The lung nitric oxide (NO) diffusing capacity (DlNO) mainly reflects alveolar-capillary membrane conductance (Dm). However, blood resistance has been shown in vitro and in vivo. To explore whether this resistance lies in the plasma, the red blood cell (RBC) membrane, or in the RBC interior, we measured the NO diffusing capacity (Dno) in a membrane oxygenator circuit containing ∼1 liter of horse or human blood exposed to 14 parts per million NO under physiological conditions on 7 separate days. We compared results across a 1,000-fold change in extracellular diffusivity using dextrans, plasma, and physiological salt solution. We halved RBC surface area by comparing horse and human RBCs. We altered the diffusive resistance of the RBC interior by adding sodium nitrite converting oxyhemoglobin to methemoglobin. Neither increased viscosity nor reduced RBC size reduced Dno. Adding sodium nitrite increased methemoglobin and was associated with a steady fall in Dno (P < 0.001). Similar results were obtained at NO concentrations found in vivo. The RBC interior appears to be the site of the blood resistance.
- diffusing capacity for oxygen
- diffusing capacity for carbon monoxide
- lung diffusing capacity for nitric oxide
- membrane oxygenator
nitric oxide (no) and carbon monoxide (CO) lung gas transfer may be described by the Roughton and Forster relationship: (1)Where Dl is overall gas transfer, Dm is membrane conductance, θ is specific blood conductance for that gas, and Vc is pulmonary capillary blood volume (34).
The diffusing capacity for NO (DlNO) reflects Dm better than the diffusing capacity for CO (DlCO) (11). However, blood resistance to NO uptake still occurs (12): we have shown that NO diffusing capacity (Dno) increases with oxyglobin (a cell-free heme-based blood substitute) or free hemoglobin (Hb) in vitro. In collaboration with us, the Houston group has shown that DlNO increases using oxyglobin in anesthetized dogs (12).
This resistance to NO uptake must lie in the plasma, red cell membrane, or red cell interior.
Extending the Roughton-Forster model to NO blood uptake: (2)where D is diffusing capacity. The far right-hand term can be ignored because the rate of reaction of oxyhemoglobin with NO is 280 times as fast as with CO (11) i.e., 1/Dreaction ≈ 0. To date, we cannot distinguish between the other three barriers. Hemolysis disrupts the membrane and cell interior, but released Hb shortens the plasma diffusion distance. Adding oxyglobin shortens the plasma diffusion distance and “bypasses” the red cell membrane and interior.
Our oxygenator model allows us to alter one variable, but keep others constant (7). To alter extracellular fluid resistance, we can compare solutions of varying viscosity. The diffusivity depends on 1/viscosity, according to the Stokes-Einstein equation: (3)(see appendix), where D′ is Fick's first law diffusion coefficient in dimensions length2 time−1, KB is Boltzmann's constant, T is absolute temperature, η is solution viscosity, and r is particle (including gas) molecular radius.
Initially, using horse blood, we halved extracellular resistance by replacing plasma with physiological salt solution (9). To alter membrane resistance, we tried to alter surface area (SA) by creating spherocytes by heating and shrinking cells with hypertonic salt solutions, as described by Carlsen and Comroe (13). To alter the red cell interior, we added sodium nitrite to form methemoglobin (metHb). We were only able to make minor alteration to viscosity and cell size. We here present observations altering viscosity (diffusivity) 1,000-fold using red cells suspended in dextran, plasma, or physiological salt solution and doubling red cell size, comparing horse to human red cells, in addition to our observations with nitrite-induced metHb. We also confirm for human blood the curvilinear relationship at low Hb concentration ([Hb]) between [Hb] and Dno.
Our detailed circuit is described elsewhere (7, 17, 18). Briefly, two membrane oxygenators were connected in series to form a continuous circuit perfused with ∼500 ml of horse red cells (TCS Biosciences, Buckingham, UK) or human red cells (NCI, National Health Service Blood and Transplant Service, Bristol, UK) suspended in the relevant solution flowing at 2.5 l/min and 37°C. One oxygenator received a gas flow of 2.5 liters of 22.7% O2, 0.019% CO, 14 parts per million (ppm) NO, and the remainder N2. The second oxygenator scrubbed the oxygenated blood with 7% CO2 in N2. In this way, near physiological gas tensions were maintained: “PaO2” = oxygenated blood output partial pressure = 117.7 Torr (SD 47.3), venous blood input partial pressure “Pv̄O2” = 44.1 Torr (SD 11.8), “Pc̄O2” = calculated average O2 partial pressure in blood channel = 61.6 Torr (SD 10.5), Pco2 = 22.0 g·dl−1·Torr−1 (SD 1.6), K+ = 6.7 mmol/l (SD 0.48), pH = 7.22 (SD 0.3).
For these experiments, the two oxygenators used (Dideco D903 Avant, Sorin Group, Mirandola, Italy) gave near physiological Dno-to-CO diffusing capacity (Dco) ratios = 3.9 (11).
