Modeling oxygen consumption in the proximal tubule: effects of NHE and SGLT2 inhibition

Abstract

The objective of this study was to investigate how physiological, pharmacological, and pathological conditions that alter sodium reabsorption (T_Na) in the proximal tubule affect oxygen consumption (Q_O2) and Na⁺ transport efficiency (T_Na/Q_O2). To do so, we expanded a mathematical model of solute transport in the proximal tubule of the rat kidney. The model represents compliant S1, S2, and S3 segments and accounts for their specific apical and basolateral transporters. Sodium is reabsorbed transcellularly, via apical Na⁺/H⁺ exchangers (NHE) and Na⁺-glucose (SGLT) cotransporters, and paracellularly. Our results suggest that T_Na/Q_O2 is 80% higher in S3 than in S1–S2 segments, due to the greater contribution of the passive paracellular pathway to T_Na in the former segment. Inhibition of NHE or Na-K-ATPase reduced T_Na and Q_O2, as well as Na⁺ transport efficiency. SGLT2 inhibition also reduced proximal tubular T_Na but increased Q_O2; these effects were relatively more pronounced in the S3 vs. the S1–S2 segments. Diabetes increased T_Na and Q_O2 and reduced T_Na/Q_O2, owing mostly to hyperfiltration. Since SGLT2 inhibition lowers diabetic hyperfiltration, the net effect on T_Na, Q_O2, and Na⁺ transport efficiency in the proximal tubule will largely depend on the individual extent to which glomerular filtration rate is lowered.

despite intense research, the mechanisms underlying the development of chronic kidney diseases remain incompletely understood. Renal hypoxia is thought to be a unifying pathway to chronic kidney disease (15) and, in general, is due to a mismatch between changes in renal oxygen delivery and oxygen consumption (8). Oxygen consumption in the kidney serves in large part to actively reabsorb Na⁺. Since the proximal tubule is where more than half the filtered load of Na⁺ is reabsorbed, the goal of this study was to investigate how physiological and pathological changes in sodium transport alter O₂ consumption in the proximal tubule.

Sodium reabsorption along the proximal tubule is coupled to HCO₃⁻ and Cl⁻ transport: early NaHCO₃ reabsorption raises the luminal concentration of Cl⁻ and enhances the driving force for paracellular NaCl reabsorption in the later part of the tubule. Notably, changes in O₂ consumption (Q_O2) do not always correlate positively with changes in Na⁺ reabsorption. Deng et al. (4) observed that blocking carbonic anhydrase with benzolamide (a proximal tubule diuretic) lowered the energy efficiency of Na⁺ reabsorption in the kidney, as it simultaneously decreased net Na⁺ reabsorption and increased overall O₂ consumption. These effects were abolished by drugs that suppress Na⁺/H⁺ exchange or basolateral Na⁺-HCO₃⁻ cotransport. Deng et al. (4) surmised that benzolamide causes a shift from paracellular to transcellular NaCl reabsorption in the proximal tubule, which is more energetically expensive. This hypothesis was further supported by the mathematical model of Weinstein et al. (51) as well as the present study (results not shown).

A significant fraction of renal O₂ consumption is independent of Na⁺ transport. Basal O₂ consumption (Q_O2^basal) provides the energy needed for other active transport processes and for intracellular biochemical reactions. Q_O2^basal may nevertheless vary with Na⁺ transport rates. For the whole kidney, a recent compilation of 24 studies indicates that the basal-to-total Q_O2 ratio spans a wide range, from 0 to 80% (7). Part of Q_O2^basal may be utilized for the production of glucose (i.e., gluconeogenesis) or triacylglycerol, depending on the availability of other substrates and the metabolic state of the tissue (20).

In vivo, fatty acids, lactate, and glutamine are the main metabolic substrates for proximal tubule function; glucose is not a significant respiratory fuel in this segment (24). Nevertheless, understanding the link between oxygen consumption and Na⁺ transport requires a precise accounting of glucose transport, since the reabsorption of Na⁺ in the proximal tubule is partly coupled to that of glucose. Under normal conditions, the filtered load of glucose is almost entirely reabsorbed along the proximal tubule. Glucose is transported across the apical brush border into the cell by sodium-glucose cotransporters (SGLT) and subsequently diffuses into the peritubular space across basolateral glucose transport facilitators (GLUT). The early proximal convoluted tubule expresses high-capacity, low-affinity glucose transporters, namely SGLT2 on the apical side and GLUT2 on the basolateral side; together these transporters reabsorb >90% of the filtered glucose under normoglycemic conditions. The last, straight part of the proximal tubule, where the luminal concentration of glucose is significantly reduced, expresses the lower capacity, high-affinity glucose transporters SGLT1 in the luminal membrane and GLUT1 in the basolateral membrane, which act in concert to reabsorb the remainder of glucose (25, 42, 55).

In this study, we used an epithelial cell-based model of the proximal tubule to investigate the extent to which physiological, pharmacological, and pathological conditions that alter T_Na in the proximal tubule impact Q_O2 and Na⁺ transport efficiency.

MATHEMATICAL MODEL

We adapted an epithelial cell-based model of the proximal tubule of a superficial nephron in a rat kidney, which was developed by Weinstein et al. (51). The model proximal tubule consists of compliant S1, S2, and S3 segments, which all express the same type of channels, transporters, and pumps. Transport protein density, however, varies along the tubule: it is positively modulated by the flow-induced torque exerted on brush border microvilli, as observed experimentally (5). Since the flow rate decreases along the tubule, transporter activity is lower in the late proximal tubule than in the early proximal tubule. The model predicts that torque-dependent transporter density may significantly contribute to perfusion-absorption balance (i.e., glomerulo-tubular balance) in the proximal tubule (51).

Our model, however, differs from the model of Weinstein et al. (51) in several respects. We explicitly distinguish between the cortical (S1–S2) and outer medullary (S3) segments of the proximal tubule; the length of S1–S2 and S3 is, respectively, set to 0.97 and 0.13 cm. The surface areas of the apical and basolateral cell membranes per unit length are reduced by a factor of 2 in S3, relative to those in S1–S2, to account for reduced membrane infolding and therefore lower transport rates in the former segment (50). In addition, the proportionality constant between transporter density and the relative microvillous torque is set to 1.4 in S1–S2 and 0.7 in S3. The kinetic rates of carbonic anhydrase-mediated CO₂ conversion are taken to be 100 times lower in the lumen of S3, relative to that of S1–S2 (22). We assume that all interstitial concentrations increase linearly in the medulla (see Table 1). The interstitial concentration of glucose at the boundary between the outer and inner stripes of the outer medulla is set to 6 mM, which is slightly higher than the plasma glucose concentration of 5 mM and which corresponds to a glucose concentration of 8.5 mM at the outer-inner medullary boundary if interstitial glucose concentration is taken to increase linearly along the cortico-medullary axis. The permeability of the proximal tubular tight junction to glucose is low and set to 0.31 × 10⁻⁵ cm/s (10). In addition, our model includes a small (0.01 × 10⁻⁵ cm/s) basolateral Cl⁻ conductance but no apical Cl⁻/HCO₃⁻ exchangers (1, 32). In compensation, the coefficient describing the rate of apical Cl⁻/HCO₂⁻ exchange is doubled, and is equal to 10.0 × 10⁻⁹ mmol²·J⁻¹·s⁻¹·cm⁻². Finally, our model uses explicit kinetic descriptions of proximal tubule glucose transporters, as described immediately below.

