Vol. 254, No. 4 Issue of February 25, pp. 1178-1190, 1979 Printed in U.$.A.

The Rate of Oxygen Uptake by Human Red Blood Cells*

(Received for publication, May 1, 1978)

J. Thaddeus Coin* and John S. Olson

From the Department of Biochemistry, Rice University, Houston, Texas 77001

Oxygen uptake into intact and reconstituted human red blood cells was measured using dual wavelength, stopped flow techniques. The rate of oxygen uptake by human erythrocytes is roughly 40 times slower (tl,z = 80 ms at 0.125 mM 02, 25°C) than the corresponding rate of oxygen combination with free hemoglobin. Ox- ygen transport through the red cell cytoplasm accounts for part of this difference and predicts a half-time of uptake of about 15 ms, which is still 5 times smaller than that observed experimentally. Further limitation of uptake appears to be due to the presence of unstirred layers of solvent adjacent to the red cell surface. Very rapidly after mixing, these layers form and become depleted of 02 due to uptake by the cells. This requires that the bulk of the oxygen molecules must diffuse over rather large distances, 1.0 to 5.0 pm, before they can penetrate the erythrocytes.

A mathematical model was developed to take into account diffusion through an unstirred solvent layer which increases in thickness with time. This scheme can account quantitatively both for the dependence of the apparent rate of uptake on O2 concentration and for the shape of the observed time courses. In addition, the diffusion parameters which were developed for the 02 reaction can also be used to describe quantitatively the rates and time courses of CO and ethyl isocyanide uptake and the rates and time courses of O2 release from cells in the presence of sodium dithionite. Finally, the parameters used to describe the stopped flow re- sults can also be used to simulate quantitatively O2 uptake time courses obtained from previous studies with thin films of red cells (Sinha, A. K. (1969) Ph.D. dissertation, University of California, San Francisco; Thews, G. (1959) Arch. Gesamte Physiol. Mens. Tiere (Pflufgers) 268, 308-317).

In 1927, Hartridge and Roughton (1) measured the rate of O2 uptake by sheep erythrocytes in a rapid mixing, continuous flow apparatus. The observed half-time for intact cells was 20 to 40 times greater than that observed for O2 uptake by free hemoglobin. This result has been confirmed with human red cell suspensions in more modern rapid mixing devices (2, 3). While there is little doubt as to the validity of the experimental observation, there has been some controversy concerning the physical meaning of the slow rate of uptake by intact cells. This is mainly due to the fact that repeated attempts to explain the large differences between predicted rates for up-

* This work was supported by United States Public Health Service Grant HL-16093-05 and Grant C-612 from the Robert A. Welch Foundation. The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.

$ Present address, Section of Biochemistry, Molecular and Cell Biology, Cornell University, Ithaca, N. Y. 14853.

take by a theoretical membraneless packet of hemoglobin and those observed for intact cells have failed to produce a con- sistent model (4-7).

In their original paper, Hartridge and Roughton (1) pro- posed four possible explanations for the slow reaction of oxygen with red cells: 1) within the red cell, deoxyhemoglobin is altered and reacts very slowly with 02; 2) the rate of O2 diffusion is reduced more markedly within the red cell cyto- plasm than it is in an equivalent, concentrated solution of free hemoglobin; 3) the red blood cell membrane is highly resistant to oxygen diffusion; and 4) incomplete stirring of the aqueous layers adjacent to the cell surface causes a net increase in the effective diffusion path from bulk solvent to the cell center. In later work, Roughton and co-workers (4, 5) presented theo- retical arguments in favor of the third proposal, that diffusion across the red cell membrane is the major rate-limiting step in O2 uptake. However, a number of workers have criticized their analysis and proposed that the membrane offers little or no resistance to oxygen diffusion (2,6,8). The most compelling evidence against the idea of membrane resistance is the ob- servation of Kreuzer and Yahr (8) that there is no difference between the rate of O2 uptake by a 100~pm layer of a concen- trated hemoglobin solution and that by an equivalent layer of packed red cells. However, it is also clear that a simple analysis which considers the erythrocyte to be a membraneless packet of concentrated hemoglobin is not sufficient to describe the time course of O2 uptake. When the appropriate diffusion constants for hemoglobin and oxygen in the red cell interior are employed, the calculated half-time is still roughly 5 times smaller than that observed in rapid mixing experiments (5,9) (Fig. 2).

In 1969, Moll (7) suggested that the extra resistance to O2 uptake was a result of a doubling of the thickness of the cell due to deformation in the mixing chamber of his stopped flow device. However, 3 years later, Miyamoto and Moll (10) took stroboscopic photographs of red cells in the observation cham- ber during stopped and continuous flow experiments. They observed no change in cell shape, even at times as short as 10 ms after mixing. Furthermore, Moll’s original calculations (7) indicated no extra resistance to oxygen release from red blood cells in the presence of excess sodium dithionite. Using a membraneless packet model, he was able to simulate closely time courses for the reaction of oxygenated cells with dithio- nite. In contrast, this simple model was unsatisfactory for the simulation of O2 uptake time courses. Roughton (11) had observed the same discrepancy between 02 uptake and release 10 years earlier.

In 1972, Gibson’ carried out a number of unpublished calculations which suggested that an unstirred layer of buffer of the order of several micrometers would cause a marked decrease in the rate of O2 uptake by red cells. Middleman (12) and Gad-el-Hak et al. (13) have also suggested, quite inde- pendently, that a stagnant, unstirred solvent layer adjacent to

’ Q. H. Gibson, personal communication.

1178

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Red Cell Oxygen Uptake 1179

the cell surface would offer sufficient resistance to 02 diffusion to account for Roughton’s data. However, as yet no one has presented theoretical time courses which accurately describe those observed experimentally.

In view of these various interpretations and the discrepan- cies associated with previous red cell studies, a fresh set of rapid mixing experiments has been carried out, employing modern stopped flow spectrophotometric techniques and a computerized data collection system. The results have been analyzed quantitatively in terms of the four possibilities out- lined by Hartridge and Roughton (1) in their original paper. In particular we have examined for the formation of unstirred aqueous layers around the red cells after passage through the mixing device. Although Hartridge and Roughton claimed to have ruled out this possibility, our results suggest strongly that such unstirred layers do exist in rapid mixing experiments and influence markedly both the rate and the shape of the time course for O2 uptake by red blood cells.

MATERIALS AND METHODS

Red Blood Cell Preparations-Blood samples were drawn (into heparinized, evacuated tubes) from both investigators (J.T.C. and J.S.O.) at the Institute of Hemotherapy, Houston, Texas, and imme- diately placed on ice. The blood was then mixed with isotonic saline (0.9% NaCl solution) and centrifuged at 1000 x g for 10 min at 4°C. The supernatant and buffy coat were removed by aspiration. The pelleted cells were washed three times with isotonic buffer (77.5 mM NaCl, 10 pM CaC12, 58 mM sodium phosphate, pH 7.4) and suspended in the same buffer for storage.

