can we model nitric oxide biotransport? a survey …...and a “bizarre molecule” because it is a...

15 Jun 2001 16:10 AR AR136-05.tex AR136-05.SGM ARv2(2001/05/10)P1: GJB

Annu. Rev. Biomed. Eng. 2001. 3:109–43Copyright c© 2001 by Annual Reviews. All rights reserved

CAN WE MODEL NITRIC OXIDE BIOTRANSPORT?A SURVEY OF MATHEMATICAL MODELS FOR A

SIMPLE DIATOMIC MOLECULE WITH

SURPRISINGLY COMPLEX BIOLOGICAL ACTIVITIES

Donald G. BuerkDepartments of Physiology, Bioengineering, and Institute for Environmental Medicine,University of Pennsylvania, Philadelphia, Pennsylvania 19104-6085;e-mail: [email protected]

Key Words blood flow, endothelium, mass transport, nitric oxide synthases,nitrosohemoglobins, nitrosothiols, oxygen transport, oxyhemoglobin, peroxynitrite,reaction kinetics, soluble guanylate cyclase

■ Abstract Nitric oxide (NO) is a remarkable free radical gas whose presence inbiological systems and whose astonishing breadth of physiological and pathophysi-ological activities have only recently been recognized. Mathematical models for NObiotransport, just beginning to emerge in the literature, are examined in this review.Some puzzling and paradoxical properties of NO may be understood by modeling pro-posed mechanisms with known parameters. For example, it is not obvious how NO cansurvive strong scavenging by hemoglobin and still be a potent vasodilator. Recent mod-els do not completely explain how tissue NO can reach effective levels in the vascularwall, and they point toward mechanisms that need further investigation. Models helpto make sense of extremely low partial pressures of NO exhaled from the lung and mayprovide diagnostic information. The role of NO as a gaseous neurotransmitter is alsobeing understood through modeling. Studies on the effects of NO on O2 transport andmetabolism, also reviewed, suggest that previous mathematical models of transport ofO2 to tissue need to be revised, taking the biological activity of NO into account.

CONTENTS

INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110NITRIC OXIDE ENZYMES AND BIOCHEMISTRY . . . . . . . . . . . . . . . . . . . . . . . . 110

Autooxidation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Reaction with Superoxide. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112Heme-Protein Binding. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114Thiol Nitrosation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116Sources Other than NOS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

CONVECTION-DIFFUSION MODELS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117

1523-9829/01/0825-0109$14.00 109

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110 BUERK

In Vitro Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118In Vivo Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120

INTERACTION BETWEEN NITRIC OXIDE AND O2 TRANSPORT. . . . . . . . . . . 125NITRIC OXIDE IN THE LUNG . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126NITRIC OXIDE IN THE BRAIN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130THE DARK SIDE OF NITRIC OXIDE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133PHYSIOLOGICAL MEASUREMENTS OF NITRIC OXIDE . . . . . . . . . . . . . . . . . . 134FUTURE DIRECTIONS AND MODELING NEEDS. . . . . . . . . . . . . . . . . . . . . . . . . 136

INTRODUCTION

Nitrogen monoxide, or nitric oxide (NO) as it is more commonly known, waschosen in December of 1992 as “molecule of the year” bySciencemagazine (1).Research on this remarkable gas led in 1998 to the awarding of the Nobel Prizein Physiology or Medicine to Robert F. Furchgott, Louis J. Ignarro, and FeridMurad. In 1980, Furchgott & Zawadzki (2) reported that endothelial cells pro-duce a potent but unknown vasodilator, which they labeled “endothelium-derivedrelaxing factor.” Working independently, Khan & Furchgott (3) and Ignarro et al(4) identified the vasodilator as NO. Research from Moncada’s laboratory (5, 6)also conclusively identified NO as an endogenous nitrovasodilator produced bythe endothelium. A decade earlier, Murad et al had shown that nitroglycerin andrelated nitrovasodilator drugs release NO and that guanylate cyclase was activatedby NO (7).Sciencemagazine described NO as both “a startlingly simple molecule”and a “bizarre molecule” because it is a rapidly diffusing, free radical gas withone unpaired electron exhibiting a surprisingly diverse range of biological activity,including potentially harmful effects. This issue ofSciencefeatured an article onthe complex biochemistry of NO by Stamler et al (8). The redox status and bio-chemical activity of NO can be altered by adding an electron to form the nitroxylanion (NO−) or by removing an electron to form nitrosonium (NO+). The nitroxylanion reacts with sulfhydryls and redox metals. The nitrosonium cation allowsnitrosation reactions to occur at -S, -N, -O, and -C centers in organic molecules.The primary reactions for the uncharged NO molecule are with O2, superoxide(O2−), and redox metals, especially iron-sulfur centers in proteins.Despite intense research activity for the past two decades, knowledge about NO

is still evolving, and some aspects of NO biochemistry are not fully understood.Because the biological importance of NO was only recently recognized, quantita-tive mathematical models for NO biotransport are just beginning to emerge in thescientific literature. These models are reviewed and their strengths and limitationsdiscussed, along with considerations for future modeling needs.

NITRIC OXIDE ENZYMES AND BIOCHEMISTRY

The heme-containing enzyme nitric oxide synthase (NOS) is linked to NADPH-derived electron transport via flavin adenine dinucleotide and flavin mononu-cleotide to catalyze oxidation ofL-arginine to L-citrulline and NO (Table 1,

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NITRIC OXIDE BIOTRANSPORT MODELS 111

TABLE 1 Biochemical reactions as sources or sinks for NObiotransport modeling

Sources1. L-Arginine+ O2→ L-citrulline+ NO

2. 2RSNO→ RSSR+ 2NO

3. SNO-Hb(Fe2+)O2+ GSH→ HS-Hb(Fe2+)O2+ GSNO+ O2

4. GSNO+ O2− → GSH+ O2+ NO

5. NO2− + H+ + NADH→ NO+ H2O

Sinks1. 4NO+ O2+ 2H2O→ 4NO2

− + 4H+

2. NO+ O2− → ONOO−

3. NO+ ONOO− → NO2− + NO3

4. NO+ Hb(Fe2+)→ Hb(Fe2+)NO

5. NO+ Hb(Fe2+)O2→ Hb(Fe3+) + NO3−

6. NO+ Mb(Fe2+)→ Mb(Fe2+)NO

7. NO+ Mb(Fe2+)O2+ H2O→ Mb(Fe3+)OH+ ONOO− + H+

8. 2NO+ RSH+ O2→ RSNO+ ONOO−

source 1), with tetrahydrobioterin as an essential cofactor. It is the primary sourceof NO production in mammals. Several NOS isoforms are expressed by differ-ent genes. As pointed out in the brief review and recommended nomenclaturefor NO biochemistry by Moncada et al (9), it is an oversimplification to classifythe three major NOS isoforms exclusively in terms of specific physical location.However, the conventional classification is for location, either in the endothelium(eNOS, or type III) or in certain types of neurons (nNOS, or type I), or for be-ing induced in tissues by macrophages in response to endotoxins or cytokines(iNOS, or type II). All isoforms can be found at other locations in certain tissues.Activities for constitutive isoforms eNOS and nNOS are regulated by Ca2+ andcalmodulin. Nathan (10) reviewed early studies with purified NOS, which reported50% effective concentrations (EC50) for Ca2+ in the 200- to 400-nM range andfor calmodulin in the 1- to 70-nM range. Michaelis constants (Km) for L-arginineranged between 2 and 32µM. Optimum activity is in the physiological pH range(11) and increases with temperature (12). O2 availability also influences NO pro-duction, discussed later in this review. The inducible isoform iNOS is not regu-lated by Ca2+ and can produce higher amounts of NO than can eNOS or nNOS.There is evidence, reviewed by Henry & Guissani (13), for a fourth NOS iso-form that is also Ca2+ dependent and localized in mitochondrial inner membranes(mtNOS).

It is clear that the spatial location and factors that regulate NO production rates(RNO) for different NOS isoforms are necessary to develop appropriate sourceterms in mathematical models for NO biotransport. After it is produced, NO must

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112 BUERK

react with biologically relevant targets. There is still considerable debate aboutwhether this occurs by simple diffusion of NO gas or whether NO combines withthiols or another carrier system for subsequent transport and release. Some of themost pertinent reactions for NO biotransport modeling are listed as sources orsinks in Table 1 and are discussed below.

Autooxidation

The reaction between NO and O2 (Table 1, sink 1) to form nitrite (NO2−) is wellknown and has been extensively studied. In a perfectly mixed aqueous medium,the reaction is third order (first order with O2 and second order with NO),

dCNO

dt= −4kaqCO2C

2NO = −

dCNO −2

dt, (1)

where the factor of 4 comes from the stoichiometry. Values for 4kaq and the tem-perature at which the rate was determined by different investigators are listed inTable 2. A numerical simulation of NO disappearance in different O2 concentra-tions using 4kaq at 37◦C (16) are shown in Figure 1. When the initial NO is low,250 nM for this illustration, the half-life (t50%) increases as O2 decreases, andt50%

can be hours in normal physiological tissue pO2 ranges. With higher initial NOvalues,t50% would be shorter.

Liu et al (18) reported that NO autooxidation is accelerated in different hy-drophobic phases, including phospholipid liposomes and biological membranesisolated from rat hepatocytes. The enhancement was approximately 300-fold(Table 2) and was attributed to higher gas solubilities for NO and O2 compared withwater. The net increase would be smaller for tissues because membranes compriseonly a fraction of the total volume. They estimated that NO autooxidation wouldbe eight times higher for brain or liver tissues compared with the rate in water, andthat most of the reaction would take place in the membranes. On the other hand,the diffusion coefficient for NO determined by an optical method appears to belower in liposomes and red blood cell membranes, about 50% of the value for O2

(31).

Reaction with Superoxide

The reaction between NO and O2− (Table 1, sink 2) to form peroxynitrite (ONOO−),

dCNO

dt= −kO −2 CO −2 CNO, (2)

was first reported by Beckman et al (32). It is unquestionably the most rapid biolog-ical reaction for NO (Table 2) and is near the maximum rate allowed by diffusion.However, the extent to which this reaction occurs is limited by the rapid reactionbetween O2− and superoxide dismutase (SOD), which has an approximately one-third lower rate constant (33). Therefore, O2

− in Equation 2 represents what hasescaped scavenging by SOD. Sources of O2

− include the mitochondrial electron

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TABLE 2 Rate constants for NO reactions

Reaction Temperature (◦C) Rate Constant Reference

With oxygenIn aqueous medium 4kaq (106 M−2 s−1)

22 6.0± 1.5 Wink et al (14)25 6.3± 0.4 Kharitonov et al (15)23 8.4± 1.6 Lewis & Deen (16)37 9.2± 1.2 Lewis & Deen (16)20 8.9± 1.0 Caccia et al (17)

In hydrophobic phase25 300∗4kaq Liu et al (18)

With superoxide kO −2(109 M−1 s−1)

20 6.7± 0.9 Huie & Padmaja (19)20 4.3± 0.5 Goldstein & Czapski (20)

With free hemoglobin kHb (107 M−1 s−1)20 1.2 Gibson & Roughton (21)20 2.5 Cassoly & Gibson (22)20 1.8 Morris & Gibson (23)20 0.3–5.0 Eich et al (24)23 2.9–3.2 Rohlfs et al (25)

With intact red blood cells krbc (105 M−1 s−1)38 1.7± 0.1 Carlsen & Comroe (26)25 0.52 Liu et al (27)25 0.00089∗kHb– Vaughn et al (28)

0.00126∗kHb

With myoglobin kMb (107 M−1 s−1)25 3.7 Doyle & Hoekstra (29)20 3.4 Eich et al (24)

With guanylate cyclase kGC (105 M−1 s−1)4 2.4 Zhao et al (30)

transport chain for oxidative metabolism, NADPH oxidase, xanthine oxidase, andNOS itself. It is known that NOS will produce O2− if no L-arginine is available,but that is highly unlikely in normal physiological states. There continues to bedebate about the biochemical mechanisms, necessary conditions, and amount ofO2− that NOS can produce.Because NO can also react with the product peroxynitrite (Table 1, sink 3), the

net change, neglecting alternate reaction pathways for ONOO−, is

dCNO

dt= −(kO −2 CO −2 + kONOO−CONOO− )CNO. (3)

The complex biochemistry of peroxynitrite has received intense scrutiny in recentyears.

