Pulmonary reduction of an intravascular redox polymer

Said H. Audi1,2, Robert D. Bongard3, Yoshiyuki Okamoto4, Marilyn P. Merker1,5,6, David L. Roerig5,6,7, and Christopher A. Dawson1,2,3,5,6,7

1 Department of Biomedical Engineering, Marquette University, Milwaukee 53201-1881; Departments of 2 Pulmonary and Critical Care Medicine, 3 Physiology, 5 Anesthesiology, and 6 Pharmacology/Toxicology, Medical College of Wisconsin, Milwaukee 53226; 7 Zablocki Veterans Affairs Medical Center, Department of Veterans Affairs, Milwaukee, Wisconsin 53295; and 4 Department of Chemistry, Polytechnic University, Brooklyn, New York 11201


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Pulmonary endothelial cells in culture reduce external electron acceptors via transplasma membrane electron transport (TPMET). In studying endothelial TPMET in intact lungs, it is difficult to exclude intracellular reduction and reducing agents released by the lung. Therefore, we evaluated the role of endothelial TPMET in the reduction of a cell-impermeant redox polymer, toluidine blue O polyacrylamide (TBOP+), in intact rat lungs. When added to the perfusate recirculating through the lungs, the venous effluent TBOP+ concentration decreased to an equilibrium level reflecting TBOP+ reduction and autooxidation of its reduced (TBOPH) form. Adding superoxide dismutase (SOD) to the perfusate increased the equilibrium TBOP+ concentration. Kinetic analysis indicated that the SOD effect could be attributed to elimination of the superoxide product of TBOPH autooxidation rather than of superoxide released by the lungs, and experiments with lung-conditioned perfusate excluded release of other TBOP+ reductants in sufficient quantities to cause significant TBOP+ reduction. Thus the results indicate that TBOP+ reduction is via TPMET and support the utility of TBOP+ and the kinetic model for investigating TPMET mechanisms and their adaptations to physiological and pathophysiological stresses in the intact lung.

lung metabolism; oxidation-reduction; mathematical modeling; superoxide; ascorbate


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TRANSPLASMA MEMBRANE ELECTRON TRANSPORT (TPMET) systems exist in various cell types (12, 18, 19, 21, 30, 31, 33, 39, 41) and have been implicated in a wide range of functions (5, 6, 11, 12, 18, 20, 21, 23, 28, 29, 32, 33, 35, 37, 39). Vascular endothelial TPMET (7-9, 15, 26, 27) is unique in its potential for influencing plasma redox status. For example, vascular endothelial cells, along with monocytes, are the key cell types involved in atherosclerotic plaque formation (38, 39). They are commonly thought to promote plasma lipoprotein oxidation (39), but in the absence of free transition metal ions, they have an antioxidant influence on plasma lipoproteins (18, 39). Both the prooxidant and antioxidant effects can be explained by TPMET systems that can either promote oxidation by reducing metal ions (15, 18, 40) or protect lipoproteins from oxidation by regenerating lipoprotein antioxidants (2, 8, 14, 19, 30). The pulmonary endothelium is particularly interesting in this regard because it is a large reactor surface upstream from the vulnerable systemic arterial system wherein the toxic effects of oxidized lipoproteins are manifest (38), but the local endothelial surface area-to-blood flow ratio is relatively very small. Additional consequences of pulmonary endothelial TPMET may include the pulmonary endothelial targeting of redox-active toxins (7, 19).

Thiazine electron acceptors have been used as probes for studying pulmonary endothelial TPMET because their redox status is easily measured (4, 7, 14, 26) and because they are electron acceptors (i.e., substrate analogs) for reductases acting on many physiologically, pharmacologically, and toxicologically important redox-active compounds (16). The TPMET system demonstrated in pulmonary arterial endothelial cells grown in culture undoubtedly contributes to the reduction of thiazine electron acceptors on passage through the lungs (4, 7, 14, 26). However, the role of endothelial TPMET within intact lungs in the overall reduction process is more difficult to assess than in cell culture. This is, in part, because the cells are not directly accessible, which contributes to the difficulty in demonstrating whether a given electron acceptor probe might have been taken up and reduced intracellularly during transit through the lungs (4, 7) and/or whether some short-lived reducing agent might have been released by the lungs (3, 10, 22, 32). Therefore, the objective of the present study was to evaluate the role of endothelial TPMET in the reduction of thiazine electron acceptors within the lungs, and, in doing so, to develop a methodological basis for future investigations into the physiological and pathophysiological adaptations of pulmonary endothelial TPMET.

Experiments were carried out with isolated rat lungs perfused with an electron acceptor, toluidine blue O (TBO) covalently bound to a polyacrylamide (TBOP) polymer (9), that was too large to enter the cells or pass through the capillary wall in a significant quantity over the time course of the experiment. Thus reduction of the TBOP polymer from its blue oxidized form (TBOP+) to its colorless reduced form (TBOPH) on passage through the lungs is indicative of reduction within the vessel lumen. The possibility that some short-lived and/or low molecular weight reductant(s) released by the lungs might contribute to TBOP+ reduction was also evaluated, and a kinetic analysis of the data was carried out to assist in their interpretation.


