Vol. 90, Issue 3, 777-788, March 2001
Microscopic modeling of NO and S-nitrosoglutathione
kinetics and transport in human airways
Hye-Won
Shin1 and
Steven
C.
George1,2
1 Department of Chemical and Biochemical Engineering and
Materials Science and 2 Center for Biomedical Engineering,
University of California, Irvine, California 92697
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ABSTRACT |
Nitric oxide (NO) appears in
the exhaled breath and is elevated in inflammatory diseases. We
developed a steady-state mathematical model of the bronchial mucosa for
normal small and large airways to understand NO and
S-nitrosoglutathione (GSNO) kinetics and transport using
data from the existing literature. Our model predicts that mean
steady-state NO and GSNO concentrations for large airways (generation 1) are 2.68 nM and 113 pM, respectively, in the
epithelial cells and 0.11 nM (~66 ppb) and 507 nM in the mucus. For
small airways (generation 15), the mean concentrations of NO
and GSNO, respectively, are 0.26 nM and 21 pM in the epithelial cells
and 0.02 nM (~12 ppb) and 132 nM in the mucus. The concentrations in
the mucus compare favorably to experimentally measured values. We
conclude that 1) the majority of free NO in the mucus, and thus exhaled NO, is due to diffusion of free NO from the epithelial cell and 2) the heterogeneous airway contribution to exhaled
NO is due to heterogeneous airway geometries, such as epithelium and
mucus thickness.
exhalation; inflammation; nitric oxide
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INTRODUCTION |
NITRIC OXIDE (NO) is
a freely diffusible molecule that performs many regulatory functions,
including smooth muscle relaxation, host defense, and inhibition of
platelet aggregation and neurotransmission (23, 57). In
addition, NO has also been detected in exhaled breath (56,
58). The fact that exhaled NO concentration increases in
inflammatory airway diseases such as asthma has generated interest in
using exhaled NO as a noninvasive marker of inflammation (11, 19,
24). However, the mechanisms underlying the production, consumption, and transport of NO within the lungs are not fully developed and have created difficulty in interpreting the exhaled NO signal.
Several isoforms of nitric oxide synthase (NOS) are found in many lung
cell types (macrophages, vascular endothelial cells, neurons,
fibroblasts, and epithelial cells) (23, 28, 43, 48, 72).
Thus exhaled NO arises from both the airway and the alveolar region of
the lungs and is strongly supported by theoretical studies aimed at
explaining the flow rate dependence of exhaled NO (49,
65). However, even within the airways, there is evidence of
heterogeneous contribution. Silkoff et al. (58)
demonstrated that the main bronchus and trachea generate more than 50%
of exhaled NO. Furthermore, DuBois et al. (14) evaluated
equilibrium NO concentrations in the gas phase and found values that
decreased from the trachea (56-266 ppb) to the respiratory
bronchioles (16-41 ppb). Currently, there is no physiological
explanation for this heterogeneous distribution of NO in the airway wall.
NO is a relatively reactive free radical and has a relatively
short in vivo half-life (0.1-15 s) (5).
S-nitrosoglutathione (GSNO) demonstrates NO-like bioactivity
(9, 22, 31) and, due to the abundance of glutathione (GSH)
in vivo, has been proposed as a possible carrier molecule for NO. GSNO
degrades in the presence of GSH in a complex manner, and the major
end-products are disulfide, ammonia, nitrous oxide, nitrite, and NO.
When the GSH-to-GSNO ratio is high (>10), ammonia, not NO, is the most
abundant end-product (61, 70). However, Gaston et al.
(24) demonstrated that tracheal S-nitrosothiol
concentration is significantly lower in asthmatic children compared
with controls, whereas expired airway NO concentration is higher. From
this result, Gaston et al. (24) proposed that
S-nitrosothiol breakdown is accelerated in asthma, which
leads to increased exhaled NO.
At present, there is adequate physical (dimensions and diffusivity) and
chemical (rate constants and concentrations) data in the literature to
begin a theoretical understanding of NO production, consumption, and
transport at the cellular level in the airways to test several
important hypotheses. The goal of this study is to design a plausible
microscopic (cellular level) steady-state model of NO, GSH, and GSNO
transport and kinetics in normal human airways. In doing so, we will
address the following hypotheses: 1) the heterogeneous
airway contribution of exhaled NO is due to heterogeneity in anatomical
structure and 2) catabolism of GSNO within the mucus is a
significant source of exhaled NO in normal subjects.
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MODEL DEVELOPMENT |
General structure.
