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J Appl Physiol 97: 293-301, 2004. First published March 19, 2004; doi:10.1152/japplphysiol.00049.2004
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Contribution of nNOS- and eNOS-derived NO to microvascular smooth muscle NO exposure

Mahendra Kavdia1 and Aleksander S. Popel2

1Biomedical Engineering Program, University of Arkansas, Fayetteville, Arkansas 72701; and 2Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, Baltimore, Maryland 21205

Submitted 16 January 2004 ; accepted in final form 15 March 2004


   ABSTRACT
TOP
 ABSTRACT
MODEL FORMULATION
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
Nitric oxide (NO) plays an important role in autocrine and paracrine manner in numerous physiological processes, including regulation of blood pressure and blood flow, platelet aggregation, and leukocyte adhesion. In vascular wall, most of the bioavailable NO is believed to derive from endothelial cell NO synthase (eNOS). Recently, neuronal NOS (nNOS) has been identified as a source of NO in the vicinity of microvessels and has been shown to participate in vascular function. Thus NO can be produced and transported to the vascular smooth muscle cells from 1) endothelial cells and 2) perivascular nerve fibers, mast cells, and other nNOS-containing sources. In this study, a mathematical model of NO diffusion-reaction in a cylindrical arteriolar segment was formulated. The model quantifies the relative contribution of these NO sources and the smooth muscle availability of NO in a tissue containing an arteriolar blood vessel. The results indicate that a source of NO derived through nNOS in the perivascular region can be a significant contributor to smooth muscle NO. Predicted smooth muscle NO concentrations are as high as 430 nM, which is consistent with reported experimental measurements (~400 nM). In addition, we used the model to analyze the smooth muscle NO availability in 1) eNOS and nNOS knockout experiments, 2) the presence of myoglobin, and 3) the presence of cell-free Hb, e.g., Hb-based oxygen carriers. The results show that NO release by nNOS would significantly affect available smooth muscle NO. Further experimental and theoretical studies are required to account for distribution of NOS isoforms and determine NO availability in vasculatures of different tissues.

model mathematical; model computational; nitric oxide; neuronal nitric oxide synthase; myoglobin; blood substitute; endothelial and neuronal nitric oxide synthase knockouts

NITRIC OXIDE (NO) IS ENZYMATICALLY synthesized from L-arginine by several isoforms of NO synthase (NOS) (for review, see Ref. 1). The isoforms of NOS are divided into inducible NOS (iNOS or NOS2) and constitutive NOS (cNOS) based on their nondependent and dependent, respectively, control of activity from intracellular calcium/calmodulin. cNOS are further classified as neuronal NOS (nNOS or NOS1) and endothelial NOS (eNOS or NOS3). Once formed, NO plays an important role in autocrine and paracrine manner in numerous physiological processes, including regulation of blood pressure and blood flow, platelet aggregation, and leukocyte adhesion (48, 52). In smooth muscle cells, NO activates enzyme soluble guanylate cyclase (sGC), which catalyzes the conversion of GTP to cyclic guanosine monophosphate (cGMP), thus causing vasodilation (35).

