Regulation of glomerulotubular balance. IV. Implication of aquaporin 1 in flow-dependent proximal tubule transport and cell volume

Abstract

The water channel aquaporin-1 (AQP1) is the principal water pathway for isotonic water reabsorption in the kidney proximal tubule (PT). We investigated flow-mediated fluid (J_v) and ${\text{HCO}}_3^{-}$ ($J_{{\text{HCO}}_3}$) reabsorption in PTs of the mouse kidney by microperfusion in wild-type (WT) and AQP1 knockout (KO) mice. Experiments were simulated in an adaptation of a mathematical model of the rat PT. An increase in perfusion rate from 5 to 20 nL/min increased J_v and $J_{{\text{HCO}}_3}$ in PTs of WT mice. AQP1 KO mice significantly decreased J_v at low and high flow rates compared with control. In contrast, $J_{{\text{HCO}}_3}$ was not reduced at either low or high flow rates. Cell volume showed no significant difference between WT and AQP1 KO mice. Renal clearance experiments showed significantly higher urine flow in AQP1 KO mice, but there was no significant difference in either Na⁺ and K⁺ or ${\text{HCO}}_3^{-}$ excretion. Acid-base parameters of blood pH, Pco₂, ${\text{HCO}}_3^{-}$, and urine pH were the same in both WT and KO mice. In model calculations, tubules whose tight junction (TJ) water permeability (P_f) was that assigned to the rat TJ, showed no difference in J_v between WT and KO, whereas TJ P_f set to 25% of the rat predicted J_v concordant with our observations from AQP1 KO. These results affirm the dominance of AQP1 in mediating isotonic water reabsorption by the mouse PT and demonstrate that flow-stimulated ${\text{HCO}}_3^{-}$ reabsorption is intact and independent of AQP1. With reference to the model, the findings also suggest that TJ water flux in the PT is less prominent in the mouse than in the rat kidney.

NEW & NOTEWORTHY We found an absence of flow-dependent modulation of fluid absorption but no effect on either proximal tubule (PT) ${\text{HCO}}_3^{-}$ absorption or acid-base parameters in the aquaporin 1 (AQP1) knockout mouse. We affirmed the dominance of the water channel AQP1 in mediating isotonic water reabsorption by the mouse PT and demonstrated that flow-stimulated ${\text{HCO}}_3^{-}$ reabsorption is independent of AQP1. With reference to the model, the findings also suggest that tight junctional water flux in the PT is less prominent in the mouse than rat kidney.

INTRODUCTION

Glomerulotubular balance refers to the proportional variation of filtered load and fluid and electrolyte reabsorption by proximal tubules (PTs); it derives in large part from flow-dependent modulation of epithelial cell transport (1–3). Specifically, increased PT flow stimulated ${\text{HCO}}_3^{-}$ absorption in the microperfused rat PT in vivo (4–6), and we have demonstrated flow-mediated Na⁺ and ${\text{HCO}}_3^{-}$ absorption in isolated mouse PTs (7). We have also demonstrated constancy of tight junction (TJ) ${\text{HCO}}_3^{-}$ permeability during flow-activated Na⁺ and bicarbonate transport, suggesting that perhaps TJ properties may not be modulated by luminal fluid flow (8). Using microperfusion, we examined the functional role of Na⁺/H⁺ exchanger (NHE) isoforms along the nephron and demonstrated that NHE3 is the predominant isoform for apical membrane Na⁺/H⁺ exchange in the PT (9). Na⁺ and ${\text{HCO}}_3^{-}$ absorption were reduced by 60% in NHE3 knockout (KO) mice compared with wild-type (WT) animals, and in its absence, neither NHE2 nor any other ethylisopropylamiloride-sensitive NHE isoform contributes to mediating PT ${\text{HCO}}_3^{-}$ absorption (10). However, a significant component of ${\text{HCO}}_3^{-}$ absorption is mediated by bafilomycin-sensitive H⁺-ATPase (10). With respect to flow-dependent transport, inhibition of NHE3 reduced flow-mediated Na⁺ absorption by 60%, and the same reduction was also observed in the NHE3 KO mouse (8). Flow-mediated ${\text{HCO}}_3^{-}$ absorption was completely abolished by inhibition of both NHE3 and H⁺-ATPase (8). In studies of flow-dependent transport, preservation of PT epithelial cell volume has been a consistent finding (8, 11), suggesting that both luminal and peritubular membrane transporters are flow modulated. In cultured mouse PT cells, fluid shear stress increases the amount of protein expression and translocation of apical NHE3 and V-ATPase from the intracellular compartment to the apical plasma membrane and Na⁺-K⁺-ATPase to the basolateral membrane (12). Disruption of actin by cytochalasin D blocks the fluid shear stress-induced translocation in NHE3 and Na⁺-K⁺-ATPase, but the fluid shear stress-induced H⁺-ATPase redistribution and expression are largely inhibited by colchicine, an agent that blocks microtubule polymerization (12). These findings identify the actin cytoskeleton as playing a critical role in fluid shear stress-induced NHE3 and Na⁺-K⁺-ATPase trafficking and the microtubule network in fluid shear stress-induced modulation of H⁺-ATPase (12).

The aquaporin (AQP)1 water channel is strongly expressed in both apical and basolateral membranes of kidney PTs as well as in the thin descending limb of Henle and endothelial cells of the descending vasa recta (13–18). It has been demonstrated that AQP1-KO mice exhibited a threefold increase in urine flow with reduced urine osmolality and 50% reduction of fluid absorption and 78% decrease in PT water permeability (19, 20). These data indicate that in the mouse PT, the high water permeability is primarily transcellular, which is mediated by AQP1 water channels, and required for near isosmolar fluid absorption in PTs (20). It has also been reported that increasing luminal flow stimulates AQP1 trafficking to the PT luminal membrane, suggesting that AQP1 plays a role in glomerulotubular balance (21). AQPs function as gas channels that increase CO₂ permeability and regulate cell pH (22). However, a role for AQP1 to facilitate PT ${\text{HCO}}_3^{-}$ absorption has not been demonstrated. To understand the significance of AQP1 in flow-dependent proximal absorption, we measured flow-mediated fluid and ${\text{HCO}}_3^{-}$ absorption by PT microperfusion in WT and AQP1 KO mice.

METHODS

Animals

All experiments from animal work were conducted according to an Institutional Animal Care and Use Committee-approved protocol at Yale School of Medicine. AQP1 KO mice were obtained from Dr. Alan Verkman at the University of California (San Francisco, CA; 19), and WT mice (C57BL) were purchased from the Jackson Lab and housed at the Yale University Animal Care facility in New Haven, CT. All mice were maintained on a normal diet and tap water until the day of the experiment and were anesthetized with an intraperitoneal injection (100–150 mg/kg body wt) of Inactin (thiobutabarbital sodium salt hydrate, Sigma, St. Louis, MO) at the time of the experiment. Male mice were used in the study, and sex differences were not studied. Mice at ages of 5–8 wk were used for the microperfusion experiments and 12–14 wk for the renal clearance experiments. Sex and ages were carefully matched between WT and KO mice.

