−27.2	64.7	18.3	68.0	0.0	−0.399	0.031
aII/−Aldo/+Na2SO4 (10 mM)
0.0	−17.1	36.7	3.9	12.4	11.2	−1.776	−0.040
0.1	−31.4	62.9	16.5	25.0	22.0	−0.979	0.006
0.2	−34.6	75.2	22.4	29.7	27.7	−0.610	0.025

V_M, transepithelial potential difference (PD); C_M, lumen concentration; F_IM(K), principal cell luminal K⁺ flux; F_EM(K), tight junction K⁺ flux.

Control of Na⁺ and K⁺ excretion requires two signals.

Figure 11, A–C, uses the full distal nephron model to undertake a more systematic examination of the interplay of DCT and principal cell transport in determining urinary Na⁺ and K⁺ excretion. For this calculation, we identify two scaling factors, ρ_DCT and ρ_PC, which will modify the parameter sets: in the DCT parameter set, NCC density is multiplied by ρ_DCT and both the DCT Na-K-ATPase and KCC densities are multiplied by 0.5·ρ_DCT; in CNT, CCD, and OMCD parameter sets, ENaC and Na-K-ATPase densities are multiplied by ρ_PC. Thus for ρ_DCT = 1.0 and ρ_PC = 1.0, we have the baseline parameters, and for the calculations of Fig. 11, these scaling factors are varied over the ranges, 0.5 ≤ ρ_DCT ≤ 2.5 and 0.5 ≤ ρ_PC ≤ 3.0. Using steps of 0.1 for both of the factors, this defines a grid of 21 × 26 = 546 solutions of the distal nephron model. In Fig. 11A, renal Na⁺ excretion for each of these calculations is displayed, with ρ_PC along the abcissa and ρ_DCT along the ordinate. Color shade indicates the intensity of Na⁺ excretion: high excretion signified by bright red in the bottom left, where both DCT and principal cell Na⁺ reabsorption are low, and low excretion signified by purple in the top right, where both DCT and principal cell Na⁺ reabsorption are high. The figure contains level curves, which identify the absolute rates of Na⁺ excretion, varying from ∼5.0 to 0.2 μmol/min over the space of these parameter choices. Of note, in the violet region in the vicinity of baseline (Na⁺ excretion ∼2.5 μmol/min), the slope of the level curves is close to −1.0, indicating a balanced dependence of Na⁺ excretion on DCT and principal cell Na⁺ transport. For these same calculations, Fig. 11B displays renal K⁺ excretion: high excretion signified by bright green in the bottom right, where DCT Na⁺ reabsorption is low and principal cell transport is high, and low excretion signified by deep blue in the top left, where DCT Na⁺ reabsorption is high and principal cell transport is low. The level curves identify the absolute rates of K⁺ excretion, varying from ∼0.3 to 2.1 μmol/min. A notable feature of each of these curves is that for any level of DCT Na⁺ reabsorption, K⁺ excretion plateaus as a function of principal cell transport. In physiological terms, K⁺ excretion is bounded by Na⁺ delivery, and aldosterone can do just so much. In Fig. 11C, the level curves for Na⁺ and K⁺ excretion have been overlaid and form a more or less orthogonal grid over the space of model results. What this implies is that if one started with dietary Na⁺ and K⁺ intake, and wanted to select model parameters which would yield those urinary excretion rates, this graph provides such a lookup function. From a conceptual point of view, the model identifies two distinct parameters to achieve the physiological objective, rather than a single rheostat to dial one excretory rate at the expense of the other.

Fig. 11.

Renal sodium and potassium excretion as a function of DCT and principal cell transporter density. Calculations use the distal nephron model with perfusion and interstitial composition of Table 1. Parameters of DCT and principal cells are modified according to 2 scaling factors, ρ_DCT and ρ_PC: In the DCT parameter set, NCC density is multiplied by ρ_DCT and both Na-K-ATPase and KCC densities are multiplied by 0.5·ρ_DCT; in the CNT, CCD, and OMCD, ENaC and Na-K-ATPase densities are multiplied by ρ_PC. These scaling factors are varied over the ranges, 0.5 ≤ ρ_DCT ≤ 2.5 and 0.5 ≤ ρ_PC ≤ 3.0 and appear as abcissa and ordinate for each of the figures. A: renal Na⁺ excretion is displayed by color shade, with high to low excretion signified by red to blue. Level curves identify absolute rates of Na⁺ excretion. B: renal K⁺ excretion, with high to low excretion signified by green to blue. Level curves identify the absolute rates of K⁺ excretion. C: level curves for Na⁺ and K⁺ excretion have been overlaid. The grid permits one to specify renal Na⁺ and K⁺ excretion, and then look to abcissa and ordinate for the model parameter set, which yields both excretion rates.

