Impact of nitric oxide-mediated vasodilation on outer medullary NaCl transport and oxygenation

Abstract

The present study aimed to elucidate the reciprocal interactions between oxygen (O₂), nitric oxide (NO), and superoxide (O₂⁻) and their effects on vascular and tubular function in the outer medulla. We expanded our region-based model of transport in the rat outer medulla (Edwards A, Layton AT. Am J Physiol Renal Physiol 301: F979–F996, 2011) to incorporate the effects of NO on descending vasa recta (DVR) diameter and blood flow. Our model predicts that the segregation of long DVR in the center of vascular bundles, away from tubular segments, gives rise to large radial NO concentration gradients that in turn result in differential regulation of vasoactivity in short and long DVR. The relative isolation of long DVR shields them from changes in the rate of NaCl reabsorption, and hence from changes in O₂ requirements, by medullary thick ascending limbs (mTALs), thereby preserving O₂ delivery to the inner medulla. The model also predicts that O₂⁻ can sufficiently decrease the bioavailability of NO in the interbundle region to affect the diameter of short DVR, suggesting that the experimentally observed effects of O₂⁻ on medullary blood flow may be at least partly mediated by NO. In addition, our results indicate that the tubulovascular cross talk of NO, that is, the diffusion of NO produced by mTAL epithelia toward adjacent DVR, helps to maintain blood flow and O₂ supply to the interbundle region even under basal conditions. NO also acts to preserve local O₂ availability by inhibiting the rate of active Na⁺ transport, thereby reducing the O₂ requirements of mTALs. The dual regulation by NO of oxygen supply and demand is predicted to significantly attenuate the hypoxic effects of angiotensin II.

nitric oxide (no) and superoxide (O₂⁻) exert opposite effects on renal vascular and tubular function. Inhibition of NO synthesis leads to a reduction in medullary blood flow (MBF), salt retention, and hypertension (27). The effects of NO on the renal medulla are mediated by several pathways: NO exerts a strong vasodilatory influence on descending vasa recta (DVR) (32), and it inhibits NaCl reabsorption in the medullary thick ascending limb (mTAL) by reducing the activity of the Na⁺-K⁺-2Cl⁻ cotransporter (30). In contrast, O₂⁻ stimulates NaCl transport across mTALs and favors reductions in MBF (29, 11). In addition, NO and O₂⁻ diminish each other's bioavailability, as they react together to form peroxynitrite. A recent study also suggests that NO reduces flow-stimulated increases in O₂⁻ production via the cGMP/PKG pathway, independently of its scavenging effects on O₂⁻ (18). The importance of NO-O₂⁻ interactions is underscored by accumulating evidence that the balance between NO and O₂⁻ is one of the key mechanisms for the development of salt-sensitive hypertension (26).

Adding to the complexity of these interactions is the role of oxygen (O₂). O₂ is a substrate for the formation of each NO and O₂⁻, yet some studies have suggested that hypoxia enhances medullary NO levels (16) and O₂⁻ production (22). Moreover, the availability of O₂ depends on the balance between O₂ supply, itself a function of blood flow, and O₂ demand, which varies with the rate of active Na⁺ transport. To better understand the three-way interactions between O_2, NO, and O₂⁻, and how they impact tubular and vascular function, we recently developed a region-based model of O₂, NO, and O₂⁻ transport in the outer medulla (OM) of the rat (14). Our results suggested that NaCl transport and the concentrating capacity of the OM are substantially modulated by basal and pathological levels of NO and O₂⁻. This previous model, however, did not account for DVR vasoactivity and subsequent changes in MBF and O₂ supply. It therefore lacked an important component of the feedback loops involving O₂, NO, and O₂⁻.

The model described herein incorporates the effects of NO on DVR diameter and DVR flow. It is first used to determine whether O₂⁻-induced vasoconstriction may be in part mediated by NO. The second part of our study centers on the impact of tubular NO synthesis. We examine in particular the hypothesis that diffusion of vasoactive agents such as NO from adjacent tubules to vasa recta plays an important role in protecting the medulla from hypoxic injury, by modulating blood flow and O₂ supply in response to variations in mTAL transport and metabolic requirements (28).

MODEL DESCRIPTION

Our “region-based” model accounts for the three-dimensional architecture of the rat OM by distinguishing four concentric regions, as originally proposed by Layton and Layton (21): the innermost region (R1) represents the central vascular bundle, where all the long DVR and a third of the long ascending vasa recta (AVR) are sequestered; the surrounding region (R2) represents the immediate periphery of the bundle and encompasses all short DVR (those that turn within the OM) and the remaining long AVR; the neighboring region (R3) contains most mTALs, both long and short, and some short AVR; and the region most distant from the vascular bundle (R4) includes all the collecting ducts and the remaining short AVR (see Fig. 1 in Ref. 14).

Fig. 1.

Postulated dependence of descending vasa recta (DVR) radius on nitric oxide (NO) concentration (C_NO) in DVR plasma, as described by Eq. 1. The radius of the vessel cannot fall below that of a single erythrocyte (∼4 μm).

The model determines flows and solute concentrations as a function of OM depth in the interstitium, the loops of Henle, collecting ducts, vasa recta, and capillaries. Blood flow in vasa recta is divided into two compartments, plasma and red blood cells (RBCs). The solutes explicitly considered in the model are NaCl, urea, deoxy- and oxy-hemoglobin (Hb and HbO₂), O₂, NO, HbNO, and O₂⁻. Detailed transport equations can be found in our previous studies (6, 14). We focus here on the new feature of our model, namely, NO-induced vasodilation of long (LDV) and short (SDV) DVR. We also briefly summarize the equations describing active Na⁺ transport and O₂ consumption in the OM.