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114 BUERK

Figure 1 Autooxidation of NO from initial value of 250 nM after instantaneousmixing is shown for different constant O2 concentrations. Numerical solutions for theautooxidation reaction kinetics (Equation 1) are shown in a physiologically relevantO2 range using 4kaq at 37◦C (Table 2). (Dashed line) The half-life (t50%); (inset)t50%

as a function of O2 or pO2.

Heme-Protein Binding

In theory, the reaction between NO and heme-containing proteins (hP) to formligand-bound hPNO is reversible,

dCNO

dt= −kaChPCNO+ kdChPNO, (4)

although the association rate constantka is several orders of magnitude higherthan the dissociation rate constantkd for both hemoglobin (Hb) and myoglobin(Mb) (21, 23, 25). Dissociation is so slow that these reactions can be consideredirreversible. Only thekas for Hb and Mb are listed in Table 2. Following instanta-neous mixing in a solution with a uniform heme-protein concentration, NO decaysexponentially:

CNO(t) = CNO(O)e−λt with t50%= ln 2/λ, (5)

whereλ = kaChP is the pseudo-first-order rate constant andt50% is the half-life. Rapid NO scavenging and very brieft50% as functions of Hb concentration

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Figure 2 Scavenging of NO from initial value of 250 nM after instantaneous mixing(Equation 5) in free hemoglobin (upper panel) or in whole blood with intact red bloodcells (bottom panel) depends on Hb concentration. The rate constant for free Hb isfrom Cassoly & Gibson (22) and for intact red blood cells from Carlsen & Comroe(26) (see Table 2). (Dashed line) The half-life (t50%); (insets)t50% as a function of Hbconcentration. Scavenging of NO is slower in whole blood.

are illustrated in Figure 2 usingkHb from Cassoly & Gibson (22) (see Table 2).AlthoughkMb for Mb is similar, the reaction is slower because Mb concentrationsin tissue are lower. There appears to be no difference between rate constants forNO binding to deoxygenated or oxygenated Hb and Mb (Table 1, sinks 4–7). Itmay be significant that in the brains of mice and humans a newly discovered “neu-roglobin” has been found (34), which may play a role similar to myoglobin inmuscle for facilitated transport of O2 in the brain, and which could also prove tobe another sink for NO.

There is a significant difference between NO reactions with free Hb and intactred blood cells (Table 2). Figure 2 illustrates NO scavenging andt50%as functionsof Hb concentration based on the rate determined by Carlsen & Comroe (26) forintact red blood cells. However, the reaction is still rapid, andt50% is∼1.8 ms for

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116 BUERK

whole blood with 45% hematocrit. The rapid reaction between oxyhemoglobinand NO to form nitrite and methemoglobin (Table 1, sink 5) was initially observedby Kon et al (35) and is considered to be the primary biochemical pathway fordeactivating NO.

The principal biological target of NO is soluble guanylate cyclase (sGC), aheme-based enzyme that converts ligand-binding free energy into protein con-formational free energy for conversion of 5′-guanosine triphosphate (GTP) tocyclic 3′,5′-guanosine monophosphate (cGMP). The intracellular second messen-ger cGMP activates protein kinases and phosphodiesterases and influences ionchannels. NO increases sGC activity several hundred-fold, with a 50% maximumactivity for NO of approximately 250 nM (99), although much lower values havebeen found (discussed below). NO binds to sGC in a two-step process. Stop flowspectrophotometric studies with recombinant sGC at 4◦C show that initial bindingto the heme is extremely rapid (k> 1.4× 108 M−1 s−1) and forms a six-coordinateintermediate (30). The intermediate converts to a five-coordinate state at a muchslower, NO-dependent rate ofkGC = 2.4 × 105 M−1 s−1 (Table 2). For sGC tobe an effective biological sensor, NO cannot remain bound and must dissociateshortly after activation. In vivo responses of vascular smooth muscle suggest thatNO dissociation must occur within 1–2 min or even faster. However, rate constantsfrom some studies predict that deactivation could take hours. Kharitonov et al (37)found much faster dissociation rates for six-coordinate nitrosyl hemes comparedwith the five-coordinate state. The fastest NO dissociation rate (0.03 s−1) for pu-rified lung sGC was measured in the presence of GTP, cGMP, and magnesiumions. Extrapolated to 37◦C, t50% was∼5 s. However, in another study using sCGextracted from bovine retina, GTP and magnesium did not accelerate deactivation(38). Furthermore, Ca2+, which is known to inhibit NO-sCG binding, prolongeddeactivation. On the other hand, Bellamy et al (39) concluded that sCG behavesmuch differently in its natural environment. Based on in vitro studies with intactcerebellar cells, EC50 for NO was∼20 nM, an order of magnitude lower than the250 nM value found by Stone & Marletta (36). Another study of sGC in vascularsmooth muscle also reports a low EC50,∼10 nM (40).

Thiol Nitrosation

There is still debate about specific mechanisms for NO reactions with thiols (RSH),and it is not clear what role nitrosothiols (RSNO) play in the transport and releaseof NO. It has been established that serum albumin and Hb carry some NO in thebloodstream (41–47), although the amount is in question (48, 49). Glutathione(GSH) is a low-molecular-weight thiol normally present at millimolar concentra-tions in tissue. Cysteine (Cys), the precursor to GSH, is also present in cells atlower concentrations. Both GSH and Cys are also present in the blood plasma atmicromolar levels. In vitro electron paramagnetic resonance spectroscopy studiesusing physiological NO (2µM) with 2 mM Cys or GSH under carefully controlledconditions preventing thiol interaction with iron or copper demonstrate that NO

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can be trapped as nitrosated cysteine (CysNO) or nitrosated glutathione (GSNO)and later regenerated (50). The authors described the mechanism as a possible “se-cret passage” for NO biotransport. Trujillo et al (51) report that xanthine oxidasecan catalyze decomposition of CysNO or GSNO to release NO under aerobic con-ditions. The involvement of superoxide was implicated for both, and the reactionfor GSNO in Table 1 (source 4) was proposed, which could be totally inhibited bySOD. The reaction for decomposition of CysNO was only partially inhibited bySOD, so an alternate mechanism may also be involved. Thus, in some locationsnitrosation could be a sink (Table 1, sink 8), or regeneration at other locationscould be a source of NO (Table 1, sources 2–4).

Sources Other than NOS

It has also been shown that xanthine oxidase can reduce nitrite back to NO (Table1, source 5) under anaerobic conditions and in the presence of NADH or xanthine(52, 53). The net production of NO from NO2

− decreased with increasing O2,consistent with greater generation of O2

−by xanthine oxidase and reaction with NOto form ONOO-. It has been shown that blood plasma nitrite/nitrate levels increaseas animals adapt to repeated periods of hypobaric hypoxia (54), but NOS activitydecreases, probably because of the O2 dependence of the enzyme. This suggeststhat another biochemical pathway is compensating for the reduced production byNOS. The amount of stored NO was estimated from relaxation of isolated rataorta at different stages of adaptation to hypoxia, using diethyldithiocarbamate toprovoke NO release from the store. The estimated size of the store increased withadaptation.

CONVECTION-DIFFUSION MODELS

The first models of NO biotransport were developed by Lancaster (55–57). Basedon point sources of NO with one-dimensional diffusion and first-order reaction,these models provided some insight into the biological activity of NO. One conclu-sion was that NO could diffuse rapidly over fairly long distances, and that the NOconcentration at any given location was determined by the sum of all NO sourcesand not necessarily by the closest source. Another aspect that was modeled wasthe strong scavenging properties of Hb, although this may have been exaggerated,because free Hb rate constants were used rather than values for intact red bloodcells (Table 2). A one-dimensional simulation showed that low Hb concentra-tions could effectively eliminate nearly all of the NO produced from endothelialcells. The logical conclusion from the modeling was that most of the NO was“wasted” by diffusing out into the bloodstream, and this fueled speculation thatthe endothelial-derived relaxing factor could not be NO but perhaps some otherrelated chemical species. This paradox has been addressed in more recent models(reviewed below).

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For the ensuing discussion, we assume that NO obeys the general mass transportequation

∂CNO

∂t+ v · ∇CNO = D∇2CNO±

∑RNO, (6)

where convection and diffusion terms are defined as usual, using the sum of allpossible reactions for NO, with a positive sign (source) for production and negativesign (sink) for loss. The mass transport equation could also be written in termsof partial pressure (pNO) using an appropriate Henry’s law solubility coefficient,but concentration (CNO) is generally used in the literature. In water at 37◦C, thediffusion coefficientD = 4.8 × 10−5 cm2 s−1 (58) and solubility coefficient=25.8× 106 mmHg NO (mol of NO)−1 per mol of H2O (59). Diffusion and solubilitycoefficients in different tissues are not known.

In Vitro Models

ONE-DIMENSIONAL DISFFUSION WITH CONSTANT O2 An in vitro model for theNO gradient as a function of time and distance in a finite layer of culture mediumabove cells was developed by Laurent et al (60), based on simplifications of theone-dimensional Fick diffusion equation

∂CNO

∂t= −D

∂2CNO

∂x2− k′C2

NO+ RNO, (7)

where a monolayer of cells (atx = 0) produce NO at a rateRNO (in nanomoles persecond per unit number of cells, or per unit volume of cells). The pseudo-second-order rate constant

k′ = 4kaqCO2, (8)

for autooxidation can be used when O2 is uniform and constant in the culturemedium. If the solution is in equilibrium with room air, the O2 concentration is220µM, and using 4kaq = 6.3 × 106 M−1 s−1 (15), the pseudo-second-order rateconstantk′ ∼ 103 M−1 s−1.

Neglecting diffusion, an upper limit for the steady state NO concentration atthe surface of the monolayer (x = 0), was estimated from

CNO0 =√

RNO/k′. (9)

If the initial NO concentration is assumed to be zero, and the cells begin to produceNO when activated att = 0, the half-time for the reaction is

t50%= (ln 3)/2√

k′RNO. (10)

Laurent et al (60) performed simulations for different NO production rates, andculture medium depths of either 3 mm or 6 mm, to find the steady state NO at thecell surface and predict mean nitrite (NO2

−) levels, which were measured experi-mentally in the medium. For parameters used in the simulation,t50% = 2.2 min,

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and the time to reach 95% of steady state was<7 min. They found that activatedmurine macrophages (∼4× 106 cells cultured in a 33-mm diameter Petri dish)produced NO2− at an average rate of 16µM h−1, which they noted was somewhathigh compared with other studies in the literature. From the model, they estimatedthat immediately adjacent to the activated macrophages,CNO∼ 4µM andRNO∼60µM h−1 (or∼4.2 nM s−1 per 106 cells). Assuming an average cell thickness of10µm, RNO would be∼490 nM s−1 cm−3.

A limitation of this closed system modeling approach is that it does not includeany loss of NO into the air over the culture medium and, therefore, may under-estimate the actual NO production rate. One simulation was performed with NOat the air/fluid interface held at zero, which predicted lower NO levels at the cellmonolayer. This simulation allowed finite NO flux at the liquid/air interface, butthe amount was not discussed in detail. An open system model that includes finiteNO flux out of the culture medium would predict higher rates for NO productionbecause the escaping NO does not form nitrite. Laurent et al (60) also noted thattheir analysis would be inaccurate if there were other NO losses, such as reactionswith O2

−.