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The isolated rat lung preparation used has been previously described (25). Each rat [314 ± 42 (SD) g] was anesthetized (pentobarbital sodium 0.040 mg/g body wt ip). The trachea was clamped, and the chest was opened. Heparin (200 IU in 0.2 ml) was injected into the right ventricle. The pulmonary artery, left atrium, and trachea were cannulated with polyethylene tubing (1.67-mm ID, 2.42-mm OD). The lungs were removed from the chest, and the respective cannulas were attached to the ventilation and perfusion system. The physiological salt solution (PSS) perfusate was maintained at 35°C and contained (in mM) 4.7 KCl, 2.51 CaCl2, 1.19 MgSO4, 2.5 KH2PO4, 118 NaCl, 25 NaHCO3, 5.5 glucose, and 5% bovine serum albumin. The initial volume (~40 ml) of perfusate pumped (MasterFlex roller pump) through the lungs was discarded until the lungs and venous effluent were visually clear of blood. The venous effluent was then sent into a reservoir, from which it was pumped back into the pulmonary artery at a flow rate of 10 ml/min. The total volume of the recirculating perfusion system including the lung vascular volume [~0.85 ml (14)] was ~16 ml. The lungs were ventilated with 8 mmHg end-inspiratory and 3 mmHg end-expiratory pressures at 40 breaths/min and a gas composition of 15% O2 and 6% CO2 in N2, giving perfusate PO2, PCO2, and pH values of 139 ± 11 (SD) Torr, 35 ± 3 Torr, and 7.36 ± 0.02, respectively. The left atrial pressure was set at atmospheric pressure. The pulmonary arterial pressure relative to the left atrium was continuously monitored during the course of the experiments and averaged 6.5 ± 0.8 (SD) mmHg at the beginning and 5.6 ± 0.9 (SD) mmHg at the end of the perfusion periods, delimiting the experimental protocols described below. At the end of the experiments, the lungs were weighed, dried, and reweighed. The lung wet weight averaged 1.45 ± 0.31 (SD) g, with a wet-to-dry weight ratio of 5.57 ± 0.76 (SD).

The TBOP polymer was synthesized as previously described (9). For the batch used in these experiments, the average molecular weight was ~35,000, and molecular weight distribution was such that the fractions passing through 3,500, 10,000 and 30,000 molecular weight cutoff filters were not detectable, 3.5%, and 31%, respectively. There were ~32 nmol redox-active TBO moieties/mg, determined as previously described (9). Absorption spectra of the oxidized form (TBOP+) and the fully reduced form (TBOPH), produced by anaerobic reduction with xanthine oxidase plus hypoxanthine in a Thunberg cuvette, are shown in Fig. 1.


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Fig. 1.   Absorption spectra for the oxidized (TBOP+) and reduced (TBOPH) forms of toluidine blue O polyacrylamide (TBOP).

To study TBOP disposition in the perfused lungs, the recirculating perfusate volume was decreased to 8 ml and then immediately replenished at time 0 by adding 8 ml of perfusate containing 4 mg/ml of TBOP+ equilibrated with the respiratory gas mixture at the perfusion system temperature. Thus the initial concentration in the total perfusate volume was 2 mg/ml. To evaluate the contribution of superoxide and ascorbate released by the lungs to the reduction process, in some experiments, the 8 ml containing the TBOP+ also contained either superoxide dismutase (SOD; 2,080 U) or ascorbate oxidase (AO; 144 U). The TBOP-containing perfusate was recirculated through the lungs for 20-60 min. At the specific times indicated in EXPERIMENTAL RESULTS, 1 ml of lung effluent was collected for spectrophotometric analysis (Beckman DU 7400). To determine the TBOP+ concentration in a sample, it was immediately centrifuged (5,500 g for 40 s in a Costar microcentrifuge), and absorbance was measured at 590 and 750 nm. The centrifugation was carried out to eliminate turbidity due to any red cells that might not have been completely removed during the washing period, and the absorbance at 750 nm was subtracted from that at 590 nm as an additional check on turbidity. The sample was then returned to the recirculating perfusion system. To determine the amount of TBOPH and the rate of TBOPH autooxidation in selected samples, the samples were placed immediately in the spectrophotometer and absorbance was recorded continuously until a steady level was achieved by a maximum of ~40 min. At that point, the sample was centrifuged, and the absorbance was measured again.

Any possible contribution of the perfusate and perfusion system tubing to the observed TBOP+ reduction under the experimental conditions was evaluated by carrying out the same experiments except with the rat lungs replaced by an additional length of tubing (sham lung) of approximately equal volume.

Additional experiments were carried out with the lungs in which the 8 ml added at time 0 was plain PSS containing no TBOP. These TBOP-free experiments were used to obtain conditioned PSS to evaluate the possibility that recirculation through the lungs might result in spectral properties interfering with the TBOP+ measurement and/or the possibility that the lungs might release some TBOP+ reductant(s) into the perfusate. Samples obtained at the usual sampling times had no above-blank absorbance at 590 nm, ruling out the first of these possibilities. The possible release of a TBOP+ reducing agent was examined by adding TBOP+ (2 mg/ml; note that this and the subsequently indicated reagent concentrations are the initial concentrations in total reaction mixture volume) to the samples removed after 0, 10, and 30 min of recirculation through the lungs, and the absorbance was continuously measured for the subsequent 25 min or longer, if necessary, to reach steady level. Because of the known release of ascorbate by perfused lungs (1, 10), the same procedure was also carried out with AO (9 U/ml) added to the conditioned medium, and the conditioned perfusate samples were also assayed for ascorbate as previously described (10).

For each of the above experiments, a sample of the PSS containing 4 mg/ml of TBOP+ that was added to the lung perfusion circuit was diluted 1:1 with plain PSS. The absorbances of the fully oxidized (TBOP+) and fully reduced (TBOPH) mixtures served to set the range for calculating the concentration of TBOP+ in the lung and sham effluents and conditioned perfusate samples and the fraction of TBOP+ recovered in the perfusate at the end of the recirculation period after complete reoxidation of any TBOPH formed during the lung perfusion. The calculated recovery of TBOP+ for the lung experiments (n = 15) was 102.2 ± 2.9% (SD).