Table l.

Interstitial concentrations

Solute	Cortex, mM	OS-IS junction, mM
Na+	140	192.6
K+	4.9	6.4
Cl−	113.2	168.3
HCO3−	24.0	24.3
H2CO3−	4.41 × 10−3	4.41 × 10−3
CO2	1.5	1.5
H2PO42− + H2PO4−	3.9	3.9
Urea	5.0	13.6
NH3 + NH4+	0.20	1.3
HCO2− + H2CO2	1.0	1.0
Glucose	5.0	6.0
pH	7.31	7.31

OS-IS junction: at the boundary between the outer and inner stripes of the outer medulla. Concentrations (in mM) in the cortical interstitium are equal to those in plasma, except that the interstitium contains in addition 2 mM protein. The luminal hydrostatic pressure is taken as 12.3 mmHg at the proximal tubule (PT) inlet and is predicted to drop to 8.8 mmHg at the PT outlet in the base case.

Glucose Transport

The fluxes of glucose and Na⁺ across SGLT1 cotransporters are computed using the kinetic model developed by Wright and colleagues (6, 31). The six-state model assumes a Na⁺:glucose stoichiometry of 2:1, does not assume rapid binding to the transporter, and includes 14 rate constants. Flux equations can be found in Ref. 31, and updated parameter values are given in Ref. 55.

The kinetic behavior of SGLT2 does not appear to have been well characterized. Based on the sodium-alanine cotransporter model (18), the SGLT2 flux is calculated as

$$J_{\text{glu}}^{\text{SGLT2}}=\frac{X_{\text{SGLT2}}{k}_{\text{u}}^{\text{f}}}{\Phi }\hspace{0.17em}\left(C_{\text{glu}}^{\text{lum}}{C}_{{\text{Na}}^{+}}^{\text{lum}}\hspace{0.17em}\text{exp}(\zeta )-C_{\text{glu}}^{\text{cyt}}{C}_{{\text{Na}}^{+}}^{\text{cyt}}\right)$$ (1)

$$J_{{\mathrm{N}\text{a}}^{+}}^{\text{SGLT}2}=J_{{\text{glu}}^{}}^{\text{SGLT}2}$$ (2)

where

$$\begin{array}{c}\zeta =\text{F}\left({\Psi }_{\text{lum}}-{\Psi }_{\text{cyt}}\right)/\left(\text{RT}\right)\end{array}$$ (3)

$$\begin{array}{l}{n}^{\text{lum}}=\frac{C_{{\text{Na}}^{+}}^{\text{lum}}}{K_{m{\text{,Na}}^{+}}^{\text{SGLT2}}},n^{\text{cyt}}=\frac{C_{{\text{Na}}^{+}}^{\text{cyt}}}{K_{m{\text{,Na}}^{+}}^{\text{SGLT2}}},g^{\text{lum}}=\frac{C_{\text{glu}}^{\text{lum}}}{K_{m\text{,glu}}^{\text{SGLT2}}},g^{\text{cyt}}=\frac{C_{\text{glu}}^{\text{cyt}}}{K_{m\text{,glu}}^{\text{SGLT2}}}\end{array}$$

$$\Phi =\left(\text{1+}{n}^{\text{lum}}+g^{\text{lum}}+n^{\text{lum}}{g}^{\text{lum}}\right)\left(\text{1+}{n}^{\text{cyt}}{g}^{\text{cyt}}\right)+\left(1+n^{\text{cyt}}+g^{\text{cyt}}+n^{\text{cyt}}{g}^{\text{cyt}}\right)\left(1+n^{\text{lum}}{g}^{\text{lum}}\text{exp}(\zeta )\right)\hspace{0.17em}\hspace{0.17em}\hspace{0.17em}$$ (4)

XSGLT2 characterizes the density of SGLT2 transporters, kuf is the forward translocation rate of the unloaded carrier; Cglulum and CNa+lum, respectively, denote the luminal concentration of glucose and Na+; Cglucyt and CNa+cyt denote the cytosolic concentration of glucose and Na+; and Ψlum and Ψcyt represent the electric potential in the lumen and cytosol. R is the ideal gas constant, F is the Faraday constant, and T is the temperature. Lastly, Km,gluSGLT2 and Km,Na+SGLT2, respectively, denote the binding affinity of SGLT2 to glucose and Na+. Equation 1 posits a simultaneous mechanism for the transport of Na+ and glucose. It also assumes that 1) the binding affinities to a given ion on the luminal and cytosolic sides of the membrane are the same; 2) the forward (kuf) and backward k(ub) translocation rates of the unloaded carrier, and the backward translocation rate of the fully loaded carrier klb, are all equal; and 3) the forward translocation rate of the fully loaded carrier (klf) is given by (kufklb/kub)·exp(ζ), so as to satisfy thermodynamics constraints (i.e., the principle of microscopic reversibility). Figure 1 depicts predicted values of the SGLT2 flux as a function of Cglulum for varying values of CNa+lum. The flux increases steeply as Cglulum is raised from 0 to 5 mM, and much less rapidly as Cglulum is raised beyond 5 mM. The predicted apparent affinity to glucose, 1.0 mM, falls within the experimental range for rat SGLT2, albeit on the lower side (26, 56). Note that the apparent affinity to glucose, which is inferred from Fig. 1, differs from the binding affinity (Km,gluSGLT2) that is specified in the flux equation and given in Table 2.

Fig. 1.

Predicted flux of Na⁺ and glucose across the sodium-glucose cotransporter SGLT2, as a function of luminal glucose concentration ([G]_lum), for different values of luminal sodium concentration ([Na]_lum). The flux is normalized by its value at [G]_lum = 5 mM, [Na]_lum = 100 mM. The cysotolic concentration of glucose and Na⁺ is, respectively, taken as 5 and 10 mM, and the lumen-to-cysotol potential difference as −50 mV.

Table 2.

Glucose transport parameters

Parameter	Value	Reference
SGLT1 density	83.3 × 10−9 mmol·cm−2	This study
SGLT2 transport rate, XSGLT2kuf	1.30 × 10−3 cm4·mmol−1·s−1	This study
SGLT2 binding affinity to glucose, Km,gluSGLT2	4.9 mM	This study
SGLT2 binding affinity to sodium, Km,Na+SGLT2	25 mM	This study
GLUT1 maximum rate, VmGLUT1	3.00 × 10−6 mmol·s−1·cm−2	This study
GLUT1 affinity to glucose, KmGLUT1	2.0 mM	(23)
GLUT2 maximum rate, VmGLUT2	1.625 × 10−6 mmol·s−1·cm−2	This study
GLUT2 affinity to glucose, KmGLUT2	17 mM	(23)
Tight junction permeability to glucose	3.1 × 10−6 cm/s	(10)

SGLT, Na⁺-glucose cotransporter.

The flux of glucose across GLUT transporters is determined based on the Maki and Keiser model (23)

$$J_{\text{glu}}^{\text{GLUT}}=V_m^{\text{GLUT}}\left(\frac{K_m^{\text{GLUT}}\left(C_{\text{glu}}^{\text{cyt}}-C_{\text{glu}}^{\text{ext}}\right)}{\left(K_m^{\text{GLUT}}+C_{\text{glu}}^{\text{cyt}}\right)\left(K_{\text{m}}^{\text{GLUT}}+C_{\text{glu}}^{\text{ext}}\right)}\right)$$ (5)

where V_m^GLUT is the maximum glucose flux, K_m^GLUT is the glucose dissociation equilibrium constant, and C_glu^ext denotes the external (peritubular) glucose concentration.