Traditionally, eNOS, which is primarily a membrane-bound protein (27), is considered the principal source of bioavailable vascular NO. NO produced by endothelial cell diffuses to vascular smooth muscle and to the flowing blood, where it rapidly reacts with Hb in red blood cells (RBCs). In recent years, a role of nNOS-generated NO in vascular function has been demonstrated (10, 34, 63). This discovery has been facilitated by the recent development of NO-sensitive dye 4,5-diaminofluorescein (DAF-2), which has allowed the visualization of NO-producing sites in living tissues (11, 36) and of selective inhibitors of NOS (66). Kashiwagi et al. (36) reported that nNOS-containing nerve fibers, which innervate arterioles, and nerve terminals are the major sources of arteriolar NO, together with nNOS-positive mast cells in rat mesentery and brain; several other studies have reported nNOS presence in perivascular nerve fibers (51). Other nonneuronal cell types, including cardiac myocytes (73) and skeletal myocytes (39), have also been shown to express nNOS (51). Both slow- and fast-twitch skeletal muscle fibers have nNOS in the sarcolemma of skeletal muscle fibers. In contracting fast-twitch mouse cremaster muscle, Grange et at. (26) demonstrated that arteriolar relaxation was attenuated in contracting muscles from mice lacking either nNOS or eNOS and suggested that NO-dependent vascular relaxation may require both nNOS and eNOS. Ebrahimian et al. (20) reported that intraluminal pressure increases eNOS and nNOS expression and subsequent NO release in rat carotid artery. In addition, several studies showed that both eNOS- and nNOS-derived NO provide mutually compensating pathways for vasodilation in mice that were genetically deficient in one of the cNOS enzymes (14, 32, 46, 47). Meng et al. (46) reported that the loss of eNOS was compensated by nNOS in the brain of eNOS-deficient mice. On the other hand, some studies showed a negligible or modest contribution of NO derived from nNOS (22, 33) in the aortic ring and in pulmonary circulation of eNOS-deficient mice.

Several experimental (7, 36, 42) and theoretical (15, 37, 40, 65, 67) studies have been performed to better understand the physiological levels of NO in different parts of the vascular wall and its surroundings. Direct measurements of NO concentration in the microcirculation with high spatial resolution are limited; porphyrinic-based microsensors were reported to be fragile and unsteady (42), and only the relative levels of fluorescence intensity have been measured by using DAF-2 without a calibration to quantify NO concentration. In recent years, studies using NO-sensitive, recessed-tipped microelectrodes developed by Buerk and coworkers (13) have demonstrated NO microelectrode sensitivity and selectivity for NO under in vivo and in vitro conditions. Bohlen and coworkers (4–9) have used this type of NO microelectrode extensively to measure NO concentrations in various regions of intestinal microvasculature of rat. In these studies, measured arterial wall NO concentrations ranged between 340 and 400 nM and parenchymal cell NO concentrations between 70 and 140 nM.

Mathematical models of NO transport have shown that free Hb in the vascular lumen scavenges NO and significantly reduces NO in the vascular wall (38, 40). However, a significant amount of NO diffuses toward smooth muscle when Hb is contained inside RBCs and when a RBC free layer is present adjacent to the endothelium (15, 67). Most of these models predicted a NO concentration in the range of ~100 nM at the smooth muscle cell. Vaughn et al. (67) also reported that NO concentration could reach 250 nM if uptake of NO by RBCs is manyfold (~100x) smaller at 15 s–1 than the predicted and measured uptake of NO by RBCs at ~1,300 s–1. The predicted NO concentration of ~100 nM is in the range of 23–100 nM reported for the half-maximal activation of sGC (3, 17) at 4°C. Recently, Griffiths et al. (28) reported a NO concentration of 1.7 nM for half-maximal activation of sGC. However, Stone and Marletta (61) reported the in vitro concentration of NO required for half-maximal activation of guanylate cyclase in vascular smooth muscle to be 250 nM at 10°C. The physiological half-maximal activation of guanylate cyclase at 37–38°C should be a higher NO concentration and remains to be determined.

The predicted NO levels are significantly lower than the experimentally measured perivascular NO concentration (~300–500 nM) in a specific tissue (3, 17). The source of such high amounts of NO in vascular wall remains to be identified. It is possible that the NO production rate in vivo is higher than in vitro; the models utilized the latter. Another possibility is additional sources of NO in the form of nNOS containing perivascular nerves or parenchymal neurons. This possibility is also supported by a recent study of Nase et al. (49) that selective impaired endothelial NO production by localized CO2 embolization. Embolization decreased the basal NO concentration from 501 to 398 nM, but, even more importantly, localized gas embolization did not fully eliminate NO release at rest. However, other possible sources may include NO transported by blood from fully intact upstream arteries (60) and nearby venular wall that can also generate NO in response to a number of stimuli (50).