Dno and Dco were measured from the difference in gas concentrations leaving and entering the first oxygenator as follows. The calculation is just the same as for the single-breath method used clinically, except that the volume of gas exposed to blood per unit time is not the alveolar volume divided by the breath-hold time. It is the volume in the gas channels per minute i.e., the gas flow rate.
Dno = gas flow rate (stpd)/(Pb − Ph2o × RH) × loge (NOin/NOout), where Pb is barometric pressure, Ph2o is saturated water vapor pressure (Torr), RH is relative humidity, and NOin and NOout are NO concentrations ([NO]) at the inlet and outlet ports, respectively. For CO, the calculations were identical, except substituting COin/COout.
O2 diffusing capacity (Do2) was measured by Bohr integration (5). (4)where Ṁo2 is O2 uptake, and the mean O2 Hb saturation in the blood channel (Sc̄O2) was calculated as a definite integral of Hb O2 saturation (So2), integrated with respect to partial pressure between the limits of O2 inlet partial pressure and O2 outlet partial pressure, divided by the inlet-outlet difference in O2 partial pressure. Pc̄O2 and mixed arterial O2 partial pressure were directly measured by the inline analyzer. The integral was calculated by estimating each infinitesimal value for saturation Si from every incremental δPo2 using an algorithm derived for human blood (37) and summing each cell value Si × δPo2 from Pv̄O2 to the oxygenator blood outlet partial pressure of O2 (PaO2) using a Microsoft Excel spreadsheet. Equation 5 shows this mathematically: (5) (6)where Pc̄O2 corresponds to Sc̄O2 estimated from the algorithm, Pa is the geometric mean partial pressure of O2 between gas inlet and outlet, SaO2 is arterial So2, and Sv̄O2 is mixed venous So2. PaO2 (blood outlet O2 tension) and Pv̄O2 (blood inlet O2 tension) together with potassium (K), “in-line” Hb, and pH were measured by an inline fluorometric analyzer (CDI 500 Terumo Cardiovascular Systems UK, Egham Surrey, UK). metHb, carboxyhemoglobin (COHb), oxyhemoglobin, Po2 (extracellular), and percentage saturation (S) were measured by a combined co-oximeter and blood-gas analyzer (Roche Cobas b221, Roche Diagnostics, Indianapolis, IN). Intracellular Po2 was calculated from S using a formula originally developed for human blood (37). O2 concentrations ([O2]) at the inlet valve and outlet were measured by a Medical Oxygen Monitor (Viamed Sensotec MX300 Cambridge Sensotec, St. Ives, UK).
Progressive Addition of Red Cells
The circuit was primed with 1,400–1,500 ml of Hartmanns solution. Aliquots were exchanged to give the desired hematocrit, e.g., 14 ml drawn off and replaced with 14 ml red cells to give 1% hematocrit. Thus hematocrits of 1–30% were generated. One estimate of Dno, Dco, and Do2 was made per exchange. Three control estimates of Dno, Dco, and Do2 were made once the final [Hb] was reached. Because the inline analyzer did not detect very low [Hb], these were calculated from the control value multiplied by the dilution.
Two hundred fifty-seven grams of either dextran 40 or dextran 500 (Pharmacosmos A/S DK-4300, Holbaek, Denmark) were added to 771 ml of Hartmanns solution to give a 30% wt/vol solution. The plasma was removed by separator (4R4414 Fenwall Laboratories, Deerfield, Illinois) from 1 liter of horse blood (TCS Biosciences, Buckingham, UK) and replaced with 30% dextran solution. The red cells suspended in dextran were added to the primed circuit with Hartmanns, and the Hartmanns drawn off. Three estimates of Dno, Dco, and Do2 were made. Five hundred milliliters of perfusate were drawn off and replaced with 500 ml of horse cells suspended in Hartmanns, giving a 20–25% dextran solution. Three further estimates of Dno, Dco, and Do2 were made. A final 500 ml of perfusate were drawn off and replaced with 500 ml of horse cells in Hartmanns to give 10–15%, and the final three estimates of Dno, Dco, and Do2 were made.
Varying Red Cell Size
Red cells of differing mean corpuscular volume (MCV) will have differing SAs. Chakraborty et al. (14) have modeled the human red cell as a discoid cylinder of diameter (d) 8 μm (8 × 10−6 M) and thickness (height) (t) 1.6 μm (1.6 × 10−6 M). This has volume π (d/2)2 t = 80 fl. Its SA will be 2 π(d/2)2 + πdt =1.41 × 10−10 M2. From the volume (MCV) of a human red cell, and assuming its ratio of t/d is the same as in the model of Chakraborty et al., i.e., 0.2, it is possible to determine its SA. Horse red cells are uniform in size with d = 5–6 μm. Knowing the MCV and using this value for d, t and hence SA can be calculated. The circuit was emptied and reprimed with horse or human cells suspended in Hartmanns, whichever had not been used for the varying [Hb] study. Three estimations of Dno, Dco, and Do2 were made. The Hb, Hct, and MCV were measured from a 2-ml aliquot (Beckmann LH 500, Miami, FL).
