Sex-specific computational models of the spontaneously hypertensive rat kidneys: factors affecting nitric oxide bioavailability

Abstract

The goals of this study were to 1) develop a computational model of solute transport and oxygenation in the kidney of the female spontaneously hypertensive rat (SHR), and 2) apply that model to investigate sex differences in nitric oxide (NO) levels in SHR and their effects on medullary oxygenation and oxidative stress. To accomplish these goals, we first measured NO synthase (NOS) 1 and NOS3 protein expression levels in total renal microvessels of male and female SHR. We found that the expression of both NOS1 and NOS3 is higher in the renal vasculature of females compared with males. To predict the implications of that finding on medullary oxygenation and oxidative stress levels, we developed a detailed computational model of the female SHR kidney. The model was based on a published male kidney model and represents solute transport and the biochemical reactions among O₂, NO, and superoxide (${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$) in the renal medulla. Model simulations conducted using both male and female SHR kidney models predicted significant radial gradients in interstitial fluid oxygen tension (Po₂) and NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ concentration in the outer medulla and upper inner medulla. The models also predicted that increases in endothelial NO-generating capacity, even when limited to specific vascular segments, may substantially raise medullary NO and Po₂ levels. Other potential sex differences in SHR, including ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production rate, are predicted to significantly impact oxidative stress levels, but effects on NO concentration and Po₂ are limited.

hypertension is a complex and multifaceted disease that affects 33% of US adults and is the leading cause of premature death in the world. It is generally believed that men typically have higher blood pressure than age-matched women, putting them at greater risk for hypertension-related cardiovascular and renal disease. However, recent studies have indicated no significant difference in the incidence and progression of chronic kidney diseases (CKD) between sexes (with some exceptions noted below), although more men have advanced-stage CKD than women (34). Furthermore, studies have indicated that women have a lower risk of progression than men (39), that CKD progresses more rapidly in women of postmenopausal age than in men (20), and that men with CKD of various etiologies show a more rapid decline in renal function than women with CKD over time (33). Despite these well known sex differences, men and women are typically treated using the same approach. Strikingly, only 45% of treated women achieve blood pressure control compared with 51% of men (18). In this study, we consider sex differences in blood pressure control, with a focus on renal bioavailability of nitric oxide (NO), a powerful vasodilator.

The kidney plays a central role in long-term control of blood pressure. By a mechanism called pressure natriuresis, elevated blood pressure increases sodium (Na⁺) excretion. This is followed by decreased water excretion, decreased extracellular fluid volume, and decreased blood pressure. Thus the kidney’s function, in particular its ability to regulate Na⁺ excretion, is critical in blood pressure control. It is noteworthy that, although Na⁺ retention may lead to hypertension, this is not the only mechanism that regulates blood pressure, especially in the long term; others include changes in vascular tone, which impacts hemodynamics.

NO contributes to blood pressure control by regulating vascular tone and hemodynamics; NO also promotes natriuresis and diuresis by inhibiting tubular Na⁺ reabsorption. Indeed, NO has a central role in hypertension-related end-organ damage. Female spontaneously hypertensive rats (SHR) are known to have greater levels of NO than males (42). We hypothesize that the discrepancy may be attributable to the sex differences in the NO-generating capacity of renal microvessels.

In this study, we used a combination of experimental and computational modeling techniques to assess the validity of the above hypothesis. Additionally, we sought to assess the potential of other physiological factors, including superoxide (${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$) production rate and antioxidant capacity, in explaining the higher NO bioavailability in the female SHR kidneys. To accomplish these goals and provide data to inform the computational model, we first measured NO synthase (NOS) protein expression in the vascular tree isolated from the whole kidneys in male and female SHR. We also developed and applied computational models of the renal medulla of the male and female SHR kidneys. We conducted model simulations to assess the extent to which sex differences in SHR may contribute to the lower levels of oxidative stress and the higher level of NO bioavailability reported in female SHR (42).

METHODS

Experimental Methods

Animals.

Thirteen-week-old male and female SHR were used in this study (Harlan Laboratories, Indianapolis, IN). Male and female SHR weighed 310 ± 5 and 176 ± 8 g, respectively. All experiments were conducted in accordance with the National Institutes of Health’s Guide for the Care and Use of Laboratory Animals and were approved and monitored by the Augusta University Institutional Animal Care and Use Committee. Rats were anesthetized with ketamine-xylazine (48 mg/kg and 6.4 mg/kg ip, respectively; Phoenix Pharmaceuticals, St. Joseph, MO) and were killed by a thoracotomy. Kidneys were removed, decapsulated, and placed in ice-cold phosphate-buffered saline (PBS; pH 7.4) containing phenylmethylsulfonyl fluoride (PMSF; 1 mM). The kidneys were minced and filtered through a mesh filter (200 m) in ice-cold PBS; the vascular bed was retained on the mesh. The isolated microvessels (which contains glomeruli, arteries, arterioles, veins, and venules) were placed in a tube containing 1 ml of homogenization buffer (50 mM Tris·HCl, pH 7.4, 0.1 mM EDTA, 0.1 mM EGTA, 250 mM sucrose, and 10% glycerol) in the presence of protease inhibitors (1 mM PMSF, 1 M pepstatin A, 2 M leupeptin, and 0.1% aprotinin) and then snap-frozen in liquid nitrogen. Note that this vascular preparation is not a microdissected arterial preparation from one region of the kidney, but instead includes glomeruli, arteries, arterioles, veins, and venules from the entire kidney. The preparation also includes some nonvascular components, although it is a highly enriched vascular preparation.