Parameter values for glucose transport are listed in Table 2. The expression levels of SGLT1 and SGLT2, and the SGLT2 binding constants are chosen so that 1) the fraction of the glucose load that is reabsorbed by the S3 segment during SGLT2 inhibition is consistent with experimental measurements in mice (37), and 2) glucosuria begins when plasma glucose reaches ∼16 mM (see below).

Oxygen Consumption

The measurements of Welch et al. (52) suggest that, in rats, the whole kidney basal-to-total O₂ consumption ratio is 25–30% (52). By extrapolation, Evans et al. (7) estimated that this ratio ranges between ∼10 and 45% in rats under normal conditions (i.e., with FE_Na = 1%). We assume here that, in the proximal tubule, Q_O2^basal remains constant and equal to 20% of total O₂ consumption (Q_O2) under baseline conditions. That is

$${\text{Q}}_{\text{O2}}^{\text{basal}}=\text{0.20}\left({\text{Q}}_{\text{O2}}^{\text{basal}}+{\text{Q}}_{\text{O2}}^{\text{active*}}\right)=\left(0.20/0.80\right){\text{Q}}_{\text{O2}}^{\text{active*}}$$ (6)

where Q_O2^active is the rate of O₂ consumption for active Na⁺ reabsorption and the asterisk denotes base-case conditions. In turn, Q_O2^active is determined based on the ATP consumption of the basolateral Na-K-ATPase and the apical H-ATPase. Oxidative metabolism yields about 5 mol of ATP per mol of O₂ consumed, depending on the substrate (36). Furthermore, 1 mol of ATP is required to pump out 3 mol of Na⁺ via the Na-K-ATPase, and the vacuolar H-ATPase has a 1 ATP:2 H⁺ stoichiometry. We thus have

$${\text{Q}}_{\text{O2}}^{\text{active}}={\text{T}}_{\text{Na}}^{\text{active}}/\text{15+}{\text{T}}_{\text{H}}^{\text{active}}/\text{10}$$ (7)

where T_Na^active is the rate of Na⁺ transport across Na-K-ATPase pumps and T_H^active is the rate of H⁺ transport across H-ATPase pumps. Note that T_Na^active differs from the overall rate of Na⁺ reabsorption (denoted T_Na), as a significant fraction of Na⁺ is passively transported across the paracellular pathway.

Sodium transport-to-oxygen consumption ratios.

The efficiency of oxygen utilization is often assessed by determining the number of Na⁺ moles reabsorbed per O₂ moles consumed. We distinguish between two ratios:

$${\text{T}}_{\text{Na}}/{\text{Q}}_{\text{O2}}^{\text{active}}=\frac{{\text{T}}_{\text{Na}}^{\text{active}}{\text{+T}}_{\text{Na}}^{\text{passive}}}{\left({\mathrm{T}}_{\text{Na}}^{\text{active}}/\text{15+}{\mathrm{T}}_{\text{H}}^{\text{active}}/10\right)}$$ (8)

and

$${\text{T}}_{\text{Na}}/{\text{Q}}_{\text{O}2}=\frac{{\text{T}}_{\text{Na}}^{\text{active}}{\text{+T}}_{\text{Na}}^{\text{passive}}}{\left({\text{T}}_{\text{Na}}^{\text{active}}/\text{15+}{\text{T}}_{\text{H}}^{\text{active}}/{\text{10+Q}}_{\text{O2}}^{\text{basal}}\right)}$$ (9)

RESULTS

Base-Case Results

Under base-case conditions, the model predicts that 79% of filtered water is reabsorbed along the proximal tubule, assuming a single nephron glomerular filtration rate (SNGFR) of 30 nl/min. The model proximal tubule also, respectively, reabsorbs 72, 72, and 70% of the filtered loads of sodium, potassium, and chloride. Over the 1.1-cm-long model proximal tubule, basolateral Na-K-ATPase pumps actively transport 1,369 pmol Na⁺/min or 124 pmol Na⁺·min⁻¹·mm⁻¹; apical H-ATPase pumps secrete 56 pmol H⁺/min into the lumen or 5 pmol H⁺·min⁻¹·mm⁻¹. The rate of oxygen consumption for active Na⁺ transport (Q_O2^active) is therefore estimated as 1,369/15 + 56/10 = 96.8 pmol O₂/min or 8.8 pmol O₂·min⁻¹·mm⁻¹. Assuming that the basal O₂ consumption rate (Q_O2^basal) represents 20% of the total O₂ consumption rate (Q_O2) in the proximal tubule, the latter is estimated as 121.0 pmol O₂/min or 11.0 pmol O₂·min⁻¹·mm⁻¹.

By comparison, experimental values of Q_O2 in isolated proximal tubules range from 6 (2, 14) to ∼20 pmol·min⁻¹·mm⁻¹ (4), assuming a conversion factor of 0.23 μg protein/mm (48). Our predicted value is in the middle of this experimental range.

Our model predicts that about half of Na⁺ reabsorption along the full proximal tubule is passive (Table 3), the latter being mostly paracellular. Sodium transport across the tight junction is driven by both electrodiffusion and convection. Convection, which results from hydrostatic, osmotic, and oncotic pressure gradients and requires nonzero paracellular permeabilities to water and electrolytes, mediates reabsorption across the paracellular pathway. The lumen-to- intercellular space Na⁺ concentration gradient favors Na⁺ secretion; when the transepithelial voltage (ΔV_te) is not sufficiently positive to overcome the effects of the concentration gradient (as in the early proximal tubule, where ΔV_te is negative), electrodiffusion drives Na⁺ secretion. In the late proximal tubule (S2/S3), where ΔV_te is positive, electrodiffusion mediates Na⁺ reabsorption.

Table 3.

Normal rat proximal tubule function

Condition	TNaactive	TNapassive	TNa	QO2active	QO2basal	QO2	TNa/QO2
Base case
Full PT	1,369	1,661	3,030	96.8	24.2	121.0	25.0
S1–S2/S3	1,298/71	1,459/202	2,757/273	91.8/5.0	23.0/1.2	114.8/6.2	24.0/43.9
90% NHE inhibition
Full PT	1,076	255	1,331	85.0	24.2	109.2	12.2
S1–S2/S3	1,016/60	198/57	1,214/117	80.3/4.7	23.0/1.2	103.3/5.9	11.8/19.5
90% Na-K-ATPase inhibition
Full PT	435	1,275	1,710	66.3	24.2	90.5	18.9
S1–S2/S3	412/23	1,109/166	1,521/189	62.5/3.8	23.0/1.2	85.5/5.0	17.8/37.4
Full SGLT2 inhibition
Full PT	1,539	1,082	2,621	108.4	24.2	132.6	19.8
S1–S2/S3	1,383/156	1,020/62	2,403/218	97.0/11.4	23.0/1.2	120.0/12.6	20.0/17.3

T_Na^active, T_Na^passive, and T_Na: active, passive, and total Na⁺ reabsorption (in pmol·min⁻¹·nephron⁻¹); Q_O2^active, Q_O2^basal, and Q_O2: O₂ consumption for active Na⁺ reabsorption, other cellular processes, and total (in pmol·min⁻¹·nephron⁻¹); NHE, Na⁺/H⁺ exchanger.