To evaluate the effect of the concentration of SOD used in the lung experiments on the superoxide dismutation rate, the superoxide-generating system xanthine oxidase (0.04 U/ml) plus hypoxanthine (70 µM), the superoxide detector ferricytochrome c (23.5 µM), and catalase (7,950 U/ml) were added to PSS with and without SOD (130 U/ml) present. The resulting evolution of ferrocytochrome c was measured spectrophotometrically (550 nm) (24).

The possible role of hydrogen peroxide (H2O2) as a TBOPH oxidant was evaluated by adding ascorbate (30 µM) and TBOP+ (2 mg/ml) to the PSS solution while monitoring TBOP+ absorbance. Two minutes after the ascorbate was added, H2O2 (4 mM) was added followed by horseradish peroxidase (4.6 U/ml) 3 min later.

Because nitric oxide (NO) is another redox-active substance released by the lung endothelium, the possibility that NO might be a TBOP+ reductant was evaluated by adding TBOP+ (2 mg/ml) to a buffer solution that was equilibrated with 200 parts/million NO in N2 in a Thunberg cuvette. The sample absorbance was measured for 5 min, and no TBOP+ reduction could be detected.


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Figure 2, left, shows lung and sham effluent TBOP+ fractions after the addition of TBOP+, TBOP+ plus SOD, or TBOP+ plus AO to the recirculating PSS perfusate. The 100% level is the initial amount of TBOP+ added to the recirculating perfusate at time 0 divided by the perfusate volume and is approximately equal to the TBOP+ concentration entering the lung or lung replacement tubing (sham) at time 0. Initially, the effluent had no TBOP+ until the first lung or sham transit after time 0. Then the sham effluent TBOP+ fraction jumped to 100% and remained virtually constant for the duration of the recirculation period. On the other hand, the lung effluent TBOP+ fraction jumped to a level somewhere below 100% as a result of reduction in the lungs. This was followed by a decrease in the lung effluent TBOP+ fraction to a plateau level, which was achieved by 15 min under all the experimental conditions studied. The plateau level appears to be determined by two competing processes, namely TBOP+ reduction in the lungs and TBOPH autooxidation throughout the perfusion system. This is revealed by the data in Fig. 2, right, which show the TBOP+ fraction versus time in the lung and sham effluent samples after the samples had been removed from the perfusion system. When the TBOPH formed during circulation through the lungs was removed from the lung perfusion circuit, it fully autooxidized within 30 min as indicated by the increase in the TBOP+ fraction to nearly 100%. Thus the TBOP+ fraction in Fig. 2, left, is that resulting from both TBOP+ reduction on passage through lungs and the simultaneous autooxidation of TBOPH, whereas the TBOP+ fraction in Fig. 2, right, reflects only the TBOPH autooxidation independent of lung TBOP+ reduction. Within an experiment, TBOPH autooxidation rates in lung effluent samples removed from the perfusion system at times ranging between 10 and 60 min during the recirculation period were not significantly different. For each lung, the autooxidation data obtained at the different sample times were averaged to provide a mean autooxidation data set for that lung. Figure 2, right, is the average of these autooxidation data sets from all lungs for a given experimental condition. In the presence of SOD, the lung effluent plateau TBOP+ fraction was higher and autooxidation of TBOPH was more rapid than in the absence of SOD. AO, on the other hand, had little effect. The sham effluent TBOP+ fraction was virtually 100% during perfusion and after removal from the perfusion system under all experimental conditions studied. Only the PSS sham TBOP+ data are shown in Fig. 2 because data with and without either SOD or AO added to the PSS perfusate were virtually superimposed. Quantitative descriptors of the data in Fig. 2 are given in Table 1.


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Fig. 2.   Left: lung and sham effluent TBOP+ concentrations expressed as a percentage of the initial concentration of TBOP+ ([TBOP+]) added to the perfusate vs. recirculation time with no additions other than TBOP [physiological salt solution (PSS)] and with superoxide dismutase (SOD) or ascorbate oxidase (AO) added. Right: [TBOP+] vs. time in effluent samples after they had been removed from the perfusion system. Only the PSS sham TBOP+ data are shown because PSS, PSS+SOD, and PSS+AO data are virtually superimposed. Values are means ± SE.


                              
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Table 1.   Descriptors of TBOP+ data from lung perfusion studies

To determine whether some relatively stable TBOP+ reductant(s) might be released from the lungs into the perfusate, the lungs were perfused in the same manner as in Fig. 2 but with no TBOP+ added to the perfusate so that the lung-conditioned perfusate could be sampled. Figure 3 shows that when TBOP+ was added to the conditioned perfusate removed from the recirculating system after 10 or 30 min of recirculation, the TBOP+ concentration fell and then returned to its initial level, indicating that a TBOP+ reducing agent did, in fact, accumulate in the perfusate. The reduction was not observed in the parallel samples to which AO had been added. Thus ascorbate accumulation in the conditioned perfusate appears to quantitatively account for the TBOP+ reduction by the conditioned perfusate.


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Fig. 3.   [TBOP+] vs. time after TBOP+ addition to conditioned perfusate samples with (+; right) or without AO (-; left) present. Model represents Eqs. 9-11 fit to the data.