Renal Clearance and Acid-Base Parameter Measurements

Male mice at the ages of 12–14 wk from the WT and AQP1 KO groups were used for the renal clearance experiments. The renal clearance protocol was carefully followed as in our previously established methods (23, 24). Briefly, mice were anesthetized and then were placed on a thermostatically controlled surgical table to maintain body temperature at 37°C for surgical preparation. Surgical procedures were performed including a tracheotomy and carotid artery and jugular vein cannulation for blood collection and intravenous infusion. The bladder was catheterized for timed urine collections. After surgical preparation, 0.05 mL of isotonic saline was administered by intravenous infusion to replace surgical fluid loss. Subsequently, a priming dose of 0.1 mg FITC-inulin (Sigma) in 0.05 mL of isotonic saline was given, and a maintenance dose of isotonic solution containing 2 mg/mL of FITC-inulin was infused at a rate of 0.41 mL/h throughout the experiment. After a 45-min equilibration period, blood and urine collections were made every 30 min. Two 30-min collections were made, and the data were summarized as the mean of these two collection periods. Urine and plasma Na⁺ and K⁺ concentrations were measured using a flame photometer (type 480, Corning Medical and Scientific, Corning, NY). These data are presented in Table 1. FITC-inulin concentrations were measured using a 96-plate reader. Urine volume (UV), glomerular filtration rate (GFR), absolute Na⁺ and K⁺ (E_Na and E_K), and fractional Na⁺ and K⁺ (FE_Na and FE_K) were measured and calculated by standard methods (23). Urine pH was measured by a micro pH meter (Fisher Scientific), and urinary ${\text{HCO}}_3^{-}$ concentration was measured by a nanoflow spectrometer [World Precision Instruments (WPI)]. Blood Na⁺, K⁺, pH, ${\text{HCO}}_3^{-}$, and Pco₂ were measured by an iSTAT blood analyzer (Abbott), and blood was freshly collected by a retroorbital bleeding (25). These data are shown in Table 2.

Table 1.

Renal clearance measurements of UV, GFR, E_Na, E_K, FE_Na, and FE_K in WT and AQP1 KO mice

	n	UV, µL/min	GFR, mL/min/100 g Body Wt	ENa, µeq/L/100 g Body Wt	EK, µeq/L/100 g Body Wt	FENa, %	FEK, %
WT	8	2.42 ± 1.1	0.76 ± 0.17	0.56 ± 0.31	1.05 ± 0.34	0.54 ± 0.09	32.6 ± 5.4
KO	10	4.15 ± 1.2*	0.71 ± 0.19	0.55 ± 0.44	0.81 ± 0.38	0.48 ± 0.38	28.4 ± 10.4

Data are presented as means ± SD; n, number of animals. AQP1, aquaporin 1; E_Na and E_K, absolute Na⁺ and K⁺ excretion; FE_Na and FE_K, fractional Na⁺ and K⁺ excretion; GFR, glomerular filtration rate; UV, urine volume. *Significant difference between wild-type (WT) and knockout (KO) mice (P < 0.01).

Table 2.

Plasma electrolytes and acid-base parameters in WT and AQP1 KO mice

	n	Body Weight, g	BNa, meq/L	BK, meq/L	BpH	Pco2, %	${\text{HCO}}_3^{-}$, meq/L	UpH	Hematocrit, %
WT	8	34.4 ± 1.7	145.5 ± 1.1	4.3 ± 0.39	7.26 ± 0.03	58.2 ± 7.1	25.1 ± 1.7	6.0 ± 0.06	43.9 ± 0.8
KO	8	31.5 ± 6.8	145.4 ± 1.4	4.7 ± 0.45	7.29 ± 0.03	51.4 ± 5.5	26.5 ± 1.9	5.5 ± 0.34	43.6 ± 1.4

Data are presented as means ± SD; n, number of animals. AQP1, aquaporin 1; B_K, blood K⁺; B_Na, blood Na⁺; B_pH, blood pH; ${\text{HCO}}_3^{-}$, blood bicarbonate; U_pH, urine pH. There were no significant differences between wild-type (WT) and knockout (KO) mice.

Microperfusion of PTs

Male mice at the ages of 5–8 wk from the WT and AQP1 KO groups were deeply anesthetized, and the kidneys were then removed from the mouse. The kidney was sectioned into ∼1-mm thick slices, and slices were transferred to 4°C HEPES-buffered Ringer solution at a pH of 7.4 for tubule dissections. Proximal convoluted tubules (S2 segments) were isolated by microdissection, transferred to the stage of an inverted microscope, and then cannulated using a series of concentric glass capillaries. The tubules were perfused with an ultrafiltrate-like solution as previously described (8). The bath solution contained similar electrolytes as the luminal solution, with added 3 g/dL of albumin. The perfusate and bath solutions were bubbled with 95% O₂-5% CO₂, the pH was adjusted to 7.4, and the osmolalities were adjusted to 300 mosmol/kgH₂O in both solutions. All tubules were perfused at 37°C in a 1.2-mL temperature-controlled bath at a flow rate of either 5 or 20 nL/min, followed by three sample collections for measuring ³H-inulin and ${\text{HCO}}_3^{-}$ concentrations (8). The order of low or high flow rate was used randomly. Bath fluid was continuously changed at a rate of 0.5 mL/min to maintain the constancy of pH and bath osmolality. Extensively dialyzed [³H]methoxy-inulin was added to the perfusate at a concentration of 30 µCi/mL as a volume marker. A constant-bore glass capillary was used to obtain precise aliquots of initial perfusates and collection of samples to be analyzed for [³H]methoxy-inulin by liquid scintillation spectroscopy. The total CO₂ concentration of both initial and collected fluids was measured by the nanoflow spectrometer (WPI). The rates of net fluid (J_v) and sorption ($J_{{\text{HCO}}_3}$) were calculated as previously described and expressed per millimeter of tubular length (8).

Cell volume is identified with epithelial volume and was calculated as follows: [π × (OD/2)² − π × (ID/2)²], where OD is tubule outer diameter and ID is tubular inner diameter. In this estimate, it is assumed that lateral intercellular space volume is a negligible fraction of epithelial volume. In this regard, Tisher and Kokko (26) determined that in the rabbit PT, the spacing between membranes of opposing cells is ∼0.03 µm at baseline and grows or shrinks 10% with changes in transport. Thus, even with the pleated lateral membrane of the PT, whose area is expanded 20-fold over a simple cylinder (27), interspace volume is estimated to be <5% of epithelial volume.

