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Department of Chemical and Biological Engineering, Tufts University, Medford, Massachusetts 02155
Submitted 7 April 2004 ; accepted in final form 22 July 2004
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ABSTRACT |
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 TOP ABSTRACT GLOSSARYMODEL AND PARAMETERSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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60–140 nM in medullary tissues (Zou AP and Cowley AW Jr. Hypertension 29: 194–198, 1997; Am J Physiol Regul Integr Comp Physiol 279: R769–R777, 2000) and 3 nM in plasma (Stamler JS, Jaraki O, Osborne J, Simon DI, Keaney J, Vita J, Singel D, Valeri CR, and Loscalzo J. Proc Natl Acad Sci USA 89: 7674–7677, 1992), the permeabilities of red blood cells (RBCs), vascular walls, and pericytes to NO are all predicted to lie between 0.01 and 0.1 cm/s, and the NO production rate by vasa recta endothelium is estimated to be on the order of 10–14 µmol·µm–2·s–1. Our results suggest that the concentration of NO in RBCs, which is essentially controlled by the kinetics of NO scavenging by hemoglobin, is 0.01 nM, that is, 103 times lower than that in plasma, pericytes, and interstitium. Because the basal concentration of NO in pericytes is on the order of 10 nM, it may be too low to active guanylate cyclase, i.e., to induce vasorelaxation. Our simulations also indicate that basal superoxide concentrations may be too low to affect medullary NO levels but that, under pathological conditions, superoxide may be a very significant scavenger of NO. We also found that although oxygen is a negligible NO scavenger, medullary hypoxia may significantly enhance NO concentration gradients along the corticomedullary axis. kidney; mathematical model; transport; medullary hypoxia
The interactions between NO and oxygen are complex. Oxygen serves as a substrate for the production of both NO and reactive oxygen species (ROS) such as superoxide, which has been shown to modulate NO levels in isolated outer medullary (OM) DVR walls (51). By incubating bovine aortic endothelial cells in gas mixtures, Whorton et al. (63) found that NOS activity rises with increasing oxygen tension (PO2) if the latter remains below its value in room air; beyond this point, PO2 does not seem to affect NOS activity. It is therefore possible that the hypoxic conditions in the renal medulla inhibit NO synthesis. Conversely, the supply and consumption of oxygen in the medulla depend on the effects of NO on vasoconstriction and tubular solute transport. Furthermore, constrictors of the medullary microcirculation can stimulate enhancement of NO generation (45). Dickhout et al. (12) observed that vasoconstriction by angiotensin II is buffered by NO produced by surrounding tubular elements. The investigators postulated that the medullary thick ascending limb (mTAL) is capable of controlling needed oxygen delivery in the face of high circulating levels of angiotensin II, by diffusing NO to pericytes of the vasa recta.
One of the first models of NO transport in biological tissues was developed by Lancaster (32), who simulated the one-dimensional diffusion of NO from an endothelial source to smooth muscle cells, accounting for NO consumption by oxygen and hemoglobin in the aqueous phase. Lancaster found that NO could diffuse over a long distance despite significant scavenging by hemoglobin. Vaughn et al. (62) modeled the production of NO from a single, oblate endothelial cell and calculated the NO production rate as 6.8 x 10–14 µmol·µm–2·s–1; the kinetic rate constant of NO degradation by vascular smooth muscle cells was estimated to be on the order of 0.01 s–1, assuming a first-order reaction, and 0.05 µM/s assuming a second-order reaction. In the model of Tsoukias and Popel (59), an erythrocyte was depicted as a disk within a larger, surrounding disk representing plasma, the size of which was determined by the hematocrit; their simulations suggested that the concentration of NO in the erythrocyte is much lower than that in plasma. Recently, Layton and colleagues (53) simulated the transport of NO in renal afferent arterioles and predicted that the advective transport of locally produced NO is sufficient to yield physiologically significant NO concentrations along the arteriole. Given the size of vasa recta and their countercurrent arrangement, the concentration of NO in the medullary microcirculation is expected to be governed by different transport processes. In this study, we modeled the generation, transport, and consumption of NO in vasa recta to gain a better understanding of the determinants of basal NO concentration in the renal medulla.
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GLOSSARY |
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Greek Symbols
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Subscripts and Superscripts
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MODEL AND PARAMETERS |
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TOPABSTRACTGLOSSARYMODEL AND PARAMETERSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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Figure 1 represents the countercurrent exchange system of the renal medullary microcirculation. Blood flows down along the DVR from the corticomedullary junction to the papillary tip and loops back to the cortical veins along the ascending vasa recta (AVR). During transit, radial exchanges between vasa recta and the medullary interstitium allow water and solutes deposited from the loops of Henle and the collecting ducts into the interstitium to be carried away by the medullary microcirculation.
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In the renal medulla, NO is predominantly produced by vasa recta, IMCDs, and mTALs (64). A portion of NO generated within vasa recta walls is assumed to diffuse into the vessel lumen, where it reacts with scavengers such as oxygen, superoxide, and the hemoglobin contained within red blood cells. The remainder diffuses abluminally toward the interstitium. In outer medullary DVR, NO has to diffuse across pericytes before it arrives in the interstitium; within the pericytes, a fraction of NO reacts with superoxide and oxygen, as well as with guanylate cyclase (GC) to induce vasodilation, and the rest reaches the medullary interstitium. NO generated by IMCDs and mTALs is also assumed to diffuse into the interstitium. These additional sources of interstitial NO, combined with the rapid degradation of NO in blood, result in a significant concentration gradient across the vascular wall that drives NO into the lumen. Our assumptions regarding the synthesis, transport, and consumption of NO are given below. The general mathematical model of transport within the medullary microcirculation has been described previously (65), and our modifications to include NO are described in the APPENDIX.