Reconstituted red cells which contained various concentrations of hemoglobin were prepared by two methods. (a) for resealed cells containing less than 5 mM heme, permeable, hemoglobin-free mem- branes were prepared in 7.5 InM sodium phosphate, pH 7.4, according to the procedure of Dodge et al. (14) and then incubated with the appropriate concentration of hemoglobin in this buffer at 4°C for 30 min. Hemoglobin was prepared by extensive dialysis of cell-free lysate against 0.1 M Na2HP04 followed by dialysis against several changes of 7.5 mM sodium phosphate pH 7.4. The red cell membranes were resealed by the addition of concentrated salts to give a final concen- tration of 78 mM NaCl, 10 pM Ca&, 58 mM sodium phosphate, pH 7.4, and incubated at 37°C for 30 min. These resealing conditions are similar to those used by Bodemann and Passow (15). The reconsti- tuted cells were washed extensively in isotonic buffer with centrifu- gations at 1000 to 3000 x g for 10 min at 4°C. (b) for resealed cells containing 5 to 12 mM heme, packed red cells were rapidly diluted into an appropriate volume of cold 7.5 mM sodium phosphate pH 7.4 buffer and incubated with stirring at 0°C for 30 min. This hypotonic suspension of cells was then rapidly diluted into a 5-fold excess of warm isotonic buffer and incubated at 37°C for 10 min. Finally, the resealed cells were washed extensively with cold isotonic buffer as in Procedure a. The internal hemoglobin concentration was controlled by varying the ratio of the volume of lysing buffer to that of the original packed cells.

The internal heme concentrations of both native and reconstituted red cells were calculated from total heme and packed cell volume measurements. Total hemoglobin concentration was determined by lysing an appropriately diluted cell suspension with glass-distilled water and measuring the absorbance of the resulting hemolysate at 577 nm. Packed cell volumes were determined by sedimentation of the cell suspensions in Wintrobe hematocrit tubes. Mean corpuscular hemoglobin concentrations determined this way give normal values (16) for intact red cells (21 mM heme for J.S.O.‘s cells, 20 mM heme for J.T.C.‘s cells). The values for the reconstitued cells are given in Fig. 3.

Concentrated suspensions of native and resealed red blood cells were deoxygenated in glass tonometers by alternatively evacuating and flushing with NS. Aliquots of deoxygenated cell suspension were transferred anaerobically to 20-ml glass syringes containing anaerobic isotonic buffer (77.5 mM NaCl, 10 pM CaCls, 58 mM sodium phosphate, pH 7.4) to make a final concentration of 40 PM hemoglobin.

Carbon monoxide-treated cells were prepared anaerobically by injecting subsaturating quantities of carbon monoxide-saturated (0.96 InM CO) isotonic buffer into previously prepared syringes containing diluted, deoxygenated red blood cells. The syringes were shaken and

allowed to stand at room temperature for at least 1 h before use to allow complete equilibration of the carbon monoxide with all of the hemoglobin molecules present inside the cells.

Reactant Solutions-Oxygen dilutions were made by anaerobic mixture of either air-equilibrated (0.25 mM 02) or Oz-saturated (1.25 mM) isotonic buffers with anaerobic buffer. Carbon monoxide solu- tions were prepared similarly using CO (0.96 mivf)-saturated buffer. Stock solutions of ethyl isocyanide (25 mM) were prepared by injecting 37 d of pure liquid into a syringe containing 20 ml of anaerobic isotonic buffer. The pure isonitrile was prepared in this laboratory by P. Reisberg.

Dithionite Solutions-Stock dithionite solutions were prepared in a tonometer equipped with a side arm and a serum stopper. 0.3 g of sodium dithionite (Eastman, 90%~ pure) was placed in the side arm and the following were placed in the main compartment: 15 ml of isotonic sodium phosphate buffer, pH 7.4 (prepared from 0.155 M

NaHZOn and 0.103 M Na,HP04); 15 ml of glass-distilled water; and 8.8 ,ul of 0.034 M CaCly. Oxygen was eliminated from the tonometer before the contents were mixed. After mixing, the resultant solution contained 0.052 M NaZS204, 0.058 M sodium phosphate, and 10 PM CaC12 (0.310 iosM). This solution was withdrawn anaerobically and either used directly or diluted into isotonic anaerobic buffer,

Suspensions of Red Blood Cells in Dense, Anaerobic Media-Ten grams of “fatty acid-free” bovine serum albumin (Sigma Chemical Co.) were dissolved in 40 ml of isotonic buffer. The solution was centrifuged to eliminate bubbles and loaded into a tonometer. This 20% solution had a density of 1.054 g/ml. Humid N, gas was blown over the surface of the albumin solution for several hours with intermittent, gentle shaking to remove oxygen.

A 50% by weight, aqueous solution of Stractan II (an arabinose- galactose polymer with an average molecular weight of about 30,000, St. Regis Paper Co.) was treated with Rexyn I-300 (a mixture of anion and cation exchange resins, Fisher Chemical Co.) to remove small molecular weight contaminating ions (17). After filtering out the resin beads, 3% (w/v) albumin and 60 rnM NaHZPO1 were added to the solution. The pH was adjusted to 7.4 by 1.0 M NaOH and solid NaCl was then added to bring the ideal osmolarity to 0.310. To achieve the correct osmotic activity, the final concentrations of salts are based on the volume of water present in the solution, not the volume of the entire solution. Red blood cells were suspended in a few drops of the final Stractan II stock solution and examined under a microscope. The cells appeared to retain normal shape and size. The 50% Stractan II solution (density, 1.125 g/ml) was deoxygenated as described above for the albumin solutions.

Dual Wavelength Stopped Flow Experiments-In order to cancel out light-scattering artifacts, the reactions were monitored simulta- neously at two wavelengths (560 and 577 nm for oxygen and ethyl isocyanide reactions; 532 and 590 nm for carbon monoxide binding) using the dual detection attachment (model D-137) for a Durrum stopped flow apparatus. An example of a typical experiment is shown in Fig. 1. Transmittance signals from the two photomultipliers were collected by an OLIS model 3600 A/D converter interface and depos- ited in the memory of a Nova 2/10 minicomputer. The two signals were converted digitally to absorbance changes (Fig. 1A) and then subtracted (Fig. 1B). Control experiments in which deoxygenated cells were mixed with anaerobic buffer showed that the resultant time course (AA560 - AAs;i) exhibits no light-scattering artifacts. For example, the initial, rapid absorbance decreases seen at both wave- lengths in Fig. 1A and the apparent drift of the baselines (AA = 0) are the result of light-scattering artifacts. Neither of these features is observed in the corrected time course shown in Fig. 1B. Finally, in all cases, five to seven replicate runs for each experiment were averaged and used for analysis.

In order to prevent cell membrane rupture during passage through the stopped flow apparatus mixing chamber, the pneumatic ram was driven at low pressures (about 35 p.s.i.) and the stopping syringe assembly was tightened to minimize recoil as flow stopped. In all cases, samples of effluent were collected and examined for lysis. For the data reported, there was less than 5% lysis. These precautions, however, required decreased flow rates and hence increased dead times. The stopped flow apparatus was calibrated by use of the metmyoglobin-azide reaction and under our operating conditions a 6- ms dead time was observed. Consequently, at very high ligand con- centrations significant portions of the uptake time courses were unobservable. Therefore, for the sake of uniformity, most of the data presented have been normalized to the fist collected data point (zero time after flow stops, which represents 6 ms after the reaction commenced to take place). In addition, all theoretical analyses take

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1180 Red Cell Oxygen Uptake

TIME (ml) TIME (ma)

FIG. 1. Typical time course for oxygen uptake by human red blood AA577); B, light scattering corrected A absorbance signal obtained by cells. Red cells (J.T.C., 20 mM heme inside) in deoxygenated isotonic subtracting the two signals shown in A (AA~w - AA577). Since the buffer (77.5 mM NaCl, 10 pm of CaC12, 58 mM Nap,, pH 7.4) were absorbance changes due to oxygen binding have opposite signs at the mixed at 25°C with oxygenated buffer to give a final concentration of two wavelengths of observation, the resultant, corrected signal rep- 0.020 mM heme (total in solution) and 0.469 m&r 02 after mixing. A, resents the sum of absorbance changes at 560 nm and 577 nm. These A absorbance signals derived from each photomultiplier (AASSO and data represent the average of seven replicate experiments.

into account this 6-ms dead time when comparing observed with calculated results

Digital Computations-In order to simulate the time course of oxygen uptake, the following set of differential equations had to be solved numerically:

a*m ato4 _

at Do

- - k’(Oz)(Hb) + k(HbOn) * a2 (14

a(HbO2) - =

at DHbO 2 + + k’(Oz)(Hb) - k(HbOz) (lb)

A detailed discussion of the various algorithms employed is given in the miniprint supplement.’ However, a number of points should be made. The reaction of 02 with hemoglobin was simulated by a simple binding process. This has been shown to be a reasonable assumption when diffusion is the rate-limiting process for ligand uptake and when high levels of saturation are achieved (Refs. 9 and 11 and miniprint supplement).