Mathematical Model of the PT

The mathematical model of the rat proximal convoluted tubule (PCT) used for the simulations of this work is that presented by Weinstein et al. (28). The novel feature of that model was the representation of the effect of luminal flow on reabsorptive fluxes, specifically, fluid drag on PCT brush border-modulated transporter density on both luminal and peritubular cell membranes. The luminal membrane drag (D_M) is proportional to mean luminal fluid velocity and is provided by the following formula:

$$D_{\text{M}}=\frac{8\text{η}{F}_{\text{vM}}}{R_{\text{M}}^2}=\frac{8\text{πη}{F}_{\text{vM}}}{A_{\text{M}}}=8\text{πη}{v}_{\text{M}}$$ (1)

in which F_vM is tubule fluid flow, R_M is tubule radius, η is fluid viscosity, A_M is the lumen cross-sectional area, and v_M is mean fluid velocity. The drag relates to local shear stress (τ_M) according to the following formula:

$${\tau }_{\text{M}}=\frac{D_{\text{M}}}{2\text{π}{R}_{\text{M}}}$$ (2)

To translate this into microvillous torque, the drag is multiplied by a factor proportional to brush border height [Eq. 37 in Weinstein et al. (28)]. Tubule compliance provides that its radius varies according to transmural pressure, according to an elasticity coefficient (ν_M). Although the original formula for tubule compliance was linear [Eq. 38 in Weinstein et al. (28)], it had been updated [Eq. 4 in Weinstein (29)] to a hyperbolic tangent to reflect limits of tubule stretch:

$$R_{\text{M}}=R_{\text{M}0}\{\text{1}.0+\text{ tanh}[{\mathrm{\nu }}_{\text{M}}({\text{P}}_{\text{M}}-{\text{P}}_{\text{S}})]\}$$ (3)

where R_M is the tubule radius, R_M0 is a reference radius, ν_M is tubule compliance, and P_M and P_S are luminal and peritubular hydrostatic pressure, respectively. For small transtubular pressure differences compliance is approximately linear, whereas at larger pressures distensibility is reduced. Torque-dependent transporter densities were specified in both luminal and peritubular cell membranes since coordinate changes in entry and exit flux are necessary to capture the constancy of PT cell volume during changes in luminal flow. Notably, the model included flow-dependent modulation of AQP1 density in both luminal and peritubular cell membranes, a feature that anticipated the findings of Pohl et al. (21). For each cell membrane channel, cotransporter, or pump, its membrane density (H) depends on microvillous torque (T_M) according to the following formula:

$$H=H_0\left[1.0+{\mathrm{\nu }}_{\text{T}}\left(\frac{T_{\text{M}}}{T_{\text{M}0}}-1.0\right)\right]$$ (4)

where H₀ is a reference density, ν_T is the sensitivity to microvillous torque, and T_M0 is torque at the reference velocity and reference radius. Of note, ν_T and T_M0 are uniform for the entire cell and not specified for each transporter; model TJ properties are not modulated by luminal flow.

The Fortran code for the PT model used in these calculations is available on Github at https://github.com/amweins/kidney-models-amw/tree/master/tubules/pctub/torque.

Statistics

Data are presented as means ± SD. A Student’s t test was used to compare control and experimental groups. An ANOVA test was used for comparison of several experimental groups with a control group followed by Dunnett’s test. The difference between the mean values of an experimental group and a control group was considered significant if P < 0.05.

RESULTS

Impact of AQP1 on Urinary Na⁺ and K⁺ Excretion and Acid-Base Parameters

The general phenotype of body weight, plasma Na⁺, K⁺, and ${\text{HCO}}_3^{-}$, blood pH, urine pH, and hematocrit in WT control and AQP1 KO mice are shown in Table 2 and showed no significant difference between WT and AQP 1KO mice. Blood samples were collected by retroorbital bleeding and immediately measured by an iSTAT blood analyzer (Abbott). As shown in Table 2, P_Na was 145.5 and 145.4 meq/L, P_K was 4.3 and 4.7 meq/L, and $P_{{\text{HCO}}_3}$ was 25.1 and 26.5 meq/L in WT control and AQP1 KO mice, respectively (n = 8, P > 0.05; Table 2). Blood pH was 7.26 and 7.29, urine pH was 6.0 and 5.5 (P > 0.05), and hematocrit was 43.9% and 43.6% in WT control and AQP1 KO mice, respectively.

Overall kidney function, including UV, GFR, E_Na, E_K, FE_Na, and FE_K, by renal clearance in WT and AQP1 KO mice is shown in Table 1 and Fig. 1. Mice were under anesthesia and infused with FITC-inulin. After the equilibration time, two 30-min urine collections and blood collections were made. AQP1 KO mice exhibited higher urine output, and the amount of UV was doubled compared with WT control mice (4.15 vs. 2.42 mL/min, P < 0.01). In contrast, GFR, Na⁺ excretion, and K⁺ excretion were not significantly changed in AQP1 KO mice compared with control mice. GFR was 0.76 and 0.71 mL/min/100 g body wt, E_Na was 0.56 and 0.55 µeq/L/100 g body wt, and E_K was 1.05 and 0.81 µeq/L/100 g body wt in WT control and AQP1 KO mice, respectively (P > 0.05). FE_Na was 0.54% and 0.48% and FE_K was 32.6% and 28.4% in WT control and AQP1 KO mice, respectively (P > 0.05). These results are consistent with the plasma measurements; plasma Na⁺ and K⁺ were same in KO and WT control mice and were within the normal range.

Figure 1.

General renal functions measured by renal clearance from wild-type (WT) control and aquaporin 1 (AQP1) knockout (KO) mice. Urine volume (UV; A), glomerular filtration rate (GFR; B), absolute Na⁺ and K⁺ excretion [E_Na (C) and E_K (D)], and fractional Na⁺ and K⁺ excretion [FE_Na (E) and FE_K (F)] were elucidated in WT control mice (solid bars) and AQP1 KO mice (open bars). There was higher UV in AQP1 KO mice compared with WT control mice (P < 0.01). There was no significant difference (NS) in GFR or Na⁺ and K⁺ excretion between WT and KO mice (P > 0.05). FE_Na and FE_K, fractional Na⁺ and K⁺.

Impact of AQP1 on Flow-Mediated Water Absorption in the PT

Flow-stimulated fluid absorption in the PT was measured by in vitro microperfusion in WT and AQP1 KO mice. S2 segments of the PT were perfused at low (5 nL/min) and high (20 nL/min) rates, and J_v was measured and analyzed by the difference of inulin concentrations in the collected fluid and original perfusate. Tubule dimensions at the two perfusion rates are shown in Table 3. As shown in Fig. 2 and Table 4, when the perfusion rate increased from 5 to 20 nL/min, J_v increased by 66% in WT mice, which is the same as we have previously reported (8, 30). In AQP1 KO mice, J_v was reduced by 30% (0.57 vs. 0.83 nL/min/mm) at the low flow rate compared with tubules from WT control mice (P < 0.01; Table 4). When the perfusion rate increased from 5 to 20 nL/min, the flow-stimulated increase in J_v was completely absent in KO mice. J_v was even significantly reduced at the high flow rate compared with the low flow rate, 0.38 versus 0.57 nL/min/mm (P < 0.01). These results confirmed that axial flow stimulates transcellular water absorption, and this transcellular water movement is through AQP1. The reduced J_v at the high perfusion rate in AQP1 KO mice may reflect the fact that the transtubular osmotic gradient, required to drive water absorption, cannot fully develop when axial fluid velocity is this high (see Model Calculations).