DIFFUSION AND REACTION IN STIRRED CELL SUSPENSIONS Chen et al (61) devel-oped a more complicated model to simulate complex biochemical interactions ina stirred suspension of cultured macrophages. A stagnant film model was used torepresent steady state mass transfer of NO, O2

−, and peroxynitrite from an acti-vated monolayer of macrophages∼15µm thick attached to a 175-µm-diametermicrocarrier bead into the external culture medium. The beads were assumed to beuniformly suspended and well mixed. Because the experimental system was opento the atmosphere, NO gas escaping from liquid to the head-space gas above theculture medium was also included in the mass balance. This NO loss was quanti-fied by Lewis et al (62) with a chemiluminescence detector. Production rates forNO and O2

− used in the model were also determined experimentally, and otherparameters were taken from the literature. The model also included nitrosation ofan amine (morpholine). Summations of steady state diffusion equations assumingangular symmetry in spherical coordinates∑ Di

r 2

d

dr

(r 2 dCi

dr

)±∑

Ri = 0 for rbead< r < rbead+ δ (11)

were used to model diffusion and reaction of the three species (NO, O2−, ONOO−)

around the beads in a film 63µm thick. Algebraic expressions were used to char-acterize reaction rates, based on interactions between all relevant species. Becausethe nitrosation of morpholine depends on the uncharged amine, acid-base equilib-ria was required, including CO2/bicarbonate (H2CO3). Algebraic expressions forreaction products nitrite (NO2−), nitrate (NO3

−), and nitrosated morpholine werewritten. An intermediate species, nitrous anhydride (N2O3), thought to be requiredfor nitrosation of the amine, was also included in the coupled chemical reactions,although it was probably only present in trace amounts.

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The model equations were solved numerically and compared with experimen-tal results for different conditions. Although there was generally good correspon-dence between predicted and experimental results, there was a tendency to over-estimate nitrate and underestimate nitrite formation, so that the predicted ratio ofNO3

−/NO2− was higher than that found experimentally. The authors attributed

this to conditions that favored ONOO− formation, which is the principle source ofNO3

− formation, especially when NO flux is low.Predicted concentration profiles in the stagnant film were very informative. The

simulation showed that superoxide was consumed rapidly, falling from an initiallevel of 3.32 nM to near zero only 2µm away from the cell monolayer surface.Peroxynitrite concentration, initially at 51 nM, declined more gradually, fallingto near zero∼30 µm away from the surface. The model predicted that neitherspecies should have reached the culture medium in any appreciable amount. Thiswas supported from experimental measurements where no O2

− could be detected,and only 0.53 pM of peroxynitrite was found. In contrast, the NO concentration washigh throughout the film, dropping from 1.13µM at the cell surface to 0.95µMat the outer edge of the film to match the bulk solution NO concentration. Thepredicted bulk solution NO was a little higher than that found experimentally. Themodel was able to predict higher NO and lower nitrate when SOD was added tocompete for the reaction between NO and O2

−, although the model did not exactlymatch experiment values. Liu et al (27) commented that perhaps discrepancies inthe model by Chen et al (61) might be smaller with a higher autooxidation rate.In terms of the model, this would mean that most of the reaction between NOand O2

− would occur in the cell membranes, rather than in the stagnant film layeraround the cells.

In Vivo Models

NO PROFILE INTO VASCULAR WALL If NO loss in the vascular wall and surroundingtissue is due to autooxidation alone, the following steady state, one-dimensionalradial diffusion equation,

D

r

d

dr

(r

dCNO

dr

)− 4kaqCO2C

2NO = 0 for r > Re (12)

could be used to model the NO gradient for a vessel with inner radiusRe. One caneither assume homogeneous properties or use a multilayered model with differentproperties for the vascular wall and surrounding tissue. This simple model alsoassumes that there are no other sources of NO from nearby neurons, no inducedNOS in surrounding tissue, and no interaction with NO diffusing from nearbyblood vessels.

Even with these simplifying assumptions, the model is complicated by thefact that pO2 varies across the vascular wall as a function of tissue properties(O2 diffusion and solubility coefficients) and O2 consumption rates (63, 64). ThepO2 profile will depend on the type of blood vessel, O2 consumption rates in

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the vascular wall and surrounding tissue, blood flow in the vessel lumen, bloodO2 saturation, pH, pCO2, etc. Autooxidation of NO will also consume some O2,although this is probably negligible compared with the metabolic use of O2. A fullydeveloped model incorporating all these variables would be a difficult challenge.One simplifying assumption would be to use the average O2 concentration acrossthe wall. For example, in 25-µm-diameter arterioles in rat mesentery, the lumenpO2 is 43 torr (∼63µM), and there is a steep drop in pO2 across the wall to 25 torr(∼37µM), as measured by an optical method (65). Using an average O2 value of50µM, the pseudo–second-order rate constant would be 4.6× 102 M−1 s−1, witht50% = 36.8 min (Figure 1). This would cause a negligible loss of NO, especiallybecause the pO2 will be even lower further out in the tissue. If autooxidation is anorder of magnitude higher because of an enhanced reaction in membranes (67),t50%would be only 3.3 min, which is still slow compared with expected half-lives,on the order of a few seconds.

To simplify the task of modeling NO in tissue, Vaughn et al (66, 67) used twoapproaches. As a first approximation, a pseudo–first-order reaction with rate con-stantλ = 0.01 s−1 was used, equivalent tot50%= 69.3 s. This permits an analyticalsolution, as discussed in the next paragraph. Alternately, a pseudo–second-orderreaction with a rate constant of 0.05µM−1 s−1 was used. Both rate constants wereestimated from experimental data reported by Malinski et al (68). The profile wassolved numerically, assuming zero NO flux at infinite radius, coupled to endothelialNO production and NO flux into the bloodstream, as described below.

Butler et al (69) took another approach toward modeling the NO profile in thevascular wall and surrounding tissue. They assumed that NO reacts with guanylatecyclase,

D

r

d

dr

(r

dCNO

dr

)− kGCCGCCNO = 0 for r > Ra, (13)

whereRa is the radius on the abluminal side of the endothelium with thicknessRa = Re+. Guanylate cyclase was assumed to be uniformly distributed in tissue atCGC = 100 nM, based on unpublished data from their laboratory, with a second-order rate constantkGC for the reaction. Autooxidation and dissociation of NOfrom sGC were not considered. In their simulation,λ = kGCCGC = 0.01 s−1,which is exactly equivalent to the first-order simulation by Vaughn et al (66).

The general solution to Equation 13 is

CNO(r ) = a1I0(br)+ a2K0(br), (14)

as described by Butler et al (69), whereI0 andK0 are zero-order modified Besselfunctions of the first and second kind with the scaling factor

b =√λ/D. (15)

The coefficientsa1, a2 can be evaluated from the boundary conditions. Butler et al(69) assumed that the NO profile extended to infinity, requiring thata1 = 0. Using

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the NO concentrationCNO(Ra) at the abluminal side of the endothelium to evaluatea2, the NO profile is

CNO(r ) = CNO(Ra)K0(br)/K0(bRa). (16)

For a blood vessel with lengthL and abluminal surface area 2πRaL, radial fluxinto the wall is

Jwall = −(2πRaL)DdCNO

dr|r=Ra. (17)

From the derivative of Equation 16 evaluated atr = Ra, NO flux into the wall is

Jwall = 2πRaLCNO(Ra)

√λDK1(bRa)/K0(bRa), (18)

whereK1 is the first-order modified Bessel function of the second kind.

NO PROFILE INTO BLOODSTREAM Using the first-order molar rate constantkHb

(per moles per second) and constant concentrationCHb, the steady state, one-dimensional radial diffusion equation with first-order scavenging of NO by Hbcan be expressed as

D

r

d

dr

(r

dCNO

dr

)− kHbCHbCNO = 0 for 0< r < Re, (19)

and can also be solved analytically. Vaughn et al (66) used the analytical solutionto check the convergence of their numerical simulation at steady state but didnot publish details for the complete solution. As shown previously, the generalsolution is the sum of modified Bessel functions (Equation 16) with a differentscaling factor

b =√

kHbCHb/D, (20)

and with different boundary conditions to evaluate the coefficientsa1, a2. Becausethe analytical solution must be finite atr = 0, a2 is zero. For a specified NOconcentrationCNO(Re) at the endothelial surface (r = Re), the NO gradient in thebloodstream is given by

CNO(r ) = CNO(Re) I0(br)/I0(bRe). (21)

The radial flux from the endothelium into the bloodstream is

Jblood= 2πReLCNO(Re)

√kHbCHbDI1(bRe)/I0(bRe), (22)

whereI1 is the first-order modified Bessel function of the first kind. In the modelby Vaughn et al (66, 67), the NO source was from two concentric surfaces, one atthe blood interface (Re) and the other between the endothelium and vascular wall(Ra). Taking both fluxes into account and dividing by the volume of endothelialcells, the total rate of NO production is

RNO = (Jblood+ Jwall)/π(R2

a − R2e

)L . (23)

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Figure 3 NO profiles in blood and tissue predicted from models by Butler et al (69)and Vaughn et al (66) are shown for a 100-µm-diameter blood vessel with differentparameters (see text and Table 2). Casea uses the Hb scavenging rate constant for freeHb from Cassoly & Gibson (22). (Inset, top left) Detail of the extremely steep gradient.Whole blood Hb scavenging rates used for casesb [Carlsen & Comroe (26)],c [Liuet al (27)], andd [Vaughn et al (28)] predict lower NO fluxes into the bloodstream.Casee is for the lowest Hb scavenging rate used in the simulations by Vaughn et al(66). The NO profile into the vascular wall and surrounding tissue for casef is for thesame first-order reaction rate used by Butler et al (69) and Vaughn et al (66). Casegis for the second-order rate used by Vaughn et al (66). Caseh is for a rate one order ofmagnitude lower, equivalent to autooxidation accelerated by hydrophobic membranesin the range predicted by Liu et al (18). (Inset, lower right) NO profiles in tissue outto a 500-µm radius, assuming uniform properties for profiles extending to an infiniteradius.

NO profiles into the bloodstream and vascular wall predicted for different pa-rameter values are illustrated in Figure 3 for a 100-µm-diameter blood vessel. Anormal hematocrit of 45% with 15 g of Hb/ml of blood was used, correspondingto a concentration of 2.25 mM, and NO was fixed at 250 nM on both sides ofthe endothelium. Casea is based on the free Hb value of Cassoly & Gibson (22).The NO profile drops to near zero within 1µm. Scavenging of NO by free Hb insolution is very effective because the reaction rate is so high (Table 2). Although

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124 BUERK

this case is not appropriate for simulating normal in vivo conditions, it illustrates apotential problem for modified Hb-based synthetic blood substitutes, which couldimpair NO delivery to the vascular wall (70). More realistic NO profiles are shownusing the lower rate constants for intact red blood cells from Carlsen & Comroe(26) (caseb), Liu et al (27) (casec), and Vaughn et al (28) (cased). Cased isbased on 0.00089 times the free Hb value of Cassoly & Gibson (22). NO con-centrations at the lumen center are 0.1 pM, 0.15 nM, and 3.2 nM, respectively.Casee is based on the lowest rate constant used by Vaughn et al (66), equivalentto a pseudo–first-order rateλ = kHbCHb = 15 s−1, which is∼17% of the valuefrom Carlsen & Comroe (26). NO at the center of the bloodstream would be nearly38 nM for this case, which is unreasonably high. This low scavenging rate was theonly one leading to an endothelial NO level above 250 nM for the NO productionrate used in the simulation (66).