Western blot analysis.

Slightly thawed microvessel preparations were homogenized on ice in the presence of fresh protease inhibitors with a glass-glass homogenizer for 10 strokes. Protein concentrations were determined by the Bradford assay (Bio-Rad; Hercules, CA) using bovine serum albumin as the standard. Proteins were separated on 7.5% SDS-PAGE and transferred onto polyvinylidene difluoride membranes with a trans-blot (Bio-Rad) for 45 min. The blots were allowed to air dry for 30 min and were blocked with 5% nonfat dry milk diluted in Tris-buffered saline for 1 h at room temperature. Two-color immunoblots were performed using polyclonal primary antibodies NOS1 and NOS3 (BD Biosciences, San Jose, CA). Specific bands were detected using the Odyssey infrared imager in conjunction with the appropriate IRDye secondary antibodies (LI-COR Biosciences, Lincoln, NE). β-Actin (monoclonal; Sigma) was used to verify equal protein loading, and all densitometric results are reported normalized to β-actin.

Computational Models

Our laboratory previously published a model of solute transport and oxygenation in the renal medulla of the kidney of a male rat in moderate antidiuretic state (15–17). Based on that model, we developed a computational model of the renal medulla of the female SHR kidney. The models represent the three-dimensional architecture of the renal medulla and include the loops of Henle, collecting ducts, vasa recta, and capillaries (see Fig. 1); the model vasa recta and capillaries are divided into plasma and red blood cell compartments. The models simulate the renal tubular and vascular transport of NaCl, urea, O₂, NO, and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$. Solute and water transport are represented using the single-barrier approach. The model predicts tubular and vascular flows, solute concentrations, and water and solute fluxes at all levels of the renal medulla. Below we highlight aspects of the models that are particularly relevant to medullary oxygenation and oxidative stress, and we describe the parameters that were adjusted in the male SHR kidney model to yield a female model. For other model equations, see Refs. 8 and 15.

Fig. 1.

Schematic diagram of model structure. A short loop, which consists of a descending limb and a contiguous ascending limb and which turns at the outer-inner medullary boundary, is represented. The diagram also depicts a long loop that turns within the inner medulla (at x₂). Although only one long loop is shown, the model represents one long loop that turns at every spatial point in the inner medulla. Similarly, only two representative descending vasa recta (DVR) are shown (with one terminating at x₁ and one at x₂), whereas the model represents one DVR that terminates at every spatial point. A representative collecting duct is shown; the “branches” represent the coalescence of the collecting ducts in the inner medulla. The black arrows at the corticomedullary boundary represent boundary flows. The outflow of the ascending limbs determines the inflow of the collecting duct. Collecting duct outflow becomes urine.

Active Na⁺ transport and O₂ consumption.

Active transport of Na⁺ occurs along the thick ascending limbs, proximal straight tubules, and collecting ducts. We assume that, for tubule i, active Na⁺ transport rate (${\Psi }_{i,\text{Na}}^{\text{active}}$) depends on local oxygen tension (Po₂), [NO], [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$], and luminal [Na⁺] (where brackets denote concentration), given by

$${\Psi }_{i,\text{Na}}^{\text{active}}=V_{\max ,i,\text{Na}}\left(\frac{[{\text{Na}}^{+}]}{K_{\text{M},\text{Na}}+[{\text{Na}}^{+}]}\right)·f_{\text{act}}([{\text{O}}_2])·g_{\text{act}}([\text{NO}])·h_{\text{act}}([{\text{O}}_2^{-}])$$ (1)

where V_max,i,Na (in nmol·cm^–2·s^–1) is the maximal rate of Na⁺ transport, K_M,Na is the Michaelis constant (taken here to be 70 mM), and the functions f_act ([O₂]), g_act ([NO]), and h_act ([${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$]) represent the effects of O₂, NO, and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$, respectively, on the rate of active Na⁺ reabsorption.

As in our laboratory’s previous studies (15–17), we assume that, below a critical Po₂ threshold P_c [taken to be 10 mmHg (16)], active Na⁺ transport becomes limited and is partially compensated by anaerobic metabolism. This process is modeled by

$$f_{\text{act}}([{\text{O}}_2])=\{\begin{array}{ll}1,\hfill & \text{if}\hspace{0.17em}{\text{PO}}_{\text{2}}\ge P_c\hfill \\ \frac{{\text{PO}}_{\text{2}}}{P_c}+F_{\text{AN}}\left(1-\frac{{\text{PO}}_{\text{2}}}{P_c}\right),\hfill & \text{if}\hspace{0.17em}{\text{PO}}_{\text{2}}<P_c\hfill \end{array}$$ (2)

where F_AN describes the capacity of the tubular segment for anaerobic transport and is taken to be 0.5 in the outer medullary collecting duct (44, 50), 0.4 in the inner medullary collecting duct (41), 0.1 in the thick ascending limbs (3), and 0.14 in the proximal straight tubules (12).

NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ have opposite effects on Na⁺ transport, with NO having an inhibitory effect and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ enhancing Na⁺ transport. These effects are represented by

$$g_{\text{act}}\text{([NO])=1}-\frac{\text{[NO]}}{{\text{β}}_i+\text{[NO]}}$$ (3)

$$h_{\text{act}}([{\text{O}}_2^{-}])=0.65+0.7\left(\frac{[{\text{O}}_2^{-}]}{{\text{γ}}_i+[{\text{O}}_2^{-}]}\right)$$ (4)

where the Michaelis constants β_i and γ_i are set to 47 nM and 0.2 pM in the thick ascending limbs and to 232 nM and 0.06 pM in the collecting ducts, respectively (15).

O₂ consumption consists of an active component that depends on active Na⁺ transport, and a basal component that depends on local Po₂:

$$R_{i,{\text{O}}_{\text{2}}}^{\text{active}}=\left(\frac{2\text{π}{r}_i{\Psi }_{i,\text{Na}}^{\text{active}}}{{\text{TQ}}_i}\right)\Theta ([{\text{O}}_2])$$ (5)

$$R_{i,{\text{O}}_{\text{2}}}^{\text{basal}}=R_{\max ,{\text{O}}_{\text{2}}}^{\text{basal}}\left(\frac{[{\text{O}}_2]}{K_{\text{M},{\text{O}}_{\text{2}}}+[{\text{O}}_2]}\right)$$ (6)

where r_i is the inner radius of tubule i, TQ_i denotes the number of moles of Na⁺ actively reabsorbed per mole of O₂ consumed, $K_{\text{M},{\text{O}}_{\text{2}}}$ is the Michaelis constant associated with basal metabolism, and $R_{\max ,{\text{O}}_{\text{2}}}^{\text{basal}}$ is the maximal volumetric rate of O₂ consumption. Θ([O₂]) denotes the fraction of the Na⁺ active transport supported by aerobic respiration. We assume that, below a certain threshold, aerobic respiration decreases progressively, so that Θ([O₂]) is given by

$$\Theta ([{\text{O}}_2])=\{\begin{array}{ll}1,\hfill & \text{if}\hspace{0.17em}{\text{PO}}_{\text{2}}\ge P_c\hfill \\ \frac{{\text{PO}}_{\text{2}}/P_c}{F_{\text{AN}}+(1-F_{\text{AN}})({\text{PO}}_{\text{2}}/P_c)},\hfill & \text{if}\hspace{0.17em}{\text{PO}}_{\text{2}}<P_c\hfill \end{array}$$ (7)

Generation of NO and $O_{\mathit{2}}^{-}$.

The generation rates of NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ are assumed to depend on local Po₂, such that for tubule or vessel i

$$G_{i,\text{NO}}=G_{{}^{{}_{i,\text{NO}}}}^{\max }\left(\frac{[{\text{O}}_2]}{K_{\text{M},\text{NO}}+[{\text{O}}_2]}\right)$$ (8)

$$G_{i,{\text{O}}_2^{-}}=G_{{}^{{}_{i,{\text{O}}_2^{-}}}}^{\max }\left(\frac{[{\text{O}}_2]}{K_{\text{M},{\text{O}}_{\text{2}}^{-}}+[{\text{O}}_2]}\right)$$ (9)

where $G_{{}^{{}_{i,\text{NO}}}}^{\text{max}}$ and $G_{{}^{{}_{i,{\text{O}}_{\text{2}}^{-}}}}^{\text{max}}$ are the maximal rates of NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production, which vary among different types of tubule and vessel (15), and K_M,No and $K_{\text{M},{\text{O}}_{\text{2}}^{-}}$ are the associated Michaelis constants, set to 50.9 and 20.6 μM, respectively (9, 48). In SHR, $G_{{}^{{}_{i,\text{NO}}}}^{\text{max}}$ is divided by a factor of 2 and $G_{{}^{{}_{i,{\text{O}}_2^{-}}}}^{\text{max}}$ is increased by a factor of 10, relative to values in normotensive rats.

NO-induced vasodilation.

Following our laboratory’s previous phenomenological approach (17), we assume that the descending vasa recta (DVR) radius (denoted R_DVR) increases with local increases in [NO]. We further assume that R_DVR cannot fall below the radius of a single erythrocyte, or 3.5 μm. Because [NO] varies throughout the medulla, R_DVR varies spatially. Thus, at a given medullary level, the model R_DVR is given (in μm) by

$$R_{\text{DVR}}=R^{*}\times \max \left\{3.5,\frac{A\left({[\text{NO}]}_{\text{avg}}/{[\text{NO}]}^{*}\right)}{(A-1)+\left({[\text{NO}]}_{\text{avg}}/{[\text{NO}]}^{*}\right)}\right\}$$ (10)

where [NO]_avg denotes the average of the DVR plasma and local interstitial [NO], and [NO]* denotes the reference [NO], taken to be 15 nM for both male and female. R* denotes the reference radius, taken to be 7.5 and 6.15 μm, for male and female, respectively. A is a dimensionless parameter, chosen to be 1.0962 so that the baseline DVR volume flow at the corticomedullary boundary is ~8 and 6 nl/min, for male and female, respectively.