In all cases, the values of k’ and K were taken to be 3 x lo6 M-’ s-’ and 40 s-l at 25°C. These values were chosen for the followina reasons: 1) they predict half-times which are consistent with those which we have observed experimentally for 02 binding to free hemo- globin; 2) they are consistent with reported literature values (18); and 3) the fractional saturation predicted at 0.125 mM 02 by the ratio of these constants is consistent with that observed in our kinetic exper- iments. A detailed description of the influence of cooperativity on 02 uptake and release time courses is given in the miniprint supplement, section III. The diffusion constants for 02 and hemoglobin were taken from the data tabulated by Kreuzer (19). Unless stated otherwise, the following values were used: DO* in buffer = 2.1 X 10e5 cm*/s; DO, in 20 mM hemoglobin (J.T.C.‘s cells) = 7.8 X 10M6 cm*/s; DO, in 21 mM hemoglobin (J.S.O.‘s cells) = 7.4 X 10M6 cm’/s; DH~o* in 20 mru hemoglobin = 6.4 X 10e8 cm2/s; Dnbo* in 21 miu hemoglobin = 5.5 X

10e8 cm*/s. The uptake of oxygen by red cells was formulated in terms of

diffusion into a volume element surrounded by two plane sheets representing the cell-buffer interfaces. Forster (9) and Kutchai (6) have argued that this formulation gives results equivalent to more complex cylindrical or torus models. Thus, diffusion from the ends of the cell is neglected, and the concentrations of HbOa and 02 are symmetrical with respect to the cell center (i.e. diffusion from both sides of the cell surface occurs at identical rates). The thickness of the red cell was taken to be 1.6 pm (9). The various boundary conditions and other restrictions were taken from previous work (7, 20) or derived using the principles described by Crank (21). Particular

* Portions of this paper (including Figs. IS, 2S, 3S, 4S, and 5s are presented in miniprint at the end of this paper. Miniprint is easily read with the aid of a standard magnifying glass. Full size photocopies are available from the Journal of Biological Chemistry, 9650 Rockville Pike, Bethesda, Md. 20014. Request Document No. 78 M-697, cite author(s), and include a check or money order for $2.85 per set of photocopies.

0

: VARIABLE LAYER

2 a

TINE (1)

FIG. 2. Comparison of time courses for 02 binding to free hemo- globin, a theoretical membraneless packet of 20 mM (heme) hemoglo- bin, and intact red blood cells (J.T.C., 20 mru heme inside). Conditions: isotonic buffer (see Fig. l), pH 7.4, 25°C 0.125 IIIM 02 and 0.02 mM

heme (total in solution) after mixing. The time course for a 1.6+m- thick packet (- - -) was calculated using the following constants: DO, in 20 mru hemoglobin = 7.8 X 10e6 cm2 s-‘; DHL,O* in 20 mM hemoglobin = 6.4 x 10-s cm2 s-l; k’ = 3 X lo6 M-’ s-’ and iz = 40 s-‘. The variable unstirred layer time course (----) was calculated using the intracelhrlar parameters given for the packet model, an external D = 2 1 x 10e5 cm* s-r, and a variable layer whose thickness is de%ned by Equation 2. The observed data for red blood cells (RBO and free hemoglobin (Hb, + - - - ) are given by the circles. Time courses in this case were normalized to the total absorbance change expected or observed after flow stops.

features of each model are described in the text, figure legends, and miniprint supplement,* section I. It should be noted that all simula- tions take into account the depletion of the total amount of oxygen present due to oxyhemoglobin formation (i.e. corrections are made for second order conditions when the total hemoglobin concentration in solution approaches that of the total oxygen concentration).

RESULTS

Oxygen Uptake and Heme Concentration Depend- ence-Normalized time courses for oxygen binding to free hemoglobin and intact erythrocytes are shown in Fig. 2. The half-time for binding to free hemoglobin is of the order of 2

ms under these conditions, and most of the reaction occurs in

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Red Cell Oxygen Uptake

the dead time. The half-time for the uptake of cells is some 40 times greater, about 80 ms. The dashed line in Fig. 2 repre- sents a theoretical time course for uptake by a membraneless packet of 20 InM hemoglobin which is 1.6~pm thick. The half- time in this case would be 15 ms, which is still 5 times slower than that observed experimentally. Thus, although it is clear that diffusion into and throughout the cell must limit in part the rate of oxygen uptake, some additional process is causing a further decrease in the observed rate.

As discussed in the introductory section, Roughton (4) proposed four possible explanations for the observed slow rate of O2 uptake: 1) very slow chemical reaction with hemoglobin; 2) reduced oxygen diffusion within the red cell matrix (as compared to an equivalent, concentrated solution of isolated hemoglobin); 3) membrane resistance to oxygen diffusion; and 4) the presence of stagnant, unstirred layers adjacent to the red cell surface. The relative merit of the first explanation can be assessed qualitatively by examining the dependence of the overall half-time of 02 uptake on internal hemoglobin concen- tration. Under pseudo-first order conditions, where the total heme concentration is at least 5 to 10 times less than the total O2 concentration, the half-time of uptake should be independ- ent of internal heme concentration if chemical reaction is completely rate-limiting. On the other hand, if diffusion into or throughout the cell is much slower than chemical reaction, the observed half-time should increase linearly with increasing internal hemoglobin concentration. This would occur because greater heme concentration requires more oxygen to diffuse into the cell and, therefore, increases the total time required to achieve 100% saturation.

As shown in Fig. 3, the half-time of O2 uptake increases markedly with increasing internal hemoglobin concentration. The upward curvature shown in Fig. 3B is readily explained in terms of a decrease in the cellular, oxygen diffusion constant with increasing internal protein concentration. For example, using the values tabulated by Kreuzer (19), the internal DO, would be expected to decrease from 1.5 X low5 cm*/s to 0.74 x 10e5 cm”/s in going from 7 to 21 mM heme. This causes a further increase in the half-time over and above that due to the increased amount of O2 that must diffuse into the cell.

The idea that the major rate-limiting step is a diffusion process is further supported by the results in Fig. 4. In these experiments, the internal heme concentration was varied by fiiing a specified number of heme sites with carbon monoxide. This allowed a variation in the concentration of oxygen com- bining sites without a change in the internal protein concen-

IO

08 06 0 25 50 75 100 125 150 0 5 10 15 20 TIME (ml) ,HEMEl in rnY

FIG. 3. Dependence of the rate of oxygen uptake on internal he- moglobin concentration using reconstituted cells. Conditions: isotonic buffer (see Fig. l), pH 7.4, 25”C, 0.020 mM heme (total in solution) after mixing. The solid lines are drawn through the experimental points. A, time courses for 0.125 mM 02 after mixing. A, reconstituted cells prepared by Method a (see “Materials and Methods”) containing 4 IIIM heme inside; A, 0, reconstituted cells prepared by Method b containing 7 mM heme inside and 12 mM heme inside, respectively; 0, intact cells (J.S.O.) containing 21 mM heme inside. B, dependence of the observed half-time of oxygen uptake on internal heme concen- tration. Micromolar 02 concentrations are given beside each curve.