Total Na⁺ reabsorption is 3,030 pmol Na⁺/min, so that T_Na/Q_O2^active equals 31.3, and T_Na/Q_O2 equals 25.0. Experimental measurements of T_Na/Q_O2 ratios in the proximal tubule appear to be rare. Baines and Ho (2) estimated T_Na/Q_O2^active as 16, but acknowledged that this value is an underestimate, since it is based on oligomycin-inhibited Q_O2, whereas oligomycin inhibits the production of ATP for all purposes, not just for Na-K-ATPase pumps. If Q_O2^active is taken instead as the sum of EIPA- and phloridzin-sensitive Q_O2, the experimental ratio equals 44 (2).

The efficiency of oxygen utilization varies significantly between the early and late proximal tubule, because the balance between passive and active sodium reabsorption differs between S1–S2 and S3. In S1–S2, T_Na^passive and T_Na^active are approximately equal, whereas T_Na^passive is 2.9 times greater than T_Na^active in S3 (Table 3). As a result, the number of Na⁺ moles reabsorbed per O₂ moles consumed is 24.0 in the early proximal tubule vs. 43.9 in the late proximal tubule. Since S1 and S2 together represent 88% of the total proximal tubule length, the T_Na/Q_O2 ratio for the full proximal tubule (25.0) is close to that for S1–S2.

As illustrated in Fig. 2, the net rate of transcellular Na⁺ reabsorption differs somewhat from T_Na^active, since the basolateral membrane expresses Na⁺ transporters other than Na-K-ATPase pumps, namely sodium-bicarbonate cotransporters and sodium-dependent chloride-bicarbonate exchangers (NDCBE) (1, 32). NDCBE mediates Na⁺ entry into the cell, whereas Na⁺-HCO₃⁻ cotransporters drive Na⁺ efflux. Since their net contribution to the transcellular Na⁺ flux is small relative to that of Na-K-ATPase pumps, T_Na^active can be taken as a rough estimate of the transcellular Na⁺ flux, and the passive Na⁺ flux approximates the paracellular Na⁺ flux.

Fig. 2.

Schematic diagram of the proximal tubule cell with predicted fluxes (in pmol·min⁻¹·mm tubule⁻¹) at the midpoint of the S1–S2 segments (A) and the S3 segment (B). Transporters for solutes other than Na⁺, K⁺, Cl⁻ and glucose are not shown. Only a small fraction of the Na⁺ flux goes through SGLT2 at the midpoint of the S1–S2 segment because most of the glucose has already been reabsorbed; see Fig. 4. The relative contribution of the paracellular pathway to net Na⁺ reabsorption is higher in the S3 segment.

Effects of Sodium Transport Inhibitors

Na⁺/H⁺ exchanger inhibition.

We then examined how changes in Na⁺ reabsorption affect T_Na/Q_O2 ratios. In the first set of simulations, we progressively inhibited the expression of the apical Na⁺/H⁺ (NHE) exchanger. As shown in Fig. 3 (solid lines), the model predicts that NHE inhibition drastically reduces net Na⁺ reabsorption, but it lowers Na-K-ATPase activity only moderately (by 40% with full NHE inhibition). Indeed, since NHE inhibition lowers intracellular Na⁺ concentrations, it substantially stimulates basolateral Na⁺ uptake via NDCBE; the partial recycling of Na⁺ on the peritubular side significantly reduces the efficacy of the sodium pump. On the luminal side, NHE inhibition is slightly compensated for by increased transport across apical Na⁺-H₂PO₄⁻ cotransporters and, to a small degree, SGLT2. In the base case, NHE, SGLT2, SGLT1, and Na⁺-H₂PO₄⁻ cotransporters carry 1,381, 157, 4, and 61 pmol Na⁺/min, respectively, into the cell; when NHE is fully inhibited, SGLT2, SGLT1, and Na⁺-H₂PO₄⁻ cotransporters carry 158, 5, and 113 pmol Na⁺/min, respectively, into the cell. Because filtered glucose is almost entirely reabsorbed under baseline conditions, blocking transport across NHE has a small effect on SGLT2 and SGLT1 fluxes. In contrast, the higher tubular Na⁺ flow nearly doubles the Na⁺ flux through Na⁺-H₂PO₄⁻ cotransporters.

Fig. 3.

A: active (A1; T_Na^active) and total (A2; T_Na) Na⁺ transepithelial transport (in pmol/min) as Na⁺/H⁺ exchanger (NHE; solid lines), Na-K-ATPase (dashed lines), or SGLT2 (dotted lines) is progressively inhibited. B: corresponding active (B1; Q_O2^active) and total (B2; Q_O2) O₂ consumption (in pmol/min). C: corresponding T_Na/Q_O2^active (C1) and T_Na/Q_O2 (C2) ratios. The transcellular flux of Na⁺ is approximately equal to the active flux, so that the paracellular flux approximately corresponds to the difference between T_Na and T_Na^active. The model predicts that NHE and Na-K-ATPase inhibition lowers O₂ consumption, whereas SGLT2 inhibition raises Q_O2.

In addition, NHE inhibition is predicted to substantially lower the paracellular reabsorption of Na⁺: since it impairs bicarbonate reabsorption, it reduces the transepithelial Cl⁻ gradient and Cl⁻ reabsorption in late proximal tubule, thereby rendering ΔV_te less positive. The latter, combined with decreased Na⁺ convection (due to lower water reabsorption), significantly reduces T_Na^passive. In fact, as fractional NHE inhibition nears 100%, the paracellular Na⁺ flux changes direction, i.e., there is net Na⁺ secretion across tight junctions (Fig. 3 shows that T_Na becomes lower than T_Na^active). Since passive Na⁺ reabsorption falls more steeply than active Na⁺ reabsorption with increasing NHE inhibition, the T_Na/Q_O2^active ratio decreases (see Eq. 9) and so does the overall efficiency of oxygen utilization (T_Na/Q_O2).

Na-K-ATPase inhibition.

Inhibition of Na-K-ATPase pumps results in high intracellular Na⁺ concentrations, reduced transport across NHE and SGLT, and a large decrease in T_Na^active. The substantial increase in intracellular Na⁺ concentrations considerably reduces Na⁺ and HCO₃⁻ uptake across the basolateral cotransporter NDCBE; in fact, the direction of transport across NDCBE is reversed in the early proximal tubule, i.e., NDCBE mediates Cl⁻ secretion and Na⁺ and HCO₃⁻ reabsorption. As apical H⁺ secretion via H-ATPase pumps increases concomitantly, ΔV_te becomes less negative in the early proximal tubule, and more positive in the late proximal tubule.

The subsequent increase in the electrodiffusion of Na⁺ across the paracellular route is nevertheless counteracted by decreased convection (since reduced transcellular Na⁺ reabsorption diminishes water reabsorption). If fractional inhibition of Na-K-ATPase stays below 60%, the two effects counterbalance each other, so that T_Na^passive remains approximately constant. Under these conditions, the relative contribution of the paracellular pathway to net Na⁺ transport is augmented, and both T_Na/Q_O2^active and T_Na/Q_O2 increase slightly. As fractional Na-K-ATPase inhibition is raised beyond 60%, the effects of decreased convection become predominant, passive Na⁺ transport begins to drop more rapidly than active Na⁺ transport, and the efficiency of oxygen utilization diminishes (Fig. 3).