The NO profile into the wall and tissue for casef is based on the value ofλ =0.01 s−1 used by Butler et al (69) and Vaughn et al (66). Caseg is a numericalsolution for the second-order rate of 0.05µM−1 s−1 used by Vaughn et al (66).For caseh, a 10-fold lower rate was used in the numerical solution, close to theenhanced autooxidation rate with membranes (18) but still an order of magnitudehigher than autooxidation in an aqueous medium. Casef has the highest NO fluxinto the wall.

Most of the NO diffuses out into the bloodstream. Relative to NO diffusing intothe wall for casef, caseapredicts that 99.8% of the total endothelial NO productionwould be lost to the bloodstream. With lower rate constants for intact red bloodcells, NO losses to the bloodsteam are 97.7%, 95.8%, and 93.6%, respectively,for casesb, c, andd. Even with the unrealistically low Hb scavenging rate forcasee, 87.8% of the NO produced by the endothelium enters the bloodstream.There are possible mechanisms that might reduce this loss, including diffusionalresistance from red blood cell free plasma layers near the wall. The width of thislayer was unrealistically high for some of the vessel sizes simulated by Butler et al(69). Experiments by Liao et al (71) with pig coronary microvessels perfused witheither free Hb or whole blood suggests that the boundary layer may be a significantfactor. Another factor is the well known F¨ahraeus-Lindqvist effect, in which theparticulate nature of blood leads to a reduced hematocrit in small tubes. This canbe less than half of the systemic hematocrit in capillaries or small arterioles andvenules (diameters∼15 µm) and has significant effects in O2 transport models(72, 73). The scavenging constantλ = kHbCHb would be proportionally reducedin very small blood vessels. However, Vaughn et al (66) demonstrated that evenwhen both boundary layer and reduced hematocrit were included, it was difficultto simulate NO levels in the vascular wall above 250 nM to activate guanylatecyclase, except when very low Hb scavenging constants were used. Perhaps oneweakness in the modeling was that they did not predict how much of an increase inendothelial NO production would be needed over the fixed value used in the modelto counteract scavenging of NO by whole blood. Of course, if sGC is sensitive toNO at much lower levels, then the model would more easily predict these valueswith the scavenging rates for whole blood.

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INTERACTION BETWEEN NITRIC OXIDE AND O2

TRANSPORT

It is clear that vascular smooth muscle vasodilation by NO increases blood flowand O2 delivery, although it may not be the primary mechanism for coupling bloodflow to metabolic requirements. There is evidence that NO directly effects O2

transport to tissue by at least four mechanisms, briefly reviewed below.First, O2 is required for the enzymatic synthesis of NO fromL-arginine as well as

for its autooxidation in tissue (Table 1), and NO production rates for all three NOSisoforms are O2 dependent. If NO production follows Michaelis-Menten kineticsand other factors (such as intracellular Ca2+) remain constant, the O2-dependentproperties can be represented by

RNO = RNOmaxO2/(O2+ Km), (24)

where the Michaelis constantKm is the O2concentration at half of the maximum NOproduction rate (RNOmax), as summarized in Table 3. These values are from studieswith purified NOS except for that of Otto & Baumgardner (77), who obtained anestimate forKmbased on nitrite production by macrophages cultured at different O2

levels. It has been reported that the apparentKm for O2 of nNOS is extremely high(75), well outside of the normal physiological tissue O2 range, although anothergroup found a much lowerKm (74).

Second, NO is also transported by Hb and has an effect on O2 release. Stamlerand coworkers (8, 41–45) propose that O2-dependent interaction between NOand Hb helps regulate blood flow and O2 delivery. Two cysteine sites on the Hbtetramer can react with NO or S-nitrosothiols (SNO), depending on oxyhemoglobinsaturation, allowing release of NO or SNO as O2 is unloaded downstream. Thus,stored NO or SNO can contribute to blood flow regulation in addition to endothelialor neuronal NO production. NO can also shift the oxyhemoglobin equilibriumcurve to the right to improve O2 delivery (80).

TABLE 3 Oxygen dependence for NO production by different NOSisoformsa

nNOS iNOS eNOS(type I) (type II) (type III) Reference

23.2± 2.8 6.3± 0.9 7.7± 1.6 Rengasamy & Johns (74)

∼400 Abu-Soud et al (75)

∼135 Dweik et al (76)

∼21 Otto & Baumgardner (77)

∼88 Liao et al (78)

∼56 Whorton et al (79)

aMichaelis constants (Km, micromolar O2) for 50%RNOmax.

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126 BUERK

Third, NO has a direct effect on O2 metabolism. NO competes with O2 atthe heme site of cytochrome oxidase to reversibly inhibit tissue O2 consumption(81–84). Inhibition by NO depends on O2 availability, with increasing effect asthe O2:NO ratio decreases (81). NO has essentially no effect on respiration whenthe O2:NO ratio is>250:1. In a study of isolated mitochondria from rat brownadipose tissue (86), the following nonlinear relationship was found for the variationin mitochondrial respiration with O2:

RO2 = RO2maxC2O2

/(C2

O2+ K 2

m

), (25)

where the apparentKm for O2 increases as a linear function of NO,

Km = 16µM(1+ CNO/27 nM). (26)

The effect of increasing amounts of NO on the O2 dependence of RO2 is shown inFigure 4. It should be noted that this is not the usual Michaelis-Menten kineticsused to represent O2-dependent respiration, and that theKm in the absence of NOis considerably higher than others report. As shown in Figure 4, the inhibitoryeffect of NO is greater at low tissue O2 levels. A similar linear relationship withan intercept closer to zero can be inferred from the data of Brown & Cooper (82),who found that the O2 consumption of brain synaptosomes was 50% inhibited with270 nM NO when O2 was 150µM. At lower O2, closer to expected tissue levels(∼30µM), only 60 nM NO caused 50% inhibition.

Fourth, it is possible that NO can react with thiols when O2 is present (87, 88).Nitrosothiols in blood and tissue may serve as a reservoir for NO release undercertain conditions, and reduction of nitrite back to NO by xanthine oxidase mayoccur when tissue pO2 levels are very low.

NITRIC OXIDE IN THE LUNG

The ability of NO to relax smooth muscle is the principle behind using NO in-halation therapy for pulmonary hypertension, acute respiratory distress syndrome,and bronchial asthma. There is also keen interest in the diagnostic potential formeasuring exhaled NO, especially as an indicator of sepsis or pulmonary inflam-mation. The partial pressure of NO in gas from the lower airways is normally verylow, on the order of 6 ppb but is much higher in the nasal passages. Therefore,techniques for respiratory gas sampling have been designed to eliminate nasalcontributions. Hyde et al (89) developed a single-compartment model to predictNO partial pressure in the lower airways (pNOL) from the relationship

VLdpNOL

dt= VNO(Patm− 47)− pNOL[DCNO(Patm− 47)+ VA], (27)

whereVA is the ventilation rate (typically 12 breaths/min with tidal volume of500 ml for a total of 6 liters/min at rest),VL is the mean volume of gas in thelower airways,Patm is the barometric pressure corrected for water vapor pressure(47 mmHg or torr) at 37◦C, VNO is the rate of NO produced by lung tissue that

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Figure 4 Inhibition of O2 consumption by NO predicted from modified Michaelis-Menten kinetics (Equations 25–26) reported by Koivisto et al (86) for isolatedmitochondria are shown as a function of O2 or pO2 (bottom panel). (Dashed line)Half-maximal O2 consumption rates. The NO concentration required to inhibit O2 con-sumption by 50% predicted from these kinetics is a linear function of O2 (top panel,solid line). A similar relationship (dashed line, top panel) is inferred from the data ofBrown & Cooper (82) for NO required to inhibit O2consumption of brain synaptosomesby 50% (squares).

enters the airway gas, and DCNO is the diffusing capacity for NO (DC is not adiffusion coefficient), which is 140 ml min−1 mmHg−1 at rest. The solution isgiven by

pNOL(t) = VNO(Patm− 47)

VL

[1− e−λt

λ

], (28)

where the first-order rate constant is

λ = [DCNO(Patm− 47)+ VA]/VL . (29)

Pulmonary blood NO concentration is assumed to be zero, andVL is considered tobe constant, although it does vary as air is inhaled and exhaled. The model was also

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modified to include a step change in NO, such as a deep breath of air containingNO, or a long breath hold. In the latter case, it was calculated that NO wouldreach steady state within∼15 s. Equations for NO exchange during inspiration orexpiration were also presented.

Tsoukias & George (90) developed a more elaborate model, with the lowerairways represented by a variable volume alveolar compartment, coupled to asecond, fixed-volume compartment for the upper airways. The upper airway in-cluded NO production and reaction in a thin layer of tissue with bronchial bloodon one side and air on the other. Because the bronchial tissue layer is very thin, aone-dimensional planar model,

∂CNO,t

∂t= Dt

∂2Ct

∂x2+ St,air− λtCNO,t , (30)

was applied, whereDt is the diffusion coefficient,St,air is the NO flux from tissueinto the upper airway gas, andλt is the first-order reaction rate constant in tissue.Rates ranging between 1.38> λt > 0.046 s−1 corresponding to 0.5< t50% <

15 s were used, and an analytical solution for the time-dependent variation intissue concentration was described. A partition coefficient of 0.0416 (mol of NOin tissue/mol of NO in gas) based on the solubility of NO in water was used toconvertCNO,t to pNO, assuming instantaneous mixing as NO diffused into the gasphase. The transient response to a step change in pNO in the gas phase showedthat the NO concentration change in tissue was 90% complete in∼0.6 s, so thatfor most respiratory maneuvers, the steady state profile would provide sufficientaccuracy in the model.

The steady state NO profile across the layer is

CNO,t (x) = α[e

x√

λtDt − e

−x√

λtDt

]+ St,air

λt

[1− e

−x√

λtDt

], (31)

where the coefficient

α =[CL − St,air

[1− e

−L√

λtDt

]/λt

]/[e

L√

λtDt − e

−L√

λtDt

], (32)

whereL is the thickness of the layer, andCL is the NO concentration at the tissue/airinterface (x = L). Scavenging by Hb reaction is not directly modeled, but NOconcentration in blood is assumed to be negligible, so the boundary conditionat the blood/tissue interface (x = 0) is fixed atCNO,t(0) = 0. NO flux into thebloodstream can be determined from the derivative of Equation 31. Predicted NOprofiles are shown in Figure 5 for several cases, including casea for parametersused by Tsoukias & George (90), with the wall concentration fixed at 0.15 nM andSt,air = 0.55 nM s−1 cm−3. Caseb is for a doubling ofSt,air, and casec is for 50%of St,air. Cased is for pNO one order of magnitude higher in the gas phase than incasea.

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Figure 5 NO profiles across a thin layer of bronchial tissue in the lower airway of thelung (Equation 31), predicted from the model by Tsoukias & George (90), are shownfor different parameters. Casea is for baseline parameters with normal ventilation intheir model. Caseb is for twofold higher and casec is for half of the NO productionrate in bronchial tissue. Cased uses baseline parameters in casea with NO partialpressure one order of magnitude higher in the gas phase.

For the upper airways, the mass balance was written as

∂CNOair

∂t=[

As

Ac

]Jt :g,air+V

∂CNOair

∂V, (33)

whereAs is the wall surface area, andAc is the airway gas volume per unit axialdistance, andJt:g,air is NO flux from tissue into airway gas. The volumetric gas rateV represents either inspirationVI or expirationVE. Tissue NO flux into the upperairway gas was coupled to the gas flow in and out of the alveolar compartment.