02

FIG. 4. Dependence of the rate of oxygen uptake on internal, free heme concentration using carbon monoxide-treated cells. Conditions: J.T.C.‘s cells (20 mM heme inside), isotonic buffer (see Fig. l), pH 7.4, 25’C, 0.020 mM heme (total in solution) after mixing. The solid lines are drawn through the experimental points. A, oxygen uptake time courses for 0.125 mM 02 after mixing.3 The per cent HbCO is given beside each curve. B, dependence of the observed half-time of oxygen uptake on the concentration of free heme sites inside the cells. Micromolar 02 concentrations after mixing are given beside each curve.

tration and, therefore, presumably, also without a change in the internal oxygen diffusion constant. In this case, the half- time of oxygen uptake appears to be directly proportional to the internal deoxygenated heme concentration as one would expect for a diffusion-dependent process.3

The results suggest strongly that chemical reaction is not the major rate-limiting step in 02 uptake by cells. This idea is supported by numerical calculation. For example, if one at- tempts to simulate the observed time course of 02 uptake by using a membraneless packet model and by assuming that the “extra” slowing of the reaction (see Fig. 2) is due to slow chemical reaction, the oxygen association rate must be de- creased to roughly 8 X lo4 M-’ s-l (a corresponding decrease is also required for the dissociation rate constant). This value is roughly 40 times smaller than that observed experimentally for O2 binding to hemoglobin free in solution and, in fact, is smaller than the accepted value for carbon monoxide binding (-2 X lo5 M-’ s-l). Furthermore, NO, CO, and 02 uptake by cells exhibit roughly equal rates (11, 22). This observation provides further evidence that diffusion, not chemical reac- tion, is rate-limiting, since the association rate constants for these ligands vary from 2 X lo7 to 2 X lo5 M-l s-l, respectively.

The data in Figs. 3 and 4 do not rule out the possibility that the rate of 02 binding is altered when hemoglobin molecules are packed in a red cell. However, in the case of slower reactions (i.e. ethyl isocyanide binding, see Fig. 8 or CO and 02 displacements (9, 11)) when chemical reaction is definitely rate limiting, little difference is observed between time L~~‘)UTSBS

measured for dilute hemoglobin solutions and those for red cell suspensions. The latter observation was used originally by Roughton (4) to argue against any difference between the chemical properties of hemoglobin in solution and those in erythrocytes. Finally, Parkhurst and Gibson (23) used flash photolysis techniques to show that horse hemoglobin in red cells and in dilute solution reacts with CO at similar, if not identical, rates. In view of all of these observations and cal- culations, it seems highly unlikely that slow chemical reaction

’ The reaction of oxygen with CO-treated cells is markedly biphasic. The fast phase is indicative of oxygen uptake by unoccupied heme sites. This is followed by a slow phase (K = 0.5 s-‘) which exhibits a complicated dependence on both oxygen and CO concentration. This slow phase appears to be due to replacement of a small amount of bound carbon monoxide by oxygen. The uptake time courses shown in Fig. 3 were obtained by subtraction of these slow phases from the total absorbance changes.

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Red Cell Oxygen Uptake

0.10

A.

24 % STRACTAN

12% STRACTAN

I I I\ I\ L I\ 0 0.04 0.08 0.12

TIME (s) FIG. 5. The effects of dense media on oxygen uptake. Reaction

conditions are identical with those in Fig. 1. A, time courses for the reaction of cells with 0.312 mM 02. 0, cells suspended in anaerobic buffer and mixed with oxygenated buffer; 0, cells suspended in 20% bovine serum albumin and mixed with 02 buffer; & cells suspended in 24% Stractan II and mixed with 02 buffer; A, cells suspended in 24% Stractan II and mixed with 02 in 24% Stractan II. B, dependence of the rate of 02 uptake on oxygen concentration in the presence

accounts for the low rate of 02 uptake observed experimen- tally.

Membrane Resistance Versus Stagnant Layers-Since it is clear that diffusion is limiting oxygen uptake, the next question is what kind of diffusion resistance causes the rate of uptake to be slower than that predicted for a membraneless packet of hemoglobin (dashed line, Fig. 2).

The idea of an increased resistance to 02 diffusion in the cell cytoplasm was ruled out by the following reasons. First, there is no evidence, either experimental or conjectural, which suggests that the internal viscosity of an erythrocyte is differ- ent from that of an equivalent, concentrated hemoglobin solution. Second, in order to simulate the observed 02 uptake curve shown in Fig. 2 by using a membraneless packet model and assuming a low rate of internal 02 diffusion, the value of the 02 diffusion constant must be decreased to 10.5 x 10m7 cm*/s. This value seems unreasonable since it is roughly 8 times smaller than that observed experimentally for a com- parable solution of concentrated hemoglobin. Third, the time course of 02 release from cells in the presence of sodium dithionite can be approximated closely by using a membrane- less packet model and the experimentally observed 02 diffu- sion constant (see Fig. 9). Further evidence against cytoplas- mic diffusion being the sole limiting factor in O2 uptake is presented in Figs. 5 and 6. Although these data will be discussed in terms of ruling out membrane resistance, the same arguments apply to any type of internal diffusion proc- ess.4

4 Another possible explanation of slow 02 uptake is deformation of the red cell during flow through the mixer, perhaps by folding over as

100 B. BSA

d

0.0 0.2 0.4 0.6

.- - I C. STRACTAN

75 t

50-

25-

o- J 0.0 0.2 0.4 0.6

(021 ml4

(0) and absence (0) of 10% bovine serum albumin. C, dependence of the rate of 02 uptake on oxygen concentration in the presence and absence of Stractan II. 0, red cells in buffer mixed with 02 buffer; 0, red cells in 12% Stractan II mixed with 02 buffer; A, red cells in 24% Stractan II mixed with O2 buffer; El, red cells in 12% Stractan II mixed with O2 in 12% Stractan II (a control to see if mixing in the previous experiment was complete); A, red cells in 24% Stractan II mixed with 02 in 24% Stractan II.

Discrimination between the remaining possibilities, mem- brane resistance or unstirred layers, is more difficult. Simu- lation of the time course shown in Fig. 2 using either a membrane-packet model or an unstirred layer-packet model yields parameters which are reasonable: either a membrane, oxygen diffusion constant equal to 3.2 X lo-’ cm2/s or an unstirred layer 2.4~pm thick. In order to test for the influence of diffusion through external aqueous layers, the viscosity of the suspending solvent was increased by adding either bovine serum albumin or Stractan II (an arabinose-galactose poly- saccharide)5 to the reaction mixture. --..------...-.. -_~~ ---.---.--...--.--

originally suggested by Moll (7). This idea is mathematically similar to that of increased cytoplasmic viscosity since they both represent limiting internal diffusion processes. The arguments against defor- mation being the explanation for slow uptake are even more compel- ling. First, using a packet model and assuming an increased thickness, simulation of the observed time course requires an internal thickness of 4.4 F, which is 3 times that of the average thickness of a normal erythrocyte. Second, Miyamoto and Moll (10) observed directly no apparent change in red cell shape during rapid mixing experiments. Third, since deformation represents another type of internal diffusion process, the results in Figs. 5 and 6 also argue against its validity.