The above results raise questions as to the implications of the substantial SOD effect with regard to a possible role for superoxide released from the lungs as a TBOP+ reductant and the apparent discrepancy between the effects of AO on TBOP+ reduction in the lungs and conditioned medium. We addressed these questions with the aid of a kinetic model as described in KINETIC MODEL.


    KINETIC MODEL
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The model derivation begins with the stoichiometric expressions, included to account for the effects of the various experimental conditions on the disposition of TBOP within the lungs and perfusate. In the model, the lungs can contribute to TBOP+ reduction via three mechanisms addressed in the experiments as depicted in Fig. 4. The lungs can directly reduce TBOP+ via TPMET
TBOP<SUP>+</SUP><IT>+</IT>DH<IT>+</IT>E <LIM><OP><ARROW>→</ARROW></OP><UL><IT>k<SUB>1</SUB></IT></UL></LIM> E<IT>+</IT>TBOPH<IT>+</IT>D<SUP>+</SUP> (a)
where E is thiazine reductase; D+ and DH are the oxidized and reduced forms, respectively, of the intra-cellular electron donor [e.g., NADH/NADPH (13, 34)]. The lungs can also release superoxide and/or ascorbate into the perfusate at constant rates (kso and kas, respectively; in nmol/min), which, in turn, reduce TBOP+ via
TBOP<SUP>+</SUP><IT>+</IT>H<SUP>+</SUP><IT>+2</IT>O<SUP>−</SUP><SUB>2</SUB>· <LIM><OP><ARROW>⇄</ARROW></OP><LL><IT>k</IT><SUB>−<IT>2</IT></SUB></LL><UL><IT>k<SUB>2</SUB></IT></UL></LIM> TBOPH<IT>+2</IT>O<SUB><IT>2</IT></SUB> (b)

TBOP<SUP>+</SUP><IT>+</IT>AH<SUB><IT>2</IT></SUB> <LIM><OP><ARROW>→k</ARROW></OP><UL><IT>k</IT><SUB>3</SUB></UL></LIM> TBOPH<IT>+</IT>A<IT>+</IT>H<SUP>+</SUP> (c)
where AH2 and A are ascorbate and dehydroascorbate, respectively, and kx represents all reaction rate constants.


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Fig. 4.   Schematic diagram depicting mechanisms of TBOP+ reduction to TBOPH within the capillary region of the kinetic model. AH2 and A, ascorbate and dehydroascorbate, respectively; DH and D+, reduced and oxidized forms of the intracellular electron donor, respectively; TPMET, endothelial transplasma membrane electron transport system represented by thiazine reductase (E) in reaction a.

Reactions b and c and superoxide dismutation via reaction d occur within the perfusate independently of the lungs per se
2O<SUP>−</SUP><SUB>2</SUB>·<IT>+2</IT>H<SUP>+</SUP> <LIM><OP><ARROW>→k</ARROW></OP><UL><IT>k</IT><SUB>4</SUB></UL></LIM> H<SUB><IT>2</IT></SUB>O<SUB><IT>2</IT></SUB><IT>+</IT>O<SUB><IT>2</IT></SUB> (d)
The kinetic model assumes that the H2O2 product of reaction d does not react with TBOP+ or TBOPH under the experimental conditions studied. This assumption is supported by the data in Fig. 5, which show that the addition of H2O2 had little effect on TBOPH oxidation rate. H2O2 is, in fact, an oxidant relative to TBOPH, but the reaction is quite slow in the absence of peroxidase activity for which TBOPH is a rather good substrate (Fig. 5).


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Fig. 5.   [TBOP+] vs. time with sequential additions of ascorbate, hydrogen peroxide (H2O2), and horseradish peroxidase at times indicated (arrows).

Reactions b-d take place throughout the perfusion system volume that has two components, a lung capillary volume and a noncapillary volume made up of the reservoir, connecting tubing, arteries, and veins. Reaction a occurs only within the lung capillary volume.

The spatial and temporal variations in the concentrations of the various species within the capillary and noncapillary volumes are described by the following sets of partial (partial ) and ordinary (d) differential equations based on the above reactions and the assumptions that the concentrations of O2, DH, and H+ ([O2], [DH], and [H+], respectively) were constant under the study conditions and that within the pulmonary capillary bed, the reduction rate of TBOP+ was too fast for axial diffusion to dissipate axial concentration gradients of the various chemical species, but the radial dimensions were so small that no radial gradients develop.

Capillary volume. The spatial and temporal variations of the concentrations of the various species within the capillary volume are described by
<FR><NU>∂[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB></NU><DE><IT>∂t</IT></DE></FR><IT>+W </IT><FR><NU><IT>∂</IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB></NU><DE><IT>∂x</IT></DE></FR><IT>=</IT>−<FR><NU><IT>k</IT><SUB>red</SUB></NU><DE>Q<SUB>c</SUB></DE></FR> [TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB><IT>+k</IT><SUB>o</SUB>[TBOPH]<SUB>L</SUB><IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>L</SUB><IT>−k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[AH<SUB>2</SUB>]<SUB>L</SUB> (1)

<FR><NU>∂[TBOPH]<SUB>L</SUB></NU><DE><IT>∂t</IT></DE></FR><IT>+W </IT><FR><NU><IT>∂</IT>[TBOPH]<SUB>L</SUB></NU><DE><IT>∂x</IT></DE></FR><IT>=</IT><FR><NU><IT>k</IT><SUB>red</SUB></NU><DE>Q<SUB>c</SUB></DE></FR> [TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB><IT>−k</IT><SUB>o</SUB>[TBOPH]<SUB>L</SUB><IT>+k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>L</SUB><IT>+k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[AH<SUB>2</SUB>]<SUB>L</SUB> (2)