Impact of Glucose Transport and Metabolism

As noted above, evidence suggests that in vivo, glucose is not an important metabolic substrate in the proximal tubule (24). In fact, that segment has a large capacity for gluconeogenesis, which is activated by stimuli such as fasting, hypoglycemia, and diabetes (11, 25). Thus we did not account for intracellular glucose consumption in the simulations above. In vitro, however, glucose is sometimes the only metabolic substrate. Base-case results indicate that if glucose were to provide all the energy needed to actively pump out 1,369 pmol Na⁺/min over the 1.1-cm-long proximal tubule, the corresponding consumption rate, namely 1,369/(15 × 6) = 15.2 pmol glucose/min, would represent ∼10% of the filtered load of glucose (5 mM × 30 nl·min⁻¹·nephron⁻¹ = 150 pmol·min⁻¹·nephron⁻¹). In a set of simulations, we assumed that glucose is consumed so as to satisfy the energy requirements of Na-K-ATPase pumps. This assumption has a negligible impact on predicted T_Na/Q_O2 ratios (results not shown), since it does not significantly affect the apical entry of glucose and Na⁺ into proximal tubule cells.

We examined the effects of increasing plasma glucose concentration (C_glu^p). As illustrated in Fig. 4A, the filtered load of glucose is fully reabsorbed by the proximal tubule when C_glu^p remains <16 mM. Above that value, the proximal tubule glucose transport system is saturated and >1% of filtered glucose is delivered downstream. This predicted value is in accordance with measured values of the glucosuria threshold in the rat kidney under normal conditions, which range from 12 mM (17) to slightly <20 mM (13, 19). Note that the glucosuria threshold is higher in diabetic rats (21).

Fig. 4.

Predicted impact of glucose on the metabolic efficiency of the proximal tubule. A: fractional luminal flow of glucose (relative to filtered load) along the proximal tubule, for different plasma glucose concentrations ([G]). B: active and total Na⁺ transepithelial transport as a function of [G]. C: corresponding Q_O2^active and Q_O2. D: corresponding T_Na/Q_O2^active and T_Na/Q_O2.

The higher C_glu^p is, the greater the rate of Na⁺ reabsorption across SGLT is (up to the maximum transport rate), and the higher T_Na^active becomes (Fig. 4B). However, the effects of C_glu^p on T_Na^passive are not monotonic: passive Na⁺ transport first increases, then decreases, as C_glu^p is raised. Indeed, below the glucosuria threshold, the faster rate of transcellular Na⁺ reabsorption stimulates paracellular water transport and, therefore, Na⁺ convection. Above the threshold, however, the glucose that remains in the lumen exerts significant osmotic effects and slows down water reabsorption, which in turn reduces Na⁺ convection and T_Na^passive. As a result, the T_Na/Q_O2 ratio is predicted to first slightly rise, then to diminish with increasing C_glu^p (Fig. 4D).

SGLT2 inhibition.

The predicted impact of SGLT2 inhibition on T_Na and Q_O2 at various levels of hyperglycemia is illustrated in Fig. 5 and summarized in Table 3. As observed experimentally, the model predicts that, under normoglycemia, SGLT2 inhibition is partially compensated for by a downstream increase in transport across SGLT1 (Fig. 5D). In addition, higher luminal glucose concentrations induce osmotic diuresis, with two consequences. On the one hand, the resulting higher luminal flow increases the microvillous torque and thereby upregulates the expression of transcellular transporters. The increase in NHE density, in particular, strongly stimulates Na⁺ reabsorption across the exchanger. Since the NHE flux elevation more than compensates for reduced Na⁺ entry via SGLT2, T_Na^active and Q_O2^active increase slightly in S1–S2 and more significantly in S3 (Table 3). On the other hand, paracellular Na⁺ reabsorption decreases in tandem with water reabsorption. Thus SGLT2 inhibition is predicted to lower overall T_Na as well as T_Na/Q_O2^active. Note that when SGLT2 is fully inhibited, the proximal tubule is predicted to reabsorb 43% of the filtered load of glucose under normoglycemic conditions, which is similar to measured values in mice (37).

Fig. 5.

Predicted impact of SGLT2 inhibition on Na⁺ reabsorption and O₂ consumption in the rat proximal tubule for plasma glucose of 5 mM (black), 15 mM (red), and 25 mM (blue). A: active and total Na⁺ transport (respectively denoted by solid and dashed lines) as SGLT2 is progressively inhibited, for differing levels of hyperglycemia. B: corresponding Q_O2^active and Q_O2. C: corresponding T_Na/Q_O2^active and T_Na/Q_O2. D: percentage of glucose reabsorbed by the proximal tubule that is attributable to the S3 segment. E: fractional reabsorption of glucose by the proximal tubule (relative to filtered load) with 0, 50, and 100% SGLT2 inhibition, for differing levels of hyperglycemia.

Our model predicts that under these conditions, glucose reabsorption is almost entirely, but not fully, mediated by SGLT1. That is, the transepithelial glucose flux has a small, but not negligible, paracellular component; as shown in Fig. 5D, a nonnegligible fraction of glucose is reabsorbed upstream from the S3 segment, via the paracellular pathway, even when SGLT2 is fully inhibited. In the base case (no SGLT2 inhibition, normoglycemia), however, our model predicts that the paracellular pathway mediates net glucose secretion: the backleak of glucose across tight junctions, which occurs mainly in the late proximal tubule, amounts to 8 pmol·min⁻¹·nephron⁻¹, or 5% of the filtered load.

At higher glucose levels, SGLT2 inhibition is similarly predicted to raise T_Na^active and Q_O2^active (proportionally more in S3 than in S1–S2), to reduce paracellular Na⁺ reabsorption, and thus to lower T_Na/Q_O2^active. As plasma and interstitial glucose concentrations rise, the compensatory increase in SGLT1-mediated transport is less able to counterbalance SGLT2 inhibition, and the fractional reabsorption of glucose by the proximal tubule falls. With plasma glucose equal to 25 mM, the proximal tubule is predicted to reabsorb ∼6% of the filtered load of glucose when SGLT2 is fully inhibited (Fig. 5E).

Impact of GFR Changes

Diabetes is known to induce hyperfiltration (41). The isolated effects of increasing SNGFR are shown in Fig. 6. Given the flow dependence of transporter expression (51), transcellular Na⁺ reabsorption rises in tandem with SNGFR, even more rapidly than paracellular Na⁺ reabsorption. The predicted T_Na/Q_O2^active ratio therefore decreases. Assuming that basal O₂ consumption is unaffected by the glomerular filtration rate increase, T_Na rises slightly less, in relative terms, than Q_O2: the model predicts a 2.4- and 2.7-fold increase in T_Na and Q_O2, respectively, as SNGFR is raised from 20 to 45 nl/min. As a consequence, the overall efficiency of oxygen utilization (T_Na/Q_O2) in the proximal tubule decreases to a small extent with increasing SNGFR.

Fig. 6.

Predicted effects of the glomerular filtration rate on the metabolic efficiency of the proximal tubule. A: active and total Na⁺ transepithelial transport as single nephron glomerular filtration rate (SNGFR) is varied, at normal blood glucose (5 mM). B: corresponding Q_O2^active and Q_O2. C: corresponding T_Na/Q_O2^active and T_Na/Q_O2.