5 In preliminary experiments, red cells were suspended in concen- trated dextran solutions and then mixed with oxygenated buffer. The results were unsatisfactory. Large light scattering changes dominated the observed absorbance data so that even when the traces measured at 577 nm were subtracted from those measured at 560 mn, multiple phases were observed. These light-scattering artifacts are most likely due to red cell aggregation and disaggregation reactions which are associated with rouleau formation. Substantial red cell aggregation is known to occur in concentrated dextran solutions (24). In order to get around this problem of rouleau formation, we carried out uptake

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Red Cell Oxygen Uptake 1183

80

60 -r

F \ RI c 40 -

20

0 L

Experiment \ ,,I’ -

P

0.0 0.2 0.4 0.6

(02) mM

FIG. 6. Dependence of the rate of uptake by cells on oxygen concentrations. Conditions are given in Fig. 1. The open circles represent J.T.C.‘s cells (20 mM inside); the filled circles J.S.O.‘s cells (21 mM inside). The theoretical curves were calculated using a mem- brane model and the following constants: 20 mM heme (inside); DO*

(inside) = 7.8 X 1Om6 cm’/s; Dabo, = 6.4 X lo-’ cm’/s; DM(OZ mem- brane diffusion constant) = 3 x lo-* cm*/s; membrane thickness = 0.015 am; and partition coefficient of 02 between buffer and membrane

As shown in Fig. 5, the rate of oxygen uptake (defined as ln2/(half-time)) is observed to decrease 28 st 3% in the pres- ence of 10% bovine serum albumin at all 0s concentrations examined. Previous work (19) has shown that the 0s diffusion constant decreases from 2.1 to 1.6 X low5 cm2 s-l in going from either 0 to 10% serum proteins or 0 to 10% hemoglobin. Thus, if external diffusion through a stagnant solvent layer is a major rate-limiting step, the rate of 02 uptake would be expected to decrease by 24% when the cells are suspended in 10% bovine serum albumin. This agreement between the observed and expected decrease suggests strongly that exter- nal diffusion limits the rate of 02 uptake. If membrane resist- ance were the dominant factor, little or no effect of added serum albumin would be expected, particularly for such a moderate change in solvent viscosity. This idea is supported by the experiments carried out in the.presence of Stractan (Fig. 5). Although in this case the oxygen diffusion constants are not known, there is a monotonic decrease in the rate of oxygen uptake with increasing external polysaccharide con- centration (from 6 to 24% by weight). Again, this decrease occurs at each ligand concentration examined.

More subtle, but equally compelling evidence in favor of rate limitation due to diffusion through stagnant layers is shown in Fig. 6. As indicated by the dashed line in Fig. 6A, the observed rate of uptake appears to depend on greater than the first power of the external oxygen concentration. This is not compatible with membrane permeation being rate-limit- ing. For a model in which membrane resistance is the domi- nant rate-limiting factor, the rate of uptake would be propor- tional to the rate of permeation into the cell. The latter rate

experiments in either bovine serum albumin or Stractan II, a poly- saccharide which does not appear to interact with the red cells (17).

7.0

6.0

5.0 _

T In

N E 4.0

m 0

x 3.0

,” 2.0

I .o

0.0

B 9 I I I I -I

/ IO

-I

Experiment 8’

----+I’ /

O,/’

/‘.

8 ’ cc -6 Membrane

Model 1

I - 1.5 - 1.0 - 0.5 0.0

lag (02) mM = 4.4 (7). A, dependence of the observed rate (ln2/half time) on oxygen concentration. The DM used here is the average of the appar- ent membrane diffusion coefficient for J.S.O.‘s and J.T.C’s cells at 0.125 mM OZ. B, dependence of the apparent membrane diffusion constant (DM) on 02 concentration. The circles were obtained by varying DM to obtain fits to the half-times of the experimental time courses.

is given by the product of the 02 diffusion constant (in the membrane) times the concentration gradient across the mem- brane. Since the concentration of free 02 inside the cell would be maintained near zero due to combination with hemoglobin, the concentration gradient would be approximately propor- tional to the concentration of oxygen present in the buffer. Thus, the observed rate of uptake would be expected to be directly proportional to external 02 concentration. The solid line in Fig. 6A shows this dependence quantitatively and was calculated using a fixed membrane diffusion constant and the packet model.

The discrepancy between the observed dependence of the rate of uptake on 02 concentration and that predicted by the membrane model is quite substantial. I f the individual time courses for uptake are analyzed independently by allowing the membrane diffusion constant to vary until a good “fit” is obtained, the apparent membrane diffusion constant appears to increase over 3-fold in going from 0.031 to 0.625 mM 02 (Fig. 6B). This conclusion seems highly improbable if interpreted literally since membrane resistance should not depend on 02 concentration.

An alternative interpretation of the results in Fig. 6 is that the diffusion resistance to 02 uptake is time-dependent. At the highest O2 concentration, 0.625 mM, the overall uptake process exhibits an 8-ms half-time and apparently much less resistance to 02 diffusion into the cells. At the lowest 02 concentration, 0.031 mM, the uptake process exhibits a 250- to 300-ms half-time and roughly a 3-fold increase in the resist- ance to O2 diffusion. This is compatible with the idea that the amount of stirring in aqueous layers adjacent to the cell surface will decrease as a function of time after mixing in stopped flow experiments. An increase in the thickness of these stagnant aqueous layers would cause a concomitant

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decrease in the apparent 02 diffusion constant if interpreted which in our apparatus shines along the axis of flow. Since no net flow is allowed after the stopping syringe hits the retaining block, the laminar flow stage is transient and the cells quickly @l/2 - 0.1 s) take on a more random orientation. The latter process accounts for the increase in scattering (decrease in transmittance) observed in the range from 0.01 to 0.5 s. This interpretation is supported by the photographs of Miyamoto and Moll(l0) which showed that, in stopped flow experiments, the red cells are oriented parallel to the sides of the cuvette at 10 ms after mixing but that more random orientations are observed at longer times.

in terms of membrane resistance (i.e. Fig. 6B). Variable Unstirred Layers and O2 Uptake-The idea of

unstirred solvent layers does not imply incomplete mixing. There can be little doubt that, in the internal cavity of the 8- jet tangential mixer, the layers of deoxygenated solvent are sheared off the membrane surface and replaced with an aqueous phase containing oxygenated buffer. Any slight in- crease in flow rate under our experimental conditions causes shearing and disruption of the cell membrane. The unstirred layers are formed after mixing has taken place and accompany the cell surface during tumbling in the observation chamber. Immediately following mixing, the layer of buffer directly adjacent to the cell does contain oxygen but this zero time concentration level decreases rapidly as 02 diffuses into the cell and combines with hemoglobin. Since the total amount of 02 present in the unstirred solvent phase is between 20 and 200 times less than the number of binding sites in the red cell, the majority of the O2 molecules which are required for complete saturation must diffuse through these external stag- nant layers. Furthermore, since the tumbling of the cells and, therefore, the amount of stirring must decrease after flow stops, the stagnant aqueous layers will increase in effective thickness with time and cause a further slowing of the rate of 02 uptake.

The time dependence of red cell tumbling can be estimated from the light-scattering changes which occur during the mixing of cells with anaerobic buffer (solid line in Fig. 7; note that this curve is drawn to mimic the transmittance pattern of the scattering changes). There is an initial rapid decrease in scattering (increase in transmittance) which is over in 5 to 10 ms after flow stops. This is interpreted to represent a change from a random cellular orientation which results from the turbulence set up in the mixer to an orientation in which the cells are lined up parallel to the walls of the observation cuvette due to laminar flow. In the latter orientation, less scattering will be observed (more transmittance) due to a minimum exposure of the cell surface to the incident light,

0 06

004

002

000

3.0

2.0

I.0

0.0

0 100 200 300

TIME or T112

(ms)

FIG. 7. Light-scattering changes and the dependence of the appar- ent thickness of the unstirred layer on the half-time of the overall

reaction. Reaction conditions are given in Figs. 1 and 6. The circles (0, J.T.C.‘s cells; 0, J.S.O.‘s cells) were obtained by varying &o, the thickness of the unstirred layer, to obtain fits to the half-times at the appropriate experimental time courses. The solid line represents a light scattering trace in which deoxygenated cells were mixed with anaerobic buffer. In this case, the absorbance changes at 560 and 577 nm were added to intensify the scattering changes. Note that the trace is presented as the inverse of the absorbance change and corresponds in sign to the observed transmittance changes.