All NO transport models only explored the NO generation from the endothelial source, except for models by Buerk et al. (12) and Wood and Garthwaite (72). In addition to eNOS-related NO production, Buerk et al. (12) modeled NO production from iNOS around an arteriole, which included mitochondrial NOS, to examine reactive oxygen and reactive nitrogen species interaction in vascular tissues. Wood and Garthwaite (72) predicted the diffusional spread of NO from a neural NO signaling perspective. According to their predictions, NO sources 200–500 µm distant can also significantly contribute to the steady-state concentration of NO within a tissue volume; they did not consider NO transport in the vascular wall.

Thus the relative importance of NO derived from nNOS and eNOS isoforms and its diffusional spread over the vascular tissues needs to be investigated. In this study, we investigate the relative contribution to smooth muscle NO concentration of eNOS and nNOS in and around an arteriole, such as brain or mesentery, where nNOS was reported to contribute to arteriolar NO (36), and address the question of whether experimentally measured levels of NO can be attributed to the nNOS.


   MODEL FORMULATION
TOP
 ABSTRACT
 MODEL FORMULATION
RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
Model geometry and governing equations.   We formulate a detailed mathematical model that represents the microvascular tissue geometry surrounding an arteriolar vessel and NO transport in the tissue. The arteriolar blood vessel is divided into the following regions: 1) luminal RBC-rich region, 2) luminal RBC-free region, 3) endothelium, 4) interstitial space between the endothelial and smooth muscle cells, 5) smooth muscle layer, 6) nerve fiber region adjacent to the outer boundary of smooth muscle, 7) perivascular nonperfused tissue region, and 8) capillary-perfused parenchymal tissue region. Here we assume nNOS is only present in the nerve fiber region, which may not be entirely accurate because nNOS may also be present in the endothelium (57) and the smooth muscle (59). However, endothelium-derived nNOS does not appear to mediate endothelium-dependent dilation (23). The bioavailable NO in the tissue is assumed to be produced by 1) membrane-associated eNOS (24), which results in shear-dependent production of NO from endothelial lining of arteriole and capillaries, and 2) nNOS in the nerve terminals and fibers that are located close to the outer layer of the smooth muscle (11, 36). The NO production from arteriolar endothelium is incorporated as surface NO release in boundary conditions at the endothelial region interfaces, whereas the NO production by capillary endothelium and nerve terminals and fibers is considered as homogenous production terms in perfused capillary tissue region and nerve fiber region, respectively.

We have shown that, because of the fast reaction with Hb, the convective transport of NO can be neglected (37). Recently, we modeled the transient release of NO in microcirculation and showed that NO profiles reach steady state within milliseconds (64). Thus it is appropriate to model steady-state profile for NO. The vessel and surrounding tissue is modeled as cylindrical geometry. For all regions, the steady-state NO mass transport equation is written as

(1)
where r is the radial distance from the center of vessel, CNO is NO concentration, DNO is NO diffusivity, QNO is NO production by nNOS in the nerve fiber region and by eNOS in the capillary endothelial cells in the capillary-perfused parenchymal tissue region, and RNO is the net NO reaction rate, the sum of individual NO reaction rates. For the luminal RBC-rich region, NO is assumed to react with Hb contained inside RBCs, and RNO is

(2)
where kCR is the effective NO reaction rate in the RBC-rich region and is a function of NO reaction rate with RBC Hb, Hb concentration in a single RBC, and core hematocrit.

In the luminal RBC-free region, we assume zero hematocrit. We assume that NO reacts with O2 in this region and also in the endothelium, interstitial, nerve fiber, and perivascular nonperfused tissue regions. RNO for these regions is

(3)
where kO2 is the NO reaction rate with O2, and CO2 is the O2 concentration in a region. The reaction between NO and O2 is second order in NO (41).

In the smooth muscle region, NO is consumed by a second-order reaction with vascular smooth muscle sGC (68), and RNO is

(4)
where ksm is the second-order rate constant of NO with sGC.

For capillary-perfused parenchymal tissue region, we assume NO is consumed by blood flowing in capillaries. For this region, RNO is

(5)
where kcap is effective NO reaction rate with blood flowing in capillaries in parenchymal tissue and is a function of capillary hematocrit and fractional capillary volume.