The human conducting airways are generally considered to represent
generations 0 (trachea) to 17 (nonrespiratory
bronchiole). Each airway is regarded as a cylindrical tube whose wall
consists of a mucus layer, the epithelium, the lamina propria
(subepithelial connective tissue), and the smooth muscle. Although the
fibroblast and smooth muscle cell express NOS, they are unlikely
sources of exhaled NO due to the presence of the bronchial circulation in the lamina propria and smooth muscle. NO reacts rapidly with hemoglobin, and blood is generally considered to be an infinite sink
for NO (partial pressure of free NO in red blood cell < 0.5 ppb).
Mitochondria have been suggested as an important sink of NO due to
binding to cytochrome oxidase. However, the mitochondria content in the
lung is considerably lower compared with mitochondria-rich tissues such
as the heart and liver. In addition, ~50% of the total mitochondria
in the lung are estimated to be present within the type II alveolar
cells (18). Thus we predict a small number of mitochondria
in the conducting airway epithelial cells and neglect the mitochondrion
sink of NO in our model.
In addition, GSNO exists as a predominantly charged molecule in vivo
(acidic dissociation constant = 8.75) (1); thus, if GSNO is formed in the subepithelial tissue, free diffusion across the
intercellular tight junctions (12) would be minimal. In light of the chemical and physical features of the bronchial mucosa, our model neglects the subepithelial tissue layers and considers only
the epithelium and the mucous layer in understanding NO, GSH, and GSNO
kinetics and transport relevant to exhaled NO.
Figure 1 depicts the model structure for
the chemistry and transport of NO and GSNO in the epithelium and mucous
layers. Each compartment is assumed to be "well-mixed" or of
spatially uniform concentration. Conducting airway geometries for
generations 1 and 15 are listed in Table
1 and are considered to represent large
and small airways, respectively. A smaller mucus layer thickness is
expected in the lower generation (62). Therefore, the
ratio of epithelium to mucus thickness for both generations
1 and 15 is held constant at 10. Also, because the
ratio of mucus and epithelium thickness to that of the airway diameter
is <1, a one-dimensional Cartesian coordinate system is used.
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Fig. 1.
Schematic of model for nitric oxide (NO) and
S-nitrosoglutathione (GSNO) chemistry and transport in the
epithelium and mucus. NO is produced in the epithelium from NO synthase
(NOS) isoforms and has 3 fates: 1) diffuses to the blood
(Jb:eNO), 2) diffuses to the
mucus (Je:mNO), or 3) is consumed
with oxygen or superoxide in the presence of glutathione (GSH) to
produce GSNO. GSNO also has three fates: 1) reacts with GSH
to form NO (and other nitrogen products), 2) reacts with
superoxide, or 3) is transported across the epithelial
membrane. Once in the mucus, NO can diffuse into the airway lumen
(Jm:aNO) or react with oxygen and GSH to
form GSNO, while GSNO reacts with GSH. Solid and dashed arrows
represent chemical reaction and transport, respectively.
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NO is produced from NOS from the epithelial compartment, then either
undergoes a chemical transformation that produces GSNO or freely
diffuses to the mucus or to the bronchial circulation. GSNO is
transported into the mucus via facilitated diffusion. Once in the
mucus, NO and GSNO can again undergo several chemical reactions, or NO
can freely diffuse into the gas phase of the airway lumen. Oxygen
concentration (230 µM, equilibrium concentration with atmosphere) is
identical and constant in both the epithelium and mucus due to the
oxygen-rich environment in the lungs.
Chemistry and kinetics of NO, GSH, and GSNO.
In our model, we are interested in predicting steady-state
concentrations of NO and GSNO in the epithelium and mucus. To
accomplish this, we must develop a chemical framework that captures the
kinetic rate expressions that are likely to occur in vivo. Several
reactions are documented to occur in vivo, yet most rate constants are
measured in aqueous solution. Thus we assume that, within the
epithelium and mucus, the reaction kinetics of NO are similar to those
reported in aqueous systems.
NO can be consumed by two pathways. First, NO can react with oxygen to
form the intermediate N2O3 (reaction
1) (29, 69). Second, NO can react with superoxide to
produce peroxynitrite (reaction 2) (66, 71,
72). In reaction 1, N2O3 can
react with various molecules such as water, GSH, and protein-SH. In reaction 2, peroxynitrite reacts predominantly with either
GSH or CO2. Because the intracellular and extracellular
CO2 concentrations are high (~1-2 mM), the
peroxinitrite-CO2 reaction is regarded as one of the major
routes for eliminating peroxinitrite. This reaction is well documented,
accounting for 30-40% of the intracellular initial peroxinitrite
reactivity and >90% of extracellular initial peroxinitrite
reactivity. The relatively low intracellular contribution of the
peroxinitrite-CO2 reaction is due to a higher thiol
concentration (51).