The lower alveolar compartment was assumed to be well mixed, with NOentering or leaving by convective flow and exchanging with alveolar tissue bydiffusion. The mass balance for the alveolar concentration of NO was written as

Valv(t)dCNOalv

dt= (Sapp,alv− DCNO)+ V(CNOair,end− CNOalv), (34)

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whereValv(t) is the time-varying alveolar gas volume,Sapp,alv is the rate of NOentering the alveolar gas produced by alveolar tissue, and DCNO is the diffusingcapacity for NO. Analytical solutions were presented for inspiration, expiration,and breath holding and were compared with measurements from a representativehuman subject taken from a companion paper (91). Generally, the model wasable to describe these maneuvers, with some minor discrepancies, even though noattempt was made to optimize the model parameters for the subject. One limitationdiscussed is the fact that the diffusing capacity for NO varies with surface area andHb reaction rate, so it is not a simple constant.

Recently, Hogman et al (92) used a simplified variation of the above model andreported that the use of three different expiratory flow rates (low, normal, and high)permitted extraction of reliable information about alveolar, lower airway, and nasalcontributions from the analysis of exhaled NO data. In ten healthy humans, theyreported that the average NO transfer rate of the airways was 9± 2 ml s−1, with theairway tissue contributing 75± 28 ppb and the alveolar fraction 2± 1 ppb. Valuescomputed from the three different flow rates were no different than values obtainedfrom a more extensive analysis of measurements for eleven different flow ratesin these ten subjects. They were also able to demonstrate significant differencesbetween five subjects with asthma and five cigarette smokers compared with thecontrol group.

NITRIC OXIDE IN THE BRAIN

NO has at least four possible functions in the central nervous system, including(a) coupling of neuronal activity with cerebral blood flow, (b) stabilizing synapticefficiency, (c) facilitating neurotransmitter release, and (d) directing growth ofaxonal arbors during development (93). The first evidence for a role of NO inbrain function was from Garthwaite et al (94), who found that cerebellar neuronssynthesized NO in response to N-methyl-D-aspartate release. Bredt & Snyder (95)isolated and characterized nNOS and demonstrated its widespread presence in thecentral nervous system. A role for NO in long-term potentiation in the hippocampuswas suggested from studies by Schuman & Madison (96).

Wood & Garthwaite (97) developed a point source model for NO in the brain,similar to the approach by Lancaster (55–57). For diffusion and first-order reactionin spherical coordinates with angular symmetry, the concentration as a function oftime at a fixed radial location is

CNO(r, t) = St=0

8(πDt)32

e−(

r 2

4Dt

)e−(λt), (35)

whereSt= 0 is the instantaneous strength of the point source atr = 0 and thepseudo-first-order reaction rateλ = 0.1386 s−1 for t50% = 5 s. Shorter half-livesup to an order of magnitude faster were also modeled. NO concentration at anyspatial location can be found using the principle of superposition by summing

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Figure 6 Dynamic changes in brain tissue NO are shown at a location 100µm froma point source following a single spike of NO production att = 0 (top panel) or a 2-Hztrain of five consecutive spikes separated by 500 ms (bottom panel). (Insets) Relativechange in NO near the origin for both cases based on a 5-s half-life in tissue. The NOvolume signaling resulting from repeated NO bursts is simulated by linear superpositionof the analytical solution for a single burst in spherical coordinates (Equation 35) fromthe model by Wood & Garthwaite (97). The peak NO concentration decreases withdistance from the source, with an increasing time lag from the initial burst.

repeated spikes or pulses from a single source, or by summing contributions frommultiple sources. An example for changes in NO at a location 100µm away froma single point source is shown in Figure 6 for a single spike att = 0 and for a 2-Hztrain of five sequential spikes 500 ms apart. For each case, the relative change inNO at the source is also shown. Note that the increase in NO at the source lastslonger than the change in NO farther away, and that the peak is delayed in time,depending on how far away it is from the source.

The steady state profile around a single point source atr = 0 producing NO ata continuous rate would be

CNO(r ) = S

4πDre−r√

λD , (36)

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whereS= 2.1× 10−17M−1 s−1 causesCNO to be 1µM at r = 0.5µm, and 1 nMatr = 500µm in the simulation by Wood & Garthwaite (97). Note that the solutionis singular atr = 0, where the concentration would approach infinity. Their modelsuggested that a single point source of NO could influence approximately twomillion synapses by diffusion to a volume of brain tissue 200µm in diameter.

Philippides et al (98) noted that there are problems with the singular nature ofan instantaneous point source, so they modeled a hollow spherical structure withNO produced in the outer shell of a sphere of 6µm inner diameter and 10µmouter diameter. They replaced the point source function with a volumetric NOproduction rateRNO = 1.32 × 10−4 M s−1 µm−3 to generateCNO = 1 µM onthe surface. They performed simulations with square wave pulses of NO productionand also used arbitrary functions for a smoother rise and decay of NO pulses up to100 ms in duration, but this made little difference in the qualitative results. One ofthe interesting features of the hollow sphere structure was that it caused a reservoireffect, as some of the NO diffused into the center during the pulse, then diffusedoutward after production ceased. They also varied the size and thickness of thehollow spheres and concluded that neurons with diameters in the 15- to 20-µmrange producing NO in 100-ms pulses will influence the largest relative volume oftissue.

They also extended the model to an irregular structure consisting of small cylin-drical shapes with branches emanating from a hollow sphere. The structure usedsimple geometries to represent the morphology of a neuron cell body with den-drites, and the simulation included an elliptical sink to represent NO scavenging byhemoglobin in a capillary. A three-dimensional simulation at different time pointswas performed, showing first the initial increases in NO around the elements, thenthe diffusion and decay of the “NO cloud” into the space around the structures.The NO cloud could surround and move past the sink, but the NO concentrationswere higher on the opposite side of the sink. Thus, contour plots at different timesshowing the amount of tissue around the structure with NO above the thresholdfor activation of guanylate cyclase were not symmetric because of the irregularshape and the distorting effect of the sink. Among the conclusions drawn from thismodeling approach, Philippides et al (98) pointed out that the morphology of thesource was crucial for the NO diffusion signal, but the surrounding tissue could beregarded as homogeneous. This is a marked contrast from classical synaptic neu-rotransmitters that diffuse more slowly over much shorter distances. The volumesignaling by NO therefore does not have to address a specific target, and the targetdoes not have to recognize the source of the signal it is receiving.

Because NO would appear to decrease synaptic specificity, it is not clear howNO can play a role in cerebellar learning through effects on long-term depression.Schweighofer & Ferriol (99) developed a neural model for adaptive movementcontrol, incorporating NO diffusion and first-order reaction (λt = 0.3 s−1, t50% =3.3 s). The neural model consisted of two-dimensional microzones occupying anarea of 315× 630µm, with nine columns and three rows of Purkinje cells and adistribution of synapses between Purkinje and granule cells. It was assumed that

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NO was generated by spikes from inferior olive cells. The spikes were simulatedby a stochastic Poisson spike generator, with the mean frequency modulated by anerror signal related to an arm-reaching task. A learning rule was defined in termsof parallel fiber activity and relative change in NO at the synapses. The efficiencyof learning was simulated with and without NO diffusion. It is not clear whetherpoint sources were used to generate NO in the model, and NO concentrations werenot specified. An example of relative NO levels computed for a system of fourinterconnected microzones during movement of shoulder and elbow joints wasillustrated. High NO levels were generated when the movement error signal waslarge, and low levels with small errors. The model predicted that learning efficiencywas improved for low-frequency inferior olive firing rates in the 0.5- to 2-Hz range.At higher frequencies, learning efficiency without NO diffusion improved becausemore information was received and, eventually, exceeded the efficiency computedwith NO diffusion. The model suggests that NO volume signaling acts as a low-pass filter that is unable to carry high-frequency information. The model sensitivityto variations in diffusion rates was examined at fixed reaction rateλt = 0.3 s−1,with the best learning simulated in the range 2000< Dt < 3300µm2 s−1.

The simulation suggests that NO can play a role in cerebellar learning, al-though there were some limitations. One limitation was the decrease in informa-tion with higher frequencies, and the authors suspect that they will need to in-clude the effects of protein kinase C activation on synaptic efficiency in futuremodels. Another limitation was cross interference due to NO diffusing from onemicrozone into another, which is probably a consequence of the simplified nature ofthe model compared with actual cerebellar morphology where distances aregreater.

THE DARK SIDE OF NITRIC OXIDE

Although the models discussed above have primarily focused on NO biotransportunder normal physiological conditions, there is a substantial body of literatureon the pathological aspects of NO biochemistry, which is too extensive to re-view here. The general consensus is that excessive or unregulated NO productioncontributes to numerous disease states. Septic shock is an obvious example ofNO overproduction. Endothelial dysfunction possibly associated with decreasedNO production or increased NO degradation is thought to play a role in diabetesmellitus, hypertension, hypercholesterolemia, thrombosis, and vasospasm. Neuro-generative disorders where NO is suspected to play a role include amyotrophiclateral sclerosis and Alzheimer’s, Huntington’s, and Parkinson’s diseases. Withstroke, traumatic brain injury, or cerebral ischemia, the consensus view is thateNOS can play a protective role by maintaining blood flow, while nNOS can beharmful through NO-mediated increases in glutamate neurotoxicity. Inflammationand increased NO production from iNOS can also come into play some time afterthe initial insult. A descriptive title from a paper by Beckman & Koppenol (100)

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borrowed from a Hollywood western movie characterized the key players in NObiochemistry as “good” (NO), “bad” (O2−), and “ugly” (ONOO−).

A series of kinetic modeling papers by Stanbro (101–103) suggest that “ugly”ONOO−could reach nanomolar concentrations in blood plasma and react with low-density lipoproteins. A coupled set of eight differential equations for the reactionswas solved numerically for specified baseline conditions and varying input NO.Although the actual number of low-density lipoprotein particles that react mightbe small, this could be sufficient to initiate a chain reaction with unsaturated fattyacids, contributing to the slow buildup of atherosclerotic plaques in blood vessels.The role of antioxidants in reducing ONOO− was also investigated but was foundto have little effect once it had formed. The modeling suggested that a morereasonable pharmacological strategy would be to reduce O2

− and, thus, limit lipidperoxidation by reducing the amount of ONOO− that would be formed.

Therapeutic approaches have included NO donors, such as the early use ofnitroglycerin many decades before the mechanism of its action on the cardio-vascular system was known. Viagra is another well-known drug. Alternativeapproaches for controlling NO production have been directed toward the develop-ment of pharmacological inhibitors with specificity for the individual NOS iso-forms. For example, an effective nNOS inhibitor that preserves eNOS activity maybe an effective agent for treating brain injury or stroke. Highly specific iNOS in-hibitors may be effective in reducing cell damage associated with inflammation.Gene therapy is also being considered. There have been several animal studies, re-viewed by Chen et al (104), where successful transfer of recombinant eNOS genesto blood vessels has been achieved. Areas of clinical application could include treat-ment of blood vessels damaged by atherosclerosis, pretreatment of vein grafts tomaintain patency, or treatment of stenosed vessels following balloon angioplasty.Gene transfer of recombinant iNOS has also been successful in animal studiesand could find a clinical application for accelerating wound healing. RecombinantnNOS might be a more suitable alternative for eNOS in some applications.

PHYSIOLOGICAL MEASUREMENTS OF NITRIC OXIDE

A substantial number of landmark NO studies in the literature are based on indirectmethods, such as measuring tissue or blood plasma nitrite/nitrate levels, or measur-ing other physiological parameters before and after inhibiting NOS. Archer (105)summarized direct and indirect methods for detecting NO and related products inbiological systems. Chemiluminescence detectors provide the highest resolutionand sensitivity but are limited to gas phase measurements. Electrochemical sensorsfor detecting NO in liquid phases are now available commercially and have beenminiaturized in some laboratories. Three different NO microelectrode designs fortissue NO measurements have been developed by Shibuki (106), Malinski & Taha(107), and Buerk et al (108). The operating principle for all three microsensors isthe electrochemical oxidation of NO.