Table 3.

Flow-induced changes of tubule diameter, cell volume, and torque in mouse proximal tubules

Groups	n/n	Vo, nL/min	L, mm	ID, µm	OD, µm	Volume, µm3	T/Tr
AQP1 WT	15/9 11/9	5.0 ± 1.2 20.2 ± 5.8	0.85 ± 0.15 0.88 ± 0.13	12.1 ± 1.47 17.5 ± 1.92***	38.1 ± 2.7 39.7 ± 1.75	1,026.7 ± 167 1,001.4 ± 131*	1.00 ± 0.2 1.75 ± 0.43*
AQP1 KO	9/7 18/7	5.11 ± 1.6 21.21 ± 3.1	0.86 ± 0.09 0.87 ± 0.13	12.36 ± 2.0 18.96 ± 2.42***	38.19 ± 4.0 39.51 ± 3.0	1,034.1 ± 234NS 946.3 ± 134ns	1.00 ± 0.45 1.49 ± 0.42ns, NS

Values are means ± SD; n/n, number of perfused tubules/number of mice. AQP1, aquaporin 1; ID, inner tubular diameter; KO, knockout; L, tubular length; ns, not significantly different from the low flow rate in the same group (by an unpaired t test); NS, not significantly different compared with the wild-type (WT) control group at similar flow rates (by an unpaired t test); OD, outer tubular diameter; T, estimated microvillous torque; Tr, estimated microvillous torque measured at a perfusion rate of 5 nL/min; V_o, original perfusion rate; volume, cell volume [formula is π × (OD/2)² × 1 − π × (ID/2)² × 1; 1 indicates the length is 1 µm]. Significant difference from low flow rates in the same group: *P < 0.05 and ***P < 0.0001 (by an unpaired t test).

Figure 2.

Flow-stimulated fluid absorption (J_v) in proximal tubules (PTs) of wild-type (WT) control and aquaporin 1 (AQP1) knockout (KO) kidneys. J_v was measured at low (∼5 nL/min) and high (∼20 nL/min) perfusion rates in PTs of WT (A) and KO (B) mouse kidneys. C: changes (Δ) of J_v from low to high flow rates. D: percent change of J_v from the low to high flow rate. Higher flow rate significantly increased J_v in WT PTs but reduced J_v in AQP1 KO mouse PTs (P < 0.001).

Table 4.

Flow-induced changes in fluid absorption in mouse proximal tubules

Group	5 nL/min		20 nL/min		ΔJv (Jvb − Jva)	ΔJv/Jva × 100	(ΔJv/Jva)/(ΔT/Tr)
	n	Jva, nL/min/mm	n	Jvb, nL/min/mm
AQP1 WT	13	0.83 ± 0.14	11	1.37 ± 0.22**	0.55 ± 0.25	66.32 ± 27.8	0.88 ± 0.36
AQP1 KO	9	0.57 ± 0.18†	14	0.38 ± 0.09*††	−0.19 ± 0.18††	−33.6 ± 14.8††	−0.73 ± 0.33††

Values are means ± SD; n, number of perfused tubules (numbers of mice are the same as in Table 3). AQP1, aquaporin 1; ΔJ_v, difference in J_v between perfusion rates of 5 and 20 nL/min; ΔJ_v/J_va × 100, percent change in fluid absorption from the low flow rate; J_v, fluid absorption; KO, knockout. Significant difference from the low flow rate in the same group: *P < 0.05 and **P < 0.01; significant difference compared with the wild-type (WT) control group at similar flow rates: †P < 0.01 and ††P < 0.001.

Impact of AQP1 on Flow-Mediated ${\mathbf{\text{HCO}}}_3^{-}$ Absorption in the PT

Flow-mediated ${\text{HCO}}_3^{-}$ absorption in the PT was also measured by in vitro microperfusion in WT and AQP1 KO mice. S2 segments of the PT were perfused under low (5 nL/min) and high (20 nL/min) perfusion rates, and the rate of ${\text{HCO}}_3^{-}$ absorption ($J_{{\text{HCO}}_3}$) was measured and analyzed by the difference of total CO₂ concentrations in the perfusate and in the collected fluid. Experimental results are shown in Table 5 and Fig. 3. In WT mice, when the perfusion rate was increased from 5 to 20 nL/min, $J_{{\text{HCO}}_3}$ increased from to 66.5 to 135.6 pmol/min/mm (P < 0.001; Table 5), which is the same as our previous published data (8, 30). The flow-induced change of $J_{{\text{HCO}}_3}$ was 69.4 pmol/min/mm, or 104.7% of the low-flow absorption in WT control mice (Table 5). When WT and AQP1 KO mice were compared, increasing luminal perfusion rate produced an identical increment of ${\text{HCO}}_3^{-}$ absorption in AQP1 KO mice compared with WT mice (Fig. 3). With perfusion at 5 nL/min, $J_{{\text{HCO}}_3}$ was 66.5 and 61 pmol/min/mm (P > 0.05) in WT and AQP1 KO mice, respectively, and at 20 nL/min, $J_{{\text{HCO}}_3}$ was 135.6 and 132.9 pmol/min/mm (P > 0.05; Table 5). Flow-induced changes of $J_{{\text{HCO}}_3}$ (Fig. 3C) and flow-induced percent changes of $J_{{\text{HCO}}_3}$ (Fig. 3D) were also not significantly different between WT and AQP1 KO mice. These results suggest that AQP1 plays no role in ${\text{HCO}}_3^{-}$ absorption and were also consistent with the result of no difference in acid-base parameters in AQP1 KO mice compared with WT control mice (Fig. 4).

Table 5.

Flow-induced changes in bicarbonate absorption in mouse proximal tubules

Group	5 nL/min		20 nL/min		$\Delta J_{{\text{HCO}}_3}$ (${\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{b}}-{\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{a}}$)	$\Delta {\mathit{\text{J}}}_{{\text{HCO}}_3}$/${\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{a}}$ × 100	(Δ${\mathit{\text{J}}}_{{\text{HCO}}_3}$/${\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{a}}$)/(ΔT/Tr)
	n	${\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{a}}$, pmol/min/mm	n	${\mathit{\text{J}}}_{{\text{HCO}}_3}\mathit{\text{b}}$, pmol/min/mm
AQP1 WT	13	66.5 ± 13.3	13	135.6 ± 13.3*	69.4 ± 13.4	104.73 ± 20.3	2.49 ± 0.47
AQP1 KO	9	61.0 ± 17.6NS	14	132.9 ± 23.4*NS	71.92 ± 30.6NS	117.92 ± 38.4NS	2.56 ± 0.84NS

Values are means ± SD; n, number of perfused tubules (numbers of mice are the same as in Table 3). AQP1, aquaporin 1; Δ$J_{{\text{HCO}}_3}$, difference in $J_{{\text{HCO}}_3}$ between perfusion rates of 5 and 20 nL/min; Δ$J_{{\text{HCO}}_3}$/$J_{{\text{HCO}}_3}\mathit{\text{a}}$ × 100, percent change in bicarbonate absorption from the low flow rate; $J_{{\text{HCO}}_3}$, bicarbonate absorption; NS, not significantly different compared with the wild-type (WT) control group at similar flow rates. *Significant difference from the low flow rate in the same group (P < 0.05).