In addition to the interactions of NO in various regions represented in Eqs. 2–5, we analyze the effect on the bioavailable NO level of myoglobin (Mb) present in the skeletal and cardiac muscle cells in the parenchymal tissue (perfused and nonperfused) beyond the vascular wall and of free Hb addition to the blood [e.g., administered as a Hb-based oxygen carrier (HBOC)].

To solve for the NO profile, the continuity of flux and concentration is applied at all interfaces except for 1) a zero flux condition at the outer edge of the capillary-perfused parenchymal region, and 2) at luminal RBC-free (cell-free) region endothelium (endo) (Eq. 6) and the endothelium-interstitial space (in-space) (Eq. 7) interfaces, where boundary conditions incorporated NO release from arteriolar endothelium:

(6)

(7)
where PNO is the half of total arteriolar endothelial NO release.

Model parameters and numerical solution.   The parameters of the model are summarized in Table 1. The parameters are as follows: 1) thickness of various regions, 2) diffusivity of NO, 3) chemical reaction rate constants, and 4) production rate of NO from eNOS and nNOS. The assumed thickness of endothelium (69) and interstitial space (38) regions is 0.5 µm each. As simulations are performed for an intermediate-size arteriole, a single smooth muscle layer of 6-µm thickness is assumed in the vascular wall (30). The luminal cell-free layer thickness is a function of vessel diameter and hematocrit and is estimated to be 4.5 µm for a 50-µm-diameter arteriole at 45% systemic hematocrit (58). Brown et al. (11) reported that 1.8-µm-diameter NO-producing discrete sources were positioned next to the outer surface of the vascular smooth muscle and were interconnected by 0.5- to 3.0-µm NO-producing fibers in arterioles. The NO production was attributed to the nerve fibers. Thus a nerve fiber region with a thickness of 2 µm is assumed. The perivascular nonperfused tissue region thickness is assumed to be 30 µm, based on images of mesenteric and cerebral microvessels from Kashiwagi et al. (36); for skeletal muscle, we assume that a single muscle fiber (~30-µm thickness) will not have a perfused capillary next to the arteriole. The thickness of parenchymal tissue (assumed in the calculations at 2,000 µm) is not important as the NO flux is shown to disappear within a short distance (<200 µm) from the center of the arteriole.


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  		Table 1. Model parameters

 
The diffusivity of NO is 3.3 x 10–5 cm2/s in all regions (42). The kCR is 1,230 s–1, which is obtained by multiplying the reported rate of reaction of NO with RBC Hb of 1.4 x 105 M–1/s (16), heme concentration in a single RBC of 20.3 mM, and core hematocrit of 0.45. The kO2 is 9.6 x 106 M–2/s (41), and in vivo CO2 is ~27 µM, corresponding to a partial pressure of 15.5 mmHg (53). However, due to slow reaction of NO and O2, NO profiles presented here were not affected, even for a significant change in CO2 that is present in various regions of tissue. The ksm estimated for vascular smooth muscle sGC is 5 x 104 M–1/s (68). The kcap is 12.4 s–1 and is calculated from a capillary hematocrit of 0.3 and a fractional capillary volume of 0.0146 [a capillary density of 1,435 per mm2 and a capillary radius of 1.8 µm, based on hamster retractor muscle (21)].

The basal rate of NO release (2PNO) by the arteriolar endothelium is assumed at 5.3 x 10–12 mol·cm–2·s–1 (68), which is equivalent to 106 µM/s in the endothelium region computed from dividing basal NO release rate by endothelium thickness. The release rates of NO by capillary endothelium to use as QNO in the perfused parenchymal tissue region are calculated from the rate of NO release by the arteriolar endothelium, capillary density, and capillary radius. The resulting homogenous distributed capillary endothelium NO production (multiplication of NO surface release rate, capillary NO producing area, and capillary density) is estimated to be 8.6 x 10–7 M/s. We will vary the capillary endothelium-related NO production by the same factor as the eNOS-related NO release from arteriolar endothelium.