NO Synthesis in the Renal Medulla
NO is produced from a group of enzymes called NOS that catalyze a five-electron oxidation of the guanidine nitrogen of L-arginine by NADPH and O2 (20). Three isoforms of the NOS enzyme, that is, nNOS (or NOS I), iNOS (or NOS II), and eNOS (or NOS III), have been identified throughout different structures of the renal medulla. All three enzymes can coexist in a given region and contribute to the overall production of NO within that region (64). There are numerous regulatory pathways at both the transcriptional and posttranslational levels that make pinpointing key biological factors of NO production extremely difficult.
Wu et al. (64) estimated the production of NO in the renal medulla by measuring the production of L-citrulline from microdissected segments in the rat kidney. The NO generation rates from IMCDs, vasa recta, and mTALs were reported as 11.5, 3.2, and 0.5 fmol·mm–1·h–1, respectively, based on 20-mm-long segments. Those values are equivalent to 3.4 x 10–17, 2.2 x 10–17, and 0.22 x 10–17 µmol·µm–2·s–1, respectively, based on the average surface area of IMCDs (0.094 mm2/mm length), DVR and AVR (0.041 mm2/mm length), and mTALs (0.063 mm2/mm length), given the diameters and AVR-to-DVR number ratio listed in Table 1. Based on their mathematical model of NO transport, Vaughn et al. (62) calculated the NO production flux from nonspecific vascular endothelial cells as 6.8 x 10–14 µmol·µm–2·s–1. Their estimate is therefore three orders of magnitude greater than that of Wu et al. (64). Because of this discrepancy, the rate of NO generation in vasa recta was a variable parameter in this study. In the absence of specific data, we assumed that the generation rates of NO per surface area are constant and identical along the corticomedullary axis.
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As discussed below, the mechanisms and kinetics of NO conversion by serum albumin and other thiols remain unclear. We therefore considered only the three main reactive species that can radically reduce NO concentration, that is, oxygen (O2), superoxide (O2–), and hemoglobin. In all four compartments considered here (interstitium, pericytes, plasma, and RBCs), NO reacts with O2 to form nitrite (NO2–; reaction 1) and with O2– to form peroxynitrite (ONOO–; reaction 2). The reactions of NO with hemoglobin (reactions 3 and 4) occur only in RBCs, and so does the reaction between hemoglobin and oxygen (reaction 6). In addition, NO reacts with GC in pericytes (reaction 5) to activate GTP, which is then converted to cGMP
 | (reaction 1) |
 | (reaction 2) |
 | (reaction 3) |
 | (reaction 4) |
 | (reaction 5) |
 | (reaction 6) |
 | (1) |
 | (2) |
 | (3) |
 | (4) |
 | (5) |
 | (6) |
Following the approaches of Vaughn et al. (62) and Butler et al. (5), the rate of reaction between NO and GC was assumed to be first order with respect to NO concentration, as the GC concentration was assumed to be constant. The kinetic rate product k5[GC] was taken as 0.01 s–1 and the perycite thickness as 0.5 µm, as described below.
The hemoglobin molecule is composed of four subunit proteins, two 
and two 
, each containing an iron-based heme group that can bind one O2 or NO molecule. The mechanisms by which NO and O2 bind to hemoglobin are complex and remain to be fully elucidated. In this study, we made the simplifying assumption that each individual heme group can be treated separately and that each reacts with NO independently of the binding state of the other groups. Hereafter, we use the term Hb to denote one heme protein group, as opposed to the entire hemoglobin molecule, unless otherwise specified. Therefore, the overall concentration of heme proteins is four times that of hemoglobin. NO oxidizes the Fe(II) in oxyheme (HbO2) to form metheme (met-Hb; reaction 3), whereas deoxyheme (Hb) and NO associate to form ligand-bound nitrosyl-heme (HbNO; reaction 4) in a reversible manner (4). Cassoly and Gibson (6) found no cooperativity in the binding of NO to deoxyhemoglobin; that is, the intrinsic NO addition rate constants do not vary with NO saturation; because the biological concentration of NO is at least 1,000-fold lower than that of heme, most hemoglobin molecules do not carry any NO, and those that do will carry no more than one (49). Therefore, k–4 was taken as 103/s, that is, the value of the kinetic constant for the disassociation of the T-state Hb4(NO) (52).
Following the approach of Baxley and Hellums (2), the kinetic constant k–6 was taken as 3.5 x 106 M/s. We derived k6 from the Hill equation
 | (7) |
NO Transport Resistance
As NO enters plasma, there are four diffusive steps leading to its reaction with hemoglobin in RBC: 1) diffusion through the RBC-free region created by intravascular flow, toward the bulk solution; 2) diffusion from the bulk solution to the surface of the RBC (extracellular layer); 3) diffusion across the RBC membrane; and 4) diffusion and reaction in the cytosol.