NO-Induced Changes in DVR Diameter

The relationship between NO levels and DVR diameter is complex. The DVR endothelium is surrounded by pericytes, vascular smooth muscle cells that impart vasocontractile properties to the vessels. The vasodilatory effects of NO appear to be mostly mediated by the cGMP/PKG pathway, which acts to reduce intracellular Ca²⁺ and the proportion of phosphorylated myosin light chains within pericytes (13). Moreover, vascular diameter is regulated by many other vasoactive agents, such as prostaglandins and endothelins. In light of this complexity, we opt for a simple, semiempirical approach. We assume that the local DVR radius (R_DVR) depends on local NO concentration according to

$$\begin{array}{cc}\frac{R_{\text{DVR}}(x)}{R^{*}}=\frac{A[{\text{C}}_{\text{NO}}^{\text{DVR}}(x)/{\text{C}}_{\text{NO}}^{*}]}{(A-1)+[{\text{C}}_{\text{NO}}^{\text{DVR}}(x)/{\text{C}}_{\text{NO}}^{*}]}& \text{DVR}\end{array}=\text{LDV},\text{ SDV}$$ (1)

where x denotes the position on the corticomedullary axis, C_NO^DVR is the NO concentration in DVR plasma (more generally, C_i^j is the concentration of solute i in compartment j), A is a constant to be determined, and the superscript * indicates reference values. The reference radius is taken as 5.5 μm, and the reference NO concentration as 50 nM, which is the average interstitial NO concentration at the outer-inner medullary junction that we predicted in our previous base case (14).

The study of Kakoki et al. (20) relates changes in interstitial NO concentrations in the inner medulla (at a depth of 5.5 mm, that is, close to the junction between the outer and inner medulla) to changes in MBF. To relate, in turn, changes in MBF to variations in vessel radius, we use Poiseuille's law

$$\begin{array}{cc}\frac{\text{dP}}{\text{d}x}=-\frac{8\mu }{\pi }\left(\frac{{\text{F}}_{\text{v}}^{\text{DVR}}(x)}{R_{\text{DVR}}^4(x)}\right)& \text{DVR}\end{array}=\text{LDV},\text{SDV}$$ (2)

where P is the luminal hydraulic pressure, F_v^DVR is the single-vessel blood flow, and μ is the fluid viscosity. Specifically, we assume that MBF varies in proportion to R_DVR⁴. Kakoki et al. (20) found that different doses of NOS inhibitors respectively reduced NO levels by 32 and 66%, and MBF by 32 and 40%; with our assumptions, the latter correspond to 10 and 12% reductions in R_DVR. A best fit of Eq. 1 to these data yields A = 1.0962. The postulated dependence of R_DVR on C_NO^DVR is illustrated in Fig. 1. We assume that DVR constrict along their entire OM length, since some vessels exhibit pericytes all the way to the papillary tip (33). However, it is possible that only the upper parts of OM DVR are capable of vasoconstriction. Our qualitative conclusions would nevertheless remain unaffected.

Blood flow is calculated as follows. The pressure in the efferent arteriole (denoted P_E) and that in the renal vein (denoted P_V) are respectively set to 20 and 3 mmHg (4, 10, 19). Each DVR is connected in series to a fixed downstream resistance (Γ_down), the value of which depends on the DVR length and localization. Blood flow at the DVR inlet (i.e., at the corticomedullary junction) is computed by an iterative process, so that the sum of the pressure drop across the DVR (ΔP_DVR) and that across its downstream resistance equals (P_E − P_V)

$${\text{P}}_{\text{E}}-{\text{P}}_{\text{V}}=\Delta {\text{P}}_{\text{DVR}}+{\text{F}}_{\text{v}}^{\text{DVR}}(L_{\text{DVR}}){\Gamma }_{\text{down}}$$ (3)

where L_DVR is the vessel length, and ΔP_DVR is given by

$$\Delta {\text{P}}_{\text{DVR}}=\frac{8\mu }{\pi }\left({\displaystyle \underset{0}{\overset{L_{\text{DVR}}}{\int }}\frac{{\text{F}}_{\text{v}}^{\text{DVR}}(\text{s})}{R_{\text{DVR}}^4(\text{s})}\text{ds}}\right)$$ (4)

Note that blood flow variations along DVR are calculated based upon the rate of water reabsorption (see Eqs. 3 and 4 in Ref. 14). The downstream resistance Γ_down of each DVR is chosen so that under baseline conditions, DVR blood flow at the inlet is 8 nl/min; Γ_down then remains fixed in all other simulations. The viscosity of blood flowing through vasa recta is low, not much higher than that of plasma (34); we assume μ = 2 cp. As an illustration, the pressure drop across a DVR that extends along the entire OM length would be 11.7 mmHg if its blood flow remained constant at 8 nl/min and its radius fixed at 5.5 μm. The pressure drop across the downstream resistance would then equal (20–3) − 11.7 = 5.3 mmHg. Base-case flow and pressure profiles in long and short DVR are shown in Fig. 2.

Fig. 2.

Flow and pressure profiles in long DVR (LDV) and in the short DVR (SDV) that reach the outer-inner medullary junction, for scenario A. Results are similar for both scenarios. x: Position along the corticomedullary axis; x/L = 0 at the corticomedullary junction, and x/L = 1 at the outer-inner medullary junction. A: vessel radius. The radius is a function of luminal NO concentration (Eq. 1). B: blood flow rate. Blood flow variations along the corticomedullary axis are determined based upon the rate of water reabsorption. C: luminal pressure, calculated using the Poiseuille equation (Eq. 2). The pressure gradient is steeper in SDV than in LDV, because it is inversely proportional to the 4th power of the vessel radius.