Both intermediates generate GSNO, which can subsequently be consumed by
two different paths: 1) reaction with GSH (61)
(reaction 3) and 2) reaction with superoxide
(32) (reaction 4). This system of reactions is
described as
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(Reaction 1)
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(Reaction 2)
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(Reaction 3)
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(Reaction 4)
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The formulations of the kinetic rate expressions that follow from
reactions 1-4 are presented in APPENDIX A.
Bronchial epithelium.
We assume that NO is produced from NOS at a constant rate
(
NO), can be consumed by reactions 1 and
2, and can be produced or regenerated by reaction
3. Although the intracellular concentration of GSH (>5 mM) is
high, N2O3 reacts preferentially with
protein-SH, which is at even higher concentration, to generate
protein-SNO. The steady state ratio of GSNO to protein-SNO is
approximately 1:3 (15). Further, NO can react with
superoxide to produce peroxynitrite (reaction 2)
(34). Peroxynitrite can then react with GSH to form GSNO
and disulfide (33, 34, 52, 66). Furthermore, Balazy et al.
(2) demonstrated that GSNO2 is produced
preferentially over GSNO. Two additional studies demonstrated that GSNO
formation from this reaction has a yield of <1% (27,
47). Thus we assume a mean yield of 0.2% GSNO from
reaction 2 with high uncertainty (±100%).
Generated GSNO has three fates: 1) consumed by superoxide to
give disulfide and nitrite (32), 2) degraded by
reacting with GSH, or 3) transported to the mucous layer
intact. NO is generally accepted to diffuse freely, and there is no
need for a transporter system (38, 39). However, GSNO has
a high potential to use a special carrier system due to a relatively
large molecular weight (MW = 335.3) compared with NO and a
negative charge at physiological pH. It was suggested that
intracellularly generated GSNO is actively expelled from the cell, as
are other S-substituted glutathione derivatives (60,
63). S-ethylglutathion (ethyl-SG), a low molecular
weight and relatively hydrophilic thioether, is mainly transported
across the cell membrane by an electrogenic and saturable mechanism
(3). ATP increases this transport by only 10-20%. In
contrast, S-(2,4-dinitrophenyl)-glutathione (DNP-SG), a
larger and more hydrophobic anion, is transported by both ATP and
voltage-dependent carriers. From these results, Ballatori and Truong
(3) tentatively conclude that low molecular weight
glutathione S-derivatives are transported largely by an
electrogenic carrier system. Because GSNO is a relatively low molecular
weight hydrophilic thiol, we assume GSNO to be transported by a
saturable electrogenic carrier transport system characterized by
Michaelis-Menten kinetics (Vmax and
Km) to cross the apical membrane of the
epithelium (see APPENDIX B for detail).
On the basis of these assumptions and the rate expressions derived from
reactions 1-4 in APPENDIX A, the mass
balances for NO and GSNO in the epithelium, a well-mixed constant
volume compartment, can be written as follows for NO
![−<FR><NU>[<IT>&kgr;</IT><SUB>b:e</SUB>C<SUB>e,NO</SUB><IT>+&kgr;</IT><SUB>e:m</SUB>(C<SUB>e,NO</SUB><IT>−</IT>C<SUB>m,NO</SUB>)]</NU><DE><IT>l</IT><SUB>e</SUB></DE></FR>](/content/vol90/issue3/fulltext/777/img012.gif)
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(1)
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and for GSNO
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(2)
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where Ce,NO, Cm,NO, Ce,GSNO,
Ce,GSH, and
CO 2
represent the molar concentrations of each species in either the
epithelium (subscript e) or mucus (subscript m) and
le is the epithelium thickness. The rate
constants (k) are defined in reactions 1-4
or in APPENDIX A. For NO, the first term on the left-hand
side represents free diffusion to either the blood or the mucus.
b:e and
e:m represent mass transfer coefficients
between epithelium and blood and between epithelium and mucus,
respectively. The mass transfer coefficients are calculated from the
diffusion coefficient divided by the average length of diffusion
(APPENDIX B). The second term represents consumption and
production due to chemical reaction. The reaction between NO and oxygen
is accelerated ~300-fold in pure hydrophobic environments such as
liposomes and lipid bilayers (21, 41). However,
considering that the hydrophobic membrane makes up only 4% of the
volume in tissue, the actual acceleration will be a maximum of 10-fold.
Although our central value for the reaction rate of NO autoxidation
will be that in aqueous solution, we will consider the case in which
this reaction rate is increased by ~10-fold. The third term,
NO, represents the production rate of NO from NOS
isoforms per unit volume of tissue (55, 64).
For GSNO, the first term represents transport by an electrogenic
carrier. Vmax/Km is
a transport constant defined by Michaelis-Menten kinetics
(APPENDIX B). The second and third terms represent consumption and production, respectively, from chemical reaction. k1d and k2b describe GSNO
formation from the reaction of NO with oxygen and/or superoxide.
k3 represents NO formation from GSNO decomposition due to reaction with GSH, and k4
is the GSNO consumption rate constant by superoxide. Central or mean
values for all parameters are listed in Table
2.