Addition of Sodium Nitrite and Sodium Dithionite
Three percent (0.43 M) sodium nitrite (Pharmacy Department, Ipswich Hospital) were added to the circuit in diluted aliquots at 5-min intervals to give a range of metHb concentrations from 1 to 100%. Single estimations of Dno, Dco, and Do2 were made.
To confirm that changes in D were due to oxidation of heme, following control human blood estimations, 20 ml of 1.5% (0.1 M) sodium dithionite (molecular weight 174) followed by 20 ml of 1:5 dilution of 3% sodium nitrite, followed by 80 ml of dithionite solution and finally 80 ml of sodium nitrite were added. Single estimations of Dno, Dco, and Do2 were made after each addition.
Precautions to Avoid Hemolysis
Special precautions were taken to avoid hemolysis and eliminate free Hb from our circuit. In our preliminary experiments, free [Hb] (27) ranged from 12 mg/dl (horse red cells suspended in Hartmanns) to 100 mg/dl (heated whole horse blood). Cells were separated from plasma to remove free Hb arising during transport and storage. They were then resuspended in Hartmanns solution. All washing and priming was performed with Hartmanns. We accounted for hemolysis by measuring K using the inline analyzer and including K as an independent covariate in all analyses.
Dno was entered as a dependent variable in one-way ANOVA to examine between-day variation. Because the associations are not linear, nonparametric correlation was used to look at the relationship between Dno and Dco and Hb, metHb, and O2, and Spearman's ρ was quoted. Linear regression was used to examine the relationship between Dno, Dco, and Do2 (dependent variables) and viscosity, MCV, and estimated thickness of the COHb and metHb layer as independent variables; human/horse and nitrite/dithionite entered as dummy variables; and K entered as a proxy for red cell damage as a covariate. All analyses were done using SPSS Statistics 21.0 (Chicago, IL).
Sequence of Experiment
The experiments were performed on 7 separate days. On 3 separate days, the following solutions were tested in a single run using a pair of oxygenators: control whole horse blood, horse red cells resuspended in Hartmanns, horse red cells resuspended in 3% saline, whole blood heated to 54°C for 20 min, and whole blood to which 3% sodium nitrite was progressively added. Three measurements of Dno, Dco, and Do2 were made for each solution. The solution was then drained, and the circuit flushed with 1 liter of Hartmanns. The order of solution was randomized. Finally 700 ml of tap water were added to achieve complete hemolysis and hence estimation of “Dno Max” ≈ Dm for the circuit. On the final run on the 3rd day, after 10 ml of 3% sodium nitrite had been added to the circuit containing whole blood, 700 ml of tap water were added to the circuit to achieve hemolysis, and, subsequently, a further 15, 20, 25, or 30 ml of 3% sodium nitrite were added. Because of concern that 3% salt solution and heated cells did not alter cell size, the results for these suspensions are not presented further here, but are published in abstract form (9). On 3 subsequent separate days, the circuit was initially primed with Hartmanns, and either horse or human red cells added. Once physiological Hb was achieved and measurements taken, nitrite and dithionite were added if human cells were used at the start, or dextran solutions if horse cells were used. Finally, the circuit was emptied, and remaining solution tested. On a 4th day, these experiments were repeated, but using a mixture of 100 parts per billion (ppb) NO in nitrogen (BOC Spectraseal Guildford, Surrey, UK) diluted in CO/N2/O2 to give 25 ppb.
Calculation of Depth of metHb and COHb Layer
The thickness of the metHb + COHb layers can be estimated as follows. The total number of molecules will be directly proportional to the percent concentration. If the molecules form a layer just inside the red cell membrane, the total number of molecules will be proportional to the cube of the depth of the layer. If all of the Hb in the red cell was replaced by metHb and COHb, then the depth would be the half thickness (1 μm). Rearranging: (7)
The work used human blood, so it fell within the UK use of human tissue legislation. National ethics approval was obtained for UK Research Governance, Human Tissue, Good Clinical Practice, Confidentiality and Data Protection Law via National Research Ethics Service Yorkshire and the Humber South Yorkshire research ethics committee. Local ethics approval was obtained from Papworth Hospital National Health Service Foundation Trust ethics committee.
The average calculated MCV for horse red cells was 49.7 fl (SD 0.18) and human red cells 91.8 fl (SD 0.18). The calculated SA was 83.5 μm2 (horse) and 153.7 μm2 (human).
As with previous studies (7), there was a significant regression of Dno on day number (t = 5.72, n = 225, P < 0.001), partly explained by varying amounts of free Hb as estimated by K (t = 2.34, n = 225, P < 0.02) milliequivalents per liter.