The amount of NO release from nNOS in the parenchyma is not available. Therefore, as a first approximation, the release rates of NO by nNOS in the nerve fiber region are assumed to be equal to the arteriolar endothelium NO release rate per unit volume and is taken as 53 µM/s, computed from dividing endothelium release rate of 106 µM/s by nerve fiber region thickness. This is qualitatively consistent with DAF-2 intensity observation around the arteriolar vessel, followed by specific NOS inhibition (36).

Equation 1, with appropriate boundary conditions was solved numerically by using FlexPDE software package (PDESolutions, Antioch, CA) with a relative accuracy of 0.001. Because the vasoactivity of NO is related to the activation of sGC in smooth muscle, the primary aim of the model is to predict NO concentration in the smooth muscle region.


   RESULTS
TOP
 ABSTRACT
 MODEL FORMULATION
 RESULTS
DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 
Effect of multiple NO sources.   We used the model to estimate the relative contribution of each of the NO sources on the NO concentration in and around the arteriolar vessel. First, we considered a control case that has NO production from all sources. We used an eNOS NO production of 5.3 x 10–12 mol·cm–2·s–1 and 8.6 x 10–7 M/s, respectively, in the arteriolar endothelium (2PNO) and the capillary-perfused parenchymal tissue region (QNO). In the nerve fiber region, NO production from nNOS of 53 x 10–6 M/s was used. As shown in Fig. 1, predicted NO concentration is 427 and 69 nM, respectively, at the smooth muscle (maximum) and in the parenchymal tissue region for the control case.



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  		Fig. 1. Nitric oxide (NO) concentration profiles are shown for a 50-µm-diameter arteriole. The vessel center is at radius = 0. NO is derived from endothelial NO synthase (eNOS) in the endothelium lining of the arterioles [left of smooth muscle (SM)] and from the neuronal NOS (nNOS) in the perivascular nerves adjacent to the SM [between SM and nonperfused tissue (NPT)]. The NO generation from eNOS and nNOS is the maximum in the control case at 5.3 x 10–12 mol·cm–2·s–1 and 53 µM/s, respectively. Shown are the effects of change of nNOS- (A) and eNOS-derived (B) NO generation, while the NO generation from the other constant is kept. Solid lines, NO profiles for eNOS- and nNOS-related NO production of 5.3 x 10–12 mol·cm–2·s–1 and 53 µM/s, respectively. Lines show decreased NO production in increments of 25% that is 75 (dotted), 50 (dashed), and 25% (dashed-dotted) of the maximum nNOS- (A) and eNOS-related (B) production. Only eNOS- and nNOS-related NO profiles are shown as zero nNOS- and zero eNOS-related NO production, respectively, in Fig. 2 (solid lines).

 
We also varied the NO production rate from two NO production mechanisms to study the effect of inhibiting NO production from these pathways. Figure 1A shows the NO profiles obtained by keeping eNOS NO production constant and varying nNOS NO production to 13.25, 26.5, and 39.75 x 10–6 M/s, respectively, corresponding to 25, 50, and 75% of the control case. The NO profiles obtained by varying eNOS NO production (and keeping nNOS NO production at the control case level) are shown in Fig. 1B. In both cases, the nature of the NO production has a different effect on the levels of NO in all regions around the arteriole.

Effect of deletion of eNOS- or nNOS-related NO production.   To study the NO production from specific NOS, we can either block NO release by the use of a specific NO inhibitor or use the specific NOS-deficient mice. We examined the effect of deletion of the eNOS-related NO production to smooth muscle cell NO contribution. For this purpose, we reduced the amount of NO produced by eNOS (2PNO) to 0, 0.265, and 0.53 x 10–12 mol·cm–2·s–1, which is 0, 5, and 10%, respectively, of the endothelium NO production for the control case. NO production in the perfused parenchymal tissue region is reduced to the same extent, and the resulting QNO is 0, 0.43, and 0.86 x 10–7 M/s in the region. The nNOS-related NO production (QNO) remained at 53 x 10–6 M/s in the nerve fiber region. Figure 2A shows the NO profiles for this case. The NO concentration has reduced by ~100 nM in all regions of the vascular wall compared with the control case. In addition, the resulting parenchymal tissue NO concentration is in the range of 0–10 nM. Once the eNOS-related NO production is blocked, the trace amount of NO released by this mechanism has no effect on the smooth muscle NO concentration, as demonstrated by nearly superimposed curves.