Diabetic Rat Proximal Tubule

Baines and Ho (2) found that oligomycin-sensitive Q_O2 is 30–40% higher in proximal tubules from diabetic rats, compared with those from control rats. The rate of active Na⁺ transport is also higher in the diabetic rat proximal tubule, but its relative increase is less than that in Q_O2^active. Their findings indicate that the number of Na⁺ moles actively reabsorbed per O₂ moles consumed (taken as 15 in our base case) is reduced from 16.2 to 13.2 in diabetic rat proximal tubules. Diabetes also induces renal hypertrophy and alters the expression of glucose transporters. Seyer-Hansen et al. (39) reported a 17% increase in the proximal tubule diameter of rats after 47 days of diabetes. Vallon et al. (44) observed that in diabetic mice with glucosuria, the protein expression of SGLT2 was augmented by 38% compared with control mice, whereas that of SGLT1 was reduced by 33%; these changes were basically maintained during chronic SGLT2 inhibition.

As recapitulated in Table 4, we simulated diabetic conditions by simultaneously raising plasma glucose (to 22 mM) (45) and SNGFR (to 45 nl/min), varying the expression of SGLT2 and SGLT1 as observed by Vallon et al. (44), raising the proximal tubule diameter from 25 to 30 μm, increasing basal O₂ consumption, and decreasing the T_Na^active/Q_O2^active ratio by 20%. The effects of SGLT2 inhibition (0, 50, and 100%) on Na⁺ transport and O₂ consumption are shown in Fig. 7.

Table 4.

Normal vs. diabetic rat PT parameter values

	Normal	Diabetic
Tubule diameter	25 μm	30 μm
SNGFR	30 nl/min	45 nl/min
QO2basal	24.2 pmol/min	33.9 pmol/min
Plasma glucose	5 mM	22 mM
SGLT1 density	83.3 × 10−9 mmol/cm2	55.8 × 10−9 mmol/cm2
SGLT2 transport rate	1.30 × 10−9 cm4·mmol−1·s−1	1.80 × 10−9 cm4·mmol−1·s−1
TNaactive/QO2active	15	12

SNGFR, single nephron glomerular filtration rate.

Fig. 7.

A: total Na⁺ transepithelial transport for base case and three diabetic cases. The diabetic rat proximal tubule is simulated as described in Table 4. “Diabetes-A,” “Diabetic-B,” and “Diabetic-C”: diabetic parameters with 0, 50, and 100% inhibition of SGLT2, respectively. B: corresponding Q_O2^active. C: corresponding T_Na/Q_O2. Diabetes is predicted to substantially increase O₂ consumption in the proximal tubule and to lower the metabolic efficiency of Na⁺ transport. These effects are accentuated by SGLT2 inhibition.

In the absence of inhibition, the proximal tubule of diabetic rats is predicted to reabsorb ∼75% more Na⁺ than that of normal rats, and to consume 2.8 times more O₂ for Na⁺ transport (Table 5). As a result, T_Na/Q_O2^activeand T_Na/Q_O2 are 37% and 30% lower in diabetic rat proximal tubules. The largest contributor to the T_Na and Q_O2^active increase is the augmented SNGFR (Fig. 8), which increases the tubular sodium and glucose loads. The increase in Q_O2^active occurs primarily along the S1–S2 segment, both in absolute and relative terms. If SNGFR were maintained at 30 nl/min while all other “diabetic” parameters were left unchanged, proximal Na⁺ reabsorption would be only 5% higher in diabetic rats than in control rats, due to increased sodium-glucose cotransport, and active O₂ consumption by the proximal tubule would be 57% higher (owing mostly to the lower T_Na^active/Q_O2^active ratio). By contrast, if the expression of SGLT1 and SGLT2 were kept at control levels while all other “diabetic” changes were accounted for, the model predicts that net Na⁺ reabsorption would be 8% lower than in the fully diabetic rat proximal tubule. Glucose reabsorption would decrease by 19% in S1–S2 and would increase by a factor of 1.7 in S3. Net glucose transport would decrease by 16%, from 923 pmol/min (fully diabetic rat proximal tubule) to 774 pmol/min (diabetic rat proximal tubule without changes in SGLT expression). Stated differently, fractional glucose excretion is predicted as 6.8% in the fully diabetic rat proximal tubule and would be significantly higher (21.8%) if SGLT expression were not modified.

Table 5.

Diabetic rat PT function

Condition	TNaactive	TNapassive	TNa	QO2active	QO2basal	QO2	TNaactive/QO2active
Diabetes
Full PT	3,100	2,194	5,294	269.8	33.9	303.7	17.4
S1–S2/S3	2,996/104	1,888/306	4,884/410	260.7/9.1	32.2/1.7	292.9/10.8	16.7/37.9
Diabetes and 90% NHE inhibition
Full PT	2,558	863	3,421	244.1	33.9	278.0	12.3
S1–S2/S3	2,477/81	619/244	3,096/325	236.1/8.0	32.2/1.7	268.3/9.7	11.5/33.3
Diabetes and 90% Na-K-ATPase inhibition
Full PT	1,006	1,278	2,284	159.5	33.9	193.4	11.8
S1–S2/S3	953/53	1,262/16	2,215/69	150.5/9.0	32.2/1.7	182.7/10.7	12.1/6.4
Diabetes and full SGLT2 inhibition
Full PT	3,349	299	3,648	288.0	33.9	321.9	11.3
S1–S2/S3	3,145/204	461/−162	3,606/42	270.5/17.5	32.2/1.7	302.7/19.2	11.9/2.2

A negative T_Na^passive value signifies that Na⁺ is secreted via the paracellular pathway.

Fig. 8.

Predicted impact of diabetes-related changes on active and total Na⁺ reabsorption and O₂ consumption in the S1–S2 segments (A and B), the S3 segment (C and D), and the full proximal tubule (E and F). The diabetic rat proximal tubule is simulated by elevating plasma glucose ([G]), increasing SGLT2 expression and decreasing SGLT1 expression, increasing proximal tubule diameter, increasing basal O₂ consumption, and increasing SNGFR, and is represented by the “All” case at the far right. The 6 cases in the center illustrate the effects of isolated changes in each of these parameters. Note the differences in the y-axis scales.

As illustrated in Fig. 7, the efficiency of oxygen utilization by the diabetic proximal tubule further decreases with increasing levels of SGLT2 inhibition, as paracellular Na⁺ transport is gradually reduced in tandem with water reabsorption (see above). We also examined the impact of inhibiting NHE or Na-K-ATPase pumps on diabetic rat proximal tubule function. The predicted profiles of T_Na and Q_O2^active as a function of the degree of inhibition were qualitatively similar to those obtained for the normal rat proximal tubule (Fig. 3) but were shifted upwards (i.e., all values were higher). Results are summarized in Table 5.

DISCUSSION

In this study, we expanded a cell-based model of the proximal tubule to examine how pharmacological inhibition of sodium and/or glucose transporters, in normal and diabetic rats, affects O₂ consumption and Na⁺ transport efficiency along the different proximal tubule segments.