Mean (SD) DNO = 3.08 ml·min−1·Torr−1 (SD 1.47), Dco = 0.83 ml·min−1·Torr−1 (SD 0.4), Dno/Dco = 3.91 (SD 2.05), Do2 = 1.23 ml·min−1·Torr−1 (SD 0.36), and Do2/Dco = 1.69 (SD 0.98). For Hb less than a concentration of 10 g/dl, there was a significant correlation between Dno and Hb (P = 0.001) (Fig. 1A) and Dco and Hb (P < 0.001, Fig. 1B). For Hb 7–15 g/dl, there was no relationship between Dno and inline Hb (ρ = 0.12, P > 0.05), but a highly significant relationship between Dco and Hb (ρ = −0.306, P < 0.001). These trends were similar for both horse and human.
There was no reduction in Dno with viscosity (Fig. 2); indeed, there was a slight rise, which was abolished when K was added as a covariate.
There was no increase in Dno, Dco, or Do2 with increasing cell size; indeed, there was a slight fall (Fig. 3).
Dithionite caused significant reversal of the nitrite-induced decline in Dno and vice versa (t = −3.07, P = 0.007, n = 19, Fig. 4).
On addition of sodium nitrite, there was a steady rise in metHb to a plateau of ∼90% (Fig. 5A). There was a rise and then decline in COHb (Fig. 5B) and steady falls in oxyhemoglobin, intracellular Po2, and %Hb saturation (Fig. 5, C and D). There was a modest decline in extracellular Po2 (Fig. 5D).
During serial sodium nitrite addition, the falls in Dno (ρ = −0.305, P < 0.05), Dco (ρ = −0.469, P < 0.01), and Do2 (ρ = 0.677, P < 0.01) were significantly correlated with the rise in metHb (Fig. 6).
Linear regression of Dno and also Dco on estimated depth of metHb + COHb layer were both highly significant (P < 0.001), but the decline in Do2 was less (Fig. 7). Hemolysis also caused reversal of the nitrite-induced decline in Dno (Fig. 8).
At low [NO] [24.8 ppb (SD 10.3)], Dno = 3.77 ml·min−1·Torr−1 (SD 1.31), Dco = 0.78 ml·min−1·Torr−1 (SD 1.01), and identical findings regarding viscosity and MCV were observed, i.e., Dno = −0.0086 (MCV) + 4.1565, and Dno = 0.0049 (η) + 4.277. In contrast to Dco, there was no statistically significant relationship between Dno and Po2 (Fig. 9, A and B).
Summary of Findings
Our findings fit with the red cell interior, rather than extracellular fluid or red cell membrane, being the site of blood resistance to NO transfer. We saw no fall in Dno, Dco, or Do2 with increasing viscosity (falling diffusivity). In fact, a small rise in Dno was seen, which was nonsignificant when K concentration was included as a covariate in the regression model. This is most likely from cell damage, as more viscous solutions were forced around the circuit at high pressure. No fall in Dno, Dco, or Do2 was found, despite halving the red cell membrane SA. A highly significant fall in Dno and Dco occurred with nitrite. This was associated with a rise in metHb and reversed by dithionite and hemolysis. We have confirmed a nonlinear relationship between Dno and Hb for human and horse red cells. This is only seen at very low [Hb]. At [Hb] found in most clinical practice (7–15 g/dl), Dno is independent of Hb.
Effect of Nitrite on NO, CO, and O2 Transfer Within the Red Cell
The fall in both Dno and Dco with increasing metHb suggests that access to the heme is limiting. This explains the reversal with dithionite, which reduces metHb to ferrous Hb (31). The rise in Dno with hemolysis (Fig. 8) shows it is not the reduction in total available Hb causing the change in Dno, but its accessibility; that is, an increase in diffusion distance to available Hb active sites. It seems likely that outer layers of Hb are converted to metHb before inner, so the layer of metHb builds up; this increases the diffusion resistance to gas transfer inside the cell. Figure 7 supports this idea. Diffusion through a layer (in this case of metHb) follows Fick's law, as applied to a biological membrane: (8)where k is a constant. The solubility of NO/CO ≈ 2.
From Eq. 8, Dno/Dco will be ≈2, and Dno will be proportional to 1/thickness. The slope and intercept of Dno/Dco are ∼2 in Fig. 7, supporting the idea that NO and CO transport obeys Fick's law inside the red cell. Because no increase in Dno occurred with the initial addition of 20 ml of dithionite (Fig. 4), the concentration of 1% of metHb occurring naturally in blood does not seem to limit diffusion. In contrast to Dno and Dco, Do2 does not appear dependent on the thickness of the metHb and COHb layer (Fig. 7). This shows a departure from Fick's law. For about fifty years, facilitated diffusion has been known to transport O2 in concentrated Hb solutions (44). Because it combines reversibly with Hb, unlike NO or CO, it can move rapidly from active site to active site, down the partial pressure gradient. Hughes and Bates (26) have suggested that DlNO may be a better surrogate for DlO2 than for CO membrane conductance (DmCO). Facilitated diffusion of O2 in the red cell and a departure from Fick's law does not support their view.