The model represents medullary blood flow as Poiseuille flow, which relates blood flow (Q_DVR) along each DVR to pressure drop (ΔP_DVR) and vascular resistance; the latter scales inversely with the fourth power of the R_DVR. That is,

$$Q_{\text{DVR}}=\frac{{\text{πΔP}}_{\text{DVR}}{\text{(}{R}_{\text{DVR}}\text{)}}^{\text{4}}}{\text{8μ}{L}_{\text{DVR}}}$$ (11)

where μ is the blood viscosity, and L_DVR denotes the DVR length. Since the DVR terminate at every medullary depth, the L_DVR can take values from 0 to 0.7 cm, the total length of the medulla. Because of the differing lengths and radii of the DVR, blood flow distribution may be inhomogeneous among the DVR. To determine the blood flow entering the DVR, we connect each DVR to a downstream resistance in series, and assume that pressures at the two ends, denoted by P_E and P_V (E, efferent arteriole; V, renal vein), are known in advance. The pressure drop (P_E − P_V) from efferent arteriole to renal vein is given by the pressure drop along that DVR and along its downstream resistance Γ_down:

$${\text{P}}_{\text{E}}-{\text{P}}_{\text{V}}{=\text{ΔP}}_{\text{DVR}}\text{+}{F}_{\text{V}}^{\text{DVR}}\text{(}{L}_{\text{DVR}}{\text{)Γ}}_{\text{down}}$$ (12)

here $F_{\text{V}}^{\text{DVR}}\text{(}{L}_{\text{DVR}}\text{)}$ is volume flow at the end of the DVR, and Γ_down is a function of L_DVR. ΔP_DVR is calculated along L_DVR:

$${\text{ΔP}}_{\text{DVR}}\text{=}\frac{\text{8μ}}{\text{π}}{\displaystyle {\int }_{\text{0}}^{L_{\text{DVR}}}\frac{F_{\text{V}}^{\text{DVR}}\text{(s)}}{R_{\text{DVR}}^{\text{4}}\text{(s)}}}\text{ds}$$ (13)

We refer readers to Ref. 17 for more details.

Sex differences in model parameters.

To produce a female SHR model, we adjusted model parameters to account for the substantial differences in size and blood flow between the male and female rat kidneys. The renal mass of a female rat is approximately one-half that of an age-matched male rat (29, 37), while the number of glomeruli per kidney is similar in both sexes (32). We assume that both male and female model SHR kidneys have 30,000 nephrons, a 17% reduction from the 36,000 nephrons that we typically assume for a normotensive rat. The lower nephron count is consistent with findings reported by Skov et al. (40). We reduce the lengths and radii of all tubules and vessels to 82% (cube root of 55%) in the female model. Additionally, we assume that single-nephron glomerular filtration rate (SNGFR) in the female kidney is 20% lower than in the male. That assumption is consistent with reports that SNGFR in female rat kidneys is a fraction of that in the male (32, 36) and yields urinary outputs that are not substantially different in both sexes (37). Medullary blood flow has not been measured in female rats; we assume that SNGFR and medullary blood flow scale proportionally, so that medullary blood flow in female is 20% lower than in male. Flows and solute concentrations for descending tubules and vessels at the corticomedullary boundary are specified in Table 1. Also, DVR hematocrit is taken to be 0.45 at the corticomedullary boundary. All other parameters are the same in both sexes, unless otherwise specified (see Refs. 8, 15, 21). Permeabilities of tubular and vascular walls to O₂, NO, and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ are given in Table 2. NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ generation rates are given in Table 3. Both model kidneys are assumed to be in a moderately anti-diuretic state.

Table 1.

Boundary conditions for descending tubules and vessels at x = 0

			DVR
	SDL	LDL	Plasma	RBC
FV male, nl/min	10 (2)	12 (11)	6 (6)	2 (6)
FV female, nl/min	8	9.6	4.8	1.6
CNa, mM	160 (2, 23)	160 (2, 23)	163.7 (2, 23)	163.7 (2, 23)
Po2, mmHg	36 (27)	36 (27)	45 (51)	45 (51)
CNO, mM	0.1 × 10–3 (13)	0.1 × 10–3 (13)	0.5 × 10–4 (54)	0.1 × 10–6 (13)
${\mathrm{C}}_{{\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}}$, mM	0.2 × 10–7 (13)	0.2 × 10–7 (13)	0.1 × 10–6 (13)	0.1 × 10–6 (13)

Citation numbers shown in parentheses. SDL, short descending limb; LDL, long descending limb; RBC, red blood cell; F_V, vessel flow; C_Na, Na⁺ concentration; C_NO, NO concentration; ${\mathrm{C}}_{{\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}}$, ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ concentration.

Table 2.