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  		Fig. 2. NO concentration profiles are shown for NOS knockout. To simulate the two types of genetic (eNOS and nNOS) knockout mice, the NO production from the respective source is reduced to zero. Shown are the NO profiles for the eNOS (A) and nNOS knockout (B). Solid lines, NO profile from NO generation from eNOS and nNOS of 0 mol·cm–2·s–1 and 53 µM/s, respectively, for the eNOS knockout, and 5.3 x 10–12 mol·cm–2·s–1 and 0 µM/s, respectively, for the nNOS knockout. Even in these knockout animals, some level of NOS activity is present. Lines represent NO profiles for 5 (dotted) and 10% (dashed) NO production to corresponding maximum NO production.

 
Next, we examined the effect of deletion of nNOS-related NO production on smooth muscle cell NO concentration. We now reduced the nNOS-related NO production (QNO) to 0, 2.65, and 5.3 x 10–6 M/s in the nerve fiber region, which is 0, 5, and 10%, respectively, of the NO production in this region for the control case, whereas the amount of endothelial NO production remained at the control level. Figure 2B shows that blocking of nNOS has reduced NO concentration significantly in the smooth muscle and the nonperfused parenchymal region compared with the control case. In addition, even a trace amount of NO derived from nNOS has some effect on the smooth muscle NO concentration in this case.

Effect of NO scavenger Mb.   Mb, a heme-containing protein, is present in high concentration (on the order of a few hundred micromolars) in cardiac and skeletal muscle. Mb's functional role is generally regarded as passive oxygen storage and facilitation of oxygen transport. Mb can also effectively scavenge NO beyond the vascular wall (i.e., beyond smooth muscle layer) because of fast reaction between oxymyoglobin and NO (38). To study whether Mb presence has any effect on the NO transport in the presence of nonendothelial sources of NO, we used a NO reaction rate of RNO = kMb CMb CNO in nonperfused and perfused parenchymal tissue region, where Mb concentration (CMb) is assumed at 0.38 mM from the measured value in the hamster retractor muscle (45), and its reaction rate constant with NO (kMb) is 4.3 x 107 M–1/s (31). Figure 3 shows the resulting NO profiles for the control case when both eNOS- and nNOS-derived NO are considered. In other cases, only one of the eNOS- and nNOS-derived NO is considered. The maximum NO concentration has dropped to <100 nM in smooth muscle and reduced to <1 nM in parenchymal region for all cases.



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  		Fig. 3. Effect of myoglobin on smooth muscle NO concentration. Myoglobin is present in the NPT and beyond. eNOS- and nNOS-derived NO are considered in different combinations.

 
Effect of NO scavenger cell-free Hb.   Patients with sickle cell disease have elevated levels of RBC-free Hb (circulating plasma Hb); the bioavailability of NO is altered in these patients (19). Cell-free Hb can also be administered as a blood substitute. In addition to NO scavenging in the lumen, cell-free Hb can extravasate into the vascular wall and beyond and scavenge NO. Experimental studies of topical administration of a small amount (at a few micromolar concentration) of cell-free Hb on the extravascular side report immediate vasoconstriction (2). To simulate the effect of cell-free Hb in different regions on NO delivery to smooth muscle, we first used a reaction rate of RNO = kHb CHb CNO in the interstitial space region between the endothelium and smooth muscle, where Hb concentration (CHb) is assumed at 10 µM, and its reaction rate constant with NO (kHb, on heme basis) is 58 x 106 M–1/s (31). Figure 4A shows that NO concentration in smooth muscle is significantly affected in all cases when 10 µM cell-free Hb is present in the interstitial space.