<FR><NU>∂[O<SUP>−</SUP><SUB>2</SUB>·]<SUB>L</SUB></NU><DE><IT>∂t</IT></DE></FR><IT>+W </IT><FR><NU><IT>∂</IT>[O<SUP>−</SUP><SUB>2</SUB>·]<SUB>L</SUB></NU><DE><IT>∂x</IT></DE></FR><IT>=</IT><FR><NU><IT>k</IT><SUB>so</SUB></NU><DE>Q<SUB>c</SUB></DE></FR><IT>+2</IT>(<IT>k</IT><SUB>o</SUB>[TBOPH]<SUB>L</SUB><IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>L</SUB> (3)

<IT>−k<SUB>&agr;</SUB></IT>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>L</SUB>)

<FR><NU>∂[AH<SUB><IT>2</IT></SUB>]<SUB>L</SUB></NU><DE><IT>∂t</IT></DE></FR><IT>+W </IT><FR><NU><IT>∂</IT>[AH<SUB><IT>2</IT></SUB>]<SUB>L</SUB></NU><DE><IT>∂x</IT></DE></FR><IT>=</IT><FR><NU><IT>k</IT><SUB>as</SUB></NU><DE>Q<SUB>c</SUB></DE></FR>−<IT>k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB>[AH<SUB>2</SUB>]<SUB>L</SUB> (4)
where [TBOPH]L(t,x), [TBOP+]L(t,x), [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]L(t,x), and [AH2]L(t,x) are the respective concentrations of TBOP+, TBOPH, O<UP><SUB>2</SUB><SUP>−</SUP></UP>·, and AH2 at distance x from the capillary inlet and at time t; Qc and W are the capillary volume and the average linear flow velocity within Qc, respectively; kred = k1[E][DH], where [E] is the thiazine reductase concentration; ko = k-2[O2]2; k-o = k2[H+]; and kalpha  = k4[H+]2.

Noncapillary volume. The temporal variations in the concentration of the various species in the noncapillary volume are described by
<FR><NU>d[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>F</IT></NU><DE>Q<SUB>R</SUB></DE></FR> ([TBOP<SUP><IT>+</IT></SUP>]<SUB>L</SUB><IT>−</IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>)<IT>+k</IT><SUB>o</SUB>[TBOPH]<SUB>R</SUB><IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB><IT>−k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB> (5)

<FR><NU>d[TBOPH]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>F</IT></NU><DE>Q<SUB>R</SUB></DE></FR> ([TBOPH]<SUB>L</SUB><IT>−</IT>[TBOPH]<SUB>R</SUB>)<IT>−k</IT><SUB>o</SUB>[TBOPH]<SUB>R</SUB><IT>+k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB><IT>+k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB> (6)

<FR><NU>d[O<SUP>−</SUP><SUB>2</SUB><IT>·</IT>]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>2F</IT></NU><DE>Q<SUB>R</SUB></DE></FR> ([O<SUP>−</SUP><SUB>2</SUB>·]<SUB>L</SUB><IT>−</IT>[O<SUP>−</SUP><SUB>2</SUB>·]<SUB>R</SUB>)<IT>+2</IT>(<IT>k<SUB>0</SUB></IT>[TBOPH]<SUB>R</SUB><IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB><IT>−k<SUB>&agr;</SUB></IT>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB>) (7)

<FR><NU>d[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT><FR><NU><IT>F</IT></NU><DE>Q<SUB>R</SUB></DE></FR> ([AH<SUB><IT>2</IT></SUB>]<SUB>L</SUB><IT>−</IT>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB>)<IT>−k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB> (8)
where [TBOPH]R(t), [TBOP+]R(t), [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]R(t), and [AH2]R(t) are the respective concentrations of TBOP+, TBOPH, O<UP><SUB>2</SUB><SUP>−</SUP></UP>·, and AH2 in the noncapillary part of the perfusion system at time t. QR and F are the combined volume of the noncapillary part of the perfusion system and pump flow rate, respectively.

The model parameters are kred (ml/min), the measure of TBOP+ reduction rate by thiazine reductase (to put the units of kred into perspective, kred is the lung perfusion rate that would result in a 1/e fraction of TBOP+ being reduced on a single passage through the lungs in the absence of any other reactions); kso (nmol/min), the rate of superoxide release by the lungs; ko (min-1), the rate constant for TBOPH autooxidation; k-o (µM-2 · min-1), the rate constant for superoxide-mediated TBOP+ reduction; kalpha (µM-1 · min-1), the superoxide dismutation rate constant; k3 (µM-1 · min-1), the rate constant for TBOP+ reduction by ascorbate; and kas (nmol/min), the rate for ascorbate release by the lungs.

In what follows, parameter estimation was carried out with a Levenberg-Marquardt optimization routine (4). At each iteration, the relevant sets of equations were numerically solved using the finite difference method (4) for the appropriate initial and boundary conditions indicated in MODEL FIT AND ESTIMATION OF MODEL PARAMETERS.


    MODEL FIT AND ESTIMATION OF MODEL PARAMETERS
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL METHODS
EXPERIMENTAL RESULTS
KINETIC MODEL
MODEL FIT AND ESTIMATION...
DISCUSSION
REFERENCES

Because all of the model parameters are not separately identifiable with the data from a single type of experiment, we used a sequential approach for fitting the model described by Eqs. 1-8 to the data in Figs. 2 and 3. We began by using the observation that when AO was added to the perfusate recirculating through the lungs (PSS plus AO), the results were nearly indistinguishable from the experiments with no enzyme added to the PSS perfusate (Fig. 2, Table 1). Thus to simplify the model initially, the ascorbate contribution to TBOP+ reduction was set to zero. The implications of this simplification are evaluated later.