Subczynski et al. (56) measured the permeability of artificial lipid membranes to NO. Their results, on the order of 77–93 cm/s, suggest that the RBC membrane itself (i.e., step 3) is not rate limiting. Vaughn et al. (60) examined the extracellular resistance to NO transport by comparing the reaction rate of NO with hemoglobin either within RBCs (that is, in a process involving steps 2–4 above) or in a continuous, cell-free solution (that is, with only extracellular diffusion). If the hematocrit was at least 7.5%, the apparent RBC-to-cell-free hemoglobin solution kinetic constant ratio was found to be 0.001, independently of the hematocrit. This suggests that the main barriers to NO transport are the RBC membrane and cytosol and that the resistance to extracellular diffusion is comparatively negligible. The permeability of RBC barriers (membrane and cytosol) to NO (PNOR) was therefore taken as 0.04 cm/s, as estimated by Vaughn et al. (61). In the absence of experimental measurements of the permeability of vasa recta walls to NO (PNOW), we used the same estimate as that to oxygen, 0.04 cm/s (23, 65). We assumed that the wall permeability implicitly accounts for the resistance of the boundary layer in the RBC-free zone adjacent to the wall (i.e., step 1 above), which has been shown to reduce NO consumption (34). In the absence of data, we also assumed that the permeability of pericytes (membrane and cytosol) to NO is the same as that of RBCs, 0.04 cm/s.
Initial Values of NO and Scavenger Concentration
Zou and Cowley (67, 68) measured tissue NO concentrations as 57–139 nM in the renal medulla and 31–95 nM in the cortex. In addition, the concentration of NO in plasma was reported as 3 nM by Stamler et al. (54). Given the high concentration of heme protein groups (on the order of 20 mM) which scavenge NO almost instantaneously, NO concentration is expected to be much lower in RBC than in plasma. As a first trial, we assumed that the initial values (i.e., at the corticomedullary junction in DVR) of CNOPand CNORare 1 nM and 0, respectively.
The initial concentration of overall heme species was taken as 20 mM (65). However, the distribution of Hb proteins at the corticomedullary junction is unknown. Because both the reaction between deoxyheme and NO (reaction 4) and the association between O2 and Hb (reaction 6) are reversible, we assumed that they are in equilibrium at the corticomedullary junction and calculated the initial value of Hb, HbNO, and HbO2 concentrations based on this hypothesis, after having specified CNOR. If initial CNORis assumed to be zero, the initial concentration of HbNO is also zero.
O2–-producing enzymes, such as NADH/NADPH oxidase, mitochondrial enzymes, and xanthine oxidase (XO), have been identified throughout the medulla (69). In their model of NO consumption by an erythrocyte, Tsoukias and Popel (59) assumed that O2– concentration in plasma was in the subnanomolar range. Intracellular O2– concentrations have been reported as 10–10-10–9 M in aerobic, SOD-proficient cells (10, 28). The concentration of O2– in vasa recta has not been reported, to the best of our knowledge, and was therefore varied between 0 and 10 nM in plasma and interstitium, and between 0 and 1 nM in RBCs, with baseline values equal to 0.1 nM in all compartments. Table 1 summarizes the baseline parameter values used in this study.
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RESULTS |
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TOPABSTRACTGLOSSARYMODEL AND PARAMETERSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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Baseline values of the parameters are listed in Table 1. As explained below, NO generation rate in vasa recta was taken as 10–14 µmol·µm–2·s–1. NO induces vasorelaxation by acting on the pericytes that surround DVR. The outer surface of DVR is only partially covered with pericytes whose thickness is 2.5 µm in the cross section that includes their nucleus and 0.7 µm in that which contains their tentacles (Dr. Tom L. Pallone, personal communication). To account as well for the fact that pericytes are disposed at intervals of 14–20 µm (57), we assumed in the baseline case that they are 0.5 µm thick but form a continuous layer. We examined two hypotheses, namely, that pericytes surround either OMDVR only, as suggested by Pallone and Silldorff (47), or both OMDVR and IMDVR, because Takahashi-Iwanaga (57) observed pericytes in the upper portion of IMDVR.
The resulting medullary NO concentration profiles in all compartments are shown in Fig. 2A for the baseline case (pericytes in OM only) and in Fig. 2B, assuming that pericytes are present throughout the medulla.
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103 greater in plasma than in RBCs. Because we assumed constant generation rates, CNO varies within a narrow range in each compartment. The predicted concentrations of NO in interstitium and pericytes (20 nM) and in plasma (8 nM) are comparable to the measurements of Zou and Cowley (67, 68) in medullary tissue (60–140 nM) and those (54) in plasma (3 nM). The abrupt variations at the OM-IM junction observed in Fig. 2A stem from the sudden disappearance of pericytes at that location. As seen in Fig. 2B, when pericytes are taken to surround both OMDVR and IMDVR, NO concentration profiles are smoother, but overall NO levels remain similar to those in the baseline case. The large plasma-to-RBC CNO gradient is due to the very rapid scavenging of NO by hemoglobin. RBCs act as a sink for NO; as shown below, the barriers formed by the RBC membrane and cytosol and the vascular wall prevent the rapid depletion of NO in plasma and interstitium. Because the RBC concentration of deoxygenated Hb is higher in AVR than in DVR given the release of oxygen for metabolic consumption, and because NO reacts with deoxygenated Hb, NO concentrations are lower in AVR than in DVR both in plasma and RBCs.