O₂, NO, and $O_{\mathit{2}}^{-}$ permeabilities of tubular and vascular walls

				DVR		AVR
	DL	AL	CD	Plasma	RBC	Plasma	RBC
${\text{P}}_{{\text{erm,O}}_{\text{2}}}$, cm/s	0.04 (8)	0.04 (8)	0.04 (8)	0.04 (8)	0.0133 (8, 51)	0.04 (8)	0.0133 (8, 51)
Perm,NO, cm/s	0.1 (13, 19)	0.0122 (13, 19)	0.0122 (13, 19)	0.496 (13, 19)	0.05 (13, 19)	0.0122 (13, 19)	0.1 (13, 19)
${\text{P}}_{{\text{erm,O}}_2^{-}}$, cm/s	5 × 10–4 (13)	5 × 10–4 (13)	5 × 10–4 (13)	5 × 10–4 (13)	5 × 10–4 (13)	5 × 10–4 (13)	5 × 10–4 (13)

Nos. in parentheses are reference nos. DL, descending limb; AL, ascending limb; CD, collecting duct, ${\text{P}}_{{\text{erm,O}}_{\text{2}}}$, O₂ permeability; P_erm,NO, NO permeability; ${\text{P}}_{{\text{erm,O}}_2^{-}}$, ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ permeability.

Table 3.

NO and $O_{\mathit{2}}^{-}$ generation rates in tubules and vessels in male and female normotensive rats and SHR

				DVR		AVR
	DL	AL	CD	Plasma	RBC	Plasma	RBC
Normal, GNO, mM/s	6.16 × 10–3 (13, 49)	4.92 × 10–4 (13, 49)	2.08 × 10–4 (13, 49)	38.24 × 10–3 (13, 49)	0	36.50 × 10–3 (13, 49)	0
Normal, $G_{{\text{O}}_{\text{2}}^{-}}$, mM/s	15.2 × 10–5 (13, 26)	3.2 × 10–5 (13, 26)	1.8 × 10–5 (13, 26)	21.0 × 10–5 (13, 26)	0	19.8 × 10–5 (13, 26)	0
SHR, GNO, mM/s	3.08 × 10–3	2.46 × 10–4	1.04 × 10–4	19.12 × 10–3	0	18.25 × 10–3	0
SHR, $G_{{\text{O}}_{\text{2}}^{-}}$, mM/s	15.2 × 10–4	3.2 × 10–4	1.8 × 10–4	21.0 × 10–4	0	19.8 × 10–4	0

Nos. in parentheses are reference nos. DL, descending limb; AL, ascending limb; CD, collecting duct.

MODEL RESULTS

Experimental Results

To inform the computational model, experiments were performed to measure NOS1 and NOS3 total protein expression in isolated renal microvessels from male and female SHR. We found that both NOS1 and NOS3 are more highly expressed in the renal vasculature of females compared with males (see Fig. 2). This result is consistent with our laboratory’s previous reports (7, 42) indicating greater blood pressure sensitivity of female SHR to NOS inhibition and greater indexes of NO production in the renal cortex and inner medulla of female SHR compared with male SHR.

Fig. 2.

Left: NOS1 protein expression (~150 kDa) in whole homogenates of isolated renal microvessels from male and female SHR. This includes the entire vascular tree isolated from the kidney. There are two immunoreactive bands: the top band is NOS1α, and the lower is NOS1β. Right: NOS3 protein expression (~130 kDa) in whole homogenates of isolated renal microvessels from male and female SHR. This includes the entire vascular tree isolated from the kidney. RDU, relative densitometric units.

Base-Case Simulation Results

Model equations were solved to obtain steady-state solutions for the male and female parameter sets. Predicted urine Na⁺ excretions for male and female normotensive rats, and male and female SHR, are shown in Table 4 and Fig. 3. Urinary Na⁺ excretions in male and female SHR are lower than the corresponding normotensive rats, consistent with data in Refs. 1 and 43. Predicted urinary outputs are shown in Table 5. The male and female SHR produced urine with similar flow rate and composition (40). Based on the DVR boundary conditions and on Eq. 11, medullary oxygen supply was computed to be 0.85 and 0.69 μmol·min⁻¹·kidney⁻¹, for male and female, respectively. Medullary oxygen consumption was computed to be 0.69 and 0.59 μmol·min⁻¹·kidney⁻¹, respectively.

Table 4.

Predicted Na⁺ excretion in male and female rats

Rat Type	Na+ Excretion, nmol·min−1·CD−1
Male normotensive	0.1780
Male SHR	0.1364
Female normotensive	0.1010
Female SHR	0.0771
Female SHR, $G_{\text{NO,all}}\times 2$	0.0943
Female SHR, $G_{\text{NO,EB-AVR}}\times 2$	0.0936
Female SHR, $G_{\text{NO,DVR}}\times 2$	0.0763
Female SHR, $G_{O_2^{-}}/2$	0.0786
Female SHR, $G_{\text{NO,all}}\times 3$	0.1098
Female SHR, $G_{\text{NO,EB-AVR}}\times 3$	0.1078
Female SHR, $G_{\text{NO,DVR}}\times 3$	0.0760
Female SHR, $G_{{\text{O}}_2^{-}}/5$	0.0809

CD, collecting duct; EB-AVR, extrabundle AVR.