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The Shibuki (106) design consists of a platinum anode and silver cathode po-larized at+900 mV inside a membrane-covered glass micropipette filled withacidic salt solution. Shibuki & Okada (109) used this electrode in cerebellar slices,finding increases in NO averaging 47 nM during electrical stimulation. These dataprovided direct evidence that NO plays a role in long-term depression of Purkinjecell neurotransmission. More recently, this type of probe measured much smallerincreases in NO, averaging 380 pM in layer V of rat auditory cortex slices duringelectrical stimulation (110).

The second design by Malinski & Taha (107) uses a carbon fiber with a flamesharpened tip of<1µm. The carbon fiber is sealed in a glass micropipette, leavingthe tip and a small length of fiber exposed. The exposed end is coated with con-ducting polymer [monomeric tetrakis (3-methoxy-4-hydroxyphenyl) porphyrin]to catalyze electrochemical oxidation of NO at 640 mV relative to an externalreference electrode. Negatively charged Nafion polymer was also coated over thepolymer to minimize interference from NO2− and catecholamines. However, tyro-sine has been reported to be a significant interfering species for this sensor (111).In vitro and in vivo studies by Malinski et al (68, 112) have provided valuableinformation used for some of the NO biotransport models in this review.

The third design by Buerk et al (108) consists of a glass micropipette with arecessed gold cathode, which is polarized at+800 to+850 mV relative to anexternal Ag/AgCl reference electrode. Tips are typically between 5 and 10µm,with recesses∼20–50µm deep. The recess acts as a diffusion barrier for higher-molecular-weight species, and Nafion polymer in the recess further minimizesinterference from ascorbate, catecholamines, NO2

−, and tyrosine. In vivo NOstudies in cat optic nerve head with simultaneous blood flow measurements bylaser Doppler flowmetry were reported (113, 108). We found that during stimula-tion of the eye by flickering light, blood flow increased by 44% and NO by an ave-rage of 88 nM. NOS inhibitors significantly attenuated the NO and blood flowresponses to flicker stimulation (108) and reduced baseline NO from an initiallevel of∼460 nM. We also reported that NO concentration is not constant, butnormally fluctuates about a mean value with a low frequency content similar to thatfor blood flow variations in cat optic nerve head (113). NO responses to hypoxiaand hypercapnia in cat optic nerve and rat brain were compared in another study(114), and the role of NO in functional activation of the brain is under investigation.The inhibitory effect of NO on O2 metabolism and the possible role of NO in O2

chemoreception in the perfused cat carotid body were also studied (115). The samerecessed design has been used by Bohlen (116) to measure NO on the outer wallsof small arteries and veins in rat intestinal mucosa. Resting levels on the outerblood vessel wall averaged 353 nM for arteries and 401 nM for veins, well abovethe 250 nM target for activating sGC in the simulation by Vaughn et al (66). NOlevels increased>500 nM for both arteries and veins during glucose absorption.In another study, Bohlen & Nase (117) report periarteriolar NO levels averaging337 nM for first-order large arterioles, and 318 nM for second-order interme-diate-sized arterioles in the intestinal microvasculature for resting conditions.

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Experimental maneuvers that caused increases in blood flow and shear stress alsoincreased NO.

As more physiological NO measurements are made, our knowledge base shouldexpand and lead to significant improvements in NO biotransport models. However,there are conflicting results in the literature that need to be resolved. The brain inparticular has produced some curious findings. For example, electron paramagneticresonance studies in normal rat forebrain found basal NO levels averaging 1.6µM,and 10-fold higher with sepsis (118). In vivo studies using microdialysis withHb to quantify NO from metHb formation found NO levels in rat cerebellumaveraging 303 nM with halothane anesthesia, and higher levels averaging 532 nMwith isoflurane anesthesia (119). We found average NO levels around 1.1µM inrat parietal cortex, increasing to 2.4µM during recovery from a short period ofsevere hypoxia (114). However, Malinski et al (68) reported baseline NO levels inrat brain<10 nM, at the detection limit of the electrode. Despite the difference inbasal levels, increases in NO following hypoxic insults were similar for the lattertwo studies. Further experimental work is needed to resolve these and many otheruncertainties in the literature.

FUTURE DIRECTIONS AND MODELING NEEDS

It is clear that reliable models will not be developed without means to verifywhether the theoretical predictions have physiological meaning, and that unre-liable physiological measurements will not improve our modeling efforts. Moresynergistic interactions between experiment and theory need to be established tovalidate proposed biochemical mechanisms. In particular, the suspected role ofnitrosothiols needs further modeling and appropriately designed experiments toinvestigate whether this “secret passage” is real.

Models need to be developed that couple NO production with O2 transport.Recently, Clementi et al (83) commented that “the classical paradigm about theindependence of oxygen consumption along a wide range of oxygen concentra-tions should be corrected in terms of NO metabolism.” As discussed above, theseinteractions include the O2 dependence of NOS isoforms, effects of NO on O2

metabolism1, oxyhemoglobin properties, and release of NO stores when tissuepO2 is low. Functional models need to be developed to predict how NO releasecontrols vascular smooth muscle tone and blood flow, with feedback from wallshear stress, intracellular Ca2+ levels in the endothelium, and O2 delivery and

1A simplified one-dimensional planar model for coupled NO and O2 diffusion from bloodvessels including reversible inhibition of O2 consumption by NO was published while thisreview was in proof, which demonstrates that tissue oxygenation can be enhanced, especiallywhen metabolic requirements are high (Thomas DD, Liu X, Kantrow SP, Lancaster JR Jr.2001. The biological lifetime of nitric oxide: implications for the perivascular dynamics ofNO and O2. Proc. Natl. Acad. Sci. USA98:355–60).

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consumption in the vascular wall. Interactions with nearby blood vessels need tobe incorporated into the boundary conditions, and diffusion of other substances thatmodify NO release should be included in the models. Further modeling work maybe needed to fully interpret NO exhalation measurements from the lung, to increasethe potential for clinical diagnosis of different respiratory diseases, or to evaluateeffectiveness of therapeutic measures. Testing standards need to be established inthe near future to evaluate the increasing database of patient information.

Modeling of the effects of NO on neurotransmission need to be extended toinclude Ca2+ homeostasis and control of ion channels, modulation of other neu-rosecretory products, and effects on other biochemical pathways. They must alsobe able to predict an outcome that can be verified experimentally.

The interactions between NO and the immune system have not been examinedin detail in this review. However, many areas can benefit from NO biotransportmodeling, including the complex behavior of leukocytes in the microcirculation,leukocyte interactions with adhesion molecules, platelet aggregation, and throm-bosis in the bloodstream, and inflammatory processes in tissue. The modeling ofNO biotransport will naturally be extended to pathological conditions and maybe useful for evaluating therapeutic approaches directed at specific molecular orbiochemical pathways.

We can anticipate that this “startlingly simple” yet “bizarre” gas and its “ugly”byproduct will continue to challenge theoreticians and mathematical modelers inthe biomedical community for many more decades.

ACKNOWLEDGMENT

This work was supported in part by grant EY 09269 from NEI, NIH.

Visit the Annual Reviews home page at www.AnnualReviews.org

LITERATURE CITED

1. Culotta E, Koshland DE Jr. 1992. Mole-cule of the year. NO news is good news.Science258:1862–65

2. Furchgott RF, Zawadski JV. 1980. Theobligatory role of endothelial cells in therelaxation of arterial smooth muscle byacetylcholine.Nature228:373–76

3. Khan MT, Furchgott RF. 1987. Addi-tional evidence that endothelium-derivedrelaxing factor is nitric oxide. InPharma-cology, ed. MJ Rand, C Raper, pp. 341–44. Amsterdam: Elsevier

4. Ignarro LJ, Buga GM, Wood KS, ByrnsRE, Chaudhuri G. 1987. Endothelium-

derived relaxing factor produced and re-leased from artery and vein is nitric oxide.Proc. Natl. Acad. Sci. USA84:9265–69

5. Moncada S, Palmer RMJ, Higgs EA.1988. The discovery of nitric oxide asthe endogenous nitrovasodilator.Hyper-tension12:365–72

6. Palmer RMJ, Ferrige AG, Moncada S.1987. Nitric oxide release accounts forthe biological activity of endothelium-derived relaxing factor.Nature327:524–26

7. Murad F, Mittal CK, Arnold WP, KatusicS, Kimura H. 1978. Guanylate cyclase:

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.


138 BUERK

activation by azide, nitro compounds, ni-tric oxide, and hydroxyl radical and in-hibition by hemoglobin and myoglobin.Adv. Cyclic Nucleotide Res.9:145–58

8. Stamler JS, Singel DJ, Loscalzo J. 1992.Biochemistry of nitric oxide and its redox-activated forms.Science258:1898–902

9. Moncada S, Higgs A, Furchgott R.1997. International Union of Pharmacol-ogy nomenclature in nitric oxide research.Pharmacol. Rev.49:137–42

10. Nathan C. 1992. Nitric oxide as a secre-tory product of mammalian cells.FASEBJ. 6:3051–64

11. Gorren ACF, Schrammel A, Schmidt K,Mayer B. 1998. Effects of pH on the struc-ture and function of neuronal nitric oxidesynthase.Biochem J.331:801–7

12. Venturini G, Colasanti M, Floravanti E,Bianchini A, Ascenzi P. 1999. Direct ef-fect of temperature on the catalytic activ-ity of nitric oxide synthases types I, II, andIII. Nitric Oxide3:375–82

13. Henry Y, Guissani A. 1999. Interactionsof nitric oxide with hemoproteins: rolesof nitric oxide in mitochondria.Cell. Mol.Life Sci.55:1003–14

14. Wink DA, Darbyshire JF, Nims JE,Saavedraand JE, Ford PC. 1993. Reac-tions of the bioregulatory agent nitric ox-ide in oxygenated aqueous media: deter-mination of the kinetics for oxidation andnitrosation by intermediates generated inthe NO/O2 reaction.Chem. Res. Toxicol.6:23–27

15. Kharitonov VG, Sundquist AR, SharmaVS. 1994. Kinetics of nitric oxide autoxi-dation in aqueous solutions.J. Biol. Chem.269:5881–83

16. Lewis RS, Deen WM. 1994. Kinetics ofthe reaction of nitric oxide with oxygenin aqueous solutions.Chem. Res. Toxicol.7:568–74

17. Caccia S, Denisov I, Perrella M. 1999.The kinetics of the reaction between NOand O2 as studied by a novel approach.Biophys. Chem.76:63–72

18. Liu X, Miller MJS, Joshi MS, Thomas

DD, Lancaster JR Jr. 1998. Acceleratedreaction of nitric oxide with O2 within thehydrophobic interior of biological mem-branes.Proc. Natl. Acad. Sci. USA95:2175–79

19. Huie RE, Padmaja S. 1993. The reactionof NO with superoxide.Free Radic. Res.Commun.18:195–99

20. Goldstein S, Czapski G. 1995. The reac-tion of NO· with O2

−· and HO2·: a pulseradiolysis study.Free Radic. Biol. Med.19:505–10

21. Gibson QH, Roughton FJW. 1957. Thekinetics and equilibria of the reactions ofnitric oxide with sheep haemoglobin.J.Physiol.136:507–26

22. Cassoly R, Gibson QH. 1975. Conforma-tion, co-operativity and ligand binding inhuman hemoglobin.J. Mol. Biol.91:301–13

23. Morris RJ, Gibson QH. 1980. The roleof diffusion in limiting the rate of lig-and binding to hemoglobin.J. Biol. Chem.255:8050–53

24. Eich RF, Li T, Lemon DD, DohertyDH, Curry SR, et al. 1996. Mechanism ofNO-induced oxidation of myoglobin andhemoglobin.Biochemistry35:6976–83

25. Rohlfs RJ, Bruner E, Chiu A, GonzalesA, Gonzales ML, et al. 1998. Arterialblood pressure responses to cell-freehemoglobin solutions and the reactionwith nitric oxide. J. Biol. Chem.273:12128–34

26. Carlsen E, Comroe JH. 1958. The rate ofuptake of carbon monoxide and of nitricoxide by normal human erythrocytes andexperimentally produced spherocytes.J.Gen. Physiol.42:83–107

27. Liu X, Miller MJS, Joshi MS, Sadowska-Krowicka H, Clark DA, Lancaster JR Jr.1998. Diffusion-limited reaction of freenitric oxide with erythrocytes.J. Biol.Chem.272:18709–13

28. Vaughn MW, Huang K-T, Kuo L, LiaoJC. 2000. Erythrocytes possess an intrin-sic barrier to nitric oxide consumption.J.Biol. Chem.275:2342–48

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.