The model represents the vasoactive effects of NO but assumes that the DVR radius is independent of the transendothelial pressure gradient. This simplifying hypothesis allows us to avoid computing local fluid pressure along the DVR and leads to substantial savings in computational cost. While elevation of luminal pressure has been shown to progressively dilate DVR ex vivo owing to the absence of a myogenic response (38), according to our calculations the effects of pressure on the radius in the scenarios simulated below are small compared with those of NO. Whereas the pressure drops from 20 mmHg in the efferent arteriole to 3 mmHg in the renal vein, pressure variations at a given medullary level are estimated to be <0.3 mmHg.

NaCl Transport Rate

The axial osmolality gradient in the OM is generated and maintained by active salt reabsorption in mTALs, which is driven by basolateral Na⁺-K⁺-ATPase pumps. As in our previous model, the rate of active Na⁺ transport along mTALs (Ψ_{mTAL, Na}^active) is expressed as

$${\psi }_{\text{mTAL,Na}}^{\text{active}}=\left[\frac{V_{\max ,\text{Na}}{\text{C}}_{\text{Na}}^{\text{mTAL}}}{K_{\text{M},\text{Na}}+{\text{C}}_{\text{Na}}^{\text{mTAL}}}\right]\cdot f\left(P_{\text{O}2}^{\text{mTAL}}\right)\cdot g\left({\text{C}}_{\text{NO}}^{\text{mTAL}}\right)\cdot h\left({\text{C}}_{\text{O}2-}^{\text{mTAL}}\right)$$ (5)

where V_{max, Na} (in mol Na⁺·m⁻²·s⁻¹) is the maximal rate of Na⁺ transport, K_M,Na is the Michaelis-Menten constant (140 mM), and the functions f(P_O2^mTAL), g(C_NO^mTAL), and h(C_O2−^mTAL), respectively, represent the effects of O₂, NO, and O₂⁻ on the mTAL reabsorption rate. P_O2^mTAL denotes the partial pressure of O₂ in mTALs. The constant V_{max, Na} is estimated as 57.0 nmol/(cm²·s) in the inner stripe, and 23.1 in the outer stripe (14). To simplify the notation, we omit the dependence of the variables on spatial position (x) in Eq. 5, as well as in the equations below.

We assume that when P_O2^mTAL falls below a critical value P_c (taken as 5 mmHg) (5), anaerobic metabolism partly takes over. We posit that in the complete absence of O₂, the anaerobic pathway produces enough energy to sustain a transport rate that is a fraction λ (taken as 0.50) of the maximum rate when O₂ supply is abundant, so that

$$f\left({\text{P}}_{\text{O}2}^{\text{mTAL}}\right)=\{\begin{array}{cc}1\hfill & {\text{P}}_{\text{O}2}^{\text{mTAL}}\ge {\text{P}}_{\text{c}}\hfill \\ \lambda +(1-\lambda )({\text{P}}_{\text{O}2}^{\text{mTAL}}/{\text{P}}_{\text{c}})\hfill & {\text{P}}_{\text{O}2}^{\text{mTAL}}<{\text{P}}_{\text{c}}\hfill \end{array}$$ (6)

With these assumptions, f(P_O2^mTAL) varies between 0.50 and 1. The function g(C_NO^mTAL) accounts for the inhibitory effect of NO on Ψ_{mTAL, Na}^active and is specified as (14)

$$g\left({\text{C}}_{\text{NO}}^{\text{mTAL}}\right)=1-\frac{{\text{C}}_{\text{NO}}^{\text{mTAL}}}{\beta +{\text{C}}_{\text{NO}}^{\text{mTAL}}}$$ (7)

where β is estimated as 46.9 nM. Similarly, the function h(C_O2−^mTAL) represents O₂⁻-induced stimulation of mTAL NaCl transport, and is chosen as (14)

$$h\left({\text{C}}_{\text{O2}-}^{\text{mTAL}}\right)=0.7+0.6\left(\frac{{\text{C}}_{\text{O2}-}^{\text{mTAL}}}{{\text{C}}_{\text{O2}-}^{\text{mTAL}}+{\text{C}}_{\text{O}2-}^{*}}\right)$$ (8)

where the reference value C_O2−^* equals 20 pM in scenario A and 350 pM in scenario B (see below), so that h(C_O2−^mTAL) equals ∼1 under baseline conditions.

The overall rate at which Na⁺ is reabsorbed along mTALs, denoted T_Na^mTAL, is calculated as the total Na⁺ molar flow (summed over all mTALs) at the inlet (x = L), minus that at the outlet (x = 0).

Active O₂ Consumption

The volumetric rate of active O₂ consumption in mTAL epithelia (γ_{mTAL, O2}^active) is given by

$${\gamma }_{\text{mTAL,O}2}^{\text{active}}=\frac{2\pi R_{\text{mTAL}}{\psi }_{\text{mTAL,Na}}^{\text{active}}\theta \left({\text{P}}_{\text{O}2}^{\text{mTAL}}\right)}{18A_{\text{mTAL}}^{\text{cpi}}}$$ (9)

where R_mTAL and A_mTAL^epi denote the mTAL radius and epithelial cross-sectional area, respectively, θ(P_O2^mTAL) is the proportion of the active transport rate that is supported by aerobic respiration, and 18 is the number of Na⁺ moles actively reabsorbed per mole of O₂ consumed under maximal efficiency. We assume that (14)

$$\theta \left({\text{P}}_{\text{O}2}^{\text{mTAL}}\right)=\{\begin{array}{cc}1\hfill & {\text{P}}_{\text{O}2}^{\text{mTAL}}\ge {\text{P}}_{\text{c}}\hfill \\ \frac{{\text{P}}_{\text{O}2}^{\text{mTAL}}/{\text{P}}_{\text{c}}}{\lambda +(1-\lambda )({\text{P}}_{\text{O}2}^{\text{mTAL}}/{\text{P}}_{\text{c}})}\hfill & {\text{P}}_{\text{O}2}^{\text{mTAL}}<{\text{P}}_{\text{c}}\hfill \end{array}$$ (10)