Figure 3.

Flow-stimulated ${\text{HCO}}_3^{-}$ absorption ($J_{{\text{HCO}}_3}$) in proximal tubules of wild-type (WT) control and aquaporin 1 (AQP1) knockout (KO) kidneys. $J_{{\text{HCO}}_3}$ was measured at low (∼5 nL/min) and high (∼20 nL/min) perfusion rates in the proximal tubules of WT (A) and KO (B) mouse kidneys. C: change (Δ) of $J_{{\text{HCO}}_3}$ from low to high flow rates in WT control and AQP1 KO groups. D: percent change of $J_{{\text{HCO}}_3}$ from low to high flow rates in WT control and AQP1 KO groups. There was no significant difference (NS) between the WT and AQP1 KO group (P > 0.05).

Figure 4.

Acid-base parameters measured from wild-type (WT) control and aquaporin 1 (AQP1) knockout (KO) mice. Blood pH (A), urine pH (B), blood ${\text{HCO}}_3^{-}$ (C), and urine ${\text{HCO}}_3^{-}$ (D) were elucidated in WT control mice (solid bars) and AQP1 KO mice (open bars). There was no significant difference (NS) in acid-base parameters between WT and AQP1 KO mice (P > 0.05).

Impact of AQP1 on Cell Volume

We measured tubule ID and OD and calculated epithelial cell volume per micrometer tubule length according to the area of the annulus between inner and outer diameters of WT and AQP1 KO mouse PTs at low and high flow rates. As shown in Table 3 and Fig. 5, there were no significant differences in ID (Fig. 5A), OD (Fig. 5B), and cell volume (Fig. 5B) between WT and KO PTs at either low or high flow rates. ID was 12.1 and 12.4 µm at the low flow rate and 17.5 and 19 µm (P > 0.05) at the high flow rate in WT and KO PTs, respectively. Increasing flow rate from 5 to 20 nL/min significantly increased ID (P < 0.001) and did not change OD in both WT and KO mouse PTs. ID increased 45%, from 12.1 to 17.5 µm, in the WT group and increased 53%, from 12.4 to 19 µm, in the KO group. OD was 38.1 and 39.7 in the WT group and 38.2 and 39.5 in the KO group at the low and high flow rates, and there was no significant difference among the groups. Cell volumes were slightly reduced in both WT and KO mouse PTs, but the changes were not statistically significant (Fig. 5).

Figure 5.

Flow-induced changes in tubule diameter and cell volume in proximal tubules (PTs) of wild-type (WT) control and aquaporin 1 (AQP1) knockout (KO) kidneys. Tubule inner diameter (ID; A), tubule outer diameter (OD; B), and cell volumes (C) in PTs of WT control and AQP1 KO mouse kidneys. Higher flow rate increased ID in both WT and KO PTs (P < 0.001) and did not change in OD or cell volumes (P > 0.05). NS, no significant difference.

Model Calculations

With respect to model parameters, three modifications were made in the parameters from the rat PCT (28), and those are shown in Table 6. The rat model was for a tubule in vivo, situated within a densely packed cortical labyrinth. For the microperfused PCT, this constraint is absent, and the tubule undergoes a 50% expansion as flow increases from 5 to 20 nL/min (Table 3). To capture this, it has been assumed that with the increase in tubule flow from 5 to 10 to 20 nL/min, tubule luminal pressure goes from 1 to 2 to 4 mmHg, and ν_M was increased from 3% to 20% per mmHg. Of note, these pressure changes cannot be attributed to the hydraulic resistance of the open tubule but must be due to constriction at the collecting end. The second modification is based on the data provided here that the mouse PCT appears to be a more briskly transporting epithelium than the rat PCT. With reference to Tables 4 and 5, the fractional absorption of volume and ${\text{HCO}}_3^{-}$ are 17% and 55%, respectively, in a 1-mm tubule perfused at 5 nL/min. Using rat model transport rates, fractional absorption is underestimated, with fractional reabsorption of volume and ${\text{HCO}}_3^{-}$ of 15% and 20%, respectively, when perfused at 5 mL/min (not shown). Basically, the rat model was parameterized for a tubule whose entering flow is typically 30 nL/min, so that with the flow dependence of transporter density, the lower flows of this study reduced model fluxes and cell membrane water permeabilities. The simplest way to remedy this was to scale up the densities of all cellular transport pathways by a similar value. When rat and mouse tubules were compared, changes in transporter density can be conceptualized as either changes in reference density or as changes in reference torque. Equation 4 provides the scaling of parameter density (H), which could have been modified by varying H₀ or T_M0. With the torque sensitivity adjusted down (from ν_T = 1.6 in the most recent rat model) to ν_T = 1 (Table 6), these two options are mathematically equivalent. In the calculations of this report, the reduction in T_M0 was done by reducing the reference velocity, v_M0, from 1 to 0.2 mm/s (Table 6), and this scales down the reference microvillous torque by a similar factor. Ideally, the modifications in cellular transport pathways for the mouse PCT would have derived from studies quantifying each transport pathway, but such data do not exist. The third modification is a reduction in the TJ water permeability. In the rat PCT, TJ water permeability was estimated to be comparable with the water permeability of the transcellular pathway (31). That estimate derived from the low reflection coefficients for Na⁺ and Cl⁻, which had been measured in rat tubules, but such studies have never been done in the mouse PCT. In the experiments of Schnermann et al. (20) and of this study (Table 4), it was found that AQP KO substantially reduces PCT volume absorption, J_v. What will be shown, in the calculations of Table 7, is that this reduction in PT volume transport (as well as its flow sensitivity) would not be compatible with a TJ water permeability (P_f) as high as that for the rat. To capture the measured J_v in AQP KO and to comport with whole epithelial P_f measurements (20), TJ P_f for this model has been set to 25% of its value in the rat (Table 6).

Table 6.