DISCUSSION

K⁺ excretion is contingent upon distal nephron Na⁺ reabsorption. During Na⁺ surfeit this is achieved easily, but with antinatriuresis K⁺ excretion is more difficult. It was a classic observation that renal K⁺ excretion decreased on a low-Na⁺ diet, and this prompted the distal micropuncture study by Malnic and coworkers (23) in Na⁺-deprived rats to understand how the hypovolemic state altered the capacity for K⁺ secretion. Their findings were that with a low-Na⁺ diet, there was a relatively minor decline in Na⁺ delivery to the distal tubule (from 8–10% of filtered load to 5–7% of filtered load), nearly constant fractional distal tubule Na⁺ reabsorption, and then a dramatic clearance of urinary Na⁺ within the inaccessible collecting duct. Compared with Na⁺-replete animals (22), K⁺ secretion was diminished in distal tubule, and collecting duct K⁺ reabsorption was enhanced. The observation emphasized by the authors was that with maneuvers that enhanced distal tubule Na⁺ delivery (e.g., mannitol or sulfate infusion), the intrinsic K⁺ secretory capacity of the distal tubule was not diminished. Ellison et al. (8) subsequently examined Na⁺-deprived rats using micropuncture and microperfusion of early distal tubule, confirming that distal Na⁺ delivery was little changed with the low-Na⁺ diet, and adding the important observation that thiazide-sensitive Cl⁻ reabsorption by the DCT approximately doubled. Subsequent work has identified DCT NCC as an angiotensin II target: DCT NaCl reabsorption is sensitive to angiotensin II (48), angiotensin II drives NCC to the luminal membrane of the DCT (36), and angiotensin II is capable of activating NCC transport activity (35, 46). Thus a secure picture has developed, in which DCT NaCl reabsorption is activated by volume depletion, but the critical question has been revisited as to the mechanism by which volume depletion compromises renal K⁺ excretion. Reconsideration of the interplay of the DCT and CNT has been prompted by interest in the kinase network underlying FHH. While there is no doubt that the FHH phenotype is contingent upon increased DCT NaCl reabsorption (and is remediated by thiazides), the hyperkalemia of this disorder has focused attention on the action of these kinases within CNT principal cells, and whether there may be a specific switch that limits CNT K⁺ secretion during hypovolemia (19, 20).

The distal nephron model of this work contributes to this discussion with a number of observations on the interplay of antinatriuresis and K⁺ excretion. The first, and perhaps the most secure prediction, is that enhanced DCT NaCl reabsorption cannot be mediated by increased NCC density alone. In the model, increased NaCl transport is achieved by coordinated increases in NCC with peritubular Na-K-ATPase and KCC, and both appear to be necessary. Of note, an increase in DCT proton secretion in response to angiotensin II has been observed, suggesting that angiotensin may also increase luminal membrane NHE2 activity (48). The model DCT does show increased proton secretion as cytosolic Na⁺ decreases, but a more substantial increase would seem to require augmentation of a complementary peritubular base exit pathway; this has not been explored here. Schultz (41) articulated the principle of coordinated luminal and peritubular transporter regulation as a means of preserving the integrity of cell volume and composition, i.e., homeostasis. Early observations obtained in intestinal epithelia focused attention on upregulation of peritubular K⁺ channels in response to increases in luminal entry of glucose and amino acids (16, 17), and these were ultimately confirmed in mammalian proximal tubule (2, 3). With respect to the distal nephron, angiotensin II has been found to stimulate peritubular K⁺ channels in principal cells from rat CCD (50). In a mathematical model of the proximal tubule, it became clear that modulation of peritubular K⁺ permeability would not suffice to represent the augmented fluxes that were actually measured, and that activation of other exit pathways, either KCl or Na⁺-3HCO₃⁻ cotransport, were required (51). The important model conclusion, as distinct from Schultz's focus, is that beyond cellular homeostasis, the model was incapable of achieving fluxes of the proper magnitude when transporter density changes were restricted to the luminal membrane. This conclusion was echoed in simulations of flow-dependent transport in the proximal tubule (59). With the exception of K⁺ channels, there has been little experimental exploration of peritubular transporters during increases in transepithelial solute flux. Of note, Duan et al. (7) did observe translocation of Na-K-ATPase to the basolateral membrane when cultured proximal tubule cells were subjected to apical shear stress. With regard to model predictions for the DCT, WNK kinases have been identified as negative regulators of KCC (5. 15); however, activation of KCC and the Na-K-ATPase during stimulated NaCl transport by the DCT remains to be examined.