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  		Fig. 4. Effect of cell-free Hb. eNOS- and nNOS-derived NO are considered in different combinations. A: NO profiles for cell-free Hb at 10 µM concentration present in the interstitial space (between endothelium and SM). B: NO profiles for cell-free Hb at 1 µM concentration present in the interstitial space (between endothelium and SM) and in the nonprefused and prefused parenchymal tissue regions (i.e., beyond nerve fiber region).

 
We also investigated the effect of cell-fee Hb in the parenchymal tissue region, which may result from extravasation of free Hb from the vascular lumen. For this purpose, we used a reaction rate of RNO = kHb CHb CNO in the interstitial space region and parenchymal tissue region (both nonprefused and prefused), and CHb is assumed at 1 µM. Resulting NO profiles are shown in Fig. 4B. Now, the NO levels are reduced even more compared with the presence of cell-free Hb, only in the interstitial space between the endothelium and smooth muscle. The parenchymal tissue region NO concentration falls to ~1 nM.


   DISCUSSION
TOP
 ABSTRACT
 MODEL FORMULATION
 RESULTS
 DISCUSSION
ACKNOWLEDGMENTS
 REFERENCES
 
In this study, we present results for NO distribution in and around an arteriolar vessel to understand the relative importance of various sources of NO production and NO consumption in tissue on the NO concentration to which arteriolar smooth muscle is exposed.

Comparison with experimental measurements of NO in the microcirculation.   The predicted average smooth muscle NO concentration is 359 nM, and parenchymal tissue NO concentration is 69 nM for the control case. These predictions are consistent with the recently reported measurement of periarteriolar and parenchymal tissue NO at 397 and 138 nM, respectively, for first-order arterioles of resting diameter of 52 µm in the rat intestinal microvasculature (49). The predicted concentrations are also quantitatively similar to several other reported measurements (7). Note that the high-NO concentration predicted in the present study, compared with previous predictions of ~100 nM (15, 67), is possible due to the NO derived from a nNOS source next to the smooth muscle cells. Compared with eNOS-related NO generation, the nNOS-related NO generation is at a distant physical location from NO's principal scavenger RBCs, which makes it relatively more significant in raising NO levels. In this study, we modeled the NO concentration in tissues where arterioles could receive NO from nNOS sources, such as the brain and mesentery. There can be several other sources of NO in the tissue, including mast cells and macrophages that synthesize NO via nNOS and iNOS pathways, respectively. Another possible source of micovascular NO can be mitochondrial NOS; however, the contribution of this mitochondrial NOS to tissue NO is controversial (25). In addition, the release of NO from all of these isoforms of NO are dependent on the CO2. Thus the NO measurements may exhibit wide regional heterogeneity reflecting variations in the distribution of NOS in various vasculatures, and a further experimental and theoretical investigation is required to determine the availability of NO in specific tissues. Although the present model predicts a significant contribution of nNOS-related NO to the smooth muscle NO exposure, we do not suggest that eNOS-related NO production is not important for maintaining vascular tone.

Alternative scenario to the sustained release from eNOS or nNOS.   Because of high diffusivity and fast binding rates, NO distribution reaches the steady state within milliseconds (18). When the release of NO is burstlike or pulsatile, there can be two pseudo-steady states: one for the time period of NO release and the other for the time period during no NO release or reduced NO release (17, 64, 72). The NO in the smooth muscle binds to the heme groups of sGC (half-maximal activity requires 23–250 nM NO) that occurs at a fast rate, leading to sGC activation within milliseconds to a few seconds, although subsequent release of cGMP is much slower (17). The deactivation of sGC (half-life, 1–2 min) is at least an order of magnitude slower than its activation (17). Thus, when NO release is switched off and the NO level reduces within milliseconds, sGC remains activated for a long time because of its slow deactivation. This could be of significant importance for maintaining vascular tone. NO sources could combine their NO release in a number of different ways with the same final outcome, resulting in similar amplitude of sGC activation.