The total consumption rate of O₂ in the OM is determined by integrating γ_{mTAL, O2}^active along the full length of short and long mTALs (that is, we neglect basal O₂ consumption). The supply of O₂ to the OM is taken as the total molar flow of O₂ (in free form or bound to Hb) in LDV and SDV at the corticomedullary junction.

Effects of Hypoxia on NO and O₂⁻

Oxygen is a substrate for NO synthesis. The volumetric rate of NO generation in compartment i (G_NOⁱ) is represented by an O₂-dependent Michaelis-Menten relationship

$$G_{\text{NO}}^i=G_{\text{NO}}^{i,\max }\left[\frac{{\text{P}}_{\text{O}2}^i}{K_{\text{M},\text{O}2}^{\text{NO}}+{\text{P}}_{\text{O}2}^i}\right]$$ (11)

where G_NO^{i, max} is the maximal NO generation rate in compartment i, P_O2ⁱ is the partial pressure of O₂ in i, and the constant K_{M, O2}^NO is taken as 38 mmHg. The mechanisms by which hypoxia raises renal medullary NO levels, as observed in anesthetized rats (16), remain to be elucidated. It has been suggested that hypoxia stimulates NO release via RBC nitrite (12) or SNOHb (35), but mathematical models of these pathways suggest that they deliver only picomolar amounts of NO to vascular smooth muscle, which is not sufficient to induce vasodilation (7, 8). In this study, we do not account for hypoxia-induced stimulation of NO release in the OM.

Given conflicting experimental data regarding the effects of hypoxia on O₂⁻ synthesis (9, 22), we consider two parallel scenarios throughout this study: scenario A assumes that low Po₂ inhibits O₂⁻ synthesis, whereas scenario B assumes instead that low Po₂ increases O₂⁻ production by 50% relative to well-oxygenated conditions. The volumetric rate of O₂⁻ generation in compartment i (G_O2−ⁱ) is thus given by

$$\begin{array}{cc}{G}_{\text{O2}-}^i=G_{\text{O2}-}^{i,\text{basal}}\left[\frac{{\text{P}}_{\text{O}2}^i}{K_{\text{M},\text{O}2}^{\text{O2}-}+{\text{P}}_{\text{O}2}^i}\right]& \text{in}scenarioA\end{array}$$ (12a)

$$\begin{array}{cc}{G}_{\text{O2}-}^i=1.5\cdot G_{\text{O2}-}^{i,\text{basal}}& \text{in}scenarioB\end{array}$$ (12b)

where G_O2−^{i, basal} is fixed, and K_{M, O2}^O2− is taken as 15.4 mmHg. The boundary conditions (such as inlet O₂⁻ concentrations) are the same in both scenarios.

Parameter Values

Aside from the effects of NO on DVR radius and blood flow, the model described herein is identical to the one we recently published (14). Tables summarizing parameter values and the description of our numerical method can be found in the latter study.

MODEL RESULTS

This study focuses on the interactions between O₂, NO, and O₂⁻ and the ways in which they affect tubular and vascular function in the OM. We first describe baseline concentration profiles and then simulate variations in production rates or reaction rates to probe the mechanisms by which blood flow and O₂ supply can be modulated by NO to match the energetic requirements of the OM. For each set of simulations, we compare results for two cases: the “vasoactive case,” which accounts for the NO-dependence of DVR radius, and the “fixed R case,” which neglects that dependence.

Base Case

The baseline mTAL Na⁺ concentration profiles, and interstitial fluid O₂, NO, and O₂⁻ concentration profiles are shown in Figs. 3 (scenario A) and 4 (scenario B) for the vasoactive case. Because model parameters were chosen so that baseline DVR inflow rates are analogous in the vasoactive case and the fixed R case, the profiles obtained in these two cases are similar. Both cases predict that the segregation of long DVR and long AVR within vascular bundles in the inner stripe gives rise to significant concentration differences between R1 (the center of the vascular bundles) and R2–R4 (the peripheral regions). The high metabolic requirements of mTALs in the interbundle regions substantially deplete O₂ therein. NO concentrations are predicted to be higher in R1 than in R2 and R3, due to the poor availability of its substrate (i.e., O₂) in the latter regions; the sharp rise in interstitial C_NO in R4 in the inner stripe is caused by tubule migration (14). When the O₂⁻ generation rate (G_O2−) is assumed to decrease with decreasing Po₂ (scenario A), interstitial C_O2− variations reflect Po₂ variations (see Fig. 3, B and D); when G_O2− is taken to be independent of Po₂ (scenario B), interstitial C_O2− varies with the fractional area occupied by vasa recta and descending limbs (i.e., the main suppliers of O₂⁻) within each region (see Fig. 4D).

Fig. 3.

Baseline concentration profiles for scenario A (vasoactive case). A: luminal Na⁺ concentrations (C_Na) in long (LAL) and short (SAL) ascending limbs. B: Po₂ in the interstitium of the 4 concentric regions (R1–R4). R1 corresponds to the center of the vascular bundle, and R4 is the outward-most region. C: NO concentrations (C_NO) in the interstitium of R1–R4. D: O₂⁻ concentrations (C_O2−) in the interstitium of R1–R4.