29. Doyle MP, Hoekstra JW. 1981. Oxidationof nitrogen oxides by bound dioxygen inhemoproteins.J. Inorg. Biochem.14:351–58

30. Zhao Y, Brandish PE, Ballou DP, Mar-letta MA. 1999. A molecular basis fornitric oxide sensing by soluble guany-late cyclase.Proc. Natl. Acad. Sci. USA96:14753–58

31. Denicola A, Souza JM, Radi R, Lissi E.1996. Nitric oxide diffusion in mem-branes determined by fluorescence quen-ching. Arch. Biochem. Biophys.328:208–12

32. Beckman JS, Beckman TW, Chen J, Mar-shall PA, Freeman BA. 1990. Apparenthydroxyl radical production by peroxini-trite: implications for endothelial injuryby nitric oxide and superoxide.Proc. Natl.Acad. Sci. USA87:1620–24

33. Fridovich I. 1995. Superoxide radicaland superoxide dismutases.Annu. Rev.Biochem.94:97–112

34. Burmeister T, Welch B, Reinhardt S,Hankeln T. 2000. A vertebrate globin ex-pressed in the brain.Nature407:520–23

35. Kon K, Maeda N, Shiga T. 1977. Effectof nitric oxide on the oxygen transport ofhuman erythrocytes.J. Toxicol. Environ.Health2:1109–13

36. Stone JR, Marletta MA. 1996. Spectraland kinetic studies on the activation ofsoluble guanylyl cyclase by nitric oxide.Biochemistry35:1093–99

37. Kharitonov VG, Sharma VS, Magde D,Koesling D. 1997. Kinetics of nitric oxidedissociation from five- and six-coordinatenitrosyl hemes and heme proteins, includ-ing soluble guanylate cyclase.Biochem-istry 36:6814–18

38. Margulis A, Sitaramayya A. 2000. Rateof deactivation of nitric oxide-stimulatedsoluble guanylate cyclase: influence of ni-tric oxide scavengers and calcium.Bio-chemistry39:1034–39

39. Bellamy TC, Wood J, Goodwin DA,Garthwaite J. 2000. Rapid desensitizationof the nitric oxide receptor, soluble guany-

lyl cyclase, underlies diversity of cellularcGMP responses.Proc. Natl. Acad. Sci.USA97:2928–33

40. Carter TD, Bettache N, Ogden D.1997. Potency and kinetics of nitric oxide-mediated vascular smooth muscle relax-ation determined with flash photolysis ofruthenium nitrosyl chlorides.Br. J. Phar-macol.122:971–73

41. Gow AJ, Luchsinger BP, Pawloski JR,Singel DJ, Stamler JS. 1999. The oxyhe-moglobin reaction of nitric oxide.Proc.Natl. Acad. Sci. USA96:9027–32

42. Gow AJ, Stamler JS. 1998. Reactionsbetween nitric oxide and haemoglobinunder physiological conditions.Nature391:169–73

43. Jia L, Bonaventura J, Stamler JS. 1996.S-nitrosohaemoglobin: a dynamic activ-ity of blood involved in vascular control.Nature380:221–26

44. Jourd’heuile D, Hallen K, Feelisch M,Grisham MB. 2000. Dynamic state of S-nitrosothiols in human plasma and wholeblood.Free Radic. Biol. Med.28:409–17

45. McMahon TJ, Stamler JS. 1999. Con-certed nitric oxide/oxygen delivery byhemoglobin.Methods Enzymol.301:99–114

46. Stamler JS, Jia L, Eu JP, McMahonTJ, Demchenko IT, et al. 1997. Bloodflow regulation by S-nitrosohemoglobinin the physiological oxygen gradient.Sci-ence276:2034–37

47. Yonetani T, Tsuneshige A, Zhou Y, ChenX. 1998. Electron paramagnetic reso-nance and oxygen binding studies ofα-nitrosyl hemoglobin. A novel oxy-gen carrier having NO-assisted allostericfunctions.J. Biol. Chem.273:20323–33

48. Gladwin MT, Ognibene FP, PannellLK, Nichols JS, Pease-Fye ME, et al.2000. Relative role of heme nitrosyla-tion and -cysteine 93 nitrosation in thetransport and metabolism of nitric oxideby hemoglobin in the human circulation.Proc. Natl. Acad. Sci. USA97:9943–48

49. Gladwin MT, Shelhamer JH, Schechter

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.


140 BUERK

AN, Pease-Fye ME, Waclawiw MA, et al.2000. Role of circulating nitrite and S-nitrosohemoglobin in the regulation of re-gional blood flow in humans.Proc. Natl.Acad. Sci. USA97:11482–87

50. Sheu F-S, Zhu W, Fung PCW. 2000.Direct observation of trapping and re-lease of nitric oxide by glutathione andcysteine with electron paramagnetic reso-nance spectroscopy.Biophys. J.78:1216–26

51. Trujillo M, Alvarez MN, Peluffo G, Free-man BA, Radi R. 1998. Xanthine oxidase-mediated decomposition of S-nitrosothi-ols.J. Biol. Chem.273:7828–34

52. Godber BLJ, Doel JJ, Sapkota GP, BlakeDR, Stevens CF, et al. 2000. Reductionof nitrite to nitric oxide catalyzed byxanthine oxidoreductase.J. Biol. Chem.275:7757–63

53. Zhang Z, Naughton D, Winyard PG,Benjamin N, Blake DR, Symons MCR.1998. Generation of nitric oxide by a ni-trite reductase activity of xanthine oxi-dase: a potential pathway for nitric oxideformation in the absence of nitric oxidesynthase activity.Biochem. Biophys. Res.Commun.249:767–72

54. Manukhina EB, Malyshev IY, Smirin V,Mashina SY, Saltykova VA, Vanin AF.1999. Production and storage of nitric ox-ide in adaptation to hypoxia.Nitric Oxide3:393–401

55. Lancaster JR Jr. 1994. Simulation of thediffusion and reaction of endogenouslyproduced nitric oxide.Proc. Natl. Acad.Sci. USA91:8137–41

56. Lancaster JR Jr. 1996. The diffusionof free nitric oxide.Methods Enzymol.268:31–50

57. Lancaster JR Jr. 1997. A tutorial on thediffusibility and reactivity of free nitricoxide.Nitric Oxide1:18–30

58. Wise DL, Houghton G. 1968. Diffusioncoefficients of neon, krypton, xenon, car-bon monoxide, and nitric oxide in waterat 10–60◦C. Chem. Eng. Sci.23:1211–16

59. National Research Council. 1928. Sol-

ubilities of gases in water. InInterna-tional Critical Tables of Numerical Data,Physics, Chemistry and Technology, ed. EWashburn, CJ West, NE Dorsey, pp. 255–61. New York: McGraw-Hill

60. Laurent M, Lepoivre M, Tenu JP. 1996.Kinetic modeling of the nitric oxide gradi-ent generated in vitro by adherent cells ex-pressing inducible nitric oxide synthase.Biochem. J.314:109–13

61. Chen B, Keshive M, Deen WM. 1998.Diffusion and reaction of nitric oxidein suspension cell cultures.Biophys. J.75:745–54

62. Lewis RS, Tamir S, Tannenbaum SR,Deen WM. 1995. Kinetic analysis ofthe fate of nitric oxide synthesized bymacrophages in vitro.J. Biol. Chem.270:29350–55

63. Buerk DG, Goldstick TK. 1982. Arterialwall oxygen consumption rate varies spa-tially. Am. J. Physiol. Heart Circ. Physiol.243:H948–58

64. Buerk DG, Goldstick TK. 1992. Spa-tial variation of aortic wall oxygen dif-fusion coefficient from transient po-larographic measurements.Ann. Biomed.Eng.20:629–46

65. Tsai AG, Friesenecker B, Mazzoni MC,Kerger H, Buerk DG, et al. 1998. Mi-crovascular and tissue oxygen gradients inthe rat mesentery.Proc. Natl. Acad. Sci.USA95:6590–95

66. Vaughn MW, Kuo L, Liao JC. 1998. Ef-fective diffusion distance of nitric oxidein the microcirculation.Am. J. Physiol.Heart Circ. Physiol.274:H1705–14

67. Vaughn MW, Kuo L, Liao JC. 1998.Estimation of nitric oxide production andreaction rates in tissue by use of a mathe-matical model.Am. J. Physiol. Heart Circ.Physiol.274:H2163–76

68. Malinski T, Bailey F, Zhang ZG, ChoppM. 1993. Nitric oxide measured by a por-phyrinic microsensor in rat brain aftertransient middle cerebral artery occlusion.J. Cereb. Blood Flow Metab.13:355–58

69. Butler AR, Megson IL, Wright PG. 1998.

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.



Diffusion of nitric oxide and scavengingby blood in the vasculature.Biochim. Bio-phys. Acta1425:168–76

70. Patel RP. 2000. Biochemical aspects ofthe reaction of hemoglobin and NO: im-plications for Hb-based substitutes.FreeRadic. Biol. Med.28:1518–25

71. Liao JC, Hein TW, Vaughn MW, HuangK-T, Kuo L. 1999. Intravascular flow de-creases erythrocyte consumption of ni-tric oxide. Proc. Natl. Acad. Sci. USA96:8757–61

72. Ye G-F, Park JW, Basude R, Buerk DG,Jaron D. 1998. Incorporating O2-Hb re-action kinetics and the F¨ahraeus effectinto a microcirculatory O2-CO2 transportmodel.IEEE Trans. Biomed. Eng.45:26–35

73. Ye G-F, Jaron D, Buerk DG, Chou M-C, Shi W. 1998. O2-Hb reaction kineticsand the F¨ahraeus effect during stagnant,hypoxic and anemic supply deficit.Ann.Biomed. Eng.26:60–75

74. Rengasamy A, Johns RA. 1996. Deter-mination of Km for oxygen of nitric ox-ide synthase isoforms.J. Pharmacol. Exp.Ther.276:30–33

75. Abu-Soud HM, Rousseau DL, Stuehr DJ.1996. Nitric oxide binding to the hemeof neuronal nitric-oxide synthase links itsactivity to changes in oxygen tension.J.Biol. Chem.271:32515–18

76. Dweik RA, Laskowski D, Abu-SoudHM, Kaneko FT, Hutte R, et al. 1998.Nitric oxide synthesis in the lung. Regu-lation by oxygen through a kinetic mech-anism.J. Clin. Invest.101:660–66

77. Otto CM, Baumgardner JE. 2001. Ef-fect of culture PO2 on macrophage (RAW264.7) nitric oxide production.Am. J.Physiol. Cell Biol.280:C280–87

78. Liao JK, Zulueta JL, Yu FS, Peng HB,Cote CG, Hassoun PM. 1995. Regulationof bovine constitutive nitric oxide syn-thase by oxygen.J. Clin. Invest.96:2661–66