In order to estimate the magnitude of the unstirred layers, various time courses of 02 uptake were simulated using a packet model and varying the thickness of the aqueous layer until the calculated half-time equalled that observed. The results of these calculations are also shown in Fig. 7 (dashed line) where the apparent thickness of the stagnant solvent layer is plotted uersus the half-time of the observed time course. As shown in this figure, there is a close correspondence between the time dependence of red cell tumbling (as mea- sured by light scattering) and that of the apparent thickness of the stagnant layers. Both processes appear to be biphasic. Rapid formation of a stagnant layer of the order of 1 ,sm appears to take place within the first 8 ms after mixing. This corresponds to the rapid increase in transmittance which we have attributed to a change from turbulent to laminar flow. This rapid phase is followed by a much slower increase in the apparent solvent thickness, from roughly 1 to 3 pm. The apparent half-time of this increase is very similar to that observed for the slow increase in transmittance observed in the light-scattering experiments. The latter increase has been assigned to a change from transient laminar flow to a more static but also more random orientation of the cells.

The following expression was derived to describe quantita- tively the time dependence of the thickness of unstirred solvent during a stopped flow experiment and is based on the results in Fig. 7:

L umtirred layer = 5.0 pm - (1.6 ~m)e-300”-i ’ - (3.4 pm)e-9s-’ ’ (2)

The initial trial values for the exponents were obtained from analyses of the fast and slow phases of light scattering time courses (i.e. solid line, Fig. 7)). Initial estimates for the am- plitudes were obtained from the fixed, unstirred layer thick- ness values obtained at high and low oxygen concentration (dashed line and symbols in Fig. 7). The final parameters given in Equation 2 represent minor alterations from the initial estimates and were obtained from multiple attempts at simulating two independent sets of Oz uptake experiments (see Fig. 1, miniprint supplement). As shown in Figs. 2 and 8A, both the observed dependence of the rate of uptake on O2 concentration and the observed shape of the time course can be described quantitatively by an unstirred layer model which incorporates the time dependence given by Equation 2. A more detailed discussion of the shape of the 02 uptake time course has been presented in a preliminary publication (25). However, it is worth noting that none of the other possible models (slow internal diffusion or membrane resistance) pre- dict time courses which are comparable in shape with those observed experimentally.

Carbon Monoxide and Ethyl Isocyanide Uptake-The var- iable unstirred layer model was tested further by examining the rate of uptake of two other ligand molecules. Equation 2 should apply to CO and ethyl isocyanide reactions with red cells even though the parameter values were derived to fit oxygen results. Diffusion constants for CO and ethyl isocya- nide were calculated from the oxygen constants using the

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Red Cell Oxygen Uptake

50

40

30

20

IO

0

I I

0

00 0 I5 0 30 0 45 0.60

(Oaygon ) , m Y

- I5 i In

c ! ; 50

.

N c

25

0.0 0.10 0.20 0.30 0.40 0.50

( Carbon Monoride) , m Y

FIG. 8. Comparison of the rate (ln2/half-time) of reactions of oxygen, carbon monoxide, and ethyl isocyanide with free hemoglobin (A) and intact red blood cells (0, J.T.C.‘s cells, 20 mM heme inside; 0, J.S.O.‘s cells, 21 mM heme inside). Conditions: isotonic buffer (see Fig. l), pH 7.4, 25”C, 0.020 m&f heme (total in solution) after mixing. Solid lines represent the concentration dependence of uptake rates predicted by the variable unstirred layer model for a 1.6~pm thick cell. The unstirred layer increases in thickness according to Equation 2.

Diffusion coefficients for CO and ethyl isocyanide were calculated using Equation 3. The second order reaction constants for CO and ethyl isocyanide which were used in the simulations are 2.0 x lo5 M-l s-l and 2.1 X lo4 M-l s-’ (experimentally determined for these buffer and temperature conditions; not all the CO points are shown here). All liganded forms of hemoglobin are assumed to have the same diffusion coefficients. A comparison of real and calculated time courses is given in the miniprint supplement, section I.

following relationship which has been shown to be valid for small gaseous molecules (11):

uptake rate is 30 to 40 times slower than the rate of oxygen combination with hemoglobin, which, in agreement with the heme concentration dependence shown in Figs. 3 and 4, pro- vides strong evidence that 02 diffusion into the cell is rate- limiting. The results with carbon monoxide are somewhat intermediate and indicate roughly equal contributions of dif- fusion and chemical reaction to the observed rate of CO uptake. As shown by the solid lines in Fig. 8, the variable, unstirred layer model (Equation 2) is compatible with all of these results and can be used to describe quantitatively the rate of uptake by red cells regardless of what ligand is exam- ined.

(3)

D, and MW, are the diffusion constant and molecular weight of the ligand molecule in question. Under the conditions examined, both the CO and ethyl isocyanide reactions with free hemoglobin can be considered irreversible and described approximately as simple, one-step association processes. Sec- ond order rate constants for CO and ethyl isocyanide binding were determined from parallel experiments with isolated he- moglobin using the same ligand solutions as those used for the red cell studies. The resultant rates (2.0 X lo5 M-’ s-’ for CO and 2.1 X lo4 M-’ s-’ for ethyl isocyanide) were then used in calculations of the expected time courses of uptake by intact erythrocytes.

A comparison of observed and calculated rates for CO uptake by red cells is shown in Fig. BB, and a set of observed and calculated time courses is presented in the miniprint supplement, Fig. 2s. The correspondence between the exper- imental and the theoretical time courses is as good as that observed for the oxygen results. In the case of O2 uptake, the reaction with free hemoglobin was approximated by a simple, one-step equilibrium. This approximation becomes inade- quate at low O2 concentrations where only low levels of saturation are achieved (see miniprint supplement, section III). On the other hand, the reaction of CO with free hemo- globin can be approximated by a simple second order process at all ligand concentrations (dashed line in Fig. 8). Thus, agreement between theory and experiment for the CO uptake data argues strongly against the objection that the parameters in Equation 2 are an artifact caused by failure to take into account cooperative oxygen binding to hemoglobin within the red cell.

In the case of isonitrile binding, chemical reaction is defi- nitely rate-limiting since there is little difference between the rate of uptake by cells and the rate of reaction with hemoglo- bin free in solution (Fig. 80. On the other hand, the oxygen

100

0

00 3.0 6 0 9.0 12 0

( Ethyl Isocyanide) , nY

Oxygen Release in the Presence of Sodium Di- thionite-There remains one apparent discrepancy in this red cell work. Why were Moll (7) and Roughton (11) able to describe oxygen release time courses by a simple membrane- less packet model and without having to invoke some kind of extra diffusion resistance? This observation is inconsistent with the idea that diffusion through the membrane is rate- limiting since equal resistance should occur with either influx

or efflux of oxygen.6 However, this observation does make

’ There is an alternative explanation for the apparently faster rates of oxygen release. In the analysis of most release experiments, it is assumed that dithionite is impermeant to the red cell membrane. If the latter assumption is not valid, dithionite diffusion into the cell could speed up the apparent 02 release by consuming free oxygen present within the cell. This effect could, in turn, mask any membrane resistance to the outward diffusion of oxygen molecules. Thus, the apparent success of the membraneless packet model in describing 02 release could be a fortuitous result of dithionite permeability across the red cell membrane.