Mucus.
We assume that the mucous layer has the physical properties of water
(i.e., diffusivity) and has a thickness of 10 µm (10) in
generation 1 and 2 µm in generation 15, such
that the epithelium-to-mucus thickness ratio remains constant. The
chemical reactions that occur in the mucus are identical to the
epithelium, except the concentrations of several substrates are
substantially different. Activated macrophages in the mucous layer may
produce superoxide and NO as well; however, we assume that these
sources are very small compared with the epithelium of normal human
airways (72). GSH concentration is substantially lower
(100-300 µM) than intracellular concentration and is assumed to
be constant (54). Thus the reaction of the nitrosating
intermediate N2O3 with GSH is competitive with hydrolysis (see APPENDIX A) (36). GSNO has a
negligible vapor pressure and thus cannot enter the gas phase; however,
free NO can enter the air stream by free diffusion. The gas phase
resistance is negligible (10), and the mass transfer
coefficient between the mucus and air is described in APPENDIX
B.
On the basis of these assumptions and the rate expressions in
APPENDIX A, the mass balance for NO and GSNO in the mucus
can be written as
![NO: <FR><NU>[−<IT>&kgr;</IT><SUB>m:a</SUB>(C<SUB>m,NO</SUB><IT>−</IT>C<SUB>air</SUB><IT>&lgr;</IT><SUB>m:a</SUB>)<IT>+&kgr;</IT><SUB>e:m</SUB>(C<SUB>e,NO</SUB><IT>−</IT>C<SUB>m,NO</SUB>)]</NU><DE><IT>l</IT><SUB>m</SUB></DE></FR>](/content/vol90/issue3/fulltext/777/img018.gif)
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(3)
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(4)
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For NO, the first term on the left hand side represents free
diffusion into either the gas phase or the epithelium, where lm is the mucous layer thickness and
Cair is the concentration of NO in the airway lumen.
Although Cair is strongly flow dependent (59,
65), we assume a mean constant value of 10 ppb for our steady-state simulation. The second term represents consumption and
production due to chemical reaction and has been previously described.
For GSNO, the first term represents transport across the
electrogenic carrier, and the second term represents consumption and
production due to chemical reaction.
Solution of governing equations.
Equations 1-4 represent the steady-state mass balances
for NO and GSNO in the epithelium and mucus. There are four dependent variables (Ce,NO, Ce,GSNO, Cm,NO,
Cm,GSNO) and eighteen independent parameters
(k1a, k1d,
k1e, k2a,
k2b, k3a,
k4a, k'w,
k'CO2,
b:e, e:m,
m:a, NO, Cair,
Ce,GSH, Cm,GSH,
CO 2 , and
Vmax/Km). These
four simultaneous nonlinear algebraic equations are solved by
computational iteration.
Sensitivity analysis.
The three major purposes of the sensitivity analysis are to
1) estimate the uncertainty ranges in our predicted
concentrations (model output) on the basis of uncertainties in the
input parameters, 2) identify the input parameters that have
the most significant impact on the output, and 3) establish
correlation among outputs. Because our system of nonlinear algebraic
equations did not have a closed form analytical solution, we chose a
statistical sampling technique called Latin Hypercube Sampling (LHS) to
perform the uncertainty and correlation of the output variables. McKay
et al. (44, 45) evaluated three Monte Carlo types of
sampling plans and demonstrated that LHS analysis is, computationally, the most efficient. LHS has been successfully used in several fields,
including physiological modeling (7).
To utilize LHS, model parameter values of importance are identified and
assigned central values and uncertainty ranges (Table 2). The
uncertainty ranges are estimated on the basis of the accuracy of
reported central values. We assigned uncertainty ranges of low
(<30%), medium (50%), or high (>80%). Rate constants involving superoxide concentration (k2a,
k2b, and k4a) have a high
uncertainty because in vivo superoxide concentration is difficult to
assess. In general, superoxide concentration is thought to range from 0.01 to 1 nM, with a mean of ~0.1 nM (34, 51). Due to
this wide range, we chose a log-normal distribution such that the
log of the superoxide concentration was equal to 
1 ± 100%. High uncertainty value was also assigned to the Michaelis-Menten
kinetic constant because no specific information is available for GSNO
transport from epithelial cell to mucus. In contrast,
k1a, k1d, and
Cair have relatively lower uncertainties (from ±10 to
±30%), and the mass transfer coefficients have medium uncertainties
(±50%) because they are relatively well characterized.