Given the small concentration variations within each compartment, in the remainder of this study NO concentration is reported as the average value for each compartment. When the differences in CNO between OM and IM are significant, concentrations in the OM and IM are reported separately.
We then performed a parameter sensitivity analysis by examining the effect of increasing and decreasing each of the parameters by 50% on NO concentration in each compartment. Results, shown in Table 2, indicate that the determinant parameters are the NO generation rates, the fraction of NO generated in vasa recta endothelium that diffuses toward the lumen (fNO), the initial hematocrit (h0), and the permeabilities of vascular walls, pericytes, and RBCs in decreasing order of importance. We therefore studied the effects of those parameters first.
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Wu et al. (64) measured the NO generation rate by vasa recta (NOP), mTALs (NOmTAL), and IMCDs (NOIMCD) as 3.2, 0.5, and 11.5 fmol·mm–1·h–1, which are equivalent to 2.2 x 10–17, 0.22 x 10–17, and 3.4 x 10–17 µmol·µm–2·s–1, respectively. The value for NOP, 2.2 x 10–17 µmol·µm–2·s–1, is 3,000 times lower that that estimated by Vaughn et al. (62) for nonspecific vascular endothelial cells, 6.8 x 10–14 µmol·µm–2·s–1. Using the generation rates obtained by Wu et al. (64), the predicted CNO in plasma and interstitium is on the order of 0.01 nM, which is several orders of magnitude lower than experimental reports. We therefore increased each parameter (NOP, NOmTAL, and NOIMCD) in turn while keeping the other two fixed at the values given above. The effects of varying NOP, NOmTAL, and NOIMCDon average medullary NO concentrations are shown in Fig. 3, A, B, and C, respectively.
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NOP. As NOPis raised from 1 x 10–17 to 1 x 10–13 µmol·µm–2·s–1, CNO increases from 10–4 to 10–2 nM in RBCs, from 0.01 to 80 nM in plasma, and from 0.01 to 200 nM in pericytes and interstitium. Because NOPis much greater than both NOmTALand NOIMCDin these simulations, vasa recta endothelium is the main source of NO; the latter diffuses from the vascular wall into the pericytes and then into the interstitium, so that CNO is slightly higher in pericytes than in OM interstitium. Our results suggest that with NOmTALand NOIMCDfixed at the values measured by Wu et al. (64), NOPshould be on the order 10–14 µmol·µm–2·s–1, that is close to the estimate of Vaughn et al. (62), to match experimental measurements of NO concentration in medullary tissue and plasma.
Because mTALs and IMCDs are located in OM and IM, respectively, increasing NOmTALraises CNO in all four compartments in the outer medulla only, as shown in Fig. 3B, whereas increasing NOIMCDraises CNO in the inner medulla only (Fig. 3C). The concentration of NO in pericytes does not vary with NOIMCDbecause the latter are taken to surround OMDVR only (baseline hypothesis).
As described below, even if we optimize the values of all the other uncertain parameters to raise medullary CNO, predictions based on the data of Wu et al. (64) cannot match the experimental measurements of both Zou and Cowley (67, 68) and Stamler et al. (54). Agreement between calculated and reported values of CNO is possible only if we increase NOP, NOmTAL, and/or NOIMCD. However, increasing the three generation rates simultaneously would introduce many more uncertainties. We therefore chose to raise only NOPand chose a value of 1 x 10–14 µmol·µm–2·s–1 as our baseline case, while keeping NOmTALand NOIMCDfixed at 0.22 x 10–17 and 3.4 x 0–17 µmol·µm–2·s–1, respectively, as reported by Wu et al. (64).
Effects of Fraction of NO Generated by Vasa Recta Wall that Diffuses Toward the Vascular Lumen
In our baseline case, we assumed that the fraction of NO generated by vasa recta endothelium that diffuses luminally (i.e., fNO) is equal to that which diffuses abluminally. Sensitivity analysis indicates that fNO affects CNO significantly (Table 2). Shown in Fig. 4 is the average CNO in plasma, interstitium and pericytes, as fNO is varied between 0 and 100%. Plasma NO concentrations remain approximately constant as equilibrium between plasma and RBCs is maintained, whereas CNO in pericytes and interstitium decreases linearly, by a factor 3 as fNO increases from 0 to 100%. In the limiting case where fNO = 100%, that is, when all NO generated by the vascular endothelium is released into the lumen, CNO is higher in DVR plasma than in interstitium. Because experimental measurements (67, 68) suggest that the concentration of NO is significantly greater in interstitium than in blood, lower values of fNO appear more reasonable.
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Variations in hematocrit affect not only the overall amount of hemoglobin but also the surface area at the interface between plasma and RBCs (65). An increase in the initial hematocrit at the corticomedullary junction increases the volume of RBCs, hence the cell-to-wall surface area ratio, thereby lowering NO concentration differences between plasma and RBCs. Because the latter act as a sink for NO, the larger surface area for exchange leads to a significant reduction in plasma NO concentration, hence in CNO in interstitium and pericytes. As shown in Fig. 5, a twofold increase in the initial hematocrit (i.e., from 25 to 50%) lowers medullary CNO by 50% in RBC and plasma and 25% in interstitium and pericytes.