Fig. 4.

Baseline concentration profiles for scenario B (vasoactive case). A: luminal C_Na in LAL and SAL. B: interstitial Po₂ in R1–R4. C: interstitial C_NO in R1–R4. D: interstitial C_O2− in R1–R4.

Since O₂⁻ is the predominant NO scavenger in the interbundle region, the fact that C_O2− is higher in scenario B than in scenario A means that conversely, C_NO is lower in R2–R4 in scenario B (compare Figs. 3C and 4C). Hence, NO inhibits NaCl reabsorption to a lesser extent in scenario B, and the concentrating ability of the OM, which is evaluated as the osmolality of the collecting duct fluid at the junction between the outer and inner medulla (denoted osm_CD^L), is higher in that scenario than in scenario A (867 vs. 789 mosmol/kgH₂O, respectively; see Table 1). Even though mTALs actively reabsorb more NaCl in scenario B, the O₂ consumption rate is slightly lower then (43 vs. 44 pmol/s per vascular bundle), because Po₂ decreases more in the inner stripe, so that a greater fraction of the mTAL energetic requirements is supported by anaerobic metabolism. The predicted O₂ consumption-to-supply ratio is 0.74 in scenario B and 0.75 in scenario A, in good agreement with the experimental estimate of 0.79 in the rat OM (3). As shown in Figs. 5 (scenario A) and 6 (scenario B), results for the vasoactive case and fixed R case are similar under baseline conditions.

Table 1.

Vascular and tubular function in the rat outer medulla

	Scenario A			Scenario B
	SDV inflow, nl/min	O2 consumption-to-supply ratio	osmCDL, mosmol/kgH2O	SDV, inflow nl/min	O2 consumption-to-supply ratio	osmCDL, mosmol/kgH2O
Base case	8.0 (8.0)	0.75 (0.76)	789 (787)	8.0 (8.0)	0.74 (0.74)	867 (867)
No NO-O2−rxn	8.0 (8.0)	0.75 (0.75)	770 (771)	8.4 (8.0)	0.59 (0.65)	666 (701)
GNOep = 0	7.5 (8.0)	0.82 (0.80)	873 (854)	7.6 (8.0)	0.78 (0.78)	967 (936)
GNOep × 2	8.1 (8.0)	0.74 (0.73)	725 (730)	8.1 (8.0)	0.70 (0.71)	800 (805)
GO2−ep× 2	7.8 (8.0)	0.80 (0.78)	856 (845)	7.6 (8.0)	0.79 (0.79)	1,096 (1,037)
GO2−ep× 2 GNOep× 2	8.1 (8.0)	0.76 (0.75)	783 (788)	7.9 (8.0)	0.76 (0.76)	1006 (995)
GO2−ep× 2 GNOep× 5	8.6 (8.0)	0.47 (0.66)	535 (694)	8.5 (8.0)	0.59 (0.71)	755 (893)

G_NO^ep and G_O2−^ep: rates of NO and O₂⁻ synthesis by tubular epithelia; osm_CD^L, osmolality of collecting duct fluid at the outer-inner medullary junction. The short descending vasa recta (SDV) inflow is averaged over all SDV. Numbers in parenthesis correspond to the “fixed R case,” which neglects DVR vasoactivity.

Fig. 5.

Predicted rates of O₂ supply, O₂ consumption, and medullary thick ascending limb of Henle's loop (mTAL) NaCl reabsorption, in pmol·s⁻¹·vascular bundle⁻¹, for scenario A. Results are shown for different cases: baseline conditions (“basal”), in the absence of reaction between NO and O₂⁻ (“no rxn”), when the rate of NO synthesis by tubular epithelia (G_NO^ep) is 0, 2, or 5 times its baseline value (NO × 0, 2, or 5) , and/or when the rate of O₂⁻ synthesis by tubular epithelia (G_O2−^ep) is twice its baseline value (O₂⁻ × 2). Black bars, “vasoactive case”; grey bars, “fixed R case.”

Fig. 6.

Predicted rates of O₂ supply, O₂ consumption, and mTAL NaCl reabsorption, in pmol·s⁻¹·vascular bundle⁻¹, for scenario B. Results are shown for different cases: baseline conditions (basal), in the absence of reaction between NO and O₂⁻ (no rxn), when G_NO^ep is 0, 2, or 5 times its baseline value (NO × 0, 2, or 5) , and/or when G_O2−^ep is twice its baseline value (O₂⁻ × 2). Black bars, vasoactive case; grey bars, fixed R case.

Indirect Effects of O₂⁻ on MBF

The mechanisms by which O₂⁻ modulates MBF remain to be elucidated (15). Could O₂⁻-induced vasoconstriction be mediated by NO, at least in part, given that O₂⁻ reduces NO levels via scavenging, thereby reducing the vasodilatory effects of NO? To probe this issue, we conducted simulations in which we eliminated the direct interactions between NO and O₂⁻ by setting their reaction rate to zero. We first consider the vasoactive case.

In scenario A, inhibiting the reaction raises C_NO (and C_O2−) by a few nanomolar in the interbundle region, not enough to raise DVR inflow (Table 1). Since NO and O₂⁻ exert counterbalancing effects on the mTAL transport rate, m_Na^mTAL and Po₂ vary only slightly. Thus, in the absence of the NO-O₂⁻ reaction, osm_CD^L and the O₂ consumption-to-supply ratio vary by <3% (Table 1).