In our simulations, LHS utilized 100 model runs to achieve greater
statistical significance. To accomplish this, the value for each input
variable was divided into 100 equal probability density regions, based
on their uncertainty. Thus, during each of the 100 model runs, a single
value for each of the 18 parameters was chosen randomly and without
replacement from the 100 possible values. The results of LHS were then
used to generate the uncertainty in our model output by determining the
mean and quartiles from the 100 runs, as well as the correlation
coefficients between the outputs.
To examine the sensitivity between the 4 model output concentrations
and the 18 input parameters, the relative sensitivity was estimated by
a finite difference approximation (4)
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(5)
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where 
is the vector of the 4 model output variables,
is the vector of the 18 input parameters, j refers
to 18 input parameters, and i represents the selected input
parameter. Our sensitivity is strictly local (i.e., evaluated at the
central values of input parameters) and based on the change in model
output concentration with a small perturbation (1%) of parameter
i with all others held constant. Then, the
sensitivity is normalized by the parameter values before perturbation
for all of the parameters used to present relative sensitivity
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RESULTS |
NO and GSNO concentration in large airways.
Mean and quartiles of NO and GSNO concentrations for large airways
(generation 1) are summarized in Table
3 and Figs.
2 and 3. It
is evident from the mean and median (50% quartile) that the
concentrations do not have a normal distribution. NO concentrations in
the epithelium are approximately one order of magnitude larger than in
mucus (Fig. 2), whereas GSNO concentrations in the epithelium are
approximately three orders of magnitude smaller than in the mucus. On
the basis of experimental evidence of a rapid reaction in the cell
(41), increasing the reaction rate of NO autooxidation (k1a) by 10-fold had a negligible effect on NO
and slightly increased GSNO concentrations in both the epithelium and
mucus (~10%). Importantly, the concentrations in the mucus compare
favorably to the experimentally measured values listed in Table
4.
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Fig. 2.
NO concentrations in the epithelium (A) and
the mucus (B) from the 100 model simulations of Latin
Hypercube Sampling (LHS) for generation 1 (large airways)
and generation 15 (small airways). Boxes represent 1 SD;
vertical bars represent 10-90th percentiles. Lines within the
boxes represent mean and median concentrations.  ,
Extreme values from the 100 simulations.
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Fig. 3.
GSNO concentrations in the epithelium (A) and
the mucus (B) from the 100 model simulations of LHS for
generations 1 and 15. See Fig. 2 for symbols.
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NO and GSNO concentration in small airways.
For generation 15, our model-predicted mean and quartiles of
NO and GSNO concentrations are summarized in Table 3 and Figs. 2 and 3.
The patterns of NO and GSNO in the epithelium and mucus are similar to
generation 1; however, the concentrations of both NO and
GSNO are substantially smaller than in generation 1. Again, increasing the rate of NO autooxidation had no discernable impact on
the predicted concentrations. As with generation 1, the
mucus concentrations still compare favorably to the experimentally
measured values listed in Table 4.
Sensitivity analysis.
The estimated relative sensitivity of each parameter is summarized in
Table 5, and the correlation coefficients
between predicted NO and GSNO concentrations in epithelium and mucus
are presented in Table 6. We are
particularly interested in the parameters that impact mucus NO
concentration. Values of 
> 0.1 are shown in Table 5. For
generation 1, NO, mass transfer, and
reaction with superoxide are important parameters for both NO and GSNO. In addition to these parameters, GSNO is also sensitive to the reaction
with GSH in the mucus, facilitated transport in the epithelium, and the
reaction with carbon dioxide in both layers.
The relative importance of consumption by superoxide for NO is
decreased from generation 1 to generation 15. For
generation 15, airway NO concentration and mass transfer
from mucus to airway (m:a) are the most important
parameters for determining mucus NO concentration. Mucus NO
concentration is approximately five times more sensitive to
Cair compared with that of the large airway. This reflects
the relative magnitude of the mucus NO concentration in these regions
(66 vs. 12 ppb) to that of Cair (10 ppb). Also, mucus layer
NO is not affected by GSNO decomposition (see reaction 3).
Mucus NO concentration is highly correlated to epithelial NO
concentration (Table 6) but not with GSNO concentration in either epithelium or mucus. This is consistent with the overall mass transfer
coefficients b:e,
e:m, and
m:a impacting the predicted concentrations for both generations (Table 5).
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DISCUSSION |
Chemical reaction.
The epithelium is a rich environment for both superoxide and oxygen;
thus NO may be consumed by either of these substrates. However, only
the superoxide-mediated reaction is important within the epithelium
(21), because the autooxidation of NO is very slow. This
is not only evident in the sensitivity indexes (Table 5) but is also
shown in Figs. 4 and
5 (NO and GSNO, respectively), which show
the relative magnitude of each term in the governing equations at
steady state. Note the magnitude of reaction 1 is negligible
for both NO and GSNO, but reaction 2 is significant in the
epithelium. In addition, a 10-fold acceleration in the rate of NO
autoxidation (41), considering that the membrane volume in
tissue is only ~4% of the total tissue volume, predicts negligible
change in the predicted concentrations of NO and GSNO. This provides
further evidence that NO autooxidation does not impact NO
concentrations in vivo.