The changes in O2, CO, and their ligands with Hb are complex (Fig. 5): as sodium nitrite is added, there is a rise in metHb mirrored by a decline in oxyhemoglobin and Po2. As Po2 falls 1), specific blood conductance for CO (θCO) increases, since θCO ∝ (CO)(Hb)/(Po2), so first COHb rises; 2) the steep part of the dissociation curve is reached so that specific blood conductance for O2 (θO2) increases. Looking at Fig. 5, despite massive reduction in oxyhemoglobin, the percentage of reduced Hb (= 100 − %oxyhemoglobin − %metHb − %COHb) is actually increased. The increase in θO2 and increase in percentage of reduced Hb serve to maintain O2 uptake.
Critique of Methods
The pH was lower than physiological conditions, because of the compensated metabolic acidosis of stored blood (4). The K was higher, due to the hyperkalemia of stored packed red cells (1). Our observations were made on horse and human blood drawn several days previously. Red cells are fragile and easily damaged by forcing them through narrow channels at high velocity. This becomes a particular problem for NO, since its reaction with free Hb is so much faster than with the intact red cell. The membrane oxygenator is designed to avoid hemolysis because of the disastrous clinical consequences. Previously, our laboratory has run a similar circuit without hemolysis (17). We have assumed that horse and human red cells are identical apart from their size. Actually horse red cells readily form rouleaux, especially with dextrans (41). However, this effect should increase the distance from cell to gas membrane interface and reduce the overall SA.
Finally, we used a spectrophotometer calibrated for Po2 and So2 in human blood for horse blood. Grosenbaugh et al. (22) show it is legitimate to do so.
Site of Blood Resistance (Work of Others)
Two groups have claimed that the extracellular fluid is the site of blood resistance (2, 3, 29). They used the stopped flow apparatus or competition methods, so boundary layers might bias their conclusions (see Critique of Others' Methodologies below). It would be odd to have extracellular resistance in vivo, but not in the continuous flow apparatus or oxygenator; gas exchange should not be more efficient in these devices than in life.
One group has claimed O2-dependent membrane limitation of NO transport by a transmembrane protein (2). While an attractive idea, we have three major concerns. First, Dno in the membrane oxygenator does not change with Po2 ranging from 20 to 500 Torr at either 14 ppm (7) or 25 ppb NO (Fig. 9). Second, we found a slight but significant increase in DlNO in humans, with a Po2 ranging from 86 to 143 Torr (10) and no difference between 133 and 488 Torr (11). Finally, facilitated diffusion across a membrane violates the Meyer-Overton rule; i.e., membrane permeability of a molecule depends on its oil-water partition coefficient. No violation of this rule has been found (30). Like ourselves, Subczinski et al. (38) found that the resistance of a simulated membrane to NO transfer was less than that of a water layer of the same thickness.
We, Carlsen and Comroe (13), Sakai et al. (35), and Liu et al. (28) have all tried to alter the red cell interior. Carlsen and Comroe found that the rate was greatly slowed when human red cells were shrunk by 3% saline, but not by spherocytes made by heating. Shrinking the red cell should alter the membrane SA and also the interior altering intraerythrocyte diffusion. We could not replicate their finding in horse red cells (9). Possibly this is a species difference, as the horse cell is small and contains less Hb than the human red cell and may not be so easy to shrink. Sakai et al. (35) measured the pseudo-second-order rate constant of NO reacting with liposome encapsulated human Hb over a range of Hb from 1 to 35 g/dl. They used a stopped-flow apparatus, but, because their particles were so much smaller than red cells, incomplete mixing and stagnant layers should not be such a problem. The rate constant decreased with increased particle diameter. Like us, they concluded that intracellular diffusion was the major barrier to NO red cell uptake. They speculated that bound heme caused an increasing diffusion barrier to NO. This seems less likely with the concentrations of NO and red cells that we have used (see Physiological Implications, below). Liu et al. (28) claimed that the NO half-life (t1/2) is independent of intracellular oxyhemoglobin. When they added NO to a red cell suspension, there was an immediate loss of signal, and then no loss as intracellular Hb was exhausted. However, looking at their Fig. 2, there was a reduced decline after the second aliquot, suggesting slowing as metHb accumulated and increased the diffusion distance. Overall, we, therefore, believe that the balance of evidence from others' work favors an intracellular barrier.
Critique of Others' Methodologies
The problem of mixing a rapidly reacting ligand with large particles, avoiding stagnant layers, was first tackled by Carlsen and Comroe (13) over 50 yr ago. They used the continuous flow rapid reaction apparatus at the University of Pennsylvania [see Hughes and Bates (26) for a fuller description]. They measured the rate constant ( in l·mol−1·s−1): (9)A dilute solution of human red cells (1/40 = 2.25 × 10−4 M Hb) was accelerated down one limb of a Y-shaped apparatus at 2.8 ms−1 = 150 ml/s, and a dilute solution of NO in deoxygenated buffer (Pno = 150 Torr = 3 × 10−4 M) (R. E. Forster, personal communication) at the same rate down the other. By moving a reversion spectroscope along the “lower limb of the Y,” the concentration of NO Hb formed at varying times after initial contact of the two reagents could be measured, and determined. It is then easy to calculate NO t1/2, second-order rate constant of NO (Kc NO), and specific blood conductance for NO (θNO) from (see Table 1). Unlike ourselves (see Table 1), they were observing a true second-order reaction, where equimolar amounts of reagent are mixed. The rate slows as the reagents are used up at a rate proportional to the multiple of the [NO] and [Hb]. In our oxygenator model, Hb is well in excess. The reaction rate is proportional only to the reagent concentration that is significantly used up (NO), i.e., the kinetics are “pseudo-first order.”