Fig. 3.

Four baseline cases: male and female normotensive rats, and male and female SHR. Interstitial [NO] (A), [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] (B), and Po₂ (C) are shown.

Table 5.

Predicted urine outputs in male and female SHR

	Male	Female
Flow, μl/min	23.8	15.9
[NaCl], mM	172.1	145.2
[Urea], mM	670.6	588.5
Osmolality, mosmol/kgH2O	1,084	950

Assuming that the NO generation rate is identical in male and female kidneys, both male and female SHR models predict similar medullary NO, Po₂, and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ levels. Figure 4 shows medullary NO, Po₂, and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ levels for all four cases: male and female normotensive rats, and male and female SHR.

Fig. 4.

Effect of varying NO generation rate (denoted G_NO) on interstitial [NO] (A), [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] (B), and Po₂ (C). Results were obtained for male SHR using baseline G_NO, and for female SHR using G_NO at baseline and at values two and three times that of baseline. The increased G_NO was applied to all cells.

Predicted Effects of Increasing NO Generation Rate in Female SHR

Motivated by our finding that NOS1 and NOS3 expression is higher in the renal vasculature of female SHR compared with males, we conducted simulations to assess the effects of higher NO generation rate in females. Specifically, we increased NO generation rate, more specifically, the maximum NO generation rate ($G_{i\text{,NO}}^{\text{max}}$ in Eq. 8, which we denote simply by G_NO below), in female SHR two- and threefold. That increase was applied to all cells. Predicted interstitial fluid [NO], [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$], and Po₂, computed as averages for the whole medulla, outer medulla, and the papillary tip (taken to be the terminal 1.5 mm of the inner medulla), are shown in Fig. 4. Elevating the NO production rate by factors of 2 and 3 increases whole medulla [NO] by 146 and 336%, respectively, with similar proportional increases predicted in the outer medulla and the papilla (see Fig. 4A).

The higher interstitial fluid [NO] induces vasodilation. The predicted medullary blood flow and O₂ supply increased 33 and 32%, and 45 and 44% when the G_NO was increased two- and threefold, respectively. In turn, whole medulla interstitial Po₂ increased by 22 and 49%, respectively.

NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ react to form ONOO⁻; thus higher NO levels, taken in isolation, would lower [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$]. However, the higher Po₂ that results from the high NO level increases ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production (see Eq. 9). These two competing factors together yielded small increases in interstitial fluid [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] as G_NO increased (see Fig. 4B).

The predicted impact of higher NO levels on water and Na⁺ excretion in female SHR is illustrated in Table 6. The G_NO-induced increase in blood flow reduces the efficiency of the concentrating mechanism, resulting in a lower urine osmolality. Since NO acts to inhibit tubular Na⁺ reabsorption in the thick ascending limb, collecting duct, and proximal straight tubule (see Eq. 3), raising G_NO enhances Na⁺ and water excretion (Table 4; Fig. 5). Somewhat paradoxically, this also results in higher medullary O₂ consumption, and a greater O₂ consumption-to-supply ratio (Table 6). The reason is that the higher the levels of NO, the higher Po₂, and the larger the contribution of aerobic metabolism (see Eq. 7); in other words, the fraction of active Na⁺ transport that is sustained by O₂ consumption (as opposed to anaerobic metabolism) increases with increasing G_NO.

Table 6.

Impact of increasing G_NO on medullary O₂ supply and consumption and on urinary excretion in female SHR

		GNO,all		GNO,DVR		GNO,EB-AVR
	Basal GNO	× 2	× 3	× 2	× 3	× 2	× 3
DVR inflow, μl·min−1·kidney−1	113.7	151.5	165.0	135.1	145.6	126.9	135.6
O2 supply, μmol·min−1·kidney−1	0.69	0.90	0.99	0.81	0.87	0.77	0.82
O2 consumption, μmol·min−1·kidney−1	0.59	0.79	0.83	0.71	0.77	0.66	0.69
Urine osmolality, mosmol/kgH2O	950	907	900	916	902	937	931
Urine flow, μl·min−1·kidney−1	2.61	2.95	3.13	2.71	2.75	2.85	3.03
Urine Na+ flow, μmol·min−1·kidney−1	0.38	0.46	0.54	0.38	0.37	0.46	0.53

G_NO, maximal volumetric rate of NO consumption. In the cases examined here, it is multiplied by a factor of 2 or 3 either in all cells (G_NO,all), in DVR only (G_NO,DVR), or in extrabundle AVR only (G_NO,EB-AVR).

Fig. 5.

Na⁺ excretion in male and female normotensive and hypertensive rats.

Predicted Effects of Selective Increases in G_NO

In the above simulations, G_NO was increased uniformly in all cells. However, regional differences in NOS1 and NOS3 expression, and hence G_NO, are likely. Thus, in the next few sets of simulations, we considered selective increases in G_NO. Based on our findings that NOS1 and NOS3 expressions are higher in renal microvessels in female SHR compared with male (Fig. 2), we selectively increased G_NO in vasa recta of female SHR.