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Fig. 4.
Magnitude of diffusion fluxes and rates of reactions of
NO at steady state for generations 1 and 15 in
the epithelium and the mucus. A: NO in the epithelium.
B: NO in the mucus. Negative and positive values refer to
either a decrease or increase, respectively, in NO within the
compartment. Note that the ranges of values for each axis are
substantially different due to the wide range of values within the
compartments.
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Fig. 5.
Magnitude of diffusion fluxes and rates of reactions of
GSNO at steady state for generations 1 and 15 in
the epithelium (A) and the mucus (B). Negative
and positive values refer to either a decrease or increase,
respectively, in GSNO within the compartment. Note that the ranges of
values for each axis are substantially different due to the wide range
of values within the compartments.
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A particularly interesting result is that GSNO catabolism (by reacting
with GSH) has minimal effect on NO concentrations. This result occurs
even under the extreme case of NO as the only nitrogen product. In
fact, a high ratio of GSH to GSNO (>1,000) occurs in the epithelium
and mucus, which would favor NH3 as the end product
(61, 70) and would further reduce the impact of GSNO
catabolism as a source of NO. The explanation for this finding is
presented in Figs. 4 and 5. It is apparent that the flux of NO due to
diffusion from the epithelium is much larger than the rate of GSNO
catabolism in the mucus (see reaction 3 and Fig. 4B). Thus, under normal conditions, free diffusion of NO is
the major source of exhaled NO, and we are forced to reject our second hypothesis.
The role of GSNO as a NO donor is under investigation, particularly in
disease states such as asthma. Gaston et al. (24) suggest
that GSNO catabolism is a source of NO in asthma and may proceed by a
different mechanism, such as enzyme catalysis. Recent experiments by
Hunt et al. (30) support this hypothesis by providing evidence for a different environment in asthma such as airway acidification. Thus the rate of reaction may be accelerated relative to
the normal lungs.
Superoxide concentration is difficult to measure due to its extremely
short half-life. Experimental estimates are difficult to make but
suggest an intracellular concentration of ~0.01-1 nM (50,
72). In light of these characteristics of superoxide, we posed a
high uncertainty (±100%) for the superoxide-mediated reactions. Under
these conditions, superoxide has a large impact on GSNO concentrations
in large and small airways and impacts NO in large airways. The lack of
an impact of superoxide on NO in small airways is due to the smaller
dimensions and, thus, an even greater role of molecular diffusion. In
other words, diffusion is rapid enough that there is not sufficient
time for chemical reaction with superoxide to be critical. In addition,
conditions that alter superoxide levels in the lung, such as
inflammatory diseases, may have a significant effect on GSNO levels.
However, this source of superoxide can be from activated macrophages in the mucus, which would be an additional term in our governing equations.
Mass transfer.
The free diffusion of NO between the bronchial circulation, the
epithelium, and the airway lumen is described using three mass transfer
coefficients (b:e,
e:m, and m:a). A linear
concentration profile is not truly valid due to chemical reaction
(6). In addition, there will also be mixing in the
epithelium and mucus. Thus the simplifying assumptions used in
APPENDIX B to estimate values for the mass transfer
coefficients are only to identify central values. Thus the uncertainty
posed by the LHS analysis considers the impact of mixing and chemical reaction.
As evidenced by the LHS analysis and Fig. 4, our model predicts that
e:m and m:a are
major parameters in determining NO in the mucus (Tables 5 and 6). In
addition, if the mucus thickness is increased from 2 to 10 microns in
the small airways, the flux between the mucus and airway per unit
volume significantly decreases from 5.4 to 2.2 nmol · l
1 · s1. This
decrease in the loss of NO to the air stream is due to increased
resistance to diffusion through a thicker mucus layer. Thus the
difference in dimensions of the epithelium and mucus in large and small
airways has a profound effect on the steady-state concentrations of NO,
which lends credence to our first hypothesis.
Interestingly, our model predicts that only ~25-30% of the NO
produced by NOS within the epithelial cell reaches the airway lumen
(Fig. 4) for generations 1 and 15. The bronchial
circulation and superoxide (reaction 2) consume the
remaining NO. There is substantial variability in the exhaled NO levels
within normal subjects. This finding might be explained by the high
sensitivity to the rate of consumption by chemical reaction with,
primarily, superoxide and hemoglobin, as well as heterogeneity in the
physical features of the airway mucosa. This also places critical
importance on developing noninvasive indexes that characterize physical
characteristics of the airways, such as tissue thickness and production
rate of NO as opposed to exhaled NO concentration, if NO is to be used as a clinical indicator of inflammatory diseases.