PCT model parameters

	Rat PCT	Present Model
Selected flow parameters
Tubule length, cm	0.1	0.1
Reference radius (RM0), µm	10.6	10.6
Compliance (νM), mmHg−1	0.03	0.20*
Viscosity, dyn·s/cm2	0.0085	0.0085
Transporter torque sensitivity (νT)	1.0*	1.0*
Reference flows and forces
Reference velocity (vM0), cm/s	0.10	0.02*
Reference shear stress (τM0), dyn/cm2	3.22	0.64
Reference drag (DM0), dyn/cm	0.0214	0.0043
Reference microvillous torque (TM0), dyn × 10−6	6.60	1.32
Reference water permeabilities (Pf0), cm/s
Tight junction	0.22	0.056*
Luminal cell membrane	0.40	0.40
Peritubular cell membrane	0.41	0.41
Inlet conditions
Volume flow, nL/min	10.0	10.0
Na+ entry, pmol/min	1,440	1,440
${\text{HCO}}_3^{-}$ entry, pmol/min	250	250
Pressure (PM − PS), mmHg	2.0	2.0
Radius (RM), µm	11.2	14.6
Velocity, cm/s	0.042	0.025
Shear stress (τM), dyn/cm2	1.28	0.58
Drag (DM), dyn/cm	0.0090	0.0053
Microvillous torque (TM), dyn × 10−6	2.84	1.59
Water permeability (Pf), cm/s
Luminal cell membrane	0.17	0.48
Peritubular cell membrane	0.18	0.49
Fractional reabsorption (in 1 mm), %
Volume	11.2	17.3
Na+	10.8	18.1
${\text{HCO}}_3^{-}$	19.5	43.9

PCT, proximal convoluted tubule. *Parameter changes from the rat model of Weinstein et al. (28).

Table 7.

Impact of inlet volume flow on transport by a 1-mm proximal convoluted tubule segment

	Inflow (5 nL/min)	Inflow (20 nL/min)	Flux Change	Fractional Flux Change	Proportional Change: Flux to Torque
Inlet conditions
Pressure (PM − PS), mmHg	1.0	4.0
Radius (RM), µm	12.7	17.6
Velocity, cm/s	0.016	0.034
Microvillous torque (TM), dyn × 10−6	1.09	2.12		94%
TJ Pf at 25% of the rat value
WT fluxes
Volume reabsorption (Jv), nL/min	1.25	2.32	1.07	86%	0.91
Na+ reabsorption (JNa), pmol/min	184	351	167	91%	0.96
${\text{HCO}}_3^{-}$ reabsorption ($J_{{\text{HCO}}_3}$), pmol/min	64	161	97	151%	1.59
KO fluxes
Volume reabsorption (Jv), nL/min	0.83	0.99	0.16	20%	0.21
Na+ reabsorption (JNa), pmol/min	154	309	155	101%	1.07
${\text{HCO}}_3^{-}$ reabsorption ($J_{{\text{HCO}}_3}$), pmol/min	62	153	91	148%	1.57
TJ Pf at 100% of the rat value
WT fluxes
Volume reabsorption (Jv), nL/min	1.75	2.98	1.23	70%	0.74
Na+ reabsorption (JNa), pmol/min	249	431	182	73%	0.77
${\text{HCO}}_3^{-}$ reabsorption ($J_{{\text{HCO}}_3}$), pmol/min	67	165	98	145%	1.53
KO fluxes
Volume reabsorption (Jv), nL/min	1.76	2.61	0.85	48%	0.51
Na+ reabsorption (JNa), pmol/min	254	448	194	76%	0.81
${\text{HCO}}_3^{-}$ reabsorption ($J_{{\text{HCO}}_3}$), pmol/min	67	163	95	141%	1.49

KO, knockout; P_f, water permeability; TJ, tight junction; WT, wild type.

Table 7 and Fig. 6 show simulations of experiments in which 1.0-mm WT and KO tubules were perfused at 5 or 20 nL/min; the top of Table 7 shows inlet conditions at the two perfusion rates. To represent AQP1 KO tubules, P_f of both luminal and peritubular cell membranes has been reduced to 1% of their values in Table 6. As described earlier, selection of hydrostatic pressures and compliance was guided by the measurements shown in Table 3. With the change in flow and radius, mean fluid velocity approximately doubled, as did microvillous torque. The middle of Table 7 contains predicted reabsorptive fluxes of volume, Na⁺, and ${\text{HCO}}_3^{-}$ in WT and KO groups, and these may be compared with their values in Tables 4 and 5. It should be emphasized that in the parameter selection process, there was only a uniform scaling of the cell transporter densities, which was applied to all luminal and peritubular transporters. Thus, if one scales the mouse PT cell so that model ${\text{HCO}}_3^{-}$ absorption agrees with the measured value for inlet flow at 5 nL/min, then all other fluxes are determined at 5 nL/min and at 20 nL/min, and that is what was done here. With that parameter anchor, increasing perfusion to 20 nL/min approximately doubled fractional ${\text{HCO}}_3^{-}$ absorption, for both WT and KO groups, as was observed. The predicted volume flows were ∼50% higher in the model tubule, but in the WT group the proportional velocity dependence was also concordant with observation. It should be noted that although perfusion increased by a factor of 4, reabsorptive rates of volume and Na⁺ increased by only a factor of 2, and this parallels the change in microvillous torque. This abrogation of glomerulotubular balance is due to tubule dilatation in vitro, which reduces luminal membrane shear stress, and which is prevented in the in vivo setting. In KO tubules, the increase in inlet flow produces only a 20% increase in volume absorption. This is substantially less than the doubling of Na⁺ absorption, although it does not capture the frank decrease in J_v that was observed (Table 4). The dissociation of volume and Na⁺ fluxes depends on the development of luminal hypotonicity and is shown in Fig. 6. The abscissa for all panels is distance along the perfused tubule. The top panels of Fig. 6 show luminal Na⁺ concentration and the bottom panels of Fig. 6 show J_v; perfusion was 5 nL/min for the left panels of Fig. 6 and 20 nL/min for the right panels of Fig. 6. With respect to luminal Na⁺ concentrations, WT tubules showed a luminal drop of ∼1 mM, whereas in KO tubules this Na⁺ drop was a little over 8 mM, and these were similar at the two perfusion rates. The difference between the two perfusion rates is that with slow flow the fall in luminal Na⁺ develops earlier along the tubule, so that for most of the tubule, the osmotic difference between the lumen and bath is greater in tubules perfused at 5 nL/min. This means that higher inlet perfusion rate delays development of the transepithelial osmotic driving force and is likely to play a role in blunting the flow-dependent increase in water reabsorption.

Figure 6.

Model simulation of 1.0-mm proximal tubules from wild-type (WT) and knockout (KO) mice perfused at 5 or 20 nL/min. The abscissa for all panels is distance along the perfused tubule (in mm). Top: luminal Na⁺ concentration (in mM); bottom: fluid absorption (J_v; in nL/min/mm). Left: perfusion was 5 nL/min; right: perfusion was 20 nL/min. C_M, concentration in the lumen.