In order to test for the permeability of dithionite, we prepared red cells containing methemoglobin by incubating native cells with so- dium nitrite and then washing thoroughly to remove residual oxidizing agent. These cells were reacted anaerobically with dithionite, and the rate of reduction to deoxyhemoglobin was used as a measure of the rate of dithionite permeation. Under the conditions given in Fig. 9A, it takes at least 50 s to half reduce the internal hemoglobin molecules. Thus, although dithionite is permeable, its rate of diffusion across the membrane is too slow to influence the time course of oxygen release, which exhibits a half-time of the order of 0.1 s. Furthermore, the

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Red Cell Oxygen Uptake 1186

l.O( A

VARIABLE

\ ‘0 0

0.1

TIME (s)

n I I

0. I 0.2 0.3

FIG. 9. The reaction of oxygenated red blood cells with sodium dithionite. Conditions are identical with those given in Fig. 1. A, observed and calculated time courses of oxygen release. Experimental data (0,O) were obtained by mixing oxygenated (0.25 mM 02 before mixing) suspensions of either red cells (RBC) or solutions of free hemoglobin (Hb) (both 40 pM heme before mixing) with a 52 IIIM (before mixing) solution of sodium dithionite. The dotted line was drawn through the data for free hemoglobin. The dashed line repre- sents a theoretical time course which was calculated using a simple packet model. The solid line represents a theoretical time course which was calculated using the variable unstirred layer model. The

sense if the extra resistance seen in uptake experiments is due to diffusion through external, stagnant solvent layers. In the release experiments, oxygenated red cells are mixed with concentrations of dithionite which are great enough to alle- viate resistance due to insufficient stirring. For example, under the conditions described in Fig. 9A, 26 mM dithionite is present at the cell surface immediately after mixing. Since the cells contain roughly 20 mM bound oxygen in a 1.6~pm layer, complete deoxygenation can be affected by the dithionite which is present in an 0.6 to 0.7~pm layer of solvent adjacent to the two sides of the cell surface. Thus, there is no need for diffusion either of O2 across large unstirred layers into the bulk solvent phase or of dithionite from the bulk phase to the cell surface. The maximum external diffusion paths of these molecules are of the order of 0.6 am. This contrasts markedly with the case of O2 uptake where the external diffusion path is of the order of 2 to 5 pm.

These ideas have been quantitated in terms of expected time courses and are presented in Fig. 9. In the presence of 26 mM dithionite, the half-time of O2 release from red cells is

addition of 75 mM salicylate to red blood cells has no influence on the time course of 02 release in the presence of dithionite. In contrast, this concentration of salicvlate decreases bv 20-fold the rate of dithi- onite permeation into methemoglobin cells. The latter observation is consistent with the observations of Wieth (26) who used salicylate to inhibit sulfate transport by intact erythrocytes.

0.25 B

\

~--_--------__-------. t PACKET

0.05 i

1.. .* . . . . . . . . . . . . . . . . . . . ‘t

. . . . . ..-..-. . . . . . . .A..

FREE Hb

0.001 I I I I I 0 5 IO 15 20 25

1 DITHIONITE (mM)

parameter values for these calculations are identical with those listed in Fig. 2, and a value of 5.1 s-’ was used for the dithionite-02 rate constant (see miniprint supplement, section II). B, dependence of the half-time of 02 release on dithionite concentration. Conditions were identical with those in A. The dithionite concentrations after mixing are given under the abscissa. A (dotted line), free hemoglobin in 0.25 mM 02 before mixing; 0, cells in 0.0625 mM 02 before mixing; 0, cells in 0.25 mM 02 before mixing; A, cells in 0.625 mru 02 before mixing. Dashed line represents the calculated dependence for a simple packet model; solid line, dependence for the variable layer model. Parame- ters for these calculations are the same as those in A.

approximately 4 times greater than that of 02 from hemoglo- bin free in solution. This contrasts with the 40-fold difference between cells and free hemoglobin which is observed in the 02 uptake studies (Fig. 2). In addition, the difference between the packet model and the observed data is quite small in the case of oxygen release (Fig. 9), whereas in the case of uptake, the rate predicted by the packet model is 5 times greater than that observed (Fig. 2).

A description of the methods used to simulate the oxygen release time course is given in the miniprint supplement, section II. The rate constant for the reaction of O2 with dithionite was determined from analyses of time courses of deoxygenation of oxymyoglobin. The latter reactions are de- scribed in detail in the miniprint supplement and were carried out under conditions identical with those used in the red cell studies. As shown in Fig. 9, a reasonably good fit is obtained between observed and calculated rates when the variable unstirred layer model is used.

More important, the results in Fig. 9B provide further qualitative evidence for the existence of stagnant solvent layers. As shown, the observed half-time of O2 release in- creases 1.5 to 2.0-fold in going from 26 to 2.6 mM sodium dithionite. I f the solvent phase were efficiently stirred, as is assumed in the packet model (dashed line, Fig. 9B), there should be no dependence on dithionite concentration over this range. The latter prediction results from the fact that the rate

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Red Cell Oxygen Uptake

of Oz consumption by dithionite (132 mM/S to 13.2 mM/S, see

miniprint supplement, section II) at the cell interface is sig- nificantly greater than the rate of 02 diffusion within the red cell. Thus, any model which assumes an extra amount of internal diffusion resistance (i.e. membrane resistance, altered cell shape, or increased viscosity), but efficient stirring, will predict no dependence of the rate of O2 release on dithionite concentration over the range presented in Fig. 9B (1 to 26 InM).

The observed dependence on dithionite concentration is most readily explained in terms of unstirred solvent layers. At a lower dithionite concentration, more solvent phase is re- quired to produce enough equivalents to reduce completely the bound oxygen molecules. For example, at 26 mM dithio- nite, a 0.6~pm layer is sufficient for complete deoxygenation of a 1.6~pm layer of 20 mM oxyhemoglobin, whereas at 2.6 mM,

a 6.0~pm layer is required. Thus, at lower levels, dithionite is depleted at the cell surface, and external diffusion of both O2 and reducing agent through stagnant solvent layers begins to lower the observed rate of deoxygenation.

DISCUSSION

In their original paper, Hartridge and Roughton (1) reported a number of control experiments which were designed to rule out the existence of appreciable oxygen concentration gra- dients in the solvent phase adjacent to the cell surface. They observed little or no apparent change in the rate of O2 uptake when: 1) the rate of flow was increased by a factor of three; 2) carbon monoxide-poisoned cells were added in an attempt to achieve additional stirring; and 3) an additional mixer was added to the flow tube to cause a second mixing of the solution approximately 25 ms after the first mixing. Failure of the latter two experiments to detect unstirred layers is readily understood in view of the results presented here. The addition of chemically inert cells to the reaction mixture should have no effect on the amount of stirring. When packed cells are diluted l/1000 and uniformly suspended, the average distance between cells is of the order of 50 pm. However, the stagnant layers of solvent which limit uptake are only of the order of 2 to 5 pm and, therefore, are not expected to be influenced by the presence of other red cells. The insertion of a second mixer would also be expected to produce little effect on the observed time course since a stagnant layer of the order of 1 to 1.5 ,am forms within 2 to 3 ms after mixing. Thus, under the reaction conditions used by Hartridge and Roughton (l), a rapid in- crease of only 5 to 10% saturation would be expected when a second mixer is placed in the flow system. The apparent lack of effect of flow rate on the time course of 02 uptake is less easily rationalized. The thickness of the unstirred solvent layer should certainly be influenced by the rate of turbulent flow; however, less dependence would be expected if only laminar flow were achieved.