In the presence of SOD, it was assumed that kalpha was fast enough that reactions b and d, which account for TBOPH autooxidation and superoxide dismutation, respectively, reduce to the unidirectional reaction
TBOPH<IT>+2</IT>O<SUB><IT>2</IT></SUB> <LIM><OP><ARROW>→</ARROW></OP><UL><IT>k</IT><SUB>−<IT>2</IT></SUB></UL></LIM> TBOP<SUP>+</SUP><IT>+</IT>H<SUP>+</SUP><IT>+2</IT>O<SUP>−</SUP><SUB>2</SUB>·
This assumption is supported by the data in Fig. 6 that evaluate the effect of SOD on the superoxide dismutation rate with the ferricytochrome c-SOD assay. The ratio of the initial rates of ferrocytochrome c generation via the reduction of ferricytochrome c by the hypoxanthine-xanthine oxidase system with and without the SOD present (Fig. 6) provides a lower bound on the ratio of catalyzed to uncatalyzed superoxide dismutation rates (Kd), which was >2 × 102.


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Fig. 6.   Ferrocytochrome c concentration vs. time after the addition of ferricytochrome c and hypoxanthine to PSS with and without SOD present. Arrow, addition of xanthine oxidase.

Under the above assumptions, the TBOP+ data obtained with SOD present provide an estimate of the contribution of the reductase (E) to TBOP+ reduction in the lungs. The parameters identifiable from the data with SOD present were then kred and ko, with the other model parameters set to zero. Thus the model was fit to the average TBOP+ data in Fig. 2, with SOD present by solving Eqs. 1, 2, 5, and 6 with the initial conditions [TBOPH]L(0,x) = [TBOP+]L(0,x) = 0, [TBOP+]R(0) = [TBOP+]0, and [TBOPH]R(0) = 0 and the boundary conditions [TBOPH]L(t,0) = [TBOPH]R(t) and [TBOP+]L(t,0) = [TBOP+]R(t), where [TBOP+]0 is the initial (time 0) concentration of TBOP+. The estimated values were kred = 1.73 ml/min and ko = 0.316 min-1. The estimated value of kred can be used to calculate a TBOP+ reduction rate of 73 nmol/min from kred[TBOP+]0.

With kred and ko known, we proceeded to evaluate the contribution of superoxide released by the lungs to TBOP+ reduction by fitting the model to the average TBOP+ data in Fig. 2 obtained from the experiments in which the lungs were perfused with no enzyme added. The identifiable model parameters were then kso and k-o, with the uncatalyzed superoxide dismutation rate (kalpha ) set to 12 µM-1 · min-1 as estimated by Fridovich et al. (17). The model fit was obtained by solving Eqs. 1-8 with the initial conditions [TBOPH]L(0,x) = [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]L(0,x) = [TBOP+]L(0,x) = 0, [TBOP+]R(0) = [TBOP+]0, and [TBOPH]R(0) = [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]R(0) = 0 and the boundary conditions [TBOPH]L(t,0) = [TBOPH]R(t), [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]L(0,x) = [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·]R(t), and [TBOP+]L(t,0) = [TBOP+]R(t). The estimated values of the rate of superoxide release by the lungs (kso) and the rate constant for superoxide-mediated TBOP+ reduction (k-o) were 26.2 nmol/min and 0.804 µM-2 · min-1, respectively. These model fits are indicated in Fig. 7.


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Fig. 7.   Model fit to the experimental data presented in the same format as in Fig. 2. Model represents Eqs. 1-8 fit to the data as indicated in text.

To return to the potential role of the ascorbate that accumulated in the conditioned perfusate (Fig. 3) in TBOP+ reduction in the lungs, we obtained an estimate of the rate of ascorbate release by the lungs and evaluated its contribution to TBOP+ reduction in lungs as follows. Under the experimental conditions in the conditioned perfusate samples, resulting in the data shown in Fig. 3, the relevant reactions are reactions b-d and Eqs. 5-8 reduce to
<FR><NU>d[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=k</IT><SUB>o</SUB>([TBOP<SUP><IT>+</IT></SUP>]<SUB><IT>0</IT></SUB><IT>−</IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>)<IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB><IT>−k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB> (9)

<FR><NU>d[O<SUP>−</SUP><SUB>2</SUB> · ]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=2</IT>{<IT>k</IT><SUB>o</SUB>([TBOP<SUP><IT>+</IT></SUP>]<SUB><IT>0</IT></SUB><IT>−</IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>)<IT>−k</IT><SUB>−o</SUB>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB><IT>−k<SUB>&agr;</SUB></IT>[O<SUP>−</SUP><SUB>2</SUB>·]<SUP>2</SUP><SUB>R</SUB>} (10)