Interpretation of experimental studies on eNOS and nNOS knock-out mice vasoactivity.   Wei et al. (71) reported that transgenic mice deficient in the endothelial and neuronal isoforms of NOS [eNOS(–/–) or nNOS(–/–), respectively] produced NO that was ~50% of wild-type mice NO production. Several studies have reported that the NO generation from one of the two isoforms can dilate blood vessels by compensatory mechanisms following the disruptions of the other isoform (14, 32, 46, 47). In contrast, studies have reported that only eNOS- and/or iNOS-derived NO and not nNOS-derived NO modulated the vascular tone in pulmonary microcirculation (22). Most of these transgenic mice express a small level of eNOS or nNOS (33, 71). As shown in Fig. 2, a small expression of deficient NOS enzyme can substantially impact the levels of NO in vascular tissue in the nNOS-deficient mice, whereas, in the eNOS-deficient mice, NO levels are not affected. The results also suggest that, in eNOS knockout animals when no other source of NO production exists in vascular tissue, NO concentrations in the parenchymal tissues will be on the order of 1 nM; these predictions need to be verified experimentally.

Interpretation of Mb knockout studies.   Wegener et al. (70) examined the effect of NO donors on cardiac contractility in wild-type and Mb-deficient mice and reported that the exogenously applied NO at concentrations <10 µM has no myocardial effect in wild-type mice as Mb scavenges NO. However, in Mb-deficient mice, NO reduced contractility via activation of the sGC/cGMP pathway. In an earlier paper (38), we predicted that Mb can effectively scavenge NO beyond the vascular wall (i.e., beyond smooth muscle layer), but not significantly change the smooth muscle concentration. According to the results presented in the present study, if a neuronal source of NO is present next to smooth muscle, the NO concentrations are significantly affected in all regions in the presence of Mb (smooth muscle and parenchymal). The prediction of this study supports the notion that NO scavenging by Mb can have important functional consequences on the maintenance of vascular tone and cardiac function in hearts lacking Mb.

Implication for HBOC.   HBOCs are being developed to temporarily replace RBCs for providing oxygen delivery and maintaining circulating volume (55, 62). These HBOCs are mainly modified cell-free Hb. The administration of HBOCs often results in hypertension, resulting from vasoconstriction (29, 54, 56). Identifying the mechanism responsible for the vasoconstriction is important for the clinical use of HBOCs. The vasoconstriction is attributed to the scavenging of NO by the Hb or oxyhemoglobin. Being small molecules, HBOCs can come close to endothelium and additionally, in many instances, can extravasate into interstitial spaces (44). Thus scavenging of NO can occur both in vascular lumen and/or in interstitial space. Our present results suggest that eliminating extravasation of HBOCs can significantly enhance smooth muscle NO availability. Thus the model results provide a possible explanation for experimental studies in which eliminating extravasation (e.g., by Hb polymerization) prevented or attenuated vasoconstriction (43). Further analysis of the effects of HBOCs on NO delivery is beyond the scope of the present study.

Finally, the present model predicts that high levels of NO in the vascular wall are possible when multiple sources of NO generation are present. The model predicts that NO from perivascular nerve fibers can significantly contribute to smooth muscle NO exposure, which can lead to vasodilatation. This could be exploited for the possible development of new therapeutic strategies involving nerve-derived NO in pathophysiological conditions.


   ACKNOWLEDGMENTS
TOP
 ABSTRACT
 MODEL FORMULATION
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
REFERENCES
 
This work was supported by National Heart, Lung, and Blood Institute Grant HL-18292.


   FOOTNOTES
 

Address for reprint requests and other correspondence: M. Kavdia, Biomedical Engineering, Dept. of Biological Engineering, Univ. of Arkansas, 203 Engineering Hall, Fayetteville, AR 72701 (E-mail: mkavdia{at}uark.edu).

The costs of publication of this article were defrayed in part by the payment of page charges. The article must therefore be hereby marked "advertisement" in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.


   REFERENCES
TOP
 ABSTRACT
 MODEL FORMULATION
 RESULTS
 DISCUSSION
 ACKNOWLEDGMENTS
 REFERENCES
 

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