In scenario B, the consequences of inhibiting the NO-O₂⁻ reaction are more pronounced: because C_O2− is two- to threefold higher in this scenario, O₂⁻ scavenging has a greater impact on interbundle NO levels (14). Thus, when the reaction is abolished, C_NO increases more (Fig. 7), and the average SDV inflow rises from 8.0 to 8.4 nl/min (LDV inflow varies by 0.04 nl/min). The inhibitory effects of NO on mTAL transport then predominate, T_Na^mTAL and O₂ consumption both decrease (Fig. 6), and osm_CD^L is reduced by 23%. Altogether, the O₂ consumption-to-supply ratio is predicted to fall from 0.74 to 0.59 (Table 1).

Fig. 7.

Impact of the NO-O₂⁻ reaction on concentration profiles (scenario B, vasoactive case). Results are shown for the base case (basal) and assuming that the NO-O₂⁻ reaction rate is zero (no rxn). A: luminal C_Na in LAL and SAL. B: interstitial Po₂ in regions R2 and R4. C: interstitial C_NO in R2 and R4. D: interstitial C_O2- in R2 and R4. In the interbundle region, inhibition of the NO-O₂⁻ reaction has a larger impact on C_NO than on C_O2−. The subsequent increase in O₂ supply is accompanied by a significant decrease in the rate of NaCl reabsorption across LAL and SAL, and in the rate of O₂ consumption.

A comparison with the fixed R case is instructive. If DVR vasoactivity is not taken into account, the O₂ consumption-to-supply ratio in scenario B is found to decrease significantly less (from 0.74 to 0.65) when the NO-O₂⁻ reaction rate is set to zero. Indeed, the fixed R case does not consider the following positive feedback mechanism: as C_NO increases, DVR dilate and carry more O₂ into the medulla, which in turn raises the generation rate of NO (G_NO) and therefore C_NO, and so on. This cycle will stop at some point, however, because the extent to which DVR can dilate, and that to which G_NO can increase, are both intrinsically limited (see the saturable expressions in Eqs. 1 and 11). Moreover, other vasoconstrictor agents, not represented in the present model, are likely to be released to limit such NO-dependent vasodilation. It is also possible that as Po₂ increases, hypoxia-induced stimulation of NO release diminishes, thus putting another break on this positive feedback mechanism.

Finally, it should be noted that inhibiting the NO-O₂⁻ reaction reduces osm_CD^L less in the fixed R case than in the vasoactive case in scenario B (Table 1): since C_NO does not rise as much, mTAL transport is less inhibited. Together, these results suggest that NO-induced vasodilation may significantly affect the O₂ balance and the concentrating capacity of the OM, and that O₂⁻-induced DVR vasoconstriction could be at least partly mediated by NO.

Impact of Epithelial NO Generation

To assess the contribution of tubular NO generation to the maintenance of medullary oxygenation, we first simulated an isolated twofold increase in the rate of NO synthesis by epithelia (G_NO^ep). Under these conditions, calculated C_NO values are 10–20 nM higher in the interbundle region (see Fig. 8 for scenario A). NO-mediated inhibition of active Na⁺ transport is then enhanced, and osm_CD^L, T_Na^mTAL, and O₂ consumption are predicted to decrease by 4–8% (Figs. 5 and 6). The impact on O₂ supply is small, and the O₂ consumption-to-supply ratio decreases in proportion to consumption (Table 1).

Fig. 8.

Impact of NO synthesis by tubular epithelia on Po₂ and C_NO in region R3, where most mTALs are located. Results are shown for scenario A. The rate of NO synthesis by tubular epithelia is either equal to its baseline value (basal), multiplied by 2 (G × 2), or 0 (G = 0). A and B: Po₂ and C_NO in the R3 interstitium, accounting for vasoactivity of DVR. C and D: Po₂ and C_NO in the R3 interstitium, assuming no vasoactivity of DVR. Results suggest that NO tubulovascular cross talk has a significant impact on O₂ balance in the outer medulla.

Conversely, in the absence of NO generation by epithelia, C_NO is predicted to decrease by 10–30 nM in R2–R4 (vasoactive case) relative to baseline conditions (Fig. 8). The resulting vasoconstriction of SDV reduces O₂ supply to the interbundle region by ∼ 5% (Figs. 5 and 6). In parallel, the rate of active Na⁺ transport (which is less inhibited by NO) rises by 10%, and so does osm_CD^L (Table 1). Overall O₂ consumption is predicted to increase only slightly (by ∼2%) for the following reason. The increase in T_Na^mTAL requires more energy, but because O₂ supply to the interbundle region decreases, in the vicinity of mTAL Po₂ falls even further below the critical pressure along most of the inner stripe (see Fig. 8A), so that a smaller fraction of active Na⁺ transport is supported by aerobic respiration. In other words, O₂ consumption does not increase in proportion to T_Na^mTAL because a greater fraction of mTAL energy requirements is provided by anaerobic metabolism. Overall, the O₂ consumption-to-supply ratio increases to 0.82 (scenario A) and 0.78 (scenario B).

In the fixed R case, the O₂ supply to the interbundle region is constant. Thus, in the absence of NO generation by epithelia, Po₂ does not fall as significantly in the tissue surrounding mTALs (see Fig. 8, A and C), and O₂ consumption increases in proportion to the rate of active Na⁺ transport, that is, more than in the vasoactive case (Figs. 5 and 6). As a result, the increase in the O₂ consumption-to-supply ratio is comparable in both cases (Table 1). Taken together, these results suggest that NO tubulovascular cross talk has a significant impact on OM O₂ balance and concentrating capacity.