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The RBC (membrane and cytosol) permeability to NO (PNOR) was taken as 0.04 cm/s (61). In the absence of reported measurements, the permeability of the pericytic cells to NO (PNOPC) was also taken as 0.04 cm/s, and we assumed that the permeability of the vasa recta wall to NO (PNOW) is equal to that to oxygen, 0.04 cm/s (23, 65). Given these uncertainties, we varied each permeability individually from 0.005 to 0.5 cm/s (as explained below) while keeping the other two constant. Shown in Fig. 6, A and B, are the average NO concentrations in the medulla as a function of PNORand PNOW, respectively.
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CNO = CNOP– CNOR; because NO concentration in RBC is 1,000-fold lower than in plasma, CNO 
CNOP, so that the product of the permeability and the plasma NO concentration remains constant. We were not able to reduce PNORbelow 5 x 10–3 cm/s. Indeed, very low PNORvalues result in higher NO concentrations throughout the outer medulla; if CNORis too large in the OM, oxygen is depleted before the papillary tip due to the balance between NO, Hb, and HbO2, and simulations fail to converge.
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CNOI], whereas that between pericytes and interstitium remains large because PNOPCis fixed at 0.04 cm/s. As a consequence, CNOP(AVR) increases more rapidly than and surpasses CNOP(DVR). As PNOW > 0.5 cm/s, simulations fail to converge for the same reasons as above. We then varied PNOPCwhile keeping PNORand PNOWfixed at 0.04 cm/s. As PNOPCincreases from 0.005 to 0.5 cm/s, CNO remains approximately constant in RBCs, plasma, and interstitium and decreases by <20% in pericytes. This decrease is not very significant because the pericytes occupy a comparatively small volume (i.e., 13% of that of OMDVR lumen and <1% of that of the overall vascular lumen).
These results indicate that the permeability of the RBC to NO is an important determinant of NO concentration in plasma, pericytes, and interstitium and that the permeability of vascular wall to NO significantly affects CNO in intersititium and pericytes. To raise interstitial NO concentrations, we would have to lower our baseline permeability values; however, assuming that NOPwere as low as 10–17 µmol·µm–2·s–1 as reported by Wu et al. (64), NO concentration would remain close to 1 nM in the interstitium and pericytes even if PNOW, PNOR, and PNOPCwere as small as 5 x 10–3 cm/s, a value that seems too low given that NO and O2 are similar in size and that the permeability of RBCs and the vascular wall to oxygen is predicted to be on the order of 10–2 cm/s (23, 65).
O2– Concentration
We assumed in this study that the concentration of superoxide remains fixed in each compartment throughout the medulla; in the baseline case, it was taken as 0.1 nM (see above). Among the species considered here, superoxide scavenges NO at a much higher rate than do oxygen and GC. In RBCs, however, the relative amount of NO scavenged by O2– is negligible. Hence, decreasing the concentration of superoxide in RBCs to zero or increasing it to 1 nM has a negligible effect on the RBC concentration of NO (results not shown).
As shown in Table 3, reducing O2– concentrations in all compartments to zero raises medullary NO levels by <1% in all compartments. Conversely, a 10-fold increase in CO2– in all compartments reduces NO concentrations by 6% in plasma and interstitium and by 3% in pericytes, whereas the fraction of NO scavenged by O2– increases from 0.6% in the baseline case to 6%. Increasing O2– concentration in each compartment separately shows that only plasma and interstitial CO2– have a measurable effect on medullary NO levels (Table 3). A 100-fold increase in all compartments increases the fraction of NO scavenged by O2– by 60% and decreases CNO by 90%.
To the best of our knowledge, measurements of O2– concentration in the renal medulla have not been reported. Our results suggest that agreement between our model predictions and NO levels reported in the literature can only be obtained with NO production rates on the order of 10–14 µmol·µm–2·s–1, because decreasing the concentration of O2– has little effect on that of NO. With lower generation flux values, no agreement is possible independently of O2– concentration.
Initial NO Concentration
The initial value (i.e., at the corticomedullary junction in DVR) of plasma CNO was chosen as 1 nM based on reported measurements of NO concentration in plasma (54). Our simulations indicate that this initial value has a negligible effect on average NO concentrations in the medulla, as a 10-fold increase or decrease in this parameter does not affect CNO in interstitium, plasma, and RBCs, independently of the NO generation rate in vasa recta (results not shown).
As described above, the initial value of CNORwas chosen as 0. Over the range of NOPvalues that we examined, our simulations did not converge if we increased the initial CNORto 0.1 nM. Indeed, because we assumed in our baseline case that both HbO2 and nitrosyl-heme are at equilibrium with NO and O2 at the corticomedullary junction in DVR, increasing the initial CNO in RBCs simultaneously raises CHbNO and reduces CHb. This enhances the dissociation of HbO2 and thus raises the concentration of free O2 at the junction; O2 is then shunted from DVR to AVR in the OM and is therefore depleted before blood reaches the papillary tip. Instead of the equilibrium hypothesis, we then assumed that the initial concentration of HbNO is 0; under these conditions, our simulations suggest that raising the initial value of CNORfrom 0 to 1 nM does not affect the average CNO in the four compartments. Given that the rate constant for the binding of NO to Hb is 10 times larger than that for the dissociation of HbNO, the equilibrium hypothesis (namely, that NO and HbNO are at equilibrium at the corticomedullary junction) is more likely to be true than the alternate assumption (namely, that the concentration of HbNO is 0 at the junction).