Oxygen Consumption

Based on in vivo experimental data (7, 52), we assumed in this study that basal O₂ consumption represents 20% of total O₂ consumption in the rat proximal tubule. Note that in vitro studies yield higher estimates. The basal-to-total O₂ consumption ratio was found to range between 0.3 and 0.5 in the rabbit proximal tubule (3, 16). In isolated rat proximal tubule, oligomycin-inhibited Q_O2, which reflects the rate of oxidative phosphorylation to produce ATP, was found to represent 45% of total Q_O2 (2). In suspensions of rat cortical cells, ouabain reduced O₂ consumption by ∼30% in one study (28) and 60% in another (30). In the latter studies, underestimation of the contribution of the sodium pump to Q_O2 can be ascribed at least partly to the fact that the (predominant) α₁-isoform of the rat Na-K-ATPase is ouabain insensitive.

The predicted rate of total oxygen consumption in the proximal tubule, 11 pmol O₂·min⁻¹·mm⁻¹, falls at the center of the experimental range (6 to 20 pmol·min⁻¹·mm⁻¹) (2, 4, 14). As shown in Fig. 3, our results suggest that whereas NHE and Na-K-ATPase inhibition each reduce active Na⁺ reabsorption and O₂ consumption, SGLT2 inhibition raises T_Na^active and Q_O2^active, because it is compensated for by increased transport across both SGLT1 and NHE. Full SGLT2 inhibition is predicted to increase Q_O2^active by 12%, and total Q_O2 by 9% under normoglycemia (Table 3).

Metabolic Efficiency of Na⁺ Transport

In the base case, the predicted T_Na/Q_O2 is 25. We did not find experimental measurements of this ratio in the rat proximal tubule specifically. Reported values of T_Na/Q_O2 for the whole kidney range between 15 and 25 in the rat (4, 7, 53). The efficiency of oxygen utilization for Na⁺ transport increases with the passive-to-active Na⁺ reabsorption ratio. As expected, partial inhibition of Na-K-ATPase pumps raises the relative contribution of passive Na⁺ transport and thereby increases the metabolic efficiency of the proximal tubule, while substantially reducing overall Na⁺ transport (Fig. 3, dashed lines). In addition, Na-K-ATPase inhibition is predicted to slightly enhance bicarbonate reabsorption via basolateral NDCBE cotransporters. In contrast, our results suggest that inhibition of NHE, instead of shifting a greater fraction of Na⁺ reabsorption to the paracellular pathway, decreases the relative contribution of the latter and thereby lowers T_Na/Q_O2. Indeed, inhibition of Na⁺/H⁺ exchange decreases bicarbonate reabsorption, which in turn lowers Cl⁻ reabsorption in the late proximal tubule. The subsequent decrease in ΔV_te (which becomes less lumen-positive) reduces the driving force for paracellular Na⁺ reabsorption. Conversely, reducing Na⁺ transport across the electrogenic transporter SGLT (e.g., by lowering the plasma concentration of glucose) augments ΔV_te, enhances paracellular Na⁺ reabsorption and thus T_Na/Q_O2. Note that the response to SGLT2 inhibition is different, as described below.

Metabolic Efficiency of the Proximal Tubule in Diabetic Rats

We simulated a diabetic rat proximal tubule by simultaneously increasing the proximal tubule diameter, SGLT2 expression, SNGFR, as well as plasma and peritubular glucose concentrations, and decreasing SGLT1 expression and the T_Na^active/Q_O2^active ratio (Table 4). There are few micropuncture studies of the proximal tubule in diabetic rats. A quantitative comparison of our results with these experimental data is difficult, because GFR and plasma glucose concentrations vary widely in these studies and the micropuncture site is not precisely identified. Nonetheless, our model predictions agree qualitatively with the observed increase in the fractional reabsorption of water and sodium (diabetic vs. normal rat proximal tubule) (34, 33, 40, 43, 45).

The simulated decrease in T_Na^active/Q_O2^active in the diabetic rat proximal tubule, by itself, lowered T_Na/Q_O2^active, but another factor further reduced this ratio: the paracellular component of T_Na rose less than the transcellular component. As shown in Fig. 8, the main factor underlying the T_Na augmentation is the SNGFR increase. Per se, the latter is predicted to raise T_Na^active more than T_Na^passive because the higher filtration rate enhances the microvillous torque, which then induces a coordinated increase in luminal and basolateral transporter expression (51).

Based on experimental data (28, 30), we assumed that basal O₂ consumption in the proximal tubule is 40% higher in the diabetic rat than in the normal rat. The hypertrophy and increased gluconeogenesis that characterize the diabetic rat proximal tubule are likely to contribute to the increase in basal O₂ consumption. With this assumption, the model predicts that T_Na/Q_O2 is 30% lower in the diabetic rat proximal tubule than in the normal rat proximal tubule. Interestingly, at the organ level, in vivo measurements suggest that the whole kidney T_Na/Q_O2 does not vary between normoglycemic and diabetic rats (27, 29).

SLGT2 inhibitors are being developed as antidiabetic drugs (42). As shown in Fig. 5E, SGLT2 inhibition considerably reduces glucose reabsorption by the proximal tubule, even if glucose transport across SGLT1 increases in partial compensation. Our results suggest that SGLT2 inhibition can reduce the metabolic efficiency of the proximal tubule, as it stimulates active transcellular Na⁺ reabsorption via NHE and increases glucose-induced osmotic diuresis, thereby reducing solute convection across tight junctions and lowering the relative contribution of the paracellular pathway to overall Na⁺ reabsorption. Thus SGLT2 inhibition can decrease the number of Na⁺ ions reabsorbed per O₂ moles consumed.

Na⁺ Transport and O₂ Consumption in the S3 Segment

As illustrated in Table 3, oxygen consumption varies significantly between the cortical and medullary portions of the proximal tubule, even when differences in length are accounted for. In our base-case scenario, the S3 segment (which represents 12% of the proximal tubule length) reabsorbs 9% of the filtered Na⁺, but it consumes <6% of the proximal tubule Q_O2, because the paracellular pathway mediates a greater fraction of Na⁺ transport, relative to the transcellular pathway, in S3 than in S1–S2. Indeed, as noted above, transcellular NaHCO₃ reabsorption predominates in the early proximal tubule, whereas NaCl reabsorption, which occurs via both transcellular and paracellular pathways, prevails in the late proximal tubule (32, 35). The oxygen consumption rates of the different proximal tubule segments correlate with the oxygen tension of their respective regions: the cortex, where the S1 and S2 segments reside, is well oxygenated with an oxygen tension of 40–50 mmHg, whereas the outer medulla, where the S3 segment is found, has a much lower oxygen tension of ∼20 mmHg. As a result, even with a relative low Q_O2, the S3 segment is more vulnerable to hypoxic injury.

Our results suggest that inhibition of NHE or Na-K-ATPase lowers O₂ consumption to the same extent in S1–S2 and S3, whereas inhibition of SGLT2 raises Q_O2; the relative increase in Q_O2 is much greater in S3 (102%) than in S1–S2 (5%), because SGLT2 inhibition shifts a significant fraction of Na⁺ reabsorption downstream.