<FR><NU>d[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB></NU><DE>d<IT>t</IT></DE></FR><IT>=</IT>−<IT>k<SUB>3</SUB></IT>[TBOP<SUP><IT>+</IT></SUP>]<SUB>R</SUB>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB> (11)
To fit Eqs. 9-11 to the Fig. 3 data, ko was set to the value estimated from the PSS plus SOD data in Fig. 2, and kalpha was set to the standard value of 12 µM-1 · min-1 (17). Thus the identifiable parameters were k3 (µM-1 · min-1), k-o (µM-2 · min-1) and [AH2]0 (µM), the concentration of ascorbate in the conditioned perfusate sample before the addition of TBOP+. The model fit to the TBOP+ data from the conditioned perfusate samples was obtained by numerically solving Eqs. 9-11 with the initial conditions [TBOP+](t = 0) = [TBOP+]0, [AH2](t) = [AH2]0, and [O<UP><SUB>2</SUB><SUP>−</SUP></UP>·](t) = 0. The estimated values of k3 and k-o were 0.146 ± 0.1 (SE) µM-1 · min-1 and 1.03 ± 0.71 µM-2 · min-1, respectively. Figure 8 shows the resulting estimate of the concentration of ascorbate ([AH2]0) in the conditioned perfusate, which increased approximately linearly with recirculation time. The model estimated rate of 0.383 µM/min is comparable to the value of 0.302 µM/min estimated by measuring the ascorbate concentration (10), which provides additional evidence for consistency in the model assumptions.


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Fig. 8.   Ascorbate concentration in conditioned perfusate vs. recirculation time estimated by fitting Eqs. 9-11 to data exemplified in Fig. 3.

Knowing the rate of ascorbate accumulation in the conditioned medium, the rate of ascorbate efflux from the lungs into the perfusate was estimated with Eq. 12, which is the solution of a nested version of Eqs. 1-8, descriptive of ascorbate kinetics in TBOP-free recirculation experiments
k<SUB>as</SUB><IT>=</IT><FR><NU>[AH<SUB><IT>2</IT></SUB>]<SUB>R</SUB>(<IT>t</IT>)(Q<SUB>R</SUB><IT>+</IT>Q<SUB>c</SUB>)</NU><DE><IT>t</IT></DE></FR> for<IT> t≥t</IT><SUB>c</SUB> (12)
where tc = Qc/F is the pulmonary capillary transit time, estimated to be ~2.4 s under the conditions of these experiments (14). The value of kas was thus estimated to be 6.1 nmol/min.

To put the contributions of each of the three TBOP+ reduction mechanisms in prospective, model simulations of the pulmonary venous effluent TBOP+ concentration were generated by solving Eqs. 1-8 with the appropriate initial and boundary conditions and with the parameters ko, kred, kso, and k-o set to values estimated from Fig. 7 fits to the lung data, with the additional parameters k3 and kas set to 0.146 µM-1 · min-1 and 6.1 nmol/min, respectively, estimated from the data in Fig. 3, and kalpha set to the standard value 12 µM-1 · min-1 (17). The objective was to determine how much each of the three reduction mechanisms contributed to the experimental data by successively eliminating it from the simulations. For simulation 1 in Fig. 9, all three reduction mechanisms (reductase, ascorbate, and superoxide) were allowed to contribute to the simulated TBOP+ reduction. Then, for simulation 2, the ascorbate contribution was eliminated. For simulation 3, the superoxide contribution was eliminated. For simulation 4, both the ascorbate and superoxide contributions were eliminated, and for simulation 5, all three reduction mechanisms (ascorbate, superoxide, and reductase) were eliminated by setting the appropriate parameters to zero (sham). Simulation 5 is a trivial result, but it is shown to emphasize the range of possibilities. These simulations demonstrate the model explanation for the experimental observations, namely, that the pulmonary endothelial TPMET dominated the pulmonary reduction of TBOP+ and that the combined effect of ascorbate and superoxide released from the lungs could account for no more than 13% of the total TBOP+ reduction.


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Fig. 9.   open circle , Pulmonary venous effluent [TBOP+] (as a fraction of the initial [TBOP+] added to the perfusate) vs. recirculation time with no additions other than TBOP+. The lines are model simulations generated with Eqs. 1-8. For simulation 1, the contributions of reductase, superoxide, and ascorbate to simulated TBOP+ reduction were set to the values estimated as described in text. For simulation 2, ascorbate contribution was eliminated. For simulation 3, superoxide contribution was eliminated. For simulation 4, both ascorbate and superoxide contributions were eliminated. For simulation 5, the contributions of all 3 mechanisms were eliminated.


    DISCUSSION
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL METHODS
EXPERIMENTAL RESULTS
KINETIC MODEL
MODEL FIT AND ESTIMATION...
DISCUSSION
REFERENCES

The experimental results and kinetic model interpretation lead to the conclusion that the major route in TBOP+ reduction within the lungs is via an endothelial TPMET system. This relative contribution of TPMET is emphasized by the model simulations shown in Fig. 9, where it can be seen that the predicted contributions of ascorbate and any superoxide that might be released by the lungs to the pulmonary reduction of TBOP+ are very small compared with that attributable to endothelial TPMET. Ascorbate and superoxide contributions to TBOP+ were specifically addressed because previous studies have demonstrated the release of ascorbate (1, 10) and, under some experimental conditions, superoxide (10, 22, 32) by isolated perfused lungs. Although the possibility that some other unidentified and very short-lived TBOP+ reducing agent might contribute to TBOP+ reduction would be difficult to rule out entirely, it is difficult to imagine what another candidate might be that would also be undetectable in the immediately sampled conditioned perfusate. Neither NO nor H2O2 are TBOP+ reductants. The steady-state release of a reducing agent in sufficient quantity to account for the reduction of the various thiazine dyes that have been studied would have to be even greater than the normal rate of O2 reduction by the lung (4, 7, 14).