In 1975 Kutchai (6) suggested that the slow rates of O2 uptake in stopped or continuous flow experiments were arti- factual and that the microspectrophotometric technique of Sinha (27) was more legitimate. In Sinha’s apparatus, a small drop of red cell suspension was placed on a specially coated cover glass. The cover slip was inverted and placed in a humidified chamber which was attached to the stage of a microscope. An adjustable diaphragm was used to mask out any light other than that which was transmitted by the cell to be examined. Absorbance measurements were made by at- taching a photomultiplier to the eyepiece of the microscope. In order to measure oxygen uptake reactions, the red cells were first deoxygenated by passing purified Nz through the chamber and then flushed with the appropriate nitrogen- oxygen mixture.

Sinha (27) carried out a number of experiments on cells for which no solvent layer could be detected. Excess plasma had been removed from the cover glass by suction. Under these conditions, the half-time for uptake at 104 mm Hg of O2 (equivalent to 0.171 mM 02 at the solvent/gas interface) was found to be 60 ms. Kutchai (6) has claimed that this data can be approximated by using as a model a membraneless packet of hemoglobin which is 1.6-,am thick. Unfortunately, he did not take into account the possibility of a residual plasma layer. Layers of the order of those postulated for the stopped flow work cannot be ruled out since Sinha’s (27) measurements could not detect coating plasma layers which were less than 1 to 2 pm. In order to achieve a reasonable fit, Kutchai (6) lowered the value of the cytoplasmic oxygen diffusion constant from 0.8 X 10e5 cm’/s to 0.5 x 10m5 cm’/s, which is equivalent to raising the internal hemoglobin concentration from 33% to between 40 and 45% (19). Even with this modification, the discrepancy between Kutchai’s (6) theoretical time course and that observed experimentally was quite pronounced, particu- larly during the initial portion of the reaction. A more reason- able interpretation of Sinha’s (27) data is to assume that a 0.5- to 1.0~pm layer of plasma covers the exposed surface of the red cell. We have been able to simulate quantitatively Sinha’s (27) time course of O2 uptake by using a 0.7~pm-thick external layer model and the same values for the oxygen diffusion constants which were used to describe the stopped flow results.

A technique similar to Sinha’s (27) had been developed by Thews in 1959 (28). In Thews’ apparatus, a thin film of blood is stretched across the inside of a small metal ring. The surface tension of the plasma causes the erythrocytes to form a single layer of cells. The thickness of the plasma portion of the film was estimated to be 2 to 3 ,am. Thews (28) reported a half- time of uptake of 40 ms after exposure of a deoxygenated cell film to 100 mm Hg oxygen. The faster rate observed in Thews’ (28) experiment is due to the fact that both sides of the red cells were exposed to OZ. In Sinha’s (27) experiments, only one side was exposed; the other side was adjacent to the glass cover slip. Again the parameters employed in the stopped flow calculations can be used to simulate Thews’ (28) experiments if, in this case, a 1.3-pm layer of plasma covered each side of the red cells. The total thickness of plasma obtained in this fashion (2.6 pm) is well within the 2- to 3-pm range estimated by Thews (28).

Thus, both types of experiments, rapid mixing and uptake by stationary, thin films, can be described by the same diffu- sion and chemical reaction parameters. In neither case does membrane resistance appear to limit, even in part, the rate of oxygen uptake.

However, the physiological significance of external diffusion through unstirred layers of solvent is less clear. Plasma thick- nesses of the order of those reported for rapid mixing experi- ments are often observed between red cells and capillary walls in studies of in uiuo microcirculation (12, 29). In the small capillaries of the lung diffusion through alveolar and vessel endothelial cell layers is probably rate-limiting. However, 02 diffusion through plasma layers may slow gas exchange sig- nificantly in larger vessels where the average distance between the red cell and capillary wall is greater than 1 to 2 pm.

REFERENCES

1. Hartridge, H., and Roughton, F. J. W. (1927) J. Physiol. (Lord) 62, 232-242

2. Gibson, Q. H., Kreuzer, F., Meda, E., and Roughton, F. J. W. (1955) J. Physiol. (Land.) 129, 65-89

3. Sirs, J. A., and Roughton, F. J. W. (1963) J. Appl. Physiol. 18, 158-165

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6. 7. 8.

9.

10. 11.

12.

13.

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15. 16.

Roughton, F. J. W. (1932) Proc. R. Sot. Land. B Biol. Sci. 111, l-36

Nicolson, P., and Roughton, F. J. W. (1951) Proc. R. Sot. Lond. B Biol. Sci. 138, 241-264

Kutchai, H. (1975) Respir. Physiol. 23, 121-132 MO& W. (1969) Respir. Physiol. 6, l-15 Kreuzer, F., and Yahr, W. Z. (1960) J. Appl. Physiol. 15,

1117-1122 Forster, R. E. (1964) in Handbook of Physiology (Fenn, W. O.,

and Rahn, H., eds) Section 3, Vol. 1, pp. 827-837, American Physiology Society, Washington, D. C.

Miyamoto, Y., and MO& W. (1972) Respir. Physiol. 16,259-266 Roughton, F. J. W. (1959) in Progress in Biophysical Chemistry

(Butler, J. A., and Katz, B., eds) Vol. 9, pp. 55-104, Pergamon Press, New York

Middleman, S. (1972) Transport Phenomena in the Cardiouus- culur System, p. 69, Wiley-Interscience, New York

Gad-el-Hak, M., Morton, J. B., and Kutchai, H. (1977) Biophys. J. 18, 289-300

Dodge, J. T., Mitchell, C., and Hanahan, D. J. (1963) Arch. Biochem. Biophys. 100,119-130

Bodemann, H., and Passow, H. (1972) J. Membrane Biol. 8,1-26 Wintrobe, M. M. (1974) Clinical Hematology, p. 1791, Lea and

Febiger, Philadelphia

17. Corash, L. M., Piomelli, S., Chen, H. C., Seaman, C., and Gross, E. (1974) J. Lab. Clin. Med. 84, 147-151

18. Wittenberg, J. B. (1966) J. Biol. Chem. 241, 104-114 19. Kreuzer, F. (1970) Respir. Physiol. 9, l-30 20. Kutchai, H. (1970) Respir. Physiol. 10, 273-284 21. Crank, J. (1975) The Mathematics of Diffusion, 2nd Ed, pp.

137-159, Oxford University Press, London 22. Carlsen, E., and Comroe, J. H. (1958) J. Gen. Physiot. 42,83-107 23. Parkhurst, L. J., and Gibson, Q. H. (1967) J. Biol. Chem. 242,

5762-5770 24. Chien, S. (1973) in The Red Blood Cell (Surgenor, D. MacN., ed)

2nd Ed, Vol. 2, pp. 1032-1121, Academic Press, New York 25. Coin, J. T., and Olson, J. S. in Clinical and Biochemical Aspects

of Hemoglobin Abnormalities (Caughey, W. S., ed) pp. 559- 576, Academic Press, New York

26. Wieth, J. 0. (1970) J. Physiol. (Land.) 207, 581-609 27. Sinha, A. K. (1969) Ph.D. dissertation, University of California

(San Francisco) 28. Thews, G. (1959) Arch. Gesumte Physiol. Mens. Z’iere (Pflufgers)

268, 308-317 29. Cliff, W. J. (1976) Blood Vessels, pp. 9-10, Cambridge University

Press, Cambridge Additional references appear on p. 1190.

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Red Cell Oxygen Uptake

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Red Cell Oxygen Uptake

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J T Coin and J S OlsonThe rate of oxygen uptake by human red blood cells.

1979, 254:1178-1190.J. Biol. Chem. 

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