Conversely, our model predicts that diabetes increases active Na⁺ reabsorption and O₂ consumption to a greater extent in S1–S2 than in S3, relative to control rats, for the following reason. Our simulations suggest that the main factor driving the changes in T_Na and Q_O2 is hyperfiltration: the subsequent increase in proximal tubule luminal flow greatly enhances the torque exerted on the microvilli and thereby stimulates transcellular transport (5, 51). Since the rate of flow decreases along the proximal tubule, T_Na^active and Q_O2^active are predicted to rise to a greater extent in the early proximal tubule than in the late proximal tubule. Assuming a 40% increase in basal O₂ consumption, Q_O2 is 2.6 times higher in S1–S2 (diabetic vs. normal rat) and 1.7 times higher in S3 (Table 5). Full inhibition of SGLT2 in the diabetic rat proximal tubule greatly enhances the fraction of O₂ that is consumed in the S3 segment: the predicted Q_O2 increases by 3% in S1–S2, and by 77% in S3. Thus, when SGLT2 is inhibited, the metabolic efficiency of Na⁺ transport, as assessed by T_Na/Q_O2, becomes higher in S1–S2 than in S3, both in the normal rat proximal tubule (Table 3) and in the diabetic rat proximal tubule (Table 5).

Paracellular Water Transport and Metabolic Efficiency

The model predicts that, under normal conditions, convection (i.e., solvent drag) contributes significantly to paracellular Na⁺ transport. In the rat a significant fraction of water reabsorption is thought to occur paracellularly, as suggested by several studies showing reflection coefficients <1 for the main solutes (9, 12, 49, 54). The role of paracellular water transport is less clear in the mouse. Experiments by Schnermann et al. (38) indicate that aquaporin 1 (AQP1) deletion in mice results in substantially decreased transepithelial proximal tubule water permeability and defective fluid reabsorption. These investigators estimated that <20% of osmotically driven transepithelial water transport in the mouse proximal tubule is paracellular. Furthermore, Vallon et al. (47) observed that AQP1 deletion in mice generates marked luminal hypotonicity in proximal tubules in vivo.

In the rat, the reflection coefficient of Cl⁻ (taken to be σ = 0.30 in the present model) is much smaller than that of other major solutes (σ = 0.75–0.90) (49). Thus the model predicts that paracellular convective solute flux contains a disproportionately large amount of Cl⁻, which, taken in isolation, raises the transepithelial voltage, enhances paracellular Na⁺ diffusion and thereby increases the metabolic efficiency of Na⁺ transport. When paracellular water transport is eliminated, ΔV_te decreases and paracellular Na⁺ reabsorption becomes negligible. Given the numerous interspecies differences between the rat and the mouse, it is not clear that the present model, which is formulated for the rat, can make meaningful predictions for the mouse. To understand the implications of the relatively small amount of paracellular water transport on the metabolic efficiency of Na⁺ transport in the mouse, a mathematical model of the mouse proximal tubule may prove useful. Likewise, any insights into the role of paracellular proximal tubule convection in humans would be highly desirable.

Tubuloglomerular Feedback

Model results indicate that glucose delivery to the S3 segment increases at higher levels of SGLT2 inhibition (Fig. 5). Glucose delivery to the S3 segment is a result of two counterbalancing processes: glucose filtration by the glomerulus and glucose reabsorption by S1–S2. The results shown in Fig. 5 were obtained assuming a constant GFR; thus filtered glucose depends only on the level of hyperglycemia. But GFR is affected by a number of factors, including tubuloglomerular feedback (TGF), which responds to changes in tubular fluid (Cl⁻) at the macula densa. Hyperglycemia enhances proximal tubular Na⁺ and Cl⁻ reabsorption in part by enhancing sodium-glucose cotransport; the latter lowers the Cl⁻ concentration at the macula densa and via TGF contributes to diabetic hyperfiltration (45).

At normoglycemia or low levels of hyperglycemia, SGLT2 inhibition induces sustained glucosuria and increased delivery of glucose to the S3 segment, because the TGF-mediated reduction in GFR is sufficiently small that the inhibition of glucose reabsorption predominates. At sufficiently high levels of hyperglycemia, however, the TGF-mediated reduction in GFR becomes more important. Indeed, studies by Vallon et al. (44, 46) have suggested an inverse relationship between initial blood glucose levels/hyperglycemia and the degree to which SGLT2 inhibition increases glucose delivery to the late proximal tubule and urine. These studies indicate that at sufficiently high levels of initial hyperglycemia decreased glucose reabsorption is compensated for by TGF-mediated reduction in the volume of filtered plasma. Moreover, glucosuria lowers blood glucose levels, which further reduces glucose filtration. Consequently, even though glucose reabsorption is reduced along the S1–S2 segment, the reduced filtered glucose results in a steady-state glucose delivery downstream of S1–S2 that is relatively unaffected by strong SGLT2 inhibition under these conditions (44, 46). To account for these results, the present model will need to be extended to include the loop of Henle and to represent the influence of glucose reabsorption on GFR via TGF.

In summary, our model of the rat proximal tubule suggests that the T_Na/Q_O2 ratio (transport efficiency) is 80% higher in S3 than in S1–S2, due to the greater contribution of the paracellular pathway to Na⁺ transport in the former segment. Inhibition of NHE or Na-K-ATPase reduces Na⁺ transport and O₂ consumption, as well as Na⁺ transport efficiency in the proximal tubule. SGLT2 inhibition also reduces proximal tubular T_Na but increases Q_O2. These effects are relatively more pronounced in the S3 vs. the S1–S2 segments. SGLT2 inhibitors reduce proximal tubule Na⁺ transport efficiency in part by lowering the relative contribution of the paracellular vs. the transcellular pathway to overall Na⁺ reabsorption. This is due to enhanced NHE- and SGLT1-mediated Na⁺ reabsorption and glucose-induced osmotic diuresis. The latter is based on the assumption of significant paracellular water reabsorption in the proximal tubule. In other words, if paracellular proximal tubule water transport is less prominent in humans than proposed for the rat, then the osmotic effects of SGLT2 inhibition on paracellular Na⁺ transport would be diminished.

Our model further predicts a significant increase in T_Na and Q_O2, and a reduction in T_Na/Q_O2, in the proximal tubule of diabetic rats, flowing mostly to hyperfiltration. This prominent influence of glomerular hyperfiltration on proximal tubule function may contribute to its proposed role as a predictor of long-term chronic kidney diseases and negative diabetic kidney outcome. SGLT2 inhibition lowers diabetic hyperfiltration (42), and thus the net effect on T_Na, Q_O2 and Na⁺ transport efficiency in the proximal tubule will largely depend on the extent to which GFR is reduced. In other words, the magnitude of the GFR decrease in response to SGLT2 inhibitors may determine whether a given individual responds with an increase or a decrease in T_Na, Q_O2, and Na⁺ transport efficiency in the PT, which especially in the highly vulnerable S3 segment may have clinical relevance for the prevention or promotion of hypoxia and negative long-term outcome.

GRANTS

This research was supported by the Department of Veterans Affairs (to V. Vallon) and by National Institute of Diabetes and Digestive and Kidney Diseases Grants R01-DK-089066 (to A. T. Layton) and R01-DK-56248 (to V. Vallon) and University of Birmingham at Alabama/University of California San Diego O'Brien Center for Acute Kidney Injury Research Grants P30-DK-079337 and R01-HL-94728 (to V. Vallon).

DISCLOSURES

No conflicts of interest, financial or otherwise, are declared by the author(s).

AUTHOR CONTRIBUTIONS

Author contributions: A.T.L., V.V., and A.E. conception and design of research; A.T.L. and A.E. performed experiments; A.T.L., V.V., and A.E. analyzed data; A.T.L., V.V., and A.E. interpreted results of experiments; A.T.L. prepared figures; A.T.L. and A.E. drafted manuscript; A.T.L., V.V., and A.E. edited and revised manuscript; A.T.L., V.V., and A.E. approved final version of manuscript.