With NOPequal to its baseline value of 10–14 µmol·µm–2·s–1, increasing the initial CNORfrom 0 to 0.01 nM only raises the average CNORfrom 0.010 to 0.013 nM and does not affect NO concentration in other compartments. However, if NOPis on the order of 10–17 µmol·µm–2·s–1, the same increase in the initial CNORraises the average NO concentration in RBCs from 2 x 10–5 to 10–3 nM. Indeed, because we assumed that at the corticomedullary junction, HbNO is in equilibrium with NO and Hb, and HbO2 is in equilibrium with O2 and Hb, the combination of these two reactions yields the following balance at the junction: HbO2 + NO 
HbNO + O2 (so that variations in the initial CNORresult in similar changes in the initial CHbNO). Although this equilibrium is not strictly maintained beyond the corticomedullary junction, deviations from it appear to be small, and our model suggests that NO is never completely scavenged by HbO2 (reaction 4) even though this scavenging reaction is not reversible. When the NO vasa recta production rate is high, NO influx from plasma is high, so that reaction of Hb and NO goes forward. With lower values of NOP, however, the NO influx is so low so that the reaction is reversed, that is, HbNO actually dissociates to release NO; as described above, the latter is not completely scavenged by HbO2. In that sense, the reversible association of Hb and O2 plays a significant role in maintaining NO concentrations in RBCs.
Because variations in initial CNOPand CNORvalues do not significantly affect plasma and interstitial NO levels, these parameters cannot be optimized to obtain agreement between calculated and measured concentrations if NOPis significantly lower than 10–14 µmol·µm–2·s–1.
Dependence of NO Synthesis on PO2
Our simulations suggest that the fraction of NO scavenged by O2 is negligible relative to that consumed by hemoglobin and O2–. As a substrate in the synthesis of both NO and O2–, O2 nevertheless plays an important role in NO transport. A NO-mediated increase in blood flow increases the supply of O2 and therefore PO2, which in turn affects medullary CNO. As such, there is a strong correlation between O2 and NO concentrations in the renal medulla. In studies of cultured bovine aortic endothelial cells, Whorton et al. (63) measured a concentration-dependent decrease in NO production as PO2 was reduced and observed that the percentage of inhibition of NO production as a function of PO2 was a sigmoidal curve, other than a Michaelis-Menten profile, if Ca2+ was saturated. A regression of the experimental data obtained by Whorton et al. (63) yields the following expression
 | (8) |
According to the review of Buerk (4), the O2-dependent NO generation rate abides by the conventional Michaelis-Menten equation. The corresponding inhibition ratio can be expressed as
 | (9) |
150 Torr.
Shown in Fig. 7A are interstitial NO concentration profiles along the corticomedullary axis in our baseline case (case a, no inhibition), using Eq. 8 based on the data of Whorton et al. (63) (case b), and assuming a Michaelis-Menten expression as given by Eq. 9 with P1/2 as 34 and 150 Torr (cases c and d), respectively. The interstitial PO2 is predicted as 46 Torr at the corticomedullary junction and 20 Torr at the papillary tip (Fig. 7B). When NO synthesis is correlated with PO2, NO concentration decreases significantly along the corticomedullary axis. For equal values of P1/2, the decrease in CNO is much steeper if Eq. 8 is used rather than the Michaelis-Menten expression, as shown by a comparison between cases b and c. However, NO concentrations at the papillary tip are similar using Eq. 8 with P1/2 = 34 Torr and Eq. 9 with the upper limit P1/2 = 150 Torr (cases b and d). The average NO concentration in interstitium is calculated to be 2.9, 6.6, and 2.2 nM in cases b, c, and d, respectively, vs. 16.9 nM in the baseline case (case a).
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DISCUSSION |
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TOPABSTRACTGLOSSARYMODEL AND PARAMETERSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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Our investigation was limited to parametric studies because there is very little experimental data related to NO in the renal medulla. We did not find in the literature estimates of several important variables, such as medullary O2– levels. O2– concentrations have been reported in aortic blood and intracellularly (10, 28) but may be significantly different in vasa recta given medullary hypoxia. Zou et al. (69) found that O2– is primarily produced in the OM but did not report O2– concentrations. Other uncertain parameters include the permeability of vasa recta, erythrocytes, and pericytes to NO, the volume, thickness, and distribution of pericytes, as well as kinetic constant values at 37°C. As summarized by Buerk (4), the kinetics of NO-scavenging reactions have been observed mostly at 20°C. In simulating the consumption of NO within erythrocytes, Tsoukias and Popel (59) extrapolated kinetic constant values to 37°C assuming a temperature coefficient of 1.4/10°C (that is, a 68% increase from 20 to 37°C) based on data for CO binding to deoxyhemoglobin reported by Cassoly and Gibson (6). Given the uncertainty of this approach, we opted to use the kinetic constant values at 20°C consistently and examined the effects of variations in these parameters on NO transport. Our simulations indicate that varying the kinetic rate constants of the reactions between NO and hemoglobin affects the relative amounts of NO scavenged by deoxyheme and oxyheme but has a negligible effect on NO concentrations in plasma, pericytes, and interstitium.
In addition, changes in medullary NO concentrations have not been measured simultaneously with changes in DVR diameter, blood flow, or PO2. We were therefore not able to correlate these variables and to simulate the effect of NO on variations in capillary size and O2 supply. We also did not model the effects of NO on the tubular system, including sodium reabsorption and oxygen consumption by mTALs.