ANG II-Mediated Increases in Epithelial Generation

We then examined the impact of tubular NO synthesis specifically in response to ANG II. ANG II stimulates the production by mTAL epithelia of not only O₂⁻ but also NO (24, 25). The ANG II-induced increase in NO synthesis is thought to help abrogate tissue hypoxia (31). We simulated first an isolated increase in the tubular production of O₂⁻, followed by an increase in that of both O₂⁻ and NO. Based on experimental measurements of O₂⁻ and NO concentrations in the presence of ANG II (24, 25, 39), epithelial G_O2− (G_O2−^ep) was multiplied by a factor of 2, and epithelial G_NO (G_NO^ep) by a factor of 2 or 5. Note that we did not consider the NO-independent mechanisms by which ANG II may induce DVR vasoconstriction in these simulations.

As expected, an isolated twofold increase in G_O2−^ep raises C_O2− in the vicinity of mTALs, thereby stimulating active Na⁺ transport, and increasing both oxygen consumption (Fig. 5 and 6) and the concentrating capacity of the medulla (Table 1). The rate of NO scavenging by O₂⁻ increases concomitantly (more so in scenario B), leading to vasoconstriction of SDV in the interbundle region and a reduction in local O₂ delivery. The O₂ consumption-to-supply ratio is thus predicted to increase by 5 percentage points in both scenarios.

A concomitant increase in G_NO^ep, however, counteracts the stimulating effects of O₂⁻ on NaCl transport and O₂ consumption in the OM. A twofold increase in G_NO^ep offsets the T_Na^mTAL increase, either fully (scenario A) or partially (scenario B) (Figs. 5 and 6). It also raises C_NO sufficiently to essentially abolish SDV constriction and restore O₂ supply to the interbundle region. Thus, when G_O2−^ep and G_NO^ep are both doubled, the O₂ consumption-to-supply ratio is predicted to remain close to its baseline value (Table 1).

If G_NO^ep is increased five times relative to its baseline level (while G_O2−^ep is doubled), O₂ supply to the interbundle region is further augmented, while active Na⁺ transport and O₂ consumption both decrease significantly below baseline levels (Figs. 5 and 6). Under these conditions, the O₂ consumption-to-supply ratio is calculated as 0.47 in scenario A and 0.59 in scenario B. The corresponding predictions, displayed in Fig. 9 (case 3), conflict with experimental findings, however: in vivo, acute subpressor doses of ANG II do not significantly alter MBF and medullary Po₂ (39). These results thus suggest that ANG II induces comparable increases in G_O2−^ep and G_NO^ep.

Fig. 9.

Impact of epithelial production of O₂⁻ (G_O2−^ep) and NO (G_NO^ep) on Po₂ and C_NO in region R3. Results are shown for scenario A. Basal denotes baseline profiles. In case 1, G_O2−^ep is multiplied by 2 (relative to its baseline value); in case 2, G_O2−^ep and G_NO^ep are both multiplied by 2. In case 3, G_O2−^ep is multiplied by 2, and G_NO^ep by 5. A and B: Po₂ and C_NO in the R3 interstitium, accounting for vasoactivity of DVR. C and D: Po₂ and C_NO in the R3 interstitium, assuming no vasoactivity of DVR. Results suggest that ANG II-induced stimulation of NO synthesis by mTAL counteracts the effects of oxidative stress.

As expected, the two- or fivefold G_NO^ep increase is predicted to have a lesser impact in the fixed R case (Fig. 9). That is, in the absence of tubulovascular cross talk, T_Na^mTAL, osm_CD^L and the O₂ consumption-to-supply ratio are much less reduced (Table 1). Taken together, our results suggest that ANG II-mediated NO synthesis acts not only to counterbalance the effects of ANG II on vasoconstriction, as observed experimentally (39, 36), but also to reduce active Na⁺ transport and thereby preserve O₂ availability in the OM.

DISCUSSION

The effects of NO and O₂⁻ on vascular and tubular function in the OM are difficult to untangle: not only do NO and O₂⁻ exert opposite actions on blood flow and sodium transport while reducing each other's bioavailability (15) but they also interact with O₂ in ways that are not fully understood. In this study, we used a mathematical model to gain more insight into the reciprocal interactions between O₂, NO, and O₂⁻.

The most significant limitations of our model stems from the paucity of experimental data. As previously discussed (14), absolute O₂⁻ concentrations in the renal medulla have not yet been reported; the quantitative effects of NO and O₂⁻ on mTAL reabsorption rates are also uncertain. Similarly, the data we extrapolated to predict the effects of C_NO on DVR diameter and blood flow (Eq. 1) are somewhat limited. In addition, the contribution of anaerobic metabolism to the energy requirements of the OM, which likely varies among species, has never been precisely determined. Further experimental studies are needed to fill those gaps, and to elucidate the effects of downstream products such as ONOO⁻ (peroxynitrite) and H₂O₂ (hydrogen peroxide) on MBF (23, 26), which our current model does not consider. Finally, conflicting experimental results regarding the effects of low Po₂ on medullary O₂⁻ synthesis (9, 22), as well as the uncertainty surrounding the mechanisms by which hypoxia raises medullary NO levels, also require additional investigation.

To circumvent some of these limitations, we considered two scenarios in parallel throughout the study: scenarios A and B assume that O₂⁻ synthesis respectively decreases and increases with decreasing Po₂. Since medullary Po₂ is low, C_O2− is significantly higher in scenario B. This distinction proved useful when we examined the indirect effects of O₂⁻ on MBF. Our results suggest that O₂⁻-induced vasoconstriction may be partly mediated by NO, provided that O₂⁻ levels are sufficiently high. When the scavenging effects of O₂⁻ on NO were eliminated, SDV inflow was predicted to remain constant in scenario A, and to increase by 5% in scenario B (from 8.0 to 8.4 nl/min).