Although the results indicate that the release of a reductant is not a major contributor to TBOP+ reduction, the data in Fig. 3 do demonstrate that a TBOP+ reductant accumulates in the perfusate recirculating through the lungs. Its elimination by AO is consistent with previous studies indicating ascorbate release by the perfused lungs (1, 10). The estimated rate of release from the data in Fig. 3 of ~4 nmol · min-1 · g wet wt-1 is on the same order as that previously reported by Arad et al. (1) in perfused rat lungs (6 nmol · min-1 · g wet wt-1) and by Bongard et al. (10) in perfused rabbit lungs (2 nmol · min-1 · g wet wt-1). The rate of TBOP+ reduction in the lungs is 50 nmol · min-1 · g wet wt-1. Although the conditioned perfusate had accumulated enough ascorbate by the end of the perfusion period to reduce the added TBOP+ to a fraction comparable to that in the perfusate recirculating through the lungs, the total amount released over the entire period was small compared with the required reduction rate during that period. This accounts for the small effect of adding AO to the recirculating perfusate in the presence of TBOP+ as shown in Fig. 2.

The higher steady-state TBOP+ fraction in the presence of SOD in Fig. 2 might be thought to suggest a significant role for superoxide in the pulmonary reduction of TBOP+. However, the kinetic analysis apparently rules out that possibility. When both TBOP+ reduction and TBOPH autooxidation rates are taken into account, the effect of adding SOD can be almost completely accounted for by its effect on the TBOPH autooxidation rate. Thus there is no reason to believe that superoxide released by the lungs is a significant TBOP+ reductant in lungs. This is explained mechanistically by including superoxide as an autooxidation by-product in the stoichiometric equations leading to the kinetic model. This explanation for the SOD effect is analogous to those of Auclair et al. (3) and Picker and Fridovich (36) for the inhibitory effect of SOD on the aerobic reduction of nitro blue tetrazolium (NBT) in the presence of NADPH and NADPH-cytochrome P-450 reductase or NADH and phenazine methosulfate, respectively. They determined that the SOD effect was on the superoxide produced by autooxidation of the intermediate monoformazan formed in the first step of the two-step NBT reduction to the diformazan. By eliminating the superoxide formed in the autooxidation reaction, SOD increases the autooxidation rate, i.e., the regeneration of NBT, and thus causes inhibition of diformazan production. A minor difference for TBOP is that TBOPH is the final two-electron reduction product, which is autooxidizable, whereas the final two-electron NBT reduction product diformazan is a stable end product. Although a superoxide release rate is a model output, the estimated rate makes such a small contribution to the model fit that its numerical value is useful only to show that it cannot be an important contributor to TBOP+ pulmonary reduction and not as an accurate measure of superoxide release by the lungs.

In the above analysis, the uncatalyzed superoxide dismutation rate (kalpha ) was set to the standard value of 12 µM-1 · min-1 (17), which may or may not be an accurate estimate under the experimental conditions of the present study. To evaluate the sensitivity of the model predictions to this value, we varied the value of kalpha from 3 to 36 µM-1 · min-1. The results of this exercise indicated that the changes in kalpha were compensated for almost exclusively by changes in k-o, with little effect on the estimated values of the other parameters or on the ability of the model to fit the data. In other words, kalpha and k-o are highly correlated with each other but not with the other model parameters. Similar analysis revealed the robustness of the model fit and data interpretation to the ratio of catalyzed to uncatalyzed superoxide dismutation rates (Kd) when Kd was >5. Thus the lower bound Kd estimate of 2 × 102 from the data in Fig. 6 is quite sufficient support for the assumption that in the presence of SOD, reaction b could be considered unidirectional.

The estimated TBOP+ reduction rate was about two orders of magnitude smaller than that previously estimated for oxidized TBO (TBO+) itself (4, 14), and the estimated TBOPH autooxidation rate constant was about half of that estimated for reduced TBO (14). The reasons for these differences are not known, but at least two factors probably contribute. One is that the TBO moieties in the polymer are no longer TBO because the primary amine is changed to a complicated secondary amine (9). This probably contributes to the shift in the absorbance spectrum in the region of TBO maximum absorbance (from 626 nm for TBO+ to 590 nm for TBOP+). The high absorbance at the low wavelengths is mainly due to the acrylamide polymer. Another likely contributor to the differences in reduction rates is steric hindrance due to the small redox-active moieties being attracted to the large polymer.

In summary, the experimental and kinetic model results are consistent in pointing to the endothelial TPMET system as the major contributor to TBOP+ reduction in lungs. The SOD effect was predominantly on autooxidation rather than on reduction, and no long-lived TBOP+ reductant was released into the perfusate in sufficient quantity to contribute significantly to the TBOP+ reduction. The basic experimental design with TBOP+ as the extracellular electron acceptor and the kinetic model for interpretation appear to provide tools for further studies of pulmonary endothelial TPMET mechanisms and their responses to physiological and pathophysiological stresses.


    ACKNOWLEDGEMENTS

This study was supported by National Heart, Lung, and Blood Grants HL-24349 and HL65537 and the Department of Veterans Affairs.


    FOOTNOTES

Address for reprint requests and other correspondence: C. A. Dawson, Research Service 151, Zablocki VA Medical Center, 5000 W. National Ave., Milwaukee, WI 53295-1000 (E-mail: cdawson{at}mcw.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 7 November 2000; accepted in final form 15 December 2000.


    REFERENCES
TOP
ABSTRACT
INTRODUCTION
EXPERIMENTAL METHODS
EXPERIMENTAL RESULTS
KINETIC MODEL
MODEL FIT AND ESTIMATION...
DISCUSSION
REFERENCES

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Am J Physiol Lung Cell Mol Physiol 280(6):L1290-L1299