Because the half-life of NO in vivo is a few milliseconds, NO should only be able to exert its effects within a few micrometers of its site of generation (17). Evidence to the contrary suggests that NO may be stored under forms that preclude its inactivation, and the conversion of NO into S-nitrosothiols (RSNOs) has been postulated to play an important role in its preservation (17, 25). RSNOs are thioesters of nitrite with the generic structure R-S-N=O, and S-nitrosoalbumin is thought to account for most of the circulating RSNOs (17). Although estimates of RSNO concentration in plasma vary widely, they are generally believed to remain under 0.15 µmol/l in control subjects (17). The mechanisms by which RSNOs are formed in vivo and by which they may release NO are unclear (25). Pawloski and colleagues (48, 49) have suggested that S-nitrosohemoglobin (SNO-Hb) is formed in RBCs by transferring NO from the nitrosyl group of the hemoglobin molecule to the highly conserved -chain cysteine 93 residue (cys-Hb), and that under anaerobic conditions, the nitroso moiety is transferred to the chloride-bicarbonate anion-exchanger 1 (AE1) protein, which carries it from the erythrocyte to vascular muscle cells to elicit vasodilation. Given that the suggested mechanisms of SNO-Hb formation remain speculative (17, 18, 29), and in the absence of experimental kinetics data on RSNO formation, we did not account for the effects of RSNOs in this model.
Our results are also limited by our compartmental approach, in that we did not take into account the radial NO concentration gradients within each compartment, which are likely to be significant because NO is a highly active free radical. Considering both radial and axial variations along the corticomedullary axis, however, is beyond the scope of this study.
Observations suggest that pericytes are disposed at intervals of 14–20 µm along DVR (57) and that their thickness varies from 2.5 µm across their nucleus to 0.7 µm across their tentacles (Dr. Tom L. Pallone, personal communication). Our baseline assumption that pericytes form a continuous, 0.5-µm-thick layer surrounding OMDVR is therefore oversimplified. However, changes in their thickness, distribution, and O2– concentration are all predicted to have a negligible effect on medullary NO levels; even when the permeability of pericytes to NO increases from 0.005 to 0.5 cm/s, pericyte CNO is reduced by only 20%, because pericytes occupy <1% of the vascular lumen volume. Although NO regulates vascular tone at the level of the pericytes, our simulations suggest that these cells do not significantly affect NO concentrations in the renal medulla.
Our results indicate that basal NO concentration in pericytes is 20 nM. The concentration of NO above which the vasodilator is able to activate GC has been reported to lie between 23 and 120 nM, as reviewed by Tsoukias et al. (58), and a value as high as 250 nM was also reported by Stone and Marletta (55). Our results thus suggest that basal NO levels are too low to activate GC and induce vasodilation. Decreasing the permeability of RBCs or vascular walls to NO, or increasing the endothelial generation rate of NO would raise CNO in pericytes, but the latter concentration would remain well below 250 nM. These results are not surprising; under basal conditions, NO is not expected to induce vasodilation.
We assumed in this study that NO is generated by both DVR and AVR endothelium. Because AVR have a highly fenestrated endothelium, it is possible that they lack the cellular machinery needed to regulate NOS; the activity of NOS has been found to be affected by the presence of caveolae (31), which may be absent in AVR. To investigate this hypothesis, we performed simulations in which the NO generation rate in AVR was eliminated. Results (not shown) indicate that the average CNO in plasma, RBC, and interstitium would then decrease by 60% relative to the baseline case, whereas that in pericytes would decrease by 40%. NO concentration profiles along the corticomedullary axis would remain similar, which suggests that the other trends described in this study would still hold.
Our model predicts that the basal concentration of NO in the RBCs of the renal medulla is 0.01 nM, due to rapid scavenging by hemoglobin. Under physiological conditions, it is the continuous generation of NO in vasa recta walls as well as the low permeability of the RBC membrane and cytosol to NO that allow basal plasma NO concentrations to be maintained at much higher levels. The precise nature of the significant resistance to NO transport across the RBC remains unclear (60). Our parametric studies indicate that the permeability of RBCs and vasa recta walls to NO should both be on the order of 0.01 cm/s to yield agreement with experimental measurements of NO concentration in medullary tissue. The three-orders-of-magnitude difference in NO concentration between erythrocytes and plasma suggests that the two compartments should be carefully distinguished; the term "biological NO concentration in blood" used by many investigators must be employed with caution.
Both experimental and theoretical limitations did not allow us to capture the multiple ways in which NO and O2 interact, such as the fact that O2 is a precursor in the synthesis of not only NO but also of O2–, an important NO scavenger, or the effects of NO-mediated changes in blood flow rate on O2 supply. However, a simple simulation suggested that O2 could play an important role as a substrate for NO production. We found that if the production flux of NO decreases with decreasing PO2 as observed in vitro by Whorton et al. (63), the average NO concentration in plasma and pericytes is about six times lower than in the baseline case (i.e., assuming no inhibition). We did not consider the possible effect of low PO2 on O2– concentration. Indeed, we found that under basal conditions, the scavenging of NO by O2– is small compared with that by hemoglobin (Table 3). However, our simulations also suggest that if O2– concentration is increased 100-fold, CNO decreases by a factor of 10 in all compartments. Under pathological conditions, the production of O2– by vascular endothelium and smooth muscle has been shown to increase >1,000-fold (11, 22), and our results suggest that O2– may then play a significant role in inactivating NO. Under these conditions, the effect of PO2 on O2– concentrations should be taken into account.