79. Whorton AR, Simonds DB, PiantadosiCA. 1997. Regulation of nitric oxide syn-

thesis by oxygen in vascular endothelialcells.Am. J. Physiol. Lung Cell Mol. Phys-iol. 272:L1161–66

80. Kosaka H, Seiyama A. 1996. Physiolog-ical role of nitric oxide as an enhancerof oxygen transfer from erythrocytes totissues.Biochem. Biophys. Res. Commun.218:749–52

81. Boveris A, Costa LE, Cadenas E, Pode-roso JJ. 1999. Regulation of mitochon-drial respiration by adenosine diphos-phate, oxygen, and nitric oxide.MethodsEnzymol.301:188–98

82. Brown GC, Cooper CE. 1994. Nanomolarconcentrations of nitric oxide reversiblyinhibit synaptosomal respiration by com-peting with oxygen at cytochrome oxi-dase.FEBS Lett.356:295–98

83. Clementi E, Brown GC, Foxwell N,Moncada S. 1999. On the mechanismby which vascular endothelial cells regu-late their oxygen consumption.Proc. Natl.Acad. Sci. USA96:1559–62

84. Shen W, Hintze TH, Wolin MS. 1995.Nitric oxide. An important signalingmechanism between vascular endothe-lium and parenchymal cells in the regula-tion of oxygen consumption.Circulation92:350512

85. Trochu J-N, Bouhour J-B, Kaley G,Hintze TH. 2000. Role of endothelium-derived nitric oxide in the regulation ofcardiac oxygen metabolism.Circ. Res.87:1108–17

86. Koivisto A, Matthias A, Bronnikov G,Nedergaard J. 1997. Kinetics of the inhi-bition of mitochondrial respiration by NO.FEBS Lett.417:75–80

87. Gow AJ, Buerk DG, Ischiropoulos H.1997. A novel reaction mechanism for theformation of S-nitrosothiol in vivo.J. Biol.Chem.272:2841–45

88. Kharitonov VG, Sundquist AR, SharmaVS. 1995. Kinetics of nitrosation of thiolsby nitric oxide in the presence of oxygen.J. Biol. Chem.270:28158–64

89. Hyde RW, Geigel EJ, Olszowka AJ,Krasney JA, Forster RE II, et al. 1997.

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.


142 BUERK

Determination of production of nitricoxide by lower airways of humans theory.J. Appl. Physiol.82:1290–96

90. Tsoukias NM, George SC. 1998. A two-compartment model of pulmonary nitricoxide exchange dynamics.J. Appl. Phys-iol. 85:653–66

91. Tsoukias NM, Tannus Z, Wilson AF,George SC. 1998. Single-exhalation pro-files of NO and CO2 in humans: effect ofdynamically changing flow rate.J. Appl.Physiol.85:642–52

92. Hogman M, Drca N, Ehrstedt C, Meri-lainen C. 2000. Exhaled nitric oxide par-titioned into alveolar, lower airways andnasal contributions.Respir. Med.94:985–91

93. Edelman GM, Gally JA. 1992. Nitric ox-ide: linking space and time in the brain.Proc. Natl. Acad. Sci. USA89:11651–52

94. Garthwaite J, Charles S, Chess-WilliamsR. 1988. Endothelium-derived relaxingfactor release on activation of NMDA re-ceptors suggest role as intercellular mes-senger in the brain.Nature336:385–88

95. Bredt D, Snyder S. 1992. Nitric oxide, anovel neuronal messenger.Neuron8:3–11

96. Schuman EM, Madison DV. 1994. Lo-cally distributed synaptic potentiation inthe hippocampus.Science263:532–36

97. Wood J, Garthwaite J. 1994. Models ofthe diffusional spread of nitric oxide: im-plications for neural nitric oxide signalingand its pharmacological properties.Neu-ropharmacology33:1235–44

98. Philippides A, Husbands P, O’Shea M.2000. Four-dimensional neuronal signal-ing by nitric oxide: a computational anal-ysis.J. Neurosci.20:1199–207

99. Schweighofer N, Ferriol G. 2000. Dif-fusion of nitric oxide can facilitate cere-bellar learning: a simulation study.Proc.Natl. Acad. Sci. USA97:10661–65

100. Beckman JS, Koppenol WH. 1996. Nitricoxide, superoxide, and peroxynitrite: thegood, the bad, and ugly.Am. J. Physiol.Cell Physiol.271:C1424–37

101. Stanbro WD. 2000. Modeling the inter-

action of peroxynitrite with low densitylipoproteins. I. Plasma levels of peroxyni-trite. J. Theor. Biol.205:457–64

102. Stanbro WD. 2000. Modeling the inter-action of peroxynitrite with low densitylipoproteins. II. Reaction/diffusion modelof peroxynitrite in low-density lipopro-teins.J. Theor. Biol.205:465–71

103. Stanbro WD. 2000. Modeling the inter-action of peroxynitrite with low densitylipoproteins. III. The role of antioxidants.J. Theor. Biol.205:472–82

104. Chen AFY, O’Brien T, Katusic ZS.1998. Transfer and expression of recom-binant nitric oxide synthase genes in thecardiovascular system.Trends Neurosci.19:276–86

105. Archer S. 1993. Measurement of nitricoxide in biological models.FASEB J.6:3051–64

106. Shibuki K. 1990. An electrochemical mi-croprobe for detecting nitric oxide releasein brain tissue.Neurosci. Res.9:69–76

107. Malinski T, Taha Z. 1992. Nitric oxiderelease from a single cell measured in situby a porphyrinic-based microsensor.Na-ture358:676–78

108. Buerk DG, Riva CE, Cranstoun SD.1996. Nitric oxide has a vasodilatory rolein cat optic nerve head during flicker stim-uli. Microvasc. Res.52:13–26

109. Shibuki K, Okada D. 1991. Endoge-nous nitric oxide release required for long-term synaptic depression in the cerebel-lum. Nature349:326–28

110. Wakatsuki H, Gomi H, Kudoh M, Ki-mura S, Takahashi K, et al. 1998. Layer-specific NO dependence of long-term po-tentiation and biased NO release in layerV in the rat auditory cortex.J. Physiol.513:71–81

111. Stingele R, Wilson DA, Traystman RJ,Hanley DF. 1998. Tyrosine confoundsoxidative electrochemical detection of ni-tric oxide. Am. J. Physiol. Heart Circ.Physiol.274:H1698–704

112. Malinski T, Taha Z, Grunfeld S, Pat-ton S, Kapturczak M, Tomboulian P.

Ann

u. R

ev. B

iom

ed. E

ng. 2

001.

3:10

9-14

3. D

ownl

oade

d fr

om a

rjou

rnal

s.an

nual

revi

ews.

org

by U

nive

rsity

of

Tex

as -

Arl

ingt

on o

n 10

/01/

07. F

or p

erso

nal u

se o

nly.



1993. Diffusion of nitric oxide in the aortawall monitored in situ by porphyrinicmicrosensors.Biochem. Biophys. Res.Commun.193:1076–82

113. Buerk DG, Riva CE. 1998. Vasomotionand spontaneous low frequency oscilla-tions in blood flow and nitric oxide in catoptic nerve head.Microvasc. Res.55:103–12

114. Buerk DG, Atochin DN, Riva CE. 2001.Investigating the role of nitric oxide inregulating blood flow and oxygen deliv-ery from in vivo electrochemical measure-ments in eye and brain. InOxygen Trans-port to TissueXXII, ed. H Swartz, J Dunn,In press. New York: Plenum

115. Buerk DG, Lahiri S. 2000. Evidence thatnitric oxide plays a role in O2 sensingfrom tissue NO and PO2 measurementsin cat carotid body.Adv. Exp. Med. Biol.475:337–47

116. Bohlen HG. 1998. Mechanism of in-creased vessel wall nitric oxide concentra-tions during intestinal absorption.Am. J.Physiol. Heart Circ. Physiol.275:H542–50

117. Bohlen HG, Nase GP. 2000. Dependenceof intestinal arteriolar regulation on flow-mediated nitric oxide formation.Am. J.Physiol. Heart Circ. Physiol.279:H2249–59

118. Suzuki Y, Fujii S, Numagami Y, Tomi-naga T, Yoshimoto T, Yoshimura T. 1998.In vivo nitric oxide detection in the septicrat brain by electron paramagnetic reso-nance.Free Radic. Res.28:293–99

119. Loeb AL, Raj NR, Longnecker DE.1998. Cerebellar nitric oxide is increasedduring isoflurane anesthesia comparedto halothane anesthesia: a microdialy-sis study in rats.Anesthesiology89:723–30

Ann

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P1: FRK

June 13, 2001 11:34 Annual Reviews AR136-FM

Annual Review of Biomedical EngineeringVolume 3, 2001

CONTENTS

THOMAS MCMAHON: A DEDICATION IN MEMORIAM, Robert D. Howeand Richard E. Kronauer i

BIOMECHANICS OFCARDIOVASCULAR DEVELOPMENT, Larry A. Taber 1

FUNDAMENTALS OF IMPACT BIOMECHANICS: PART 2—BIOMECHANICSOF THEABDOMEN, PELVIS, AND LOWEREXTREMITIES, Albert I. King 27

CARDIAC ENERGY METABOLISM: MODELS OFCELLULARRESPIRATION, M. Saleet Jafri, Stephen J. Dudycha, and Brian O’Rourke 57

THE PROCESS ANDDEVELOPMENT OFIMAGE-GUIDED PROCEDURES,Robert L. Galloway, Jr. 83

CAN WE MODEL NITRIC OXIDE BIOTRANSPORT? A SURVEY OFMATHEMATICAL MODELS FOR ASIMPLE DIATOMIC MOLECULEWITH SURPRISINGLYCOMPLEX BIOLOGICAL ACTIVITIES, Donald G.Buerk 109

VISUAL PROSTHESES, Edwin M. Maynard 145

MICRO- AND NANOMECHANICS OF THECOCHLEAR OUTER HAIR CELL,W. E. Brownell, A. A. Spector, R. M. Raphael, and A. S. Popel 169

NEW DNA SEQUENCINGMETHODS, Andre Marziali and Mark Akeson 195

VASCULAR TISSUEENGINEERING, Robert M. Nerem and Dror Seliktar 225

COMPUTERMODELING AND SIMULATION OF HUMAN MOVEMENT,Marcus G. Pandy 245

STEM CELL BIOENGINEERING, Peter W. Zandstra and Andras Nagy 275

BIOMECHANICS OFTRABECULAR BONE, Tony M. Keaveny, Elise F.Morgan, Glen L. Niebur, and Oscar C. Yeh 307

SOFT LITHOGRAPHY IN BIOLOGY AND BIOCHEMISTRY, George M.Whitesides, Emanuele Ostuni, Shuichi Takayama, Xingyu Jiang, andDonald E. Ingber 335

IMAGE-GUIDED ACOUSTICTHERAPY, Shahram Vaezy, Marilee Andrew,Peter Kaczkowski, and Lawrence Crum 375

CONTROL MOTIFS FORINTRACELLULAR REGULATORY NETWORKS,Christopher V. Rao and Adam P. Arkin 391

vii

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June 13, 2001 11:34 Annual Reviews AR136-FM

viii CONTENTS

RESPIRATORYFLUID MECHANICS AND TRANSPORTPROCESSES, JamesB. Grotberg 421

INDEXESSubject Index 459Cumulative Index of Contributing Authors, Volumes 1–3 481Cumulative Index of Chapter Titles, Volumes 1–3 483

ERRATAAn online log of corrections toAnnual Review of BiomedicalEngineering chapters (1997 to the present) may be found athttp://bioeng.AnnualReviews.org/errata.shtml.

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can we model nitric oxide biotransport? a survey …...and a “bizarre molecule” because it is a...

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