There has been much recent interest in NO kinetics with the red cell (Table 1) since cellular Hb accounts for removal of endothelial-derived NO. Stopped flow (2, 3, 35), competition (2, 3, 29, 40), NO electrode (28), and computer simulation (13, 14, 25) methods have all been used. Unfortunately, different workers have used different terms for rate constants: the second order and Kc, t1/2, and θNO. To help compare, we have presented data using all four terms (Table 1). Unlike continuous flow, the stopped flow apparatus abruptly terminates flow once the reagents have filled the observation cell at the apex of the Y. The reaction is then followed at defined times using a static spectroscope. This method allows microliter amounts of reagents to be used (42). However, because significant extracellular resistance (2, 3) has been shown, we worry about stagnant layers when reacting NO with red cells using this method. With Sakai's method, smaller vesicles are used, which could avoid this problem (35). In the competition method, the rate of formation of metHb is used to estimate the rate of release of NO from NO donor in oxygenated buffer solution, with and without a suspension of red cells (2, 3, 28). Since the rate of reaction of NO with oxyhemoglobin is known from the literature, the rate of reaction with red cells can be calculated. Because the donor molecule is equally mixed throughout the reaction vessel, it is assumed that extracellular [NO] is likewise equally mixed, and no diffusion gradients occur. This assumption is disputed (36). The calculations also implicitly assume that there is no intracellular gradient of NO or oxyhemoglobin. Our Figs. 7 and 5C strongly challenge these two assumptions. Liu et al. (28) used a rapidly reacting NO electrode in a stirred solution of red cells to which NO was added. We would again worry that this method would not achieve rapid mixing. Extracellular gradients could thus explain the lower rate constants seen using stopped flow, competition, and NO electrode methods (Table 1). Computer simulation methods use published values for rate constants for NO reacting with oxyhemoglobin, D′ of NO (D′no) from Fick's first law (appendix), and solubility of [NO] and [Hb] within the red cell. Where there are no data for NO, they are extrapolated from published data for O2. While estimating D′no from O2 using the ratio of diffusivity is reasonable for water or plasma, Fig. 7 suggests that it is unwise for intracellular diffusion. There is also inconsistency in the values used by different groups, leading to inconsistent values for the rate constants (36). Certainly our calculated value for D′no is significantly lower than that used by others.
An important computer simulation model was created by Chakraborty et al. (14, 15). They developed a generic mathematical model for θ for any reactive gas for a red blood cell of any shape surrounded by an unstirred plasma layer. They calculated a value for θNO = 4.2 × 106 ml NO·ml blood−1·min−1·Torr−1. This is clearly incompatible with others' values (Table 1). Unfortunately, their paper contains a number of math errors (V. Balakotaiah, personal communication). Their (corrected) model [Eq. 28 in their second paper (15)] is, however, sound and gives sensible θO2 and θCO values. We recalculated θNO using this equation and their parameters except 1) D′no [where we used our value (appendix)], and 2) βNO. βNO, the slope of the NO Hb dissociation curve, is a crucial variable. There are scant data in the literature (19). We used a single datum point of 0.011% NOHb saturation [S-nitrosohemoglobin (SNO)] at 40 ppm (P = 0.029 Torr, 6.3 × 10−8 M) from recent human exposure data by Gladwin et al. (20). This gives SNO/Pno = “βNO” = 3.86 × 10−3 Torr−1. This gives θNO = 3.6 ml NO·ml blood−1·min−1·Torr−1. Although this agrees with others, it may be coincidence. The reaction pathways of NO with heme and thiol depend on Pno, Po2, So2, and the allosteric conformation of the Hb molecule (21). The relationship between saturation and partial pressure may deviate from a simple reversible ligand/heme dissociation curve.
Deonikar and Kandia (16) designed an interesting reaction apparatus. Like our system, continuous gas and liquid flow are separated from one another by a semipermeable membrane. They point out that this steady-state system avoids high localized concentrations that occur with saturated NO solutions. There is no decline in concentration over time as with NO donors. Their circuit, therefore, produces a more physiological NO delivery. Like us, they found Hb dependence, but only at <5–10% hematocrit. Unlike us, they found liquid flow rate dependence of NO uptake. This suggests stagnant layers (see following paragraph), perhaps explaining their lower value for Kc. Additionally, their dimensions suggest a far smaller SA for gas exchange than our oxygenator, with corresponding loss of efficiency.