The production rate of NO was measured specifically in the renal medulla by Wu et al. (64), who incubated microdissected renal segments with L-arginine and cofactors and measured NOS activity. However, using their data, predicted medullary NO concentrations were at least one order of magnitude smaller than experimental measurements in plasma made by Stamler et al. (54) and in renal medullary tissues made by Zou and Cowley (67, 68). The release of NO is subject to short- and long-term regulation, and it remains uncertain whether the estimates of Wu et al. (64) adequately reflect basal conditions. To obtain agreement between experimental measurements of NO concentration (54, 67, 68) and our calculations, it was necessary to assume that the vasa recta production of NO is 1,000 times larger than that measured by Wu et al. (64), i.e., close to the estimates that Vaughn et al. (62) also obtained by mathematical simulation.
It is possible that the estimates of medullary NO concentration reported by Zou and Cowley (67, 68) were too high. However, it has been argued that the microdialysis technique that these investigators used underestimates NO production (21). Moreover, the measurements of Zou and Cowley (67, 68), 50–140 nM, are significantly lower than estimates of NO concentration in other parts of the microcirculation; micromolar concentrations have been reported in rat aorta (36).
It should also be noted that the study of Wu et al. (64) suggests that IMCD is the segment with the greatest NOS enzymatic activity. Dickhout et al. (12) observed that NO produced by tubular epithelial cells can be transported to and play a role in DVR pericytes. Our simulations suggest that multiplying simultaneously by a factor 103-104 the values of NOIMCDand NOmTALmeasured by Wu et al. (64) raises medullary NO concentrations in plasma and interstitium to experimental levels (67, 68). Hence, using a much larger estimate than theirs for the production of NO in vasa recta while keeping their low values for NOIMCDand NOmTALmay have led us to underestimate the relative contribution of the epithelial cells of IMCDs, mTALs, or other tubular segments to NO transport in the medullary microcirculation.
The recent model of NO transport in the renal afferent arteriole (AA) developed by Layton and colleagues (53) suggests that the advective transport of locally produced NO is sufficient to yield physiologically significant NO concentrations along much of the arteriole. Indeed, the lifetime of NO, although short, is long compared with transit time through an AA. In the medullary microcirculation, where flow velocities are much lower and the length of vasa recta destined to the inner medulla is significantly greater, the contribution of advective NO transport is expected to be much less important. Our calculations suggest that transit time in vasa recta varies between 10 and 50 s, whereas the likely range in the AA is 3–30 ms (53). To examine the effects of NO advection, we performed simulations in which the production of NO was restricted to a small region near the corticomedullary junction (more specifically, for 0 < x/L < 0.1); in that case, NO concentrations in RBCs, plasma, and interstitium were found to rapidly decrease to 0 immediately beyond the NO-producing region.
In summary, our model predicts that basal NO concentrations in renal medullary RBCs are predominantly controlled by the kinetics of NO scavenging by hemoglobin. NO concentration was found to be 0.01 nM in RBCs, on the order of nanomolar in plasma, and 20 nM in pericytes and interstitium. Our results also suggest that a low RBC membrane permeability to NO and a significant NO generation rate in vasa recta are essential for preserving large plasma-to-RBC NO concentration gradients and maintaining NO concentration within pericytes at levels just below that needed to activate GC and regulate vascular tone. Experimental determinations of medullary O2– concentration, the permeability of RBCs and vasa recta walls to NO, and NO production rates in vasa recta and tubules, as well as more specific measurements of NO concentration in pericytes and interstitium, are needed to significantly extend our mathematical model of NO transport in the medullary microcirculation.
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APPENDIX |
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TOPABSTRACTGLOSSARYMODEL AND PARAMETERSRESULTSDISCUSSIONAPPENDIXGRANTSREFERENCES |
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Our model of the renal medullary microcirculation consists of a series of conservation equations in plasma, RBCs, interstitium, and pericytes, together with flux equations. Because NO reacts with one of the four heme protein groups on the hemoglobin molecule, each heme group, such as deoxyheme (Hb), oxyheme (HbO2), nitrosyl-heme (HbNO), and metheme (met-Hb), is treated separately. In this study, we consider NO, O2, and urea as the only solutes that cross the RBC membrane. Solutes in plasma include sodium chloride, urea, plasma proteins, O2, and NO, all of which traverse vasa recta walls through a paracellular pathway shared with water. We also account for two additional pathways across RBC membranes and DVR walls: transcellular aquaporin-1 (AQP1) water channels and UTB urea transporters.
Conservation Equations
If x is the axial coordinate along the corticomedullary axis, conservation of volume in plasma and RBCs can be expressed as
 | (A1) |
 | (A2) |
represents the cell-to-vessel surface area ratio, N denotes the number of vasa recta and D their diameter, and + and – apply to AVR and DVR, respectively. The second term on the righthand side of Eqs. A1 and A2 accounts for the fact that at various depths in the medulla, DVR break up to form a capillary plexus, from which AVR are formed and ascend. Hence, part of the flow is directly shunted from DVR to AVR at various levels.
Conservation of solutes in plasma can be expressed as
 | (A3) |
 | (A4) |