The facilitated transport of GSNO through the cell membrane primarily
impacts the epithelial concentration of GSNO. This finding reflects the
relative unimportance of GSNO in determining NO concentrations that has
been previously described. GSNO concentrations in the epithelial cell
are predicted to be approximately three orders of magnitude smaller
than in the mucus (Fig. 3), due to the fact that very little GSNO is
produced (disulfide is the main oxidation product) and most of what is
produced is actively transported to the mucus. GSNO decomposition with
GSH does not impact epithelial GSNO concentration, yet it is important
in determining mucus GSNO concentration (Fig. 5). This finding reflects
the higher GSNO concentration in the mucus layer. An electrogenic
carrier for GSNO in the epithelial apical membrane does not affect
mucus NO (Table 5) because changes in
Vmax/Km are offset by opposite
changes in epithelial GSNO concentrations; thus the product (or net
flux) remains a constant.
It is important to emphasize that no direct evidence exists for an
electrogenic carrier of GSNO; however, there is strong evidence for a
carrier of similar S-substituted glutathione derivatives (3, 60, 63). Further experimentation is necessary to
document its definitive existence.
Production rate.
The production rate of NO has a substantial impact on NO and GSNO
concentrations in both the epithelial cell and the mucus. This
important prediction is consistent with experimental findings in
inflammatory diseases in which iNOS expression (and thus NO production
rate) as well as exhaled NO is increased (i.e., increased mucus
concentration of NO) (11, 72).
Previous reports reveal that the absolute amount of iNOS decreases with
increasing generation number (37, 68, 72). This might
suggest a decreasing production rate of NO. However, it is difficult to
assess whether NO production per unit volume is changed for large and
small airways. According to our simulation results, the ratio of
exhaled NO concentration in generation 1 to that of
generation 15 is ~5 (66 vs. 12 ppb). These results are
consistent with the trend in the experimental data of DuBois et al.
(14). According to their reported experimental data, the
mean equilibrium concentration of NO in the respiratory bronchioles (16 ppb) is ~1/3 of the concentration in the larger airways (56 ppb). For
our model to predict this ratio, NO production per unit volume would be
~3 times greater in the lower airways. Whereas this is certainly a
possible and nonintuitive prediction, it is unlikely. A more likely
explanation is that the experimental data of Dubois et al.
(14) represent data from in situ airways in which a
steady-state breath-to-breath NO concentration profile is established.
In this scenario, upper airway NO is convected to the lower airways
during inspiration, thus impacting Cair (note the
importance of Cair in Table 5 in determining NO
concentration in generation 15) and may impact the partial
pressure of NO in the lower airways. Our simple steady-state model does
not consider interaction between upper and lower airways.
In conclusion, our proposed model successfully predicts
endogenous NO and GSNO concentration in the epithelium and the mucus layer for different airway generations. According to our simulation, a
fraction of intracellular NO consumption leads to GSNO formation; however, the majority of free NO in the mucus layer, and thus exhaled
NO, is due to diffusion of free NO from the epithelial cell and not
from GSNO catabolism in normal subjects. In addition, decreasing
epithelial and mucus thickness decreases steady-state NO
concentrations by increasing the rate of NO lost to the blood and air
by free diffusion. We conclude that free diffusion (i.e., airway
geometry), chemical consumption by superoxide, and production by NOS
are the critical phenomenon in understanding the dynamics of NO
transport in normal human airways, and catabolism of GSNO is relatively unimportant.
| |
APPENDIX A |
Rate Expressions for NO and GSNO
Epithelium.
reaction 1.
By applying steady-state approximation for the reaction intermediates,
NO2 and N2O3, one can write the
following rate expressions for CNO and CGSNO
|
(A1)
|
|
(A2)
|
where oxygen concentration is assumed to be constant at
230 µM.
Kharitonov et al. (36) demonstrated that the rate of GSNO
formation is independent of GSH concentration if GSH concentration exceeds 5 mM. Also, Singh et al. (61) verified that, under
excess GSH concentration, N2O3 reacts
preferentially with GSH to generate GSNO. In spite of fairly high
concentrations of GSH in mammalian cells (~5 mM), protein-associated
thiols are present in ~3× larger quantities than low molecular
weight thiols, including GSNO (15). Therefore, we consider
protein-thiols as competing targets for nitrosation of
N2O3 with GSH. Also, we can neglect hydrolysis of N2O3
(k1cCH2O < k1dCGSH + k1eCprotein-SH). Therefore,
Eq. A2 simplifies to
|
(A3)
|
where k'p-SH = k1eCp-SH.
REACTION 2.