First, we conducted simulations in which G_NO was increased two- and threefold in the extrabundle ascending vasa recta (AVR) (their entire medullary length) of the female SHR kidney. G_NO was kept at baseline values in other vessels, tubules, and interstitial cells. We chose the extrabundle AVR due to their proximity to the thick ascending limbs. Simulations predicted that selectively raising extrabundle AVR G_NO elevated medullary [NO] and Po₂ to levels comparable to raising G_NO in all cells (compare Figs. 4 and 6, A1 and B1), even though extrabundle AVR account for ~30% of all vasa recta.

Fig. 6.

Effect of selective variations in NO generation rate on interstitial [NO] and Po₂. Results were obtained for male SHR using baseline G_NO, and for female SHR with baseline G_NO and with G_NO increased to two and three times above baseline in selected segments. A1 and B1: NO generation rate of extrabundle ascending vasa recta (AVR), denoted G_NO,EB-AVR, was varied. A2 and B2: NO generation rate of descending vasa recta (DVR), denoted G_NO,DVR, was varied.

Next, we simulated a two- and threefold increase in G_NO in the DVR of the female SHR kidney. G_NO was kept constant in other cells. Our results indicate that selectively raising DVR G_NO raises medullary [NO] and Po₂ to a smaller extent than raising extrabundle AVR G_NO (see Fig. 6). Indeed, the scavenging of NO by hemoglobin is greater in DVR than in AVR, as fluid uptake significantly reduces hematocrit levels in AVR, compared with DVR.

The impact of vessel-selective changes in G_NO on urinary excretion in female SHR is also shown in Table 6. The trends are similar to those described above, but the quantitative changes are smaller. A twofold increase in G_NO raises medullary blood flow (and O₂ supply) by 33, 19, or 12% (and by 32, 18, or 11%), respectively, if it occurs in all vessels, in DVR only, or in extrabundle AVR only. The corresponding decreases in urine osmolality are small: 4, 5, and 1%, respectively. Note that raising G_NO only in DVR has a negligible impact on Na⁺ transport and Na⁺ excretion.

Predicted Effects of Decreasing $O_{\mathit{2}}^{-}$ Generation Rate in Female SHR

Thus far our predictions suggest that higher endothelial NO-producing capacity, even when restricted to specific vascular segments, can yield substantially higher medullary NO and Po₂ levels. To further explore the effects of other physiological factors, we conducted additional simulations. NO bioavailability is determined by 1) the expression and activity of NOS, and 2) scavenging of NO by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$. We first sought to assess the effects of decreasing maximum ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ generation rate ${\mathit{G}}_{\mathit{i}{\mathrm{\text{,O}}}_{\mathrm{\text{2}}}\mathrm{-}}^{\mathrm{\text{max}}}$ (which we refer to as ${\mathit{G}}_{{\mathrm{\text{O}}}_{\mathrm{\text{2}}}\mathrm{-}}$) in female SHR two- and fivefold. Predicted interstitial fluid [NO], [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$], and Po₂, computed for the whole medulla, outer medulla, and papillary tip, are shown in Fig. 7. Reducing ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production rate by factors of 2 and 5 markedly decreased whole medulla [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] by 50 and 80%, respectively, with similar proportional decreases in the outer medulla and the papilla (see Fig. 7B). Interstitial [NO] increased as ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ generation rate was progressively decreased, but that effect was relatively minor (Fig. 7A).

Fig. 7.

Effect of varying ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ generation rate (denoted ${\mathit{G}}_{{\mathrm{\text{O}}}_{\mathrm{\text{2}}}\mathrm{-}}$) on interstitial [NO] (A), [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] (B), and Po₂ (C). Results were obtained for male SHR using baseline ${\mathit{G}}_{{\mathrm{\text{O}}}_{\mathrm{\text{2}}}\mathrm{-}}$, and for female SHR using ${\mathit{G}}_{{\mathrm{\text{O}}}_{\mathrm{\text{2}}}\mathrm{-}}$ at baseline and at values 1/2 and 1/5 of baseline. The lowered ${\mathit{G}}_{{\mathrm{\text{O}}}_{\mathrm{\text{2}}}\mathrm{-}}$ was applied to all cells.

${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ stimulates thick ascending limb active Na⁺ reabsorption (see Eq. 4), thereby elevating O₂ consumption. Hence, when ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ generation rate was reduced by factors of 2 and 5, whole medulla Po₂ increased by 1 and 2%, respectively, with similar increases obtained in the outer medulla and papilla (see Fig. 7C).

Predicted Effects of Higher Antioxidant Capacity in Female SHR

SOD catalyzes the dismutation of ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ into either O₂ or H₂O₂. Plasma SOD activity has been reported to be higher in females compared with males (30). In another set of simulations, we investigated the effects of increasing [SOD] two- and threefold in female SHR. Increasing the abundance of SOD in female SHR has only minor impacts on whole medulla NO, ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$, and Po₂ levels (results not shown). The only notable effect was the ~20% reduction in [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] near the papillary tip when [SOD] was increased.