In these simulations, it has been assumed that the only change in KO tubules is in AQP1 density and that TJ properties are unchanged. The experimental observations (Table 4) were that AQP1 KO mouse tubules perfused at 5 nL/min reabsorbed water at 69% of the rate in WT tubules; when perfusion was 20 nL/min, this ratio was 28%. In the model, the predicted ratios for the two perfusion rates were 66% and 43% (Table 7), and this concordance with the measured flows guided the choice of TJ P_f. Of note, prior work has not revealed flow-dependent changes in TJ properties, at least with respect to ${\text{HCO}}_3^{-}$ permeability (8). With reference to the bottom section of Table 7, if TJ P_f had been left at the value used in the rat model, then volume and Na⁺ reabsorption in both WT and KO tubules would have been higher, due to greater TJ water flow. Indeed, the rat TJ water permeability erased any J_v difference between WT and KO tubules at the 5 nL/min perfusion rate. In the model PT, the flow-sensitive cellular pathway for water reabsorption sits in parallel with a flow-insensitive TJ. The greater the contribution of the flow-insensitive pathway to overall PT water permeability, the smaller the impact of AQP1 deletion on flow-dependent reabsorption. With the TJ P_f selected for mouse tubules, AQP1 KO reduces torque sensitivity of volume reabsorption from 86% to 20%; with rat P_f, the impact of AQP1 KO on torque sensitivity is blunted (70%–48%).

The model tubule permits simulation of an epithelial water permeability determination, for comparison with perfused tubule measurements. In the calculations shown in Table 8, an impermeant at 10 mM was added to the luminal solution, which was otherwise identical to the peritubular bath. Perfusions were done at either 60 or 10 nL/min for a 1-mm tubule. As in the flux calculations, inlet pressures were 4 and 2 mmHg, respectively. The difference in volume absorption between perfusions with and without the impermeant were used to calculate whole epithelial P_f. With respect to WT tubules, it is immediately apparent that there is a strong flow dependence on the predicted transepithelial P_f, being about threefold higher at the faster perfusion rate, and this derives from the flow dependence of AQP1 density. In KO tubules, there is still flow dependence of the predicted transepithelial P_f, albeit at much lower values than for WT tubules. That flow dependence is due to the equilibration of luminal and peritubular osmolality over the length of the perfused segment. The lower P_f at the lower flow rates is due to a reduced driving force for water over the length of the segment. At the selected TJ P_f of this model (0.056 cm/s), with tubules perfused at 60 nL/min, KO and WT epithelial P_f were 0.054 and 0.199 cm/s, and these can be compared with the measurements of Schermann et al. (20), of 0.033 and 0.15 cm/s.

Table 8.

Whole tubule water permeability: dependence on TJ P_f

TJ Pf, cm/s	Epithelial Pf, cm/s
Perfused at 60 nL/min	WT	AQP1 KO
0.002	0.187	0.014
0.022	0.192	0.030
0.056	0.199	0.054
0.222 (rat)	0.234	0.154

Perfused at 10 nL/min	WT	AQP1 KO
0.002	0.050	0.004
0.022	0.055	0.019
0.056	0.063	0.040
0.222 (rat)	0.095	0.096

AQP1, aquaporin 1; KO, knockout; P_f, water permeability; TJ, tight junction; WT, wild type.

DISCUSSION

Kidney PTs are responsible for reabsorption of ∼60% of filtered salt and water, and the fractional reabsorption is relatively constant, despite large variations in GFR, and this perfusion-absorption balance has been termed glomerulotubular balance (3). The physiological importance of glomerulotubular balance has been recognized as stabilizing distal Na⁺ delivery, thus preserving distal acid and K⁺ excretion when GFR is low and avoiding natriuresis when GFR is high (32). Underlying glomerulotubular balance is the flow dependence of PT reabsorption of filtered volume and solutes, and we have demonstrated that the flow-stimulated transport persists in the isolated perfused PT, in which membrane transporter activity is sensitive to brush border shear stress. This extends to NHE3-mediated Na⁺ transport and NHE3 and H⁺-ATPase-mediated H⁺ transport (7, 8) and to AQP1 density in both luminal and peritubular membranes (19). In the present study, we investigated flow-stimulated water transport using the AQP1 KO mouse (19). In view of the observation that AQP1 can function as a CO₂ channel (22), we also examined the acid-base parameters and ${\text{HCO}}_3^{-}$ transport. Microperfusion experiments in isolated PTs from WT and AQP1 KO mice were performed, and both fluid and ${\text{HCO}}_3^{-}$ absorption were measured under low and high flow rates. We found that in AQP1 KO mice, there was reduced fluid absorption in the PT under both low and high flow rate conditions, along with an absence of flow-dependent modulation of fluid absorption. However, AQP1 KO did not affect either PT ${\text{HCO}}_3^{-}$ absorption or acid-base parameters in the AQP1 KO mouse, thus indicating little role for AQP1 in the regulation of ${\text{HCO}}_3^{-}$ transport in this segment.

The reduced J_v in the AQP1 KO mouse PT is consistent with previous reports and confirms the primacy of AQP1 as the route of transcellular water transport (20, 33). Theilig and colleagues (21) have shown in isolated perfused PT S2 segments that increasing flow from ∼5 to ∼25 nL/min increased the AQP1 immunogold signal 2.1-fold in the brush-border membrane, 3.4-fold in the subapical compartment, and twofold in the basolateral cell membrane under high flow compared with low flow rates. Our observation that AQP1 KO tubules showed no flow-mediated increase in volume flux supports a functional role of AQP1 in response to fluid shear stress-regulated transcellular water movement. In the AQP1 KO mouse PT, a flow-induced increase in J_v was not only absent, but J_v actually decreased in the transition from low to high flow rate (Table 4 and Fig. 2). In the normal PT, minor degrees of luminal hypotonicity suffice to drive isotonic water reabsorption, whereas in AQP1 KO tubules, luminal hypotonicity is demonstrable (21). Thus, AQP1 KO tubules have diminished water permeability, which fails to increase in parallel with brush border shear stress, so that the disparity between Na⁺ reabsorption and volume reabsorption is accentuated at higher luminal flows.

Our data also provide evidence that AQP1 does not impact acid-base homeostasis. There is no phenotype of blood pH, ${\text{HCO}}_3^{-}$, or urine pH in AQP1 KO mice (Fig. 4), and PT ${\text{HCO}}_3^{-}$ absorption was similar in AQP1 KO and WT control mice under low and high flow rates. We observed that higher flow rate increased ID, as previously reported (21, 30, 34), but there was no difference between WT and AQP1 KO in tubule compliance. We also saw no significant difference between WT and AQP1 KO in the constancy of cell volume during variation of luminal flow. Thus, our data also suggest that the impact of luminal shear stress on peritubular exit pathways remains intact in the AQP1 KO mouse.