A second observation from this model is that for the distal tubule to maintain constant K⁺ delivery to the collecting duct, increased CNT K⁺ secretion must accompany increased DCT Na⁺ reabsorption. In the calculations of Figs. 4 and 5, the question was put precisely: in the face of diminished Na⁺ entry to the CNT, to what extent does CNT Na⁺ transport machinery need to be scaled up to hold exiting K⁺ flow constant. The finding was that at entering concentrations <40 mM, there should be perceptible increases in ENaC and Na-K-ATPase activity, increasing about twofold over baseline as entering Na⁺ fell below 25 mM. From this perspective, the action of aldosterone is not paradoxical, but compensatory for the decreased Na⁺ delivery, or put simply, any signal that increases DCT NaCl transport should also enhance CNT K⁺ secretion. Experimental observations of sodium deprivation in the rat have documented that within 15 h, urine Na⁺ falls to near zero and urine K⁺ more than doubles above control, and this is in conjunction with an increase in plasma aldosterone and a dramatic increase in CCD principal cell ENaC activity (11). In view of the greater mass of CNT principal cells and their responsiveness to aldosterone, it is likely that overall renal solute excretion reflects CNT events that parallel the CCD findings (13). Since the low-Na⁺ diet is also likely to have increased fractional collecting duct K⁺ reabsorption (23), it is probable that tubular K⁺ secretion actually increased by more than the increase in excretion. In rats chronically infused with a thiazide and subjected to similar short-term Na⁺ deprivation, there was no compromise of immediate renal Na⁺ conservation (12). This observation suggests that aldosterone is an early responder in the process of Na⁺ conservation, providing an opportunity for a period of excess K⁺ secretion. Recently, Frindt et al. (11) found that while Na⁺ deprivation with normal K⁺ intake provoked upregulation of ENaC subunits, this response was eliminated when aldosterone secretion was suppressed by simultaneous K⁺ deprivation. In response to chronic Na⁺ and K⁺ deprivation, NCC expression was increased. The message from their work is that increased aldosterone is not a prerequisite for overall renal Na⁺ conservation, and likely not for DCT NaCl conservation.

It is important to acknowledge that in the model calculations of this work, variability in principal cell K⁺ channel density has not been featured. Early electrophysiological study of CCD principal cells by Sansom and O'Neil (37, 38) documented that mineralocorticoid increased the luminal Na⁺ conductance, the current through the Na-K-ATPase, and the K⁺ conductances of both luminal and peritubular cell membranes. However, their observations included a time component to these changes, namely, that the increase in luminal Na⁺ conductance was apparent within a day, while the K⁺ conductance was still unchanged; only after several days did luminal K⁺ conductance also increase. The impact of K⁺ conductances of luminal and peritubular membranes of principal cells has been examined in CCD and CNT models (53, 56). In qualitative terms, when luminal K⁺ concentration is low, increasing luminal membrane K⁺ permeability enhances both Na⁺ reabsorption and K⁺ secretion; when luminal K⁺ concentration is high, the impact of ROMK on transport is diminished. Decreasing peritubular K⁺ permeability enhances K⁺ secretion and can dramatically increase the limiting K⁺ concentration against which secretion can be sustained (53). In the CNT model, increasing luminal membrane ENaC fivefold over baseline increased K⁺ secretion by about a factor of 3; superimposing a fivefold increase in ROMK augmented K⁺ secretion by about a third (Fig. 9 in Ref. 56). In those calculations, the entering Na⁺ and K⁺ concentrations were 65 and 2 mM, which would be expected to highlight the ROMK effect. In the current work, entering CNT Na⁺ is close to 45 mM at baseline, and the impact on CNT K⁺ secretion with doubling of ROMK was on the order of 10%. This should not be taken to discount the significance of chronic dietary K⁺ in modulating ROMK expression (47), but it is outside the focus of the model calculations in this work. Of note, comparing FHH mice with control, there seemed to be little difference of ROMK expression on low- or high-K⁺ diets (20). Another aspect of principal cell physiology that has not been addressed in this work is a cell volume increase that may result from increasing ENaC and Na-K-ATPase. Model predictions are that this volume increase may be blunted by increasing ROMK (unpublished observations and see also Fig. 10 in Ref. 52). It must be acknowledged that an assumption in the calculations of Figs. 9 and 10 is that the low aldosterone levels measured in FHH are indicative of diminished aldosterone effect on principal cells. In oocytes, the defective WNK4 of FHH failed to inhibit ENaC and actually increased amiloride-sensitive Na⁺ reabsorption in colon (34). If that were true in the kidney, then the premise of those calculations (i.e., low ρ_PC) would need to be abandoned; the models would need to be reconfigured to accommodate a much greater role for K⁺ channels in regulation of K⁺ secretion; and the mechanism by which sulfate infusion rescues FHH K⁺ excretion would become obscure.