We are the only group to use a membrane oxygenator. It has many advantages. It can be purchased off the shelf. It allows use of in vivo concentrations of [NO], carbon monoxide ([CO]), [O2], and red cells. It is possible to change one variable, e.g., viscosity, and keep others, e.g., hematocrit, blood flow, and membrane SA, constant. It is possible to measure many aspects of O2, acid base, CO, and NO status every 5 min for several hours. Because we saw no change with solutions of differing viscosity/diffusivity, it appears free of extracellular [NO] gradients found in the stopped flow, competition, and perhaps NO electrode and simple semipermeable membrane techniques. This is confirmed by the lack of effect of changing blood flow: in an early paper, Roughton (33) thought the continuous flow apparatus free of extracellular gas gradients because the O2 uptake rate did not change if the liquid flow rate was increased threefold. He reasoned that, if significant stagnant layers existed, they would go as flow increased. We also conclude that there is no extracellular resistance in the oxygenator, since we found that a 25-fold change in blood flow rate had no effect on NO uptake (Dno) (7).
We are the only group to try to measure θNO in vivo. We calculated (10)taking NO membrane conductance (DmNO) as DlNO after successive exchange transfusions with oxyglobin in dogs (12), i.e., θNO = 0.6 × (1/0.61 − 2/4.27)/(1/2.69 − 1/4.27) = 5.1 ml NO·ml blood−1·min−1·Torr−1. We used a stopped-flow value for θCO in dogs (24). There has been less concern with the stopped flow method for the reaction of CO with red cells compared with NO, as it is a much slower reaction. In Fig. 4 of our laboratory's previous paper (12), it does not look as if we have reached maximum DlNO after three successive exchanges. If we set DmNO as 6, that would make θNO = 3.8 ml NO·ml blood−1·min−1·Torr−1.
Though we were most interested in diagnostic [NO], our results inform endogenous NO biology in vivo. Recent estimates (23) put tissue [NO] “at 100 pM (or below) up to 5 nM” (10−10 to 5 × 10−9 M). We investigated these concentrations in our last experiment using in vivo (alveolar) gas concentrations (6) 25 ppb equivalent to 42 pM tissue concentration. We showed no change in Dno with [NO], viscosity, or red cell size, but change with nitrite/dithionite, all consistent with Fick's law. We found no difference across a wide range of O2 tensions from arterial to venous values. Thus the only blood uptake mechanism we could show was red cell interior diffusion limitation. No effect of viscosity means that the extracellular diffusion gradient is zero. In other words, the plasma partial pressure of NO is the same everywhere. One of the puzzles of NO biology is how NO released from the endothelium can stay in the circulation and dilate smooth muscle when it is only separated from a massive Hb “sink” by a thin red cell membrane. Biochemical pathways have been suggested (21); here we offer an alternative. The red cell interior has long been described as “freely rotating Hb molecules in a close-packed lattice” (32). We believe this lattice impedes NO diffusion. We do not believe it can be an “advancing front” where NO “takes out” surface oxyhemoglobin molecules, progressively increasing the diffusion distance to active heme sites. In our oxygenator or in a DlNO single breath, there are a million hemes for every NO molecule.
Practical Implications for DlNO and DlCO Measurements
Correction of DlNO for Hb.
Based on these experiments, we believe that the blood resistance to NO transfer rises as the [Hb] drops <7 g/dl. This is not because the distance for diffusion to the red cells increases, nor because the effective red cell SA falls. It is because there are fewer accessible heme sites. In support of the work by van der Lee et al. (39) pre- and posttransfusion and Zavorsky's (47) advice, there appears to be no need to correct DlNO for Hb over the range in routine clinical practice. When Zavorsky recommended the range 8–15 g/dl, the only information available was rather noisy data from horse blood (7). From Fig. 1A, there actually seems to be minimal fall in Dno down to 7 g/dl and not much down to 5 g/dl. Where we disagree with van der Lee et al. (39) is their conclusion: “Because DlNO is independent of Hb concentration. . . . θNO can be considered to be infinite.” If θNO is constant over 7–15 g/dl, DlNO will likewise be independent of [Hb]. This happens from the known kinetics of the NO reaction with the red cell. Equation 9 is second order; the rate of reaction is proportional to the concentration of NO and the concentration of red cells. As both reagents combine, they are used up, and the reaction slows. This kinetic relationship holds when the concentrations of NO and red cells are roughly equal. In our experiments and diagnostic work, red cells are substantially in excess, so the concentration does not change as the reaction proceeds. The kinetics of Eq. 9 then become “pseudo-first order” rather than second order, i.e., −d(NO)/dt = × (NO), where j″ = × (Hb). In turn, θNO = × 60 × α-NO/1.1.= 4.5 ml NO·ml blood−1·min−1·Torr−1 rather than infinity (Table 1).
For DlNO, Eq. 1 needs to be adapted to the special case when θNO is constant. Additionally, Vc and Dm vary together (25). Vc is proportional to Dm3/2, since volume/SA is proportional to diameter3/2, i.e., 1/DlNO = 1/DmNO +1/θNO DmNO3/2. This reduces to DlNO = 1/[(1 + k)/DmNO]. DlNO is, therefore, approximately proportional to Dm. We have found the constant of proportionality to be ∼0.6 (12).