The rate expressions for reaction 2 can be written as
follows
|
(A4)
|
|
(A5)
|
By applying the steady-state approximation for the
intermediate peroxynitrite (ONOO), Eq. A5 can
be written as
|
(A6)
|
where
k'CO2 = k2cCCO2. Here, we
assumed that only 0.2% of the product of reaction 2 results
in GSNO formation (see text for details).
REACTION 3.
Rate expressions for reaction 3 can be written as follows,
with the simplifying assumption that GSH concentration remains constant
in either the epithelium or the mucus
|
(A7)
|
|
(A8)
|
REACTION 4.
The rate expression for reaction 4 can be written as follows
|
(A9)
|
Mucus.
reaction 1.
The reaction mechanism is the same as reaction described for the
epithelium. However, GSH concentration in the mucus (200 µM) is much
lower than that in the epithelium (5 mM) (54). Therefore, the NO consumption rate is the same, but the GSNO formation reaction with N2O3 competes with its hydrolysis, and is
described by
|
(A10)
|
where k'w = k1cCH2O. In addition, we
assume very low protein-associated thiols in the mucus due to
relatively low membrane permeability (19).
REACTION 3.
The rate mechanism is identical to that in the epithelium, with the
exception that the GSH concentration is lower (200 µM).
| |
APPENDIX B |
Transport Mechanisms
Overall mass transfer coefficients.
The flux of mass between compartments is calculated using an overall
mass transfer coefficient multiplied by the mean concentration difference between the two compartments. The overall mass transfer coefficient is equivalent to a conductance or the inverse of a resistance. For simple steady-state homogeneous diffusion without chemical reaction within a slab, the mass transfer coefficient can be
expressed by the diffusion coefficient of the solute in the slab
divided by the length of diffusion (Fick's first law of diffusion)
(6, 16). The assumption produces a linear concentration profile within the slab, which we know does not occur within a heterogeneous cell or the mucus. However, this technique can be used to
identify a central value, and the uncertainty used in the LHS analysis
accounts for mixing and chemical reactions.
Defining the mass transport from the midpoint of one compartment to the
midpoint of an adjacent one, each overall mass transfer coefficient is
then a combination of each half of adjacent layers. For example, the
central value for the overall mass transfer coefficient between the
epithelium and the mucus, e:m, is
described by
|
(A11)
|
where the first term represents the resistance from one-half of
the epithelium, and second term is the resistance from one-half of the
mucus. De and
Dm are the diffusion coefficients of the solute (i.e., NO) in the epithelium and mucus, respectively.
b:e and
m:a are obtained in an analogous
fashion. In addition, 
b:e and
e:m are assumed to = 1 (26), whereas m:a = 0.0416 for NO (64).
The diffusion coefficient of GSNO in the mucus was estimated from the
Wilke-Chang method. The molar volume of solute was obtained from the
additive method suggested by Schroeder (6, 53). Based on
these methods, and assuming that mucus has the physical characteristics
of water, the diffusion coefficient of GSNO in the mucus is
~0.54 × 105 cm2/s. The diffusion
coefficient of NO in the mucus is ~3.2 × 105
cm2/s on the basis of an experimental measurement
(42). The diffusion coefficient of NO and GSNO in the
epithelium are assumed to be one-third of their value in water
(25).
GSNO-Facilitated Transport
We assume that GSNO is transported across the epithelial cell
membrane by a transporter in the same fashion as other
S-substituted glutathione derivatives (3). This
mechanism can be expressed by Michaelis-Menten kinetics as follows
|
(A12)
|
where superscript e and m represent epithelial and
mucus, respectively, and T represents an epithelial membrane
transporter. By applying the Michaelis-Menten analysis, one can write
the following rate expression for Cm,GSNO
|
(A13)
|
where Vmax = k6CT and CT is the
concentration of transporters. Eq. A13 then reduces to
|
(A14)
|
for the case of Km > Ce,GSNO (3). As of yet, there is no exact
experimental evidence for GSNO transport. Therefore, the central values
of Vmax/Km are
estimated from previously reported values of S-substituted
glutathione derivative (3).
| |
ACKNOWLEDGEMENTS |
We thank Dr. Donald Dabdub of the Dept. of Mechanical and Aerospace
Engineering for helpful discussions regarding the sensitivity analysis.
| |
FOOTNOTES |
This work was supported by National Science Foundation Grant
BES-9875033 and National Institutes of Health Grant R29-HL-60636.
Address for reprint requests and other correspondence: S. C. George, Dept. of Chemical and Biochemical Engineering and Materials Science, 916 Engineering Tower, Univ. of California, Irvine, Irvine, CA
92697-2575 (E-mail: scgeorge{at}uci.edu).
The costs of publication of this
article were defrayed in part by the
payment of page charges. The article
must therefore be hereby marked
"advertisement"
in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.
Received 28 January 2000; accepted in final form 5 September 2000.
| |
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