Our model predicts differential regulation of vasoactivity in short and long DVR. The region-based approach allows us to take into account the specific architecture of the rat OM, with its sharp distinction between intra- and interbundle regions. The LDV, which are destined to the inner medulla, are positioned at the center of the vascular bundles, whereas the SDV peel off from the bundle periphery to supply blood flow to the OM capillary plexus. In all the simulations performed for this study, LDV inflow remained approximately constant (it was always comprised between 7.9 and 8.1 nl/min) even when SDV inflow varied significantly. That is, the segregation of LDV within the center of the vascular bundles is predicted to insulate these vessels from changes in tubular function in the OM, thereby preserving O₂ delivery to the inner medulla.

We also found that the impact of the interactions between O₂, NO, and O₂⁻ is enhanced by a positive feedback mechanism, the importance of which remains to be ascertained in vivo. Since O₂ is a precursor in the synthesis of NO, an increase in Po₂ should raise NO concentrations, thereby augmenting DVR diameter, blood flow, and O₂ supply; this should in turn further raise C_NO, and so on. This positive feedback loop should nevertheless be mitigated, if not abolished, by the combination of several factors: 1) the limited extent to which DVR can dilate, which this model accounts for; 2) other vasoconstrictor agents such as endothelins, not considered in this study; and 3) the extent to which hypoxia affects NO bioavailability. Heyman et al. (17) observed an increase in medullary NO levels when Po₂ was lowered. Hypoxia-induced NO release has been reported in other tissues and is thought to be a mechanism whereby local perfusion is adjusted to match O₂ requirements (1). The underlying signaling pathways are still controversial and remain to be fully elucidated (1, 7, 8, 12). The tight coupling between Po₂ and C_NO illustrated by the model underscores the importance of better understanding the effects of hypoxia on NO bioavailability in the renal medulla.

We used the current model to assess in particular the importance of tubulovascular cross talk in maintaining OM perfusion and O₂ availability. Cowley and colleagues (36, 39) showed that ANG II-induced increases in NO production offset the vasoconstrictor effects of ANG II and maintain MBF constant. Our results suggest that even basal production of NO by tubular epithelia acts to preserve blood flow and O₂ supply to the interbundle region (Figs. 5 and 6). In the absence of tubular NO synthesis and subsequent NO diffusion to neighboring DVR, O₂ supply to the interbundle region is predicted to decrease by 5%, and the O₂ consumption-to-supply ratio to grow by 4–7% (Table 1). These differences are not huge, but they are significant in light of the hypoxic conditions that prevail in the OM. The variations in the O₂ ratio stem not only from the reduction in O₂ supply but also from changes in O₂ consumption, as the inhibitory effects of NO on active Na⁺ transport across mTALs are abrogated; in the absence of tubular NO synthesis, the rate of NaCl reabsorption and the concentrating capacity of the outer medulla are calculated to be ∼10% higher (Table 1). In other words, NO acts to preserve O₂ availability in the interbundle region by modulating both oxygen supply and demand, not just by matching O₂ delivery to the metabolic needs of mTALs. In the presence of ANG II, the combined regulation of O₂ consumption and supply by NO is predicted to significantly attenuate the hypoxic effects of ANG II (Fig. 9), as postulated by other investigators (28, 31).

Our investigations also suggest that O₂ consumption may not systematically increase in proportion to the rate of active Na⁺ transport, in the presence of anaerobic metabolism. In those simulations where Po₂ in the vicinity of mTALs was below the critical pressure in most of the inner stripe (where the rate of NaCl reabsorption is the highest), the rate of O₂ consumption did not rise as fast as T_Na^mTAL. This prediction is contingent upon our assumption that anaerobic metabolism can be a significant source of ATP in the rat OM. The current model assumes that, when necessary, glycolysis may produce enough energy to sustain half the maximal transport rate (i.e., that at which O₂ is not rate limiting; see Eq. 6). Ex vivo, the production of lactate by isolated rat mTAL segments was found to increase markedly following incubation with the oxidative metabolism inhibitor antimycin A (2). Whether, in vivo, anaerobic metabolism is sufficient to sustain an increased rate of NaCl reabsorption even as Po₂ decreases remains to be ascertained. At the very least, the supply of glucose to the OM seems more than sufficient to satisfy the corresponding ATP requirements. Assuming a glucose concentration of 10 mM in DVR blood (37), the supply of glucose to the OM is 80 pmol·min⁻¹·DVR⁻¹, or 4.6 nmol·min⁻¹·vascular bundle⁻¹. The basal rate of Na⁺ transport across mTALs, estimated as 1,200 pmol Na⁺·min⁻¹·bundle⁻¹ (Figs. 5 and 6), requires 400 pmol ATP·min⁻¹·bundle⁻¹, which in turn necessitates the conversion of 200 pmol glucose·min⁻¹·bundle⁻¹ under anaerobic conditions, which is less than one-tenth of the glucose supply.

In conclusion, this model underlines the importance of O₂ availability in regulating the balance between NO and O₂⁻ and their effects on vascular and tubular function in the rat OM. Conversely, our results suggest that basal production of NO by tubular epithelia modulates both the supply and demand of O₂ in the interbundle region.

GRANTS

This work was supported by National Institutes of Health Grant DK-89066 and National Science Foundation Grant DMS-0715021 (to A. Layton).

DISCLOSURES

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

AUTHOR CONTRIBUTIONS

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