Which value of θNO to use.
Given the practical problem of measuring such a reactive ligand in biological solutions, the agreement among the bottom four results using differing techniques and species (Table 1) is good. Because other methods of technique may underestimate the rate constant because of extracellular [NO] gradients, we would still advise using θNO = 4.5 ml NO·ml blood−1·min−1·Torr−1 derived from the value of Carlsen and Comroe (13) for = 167 l·mM−1·s−1. The close agreement between their value and our in vivo estimate supports this view. The higher the value for θNO used, the greater the value for Vc and the lower the value for Dm. In a previous worked example (8), our laboratory showed the effects of using different values for θNO. For a healthy 45-yr-old male with Hb of 15.3 g/dl using the steady-state method DlNO = 184.1 ml·min−1·Torr−1 and DlCO = 38 ml·min−1·Torr−1. Using θNO = 4.5 ml NO·ml blood−1·min−1·Torr−1, DmCO = 184.9 ml·min−1·Torr−1 and Vc = 80 ml, whereas using θNO = infinity DmCO = 92 ml·min−1·Torr−1 and Vc = 108 ml.
Directions for Further Work
Ideally this work should be repeated in vivo. This would be impossible for the viscosity or cell size experiments. However, in animal models, it should be possible to alter the red cell interior by increasing metHb concentration to 25%. These levels are seen giving nitrite to patients with cyanide poisoning and could be readily reversed with methylene blue. It would also be interesting to look at other species’ red cells of varying shape and size to try to confirm our findings.
Taking into account our data and a critical appraisal of the literature, we believe that the balance of evidence favors blood limitation to NO transfer by the red cell interior.
No conflicts of interest, financial or otherwise, are declared by the author(s).
Author contributions: C.D.B., A.J., and A.V. conception and design of research; C.D.B., F.B., A.J., and C.S. performed experiments; C.D.B. and C.S. analyzed data; C.D.B., A.J., and C.S. interpreted results of experiments; C.D.B. prepared figures; C.D.B. drafted manuscript; C.D.B., A.J., C.S., and A.V. edited and revised manuscript; C.D.B., F.B., A.J., C.S., and A.V. approved final version of manuscript.
We are very grateful to the following for help with initial experiments: Clare Hay, David Marshall, Martin Pooley, Nick Mann, and Rosemary Murrell. We are very grateful to Dr. Helen Doyle (nee Dunningham) for original circuit design. We are extremely grateful to J. M. B. Hughes for reading our manuscripts and suggesting many improvements.
According to Fick's first law, mass transfer per unit area (J) = −D′ ΔC/dx, where D′ is the diffusion coefficient in cm2/s, ΔC is concentration gradient, and dx is infinitesimal distance, i.e., (A1)Rearranging total mass transfer (A2)where ΔP partial pressure gradient. ΔC = αH2O ΔP, and D′ is directly proportional to αH2O, the water solubility, i.e., D′ = k αH2O, i.e., k αH2O SA/x αH2O ΔP = θVcΔP.
In other words, for NO and CO, considering the diffusion element alone of θCO, ΘNO/ΘCO is proportional to (αNO/αCO)2 ≈ 4, giving ≈1 ml·ml−1·min·Torr.
D′ can be calculated from Fig. 7 by mass balance (A3)Rearranging D′ = (Dno dx)/(SA αH2O), (Dno dx) is the integral under the slope of Fig. 7, SA is the surface area of the horse red cell = mean SA × red cell count × contact volume, and αH2O is the water solubility of NO at 37°C. We get a value for Vc of 2 ml using either the Dno/Dco method or the traditional method using varying Po2 and Holland's value for ΘCO (24) = (1.77 × 10−4)/(5.46 × 10−5 × 65.19 × 10−8 × 60 × 3 × 4.63 × 109) = 8.98 × 10−6 cm2/s.
There are limited data for the diffusion coefficient derived from Fick's first law in the other solutions studied. One approach is to use Wilke and Chang's formula (43): the D′ of a solute (including a gas) within a given solvent may be predicted by (A4)where χ is “association factor”, T is temperature in °K, M is molecular weight (molecular mass) of solvent, η is viscosity (centipoise), and V is molecular volume of solute (cm3/g mol). For water as solvent χ = 2.6, T = 310°K, and V for NO is 23.6 cm3/g mol.
The η for water at 37°C is 0.6954 cP, and horse plasma at 37°C is 1.1 cP. This gives D′no (Hartmanns) = 3.9 × 10−5 cm2/s at 37°C and D′no (horse plasma ) = 2.7 × 10−5 cm2/s at 37°C. Similar calculations give dextran 500 10–30% 1.68 × 10−6 to 3.36 × 10−8 cm2/s at 20°C.
These calculated figures seem supported by direct and indirect measurements of D′no, e.g., 3 × 10−5 cm2/s (water) (46) at 37°C and 2.79 × 10−5 cm2/s (ox serum) (45) at 37°C. (We obtained this value by multiplying a value for O2 = 1.86 × 10−5 cm2/s).
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