A final model observation is that despite the capacity for CNT K⁺ secretion to compensate for diminished Na⁺ delivery and actually increase CNT K⁺ secretion above baseline, there is enhanced K⁺ reabsorption within the OMCD and IMCD due to sluggish flow (Figs. 7 and 8). This model prediction parallels the finding of Malnic et al. (23), in which chronically Na⁺-deprived rats excreted only ∼20% of end-distal K⁺; furthermore, mineralocorticoid supplementation to these rats did not impact the fractional K⁺ reabsorption within the collecting duct. Comparable observations were made by Peterson and Wright (30), who found that fractional reabsorption of late distal K⁺ within the collecting duct was 32 and 62% in control and Na⁺-deficient rats, respectively. The flow-dependent character of CD K⁺ reabsorption was apparent in the first model of the collecting duct, especially when the decrease in flow was due to a decrease in Na⁺ delivery (54). The mechanism of the increase in collecting duct K⁺ reabsorption was an increase in luminal K⁺ concentration, driven by water abstraction, to a level that promoted reabsorptive flux, and which was enhanced by increased transit time. In view of this aspect of collecting duct physiology, other causes of prolonged transit time should also be expected to compromise K⁺ excretion. In this regard, the action of vasopressin in the CCD to increase Na⁺ reabsorption (33) can be viewed as a feed-forward signal to augment tubule K⁺ secretion, concurrent with its action to reduce collecting duct fluid flow. In the case of FHH, there is no reason to believe that collecting duct flow is compromised: Na⁺ balance is normal, the patients are hypertensive, and renin and aldosterone levels are relatively depressed (32). In this case, the model suggests that even when DCT Na⁺ delivery is increased to compensate for the increase in DCT NaCl transport, so that CNT and collecting duct Na⁺ entry are normal, a relative aldosterone deficit is apparent, and renal K⁺ excretion is compromised. In the model nephron, impaired CNT K⁺ secretion can be enhanced, and CD K⁺ reabsorption can be blunted by sulfate infusion, and this is concordant with the corrective effect of sulfate infusion on renal K⁺ excretion in FHH.

From a systems perspective, the three components of the distal nephron, the DCT, CNT, and collecting duct, are responsible for Na⁺ reabsorption and K⁺ secretion over a wide range, while entering Na⁺ and K⁺ are held in relatively narrow bounds by tubuloglomerular feedback. The job of Na⁺ reabsorption is quantitatively an order of magnitude greater than either K⁺ secretion or proton secretion, so that it always dominates distal nephron transport. What has been captured by the model calculations is that increasing DCT NaCl reabsorption both blunts CNT K⁺ secretion and enhances collecting duct K⁺ reabsorption, so that overall renal K⁺ excretion is compromised. More formally, Na⁺ and K⁺ excretion, the two model outputs, require two independent control signals, but because the solute fluxes influence each other (Fig. 11), adjustments in one excretory rate will of necessity require adjustments in both signals. From a control perspective, any signal that increases DCT NaCl reabsorption should immediately increase CNT K⁺ secretion, and one can see such anticipatory regulation with the aldosterone response to volume depletion. Conversely, when an isolated K⁺ load increases aldosterone (and principal cell transport), one expects a concomitant decrease in DCT transport, and that is what is suggested by the observation of the K⁺-dependent decrease in NCC (45). What the FHH phenotype has provided is a configuration in which DCT NaCl transport is enhanced and the aldosterone response is blunted. The model calculations here suggest that this in itself compromises renal K⁺ excretion, but cannot exclude the possibility that other FHH defects of principal cell transporters further compromise CNT function.

GRANTS

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

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the authors.

AUTHOR CONTRIBUTIONS

Author contributions: A.M.W. provided conception and design of research; A.M.W. performed experiments; A.M.W. analyzed data; A.M.W. interpreted results of experiments; A.M.W. prepared figures; A.M.W. drafted manuscript; A.M.W. edited and revised manuscript; A.M.W. approved final version of manuscript.