The present study has implications for modeling of PT function and for reporting measurement of PT water permeability. The model used for mouse tubules in vitro was an adaptation of what had been developed as a simulation of the rat PT in vivo. The first adjustment was to acknowledge the fact that tubules in vitro are more compliant than in vivo. At higher perfusion rates tubules in vitro dilate, so that luminal fluid velocity (and shear stress) does not scale proportionally with flow. Indeed, in the first report on in vitro perfusion of PT from the rabbit, tubule dilatation at higher flows obliterated the finding of statistically significant flow-dependent fluid absorption (1). In tubules from the mouse, flow-dependent transport was demonstrable, but it has been a consistent finding from this laboratory that the fractional changes in absorption of fluid or ${\text{HCO}}_3^{-}$ are less than the fractional changes in fluid flow, i.e., glomerulotubular balance in vitro is not preserved. The second adjustment was to reduce the reference shear stress used to calibrate changes in transporter density. Although mouse tubule diameter is not very different from the rat PT, it functions in a nephron whose single nephron GFR is about a third that of the rat, so that the baseline shear stress is proportionally lower. With these two modifications, the model provided realistic estimates of volume and ${\text{HCO}}_3^{-}$ absorption at low and high perfusion rates. One implication of flow-dependent transporter density is that there is no single rate for Na⁺ reabsorption or H⁺ secretion along a tubule in which luminal flow varies by a factor of 2. Similarly, with the observation that AQP1 density is also flow dependent, it must also be the case that epithelial water permeability varies according to luminal flow or with luminal perfusion rate in vitro. This implies that there is also no single P_f for the PT and that measurements of P_f in vivo must also specify the perfusion rate at which measurements were made, and this was illustrated in the model P_f computation shown in Table 8. A tubule P_f determination is more complex than an epithelial P_f measurement, due to changing solute concentrations along the tubule lumen (e.g., Fig. 6). If one seeks to minimize initial to final tubule concentration differences by increasing perfusion rate, then this flow increase will perturb the epithelial AQP1 density.

In the rat PT, TJ water flow with convective paracellular transport is a substantial component of Na⁺ and Cl⁻ reabsorption. The critical measurements underlying this assertion were determinations of ionic reflection coefficients, with the finding that while ${\text{HCO}}_3^{-}$ showed little convective flow through TJs, the coefficients for Na⁺ and Cl⁻ were much less than unity (35). In analysis of these data, solute polarization within the lateral interspace could not realistically account for these observations, so that one was forced to the conclusion that TJ water flow was substantial (31). Rat PT models were most realistic when TJ water permeability was comparable with that of the transcellular pathway. About 20 years later, the biological underpinning of these conclusions came with the identification of claudin 2 within PT TJs (36). When claudin 2 was transfected into a Madin–Darby canine kidney cell layer, it localized to the TJ and rendered the cell layer water permeable (37), and when the claudin 2 gene was disrupted in mice, their perfused PTs were defective in Na⁺, Cl⁻, and water reabsorption (38). Schnermann et al. (39) used micropuncture to examine mice deficient in AQP1, in claudin 2, and with deletion of both water pathways (double knockout). They found that in all these strains, the proportional relationship between single nephron GFR and proximal reabsorption was largely preserved; however, with AQP1 KO, there was a large osmolality difference between the lumen and blood and in the double knockout this difference increased. They estimated that the TJ contribution to PT water permeability was at most 25% of epithelial water permeability. This estimate comported with their prior study of the isolated perfused PT, in which tubule P_f was measured and found to be reduced by 60% with AQP1 KO (20, 39). It should be noted that there have not been measurements of reflection coefficients in any mouse PT, so there is uncertainty in transferring this quantitative conclusion to the rat.

In the model of this report, assignment of TJ water permeability was done to achieve rough concordance with the epithelial P_f measurement from Schnermann et al. (20, 39), who found that compared with WT tubules, AQP1 KO tubules exhibited a 78% P_f reduction. The calculations shown in Table 8 show tubule fluid reabsorption at low and high flows and thus provide a range for epithelial P_f predictions. The impact of greater tubule fluid velocity to enhance water reabsorption is twofold: at faster flow, there is reduced dissipation of the imposed transepithelial osmolality gradient, and the faster flow increases microvillous drag, which increases AQP1 density. With reference to Table 8, it may be seen that with luminal perfusion at 60 nL/min, the ratio of KO to WT P_f was 27% when the ratio of TJ to transcellular P_f was 25% (0.056–0.222 cm/s); when luminal perfusion was 10 nL/min, the ratio of KO to WT P_f was 35% when TJ PF (0.022 cm/s) was 10% of transcellular P_f. Thus, the TJ P_f that provides closest agreement with the experimental finding of a 78% P_f reduction in the KO depends on the perfusion rate of the experiment, but unfortunately Schnermann et al. (20, 39) did not specify the perfusion rate of their measurements. Additional guidance for the TJ P_f here came from a comparison of volume reabsorption rates. With reference to Table 4, the ratio of KO to WT J_v, when perfused at 5 nL/min, was 0.57/0.83 = 69%. In the model (Table 7), with TJ P_f set to 25% of the rat value, the same ratio at 5 nL/min was 0.83/1.25 = 66%. The analysis of this report identified epithelial P_f as the sum of flow-dependent (transcellular) and of flow-independent (paracellular) components and that with AQP1 KO, only the transcellular component changed. (To model AQP1 KO, P_f of both luminal and peritubular cell membranes was reduced to 1% of their WT values, with no change in TJ properties.) There is no experimental guidance as to whether any TJ permeabilies are impacted in AQP1 KO. However, at the 5 nL/min perfusion rate, the flow-dependent P_f component should be at its minimum, suggesting that the 69% concordance of KO and WT water fluxes represents preservation of the flow-independent water permeability in AQP1 KO. This issue could be addressed more directly through determinations of epithelial P_f at several perfusion rates for both WT and KO tubules.

In summary, our results identify AQP1 as a critical mediator of flow-dependent water reabsorption in the PT. With AQP1 deletion, there is both loss of flow-mediated insertion of cell membrane water channels as well as an axial delay in achieving the transepithelial osmotic force that can drive water reabsorption. We also document that flow-stimulated ${\text{HCO}}_3^{-}$ reabsorption is intact and independent of AQP1. With reference to a mathematical model of an isolated perfused tubule, it is demonstrated that water permeability measurements must take cognizance of the important effect of luminal perfusion rate in assigning a value to this parameter. Our model findings also suggest that TJ water flux in the PT is less prominent in the mouse kidney than in the rat kidney.

GRANTS

This work was supported by the National Institute of Diabetes and Digestive and Kidney Diseases Grants R01DK117650 (to T.W.) and RO1DK029857 (to A.M.W.).

DISCLOSURES

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

AUTHOR CONTRIBUTIONS

Z.D., A.M.W., and T.W. conceived and designed research; Z.D., Q.Y., E.S., A.M.W., and T.W. performed experiments; Z.D., Q.Y., A.M.W., and T.W. analyzed data; Z.D., Q.Y., A.M.W., and T.W. interpreted results of experiments; E.S., A.M.W., and T.W. prepared figures; A.M.W. and T.W. drafted manuscript; E.S., A.M.W., and T.W. edited and revised manuscript; Z.D., Q.Y., E.S., A.M.W., and T.W. approved final version of manuscript.