DISCUSSION

A major contribution of this work is the development of a computational model of solute transport and oxygenation in the renal medulla of the kidney of a female SHR. To our knowledge, every published computational model of rat kidney functions is based on the male rat (e.g., Refs. 21, 22, 24, 25, 31, 46, 47). Even though not explicitly stated in the description of those models, the “sex” of the modeled kidney can be inferred from the physical dimensions and SNGFR. Male and female rat kidneys differ substantially in size, but also in many other aspects. Recent observations indicate that renal structure and function vary between the sexes under numerous physiological, pathological, and pharmacological conditions, as reviewed in Refs. 35, 37, 45. Importantly, males and females appear to have different degrees of blood pressure control (4, 5). Thus it is important to develop a computational model for the female rat kidney.

The present female SHR model is based on our laboratory’s published normotensive male rat models (15–17). First we adjusted model parameters to account for the differences in size and blood flow between the male and female rat kidneys. Tubular transport and metabolic parameters were left unchanged. Simulations using normotensive male and female rat kidney models produced urine with similar composition (results not shown), in accordance with experimental measurements (37). In the present study, we focused on SHR. We assumed higher and lower, respectively, ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ and NO production rates in SHR kidneys, relative to their normotensive counterparts. Other pathophysiological differences, such as those in the neural and hormonal systems, were not considered. The male and female SHR models also generated urine with similar composition, albeit at a much higher flow rate in male SHR. We recognize that male and female rats, whether normotensive or hypertensive, differ in many other ways, but we opted here to examine the isolated impact of a few parameters only. The models could be expanded to account for other sex-specific variations. As such, the female kidney models (normotensive and hypertensive) provide a useful simulation tool for studying sex differences in kidney function, in both health and disease.

Nitric Oxide

Our baseline simulations indicate that, given the same transport and metabolic parameters, male and female rats have similar medullary O₂ and NO bioavailability. This result suggests that sex differences in kidney size and blood flow alone cannot account for the greater NO levels observed in female SHR compared with males (42). Thus we investigated other factors that may explain sex-based differences in NO bioavailability.

It has been suggested that the greater NO bioavailability in female SHR may be the result of greater NO production and lower levels of NO scavenging by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ (10, 53). To consider the effects of higher NO-generating capacity in females, we first measured and compared total protein expressions of NOS1 and NOS3 in isolated microvessels from male and female SHR kidneys. We found that both NOS1 and NOS3 are significantly more abundant in females compared with males. This finding is consistent with previous results that indicate higher whole body production of NO in women compared with men (14, 38, 52).

A question that naturally follows is: to what extent does higher NO-generating capacity in female SHR kidneys explain their higher NO bioavailability? To answer that question, we conducted simulations using the male and female SHR computational models. Model simulation results suggest that medullary NO and Po₂ levels are highly sensitive to endothelial NO generate rates (see Fig. 4). Noticeably higher NO and Po₂ levels can be obtained even when the higher G_NO are limited to specific vascular segments (see Fig. 6).

Oxidative Stress

Oxidative stress exacerbates blood pressure elevation and related organ injuries by contributing to inflammation, hypertrophy, and apoptosis. Hypertensive males have been reported to have greater levels of oxidative stress compared with females (28). Model simulations indicate that sex differences in oxidative stress, as reflected by differences in medullary [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$], could, to a large extent, stem from greater ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production in male SHR (Fig. 7).

We also studied the effects of the potentially lower ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ production in females. While the model predicted lower medullary ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ levels and thus lower levels of NO scavenging by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$, medullary NO levels and Po₂ were not significantly increased (see Fig. 7). The relatively minor impact on NO levels may be explained, in part, by the several orders of magnitude difference in medullary [NO] (~100 nM) and [${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$] (~0.1 nM), which renders NO scavenging by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ negligible. A caveat is that the model does not consider the specific cellular localization of NO and ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$-producing enzymes. Indeed, the extent to which NO scavenging by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$ may impact NO bioavailability may be highly dependent on the cellular localization of the ROS-producing enzymes. The potential proximity of those enzymes, which is not represented in the model, may well amplify the effect of NO scavenging by ${\mathrm{O}}_{\mathrm{2}}^{\mathrm{-}}$.

In summary, we have developed the first computational model of solute transport and oxygenation of the female rat kidney. Model simulations were conducted to reveal the potential roles of various physiological factors in explaining the sex differences in oxidative stress levels and NO bioavailability observed in SHR. These sex-specific models can be used as an essential component of models of integrated renal hemodynamic and transport, especially in studies of hypertension.

GRANTS

This research was supported by the National Institute of Diabetes and Digestive and Kidney Diseases Grant R01-DK-106102 to A. T. Layton, and by American Heart Association Grant 14GRNT20480199 to J. C. Sullivan.

DISCLOSURES

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

AUTHOR CONTRIBUTIONS

Y.C., J.C.S., A.E., and A.T.L. conceived and designed research; Y.C. and J.C.S. performed experiments; Y.C., J.C.S., A.E., and A.T.L. analyzed data; Y.C., J.C.S., A.E., and A.T.L. interpreted results of experiments; Y.C., J.C.S., and A.T.L. prepared figures; Y.C. and A.T.L. drafted manuscript; Y.C., J.C.S., A.E., and A.T.L. edited and revised manuscript; Y.C., J.C.S., A.E., and A.T.L. approved final version of manuscript.