Facilitated diffusion of oxygen and its possible significance; a review

Respiration

Physiology

FACILITATED

(1970) 9, l-30; North-Holland

DIFFUSION

Publishing

OF OXYGEN

SIGNIFICANCE;

Company,

AND

Amsterdam

ITS POSSIBLE

A REVIEW

F. KREUZER Department

of Physiology,

Uniwrsity

of Nijmegen,

Nijmegen,

The Netherlands

Abstract. The experimental evidence for the facilitation of Oz diffusion in the presence of Hb or Mb was reviewed. The basic characteristics of facilitated 0~ diffusion pointed out the diffusive nature of this process and excluded other mechanisms proposed (e.g., a “bucket-brigade” mechanism). A review of the earlier attempts at a quantitative treatment of facilitated 02 diffusion showed deficiencies concerning both the premises for the theoretical approach and the availability of adequate experimental data for the basic parameters. The situation with respect to the facilitated diffusion of CO in particular suggested the possible importance of the chemical reaction rates. It was also found that the problem of the simultaneous gradients of 02 and HbOa in the diffusion layer remained unsolved. The more recent experimental data for the diffusion coefficients of 02, Hb and Mb were summarized as a basis for further quantitative treatment. The recent mathematical work by the author of the present review was briefly described and showed that a quantitative description of the experimental evidence was possible based on the facilitated 02 diffusion being interpreted as simultaneous diffusion of 02 and HbOz if the chemical reaction rates were also taken into account. The possible physiological significance of facilitated 02 diffusion in Go was discussed, including nonsteady-state conditions as present under most physiological circumstances, with particular reference to the situation concerning Hb in the red cells and concerning Mb in muscle. It was concluded that more circumstantial and direct experimental evidence is needed in order to arrive at a definite evaluation of the importance of facilitated 02 diffusion in physiological conditions. Carbon dioxide Carbon monoxide Chemical kinetics Diffusion

Facilitated diffusion Hemoglobin Myoglobin Oxygen

One of the most important interferences with the relatively simple relationships of plain diffusion in solution is, apart from convection, the presence of simultaneous chemical reaction which may be reversible or irre?,ersible (e.g., combination of 0, with or dissociation of 0, from Hb, or 0, consumption in tissue, resp.). In all these cases a capacitive factor is present, i.e., the diffusing substance not only diffuses but also Accepted for publication

13 September

1969.

F. KREUZER

2 disappears,

on its path, into “holes”

Plain diffusion

or “sinks”

only prevails when these “holes”

or “sites” (or appears from “sources”). are and remain

filled (e.g., saturation

of Hb with 0,) or inactivated (e.g., MetHb) at steady or nonsteady state. The capacitive factor is also absent without these requirements at steady state with chemical equilibrium.

These “sites” may be moving

themselves

which complicates

matters

fur-

ther since two concentration gradients have to be considered now and the rates of reaction may be important in the relationship between these two gradients. In the organism most transport phenomena are nonsteady state processes but the recent work on facilitated diffusion of 0, in the presence of Hb or Mb to be reviewed here was mostly performed in steady state condition. Facilitated diffusion in general may be defined as diffusion of a substance at a faster rate than expected from the nature of the substance and of the diffusion medium, i.e., the rate of transport is higher than proportional to the concentration difference (DAVSON, 1959, p. 234), possibly by the interference of a carrier. It will be shown that the enhancement of 0, diffusion by Hb or Mb may be fully explained by the simultaneous diffusion of 0, in physical solution and in combination with the pigment. Experimental

basis

The possible contribution of HbO, to the total transport of O2 has been considered for a long time (ROUGHTON, 1932). KLUG, KREUZER and ROUGHTON (1956a) were the first to systematically investigate this effect. Aqueous Hb solutions in concentrations between 2 and 35.5 gy/o were spread in thin layers 100 and 200 p thick at 25 “C, completely reduced, and exposed to O2 at 0.9 atm, the increasing oxygenation being followed photoelectrically by the method of KREUZERand BETTICHER (1951). The authors compared the experimental overall times for one-third saturation as plotted against Hb concentration to the corresponding times which would be obtained if 1) the Hb did not diffuse appreciably, and 2) the diffusion coefficient of the 0, varies with the Hb concentration in the same way as LONGMUIRand ROUGHTON(1952) found for the nitrogen diffusion coefficient, the vertical distance between the two curves giving a measure of the effect of the Hb diffusion which was found to be considerable in the middle range of Hb concentration, and to peter out to low values towards the range of very low and very high Hb concentration. The decrease at the lower end was attributed to decrease of the Hb concentration, and that with high Hb concentrations to the steep increase of viscosity in this range. In other experiments with the thin layer technique KLUG, KREUZERand ROUGHTON (1956b) showed that the calculated rate of uptake of CO by thin films of 3 g”,, HbO, agreed to within 5Oh with the observed rate if no allowance was made for the diffusion of Hb; if the latter was included the calculated rate was increased by about lOq;, but no definite conclusion could be drawn since the experimental curve lay between the calculated curves with and without diffusion of Hb. The recent interest in facilitated diffusion of 0, by Hb or Mb has been initiated independently by WITTENBERG (1959) and SCHOLANDER (1960a). From a study of the secretion of 0, into the swimbladder of fish, WITTENBERG (1958)

FACILITATED DIFFUSION OF

obtained

strong evidence

3

OXYGEN

for the idea that the active transport

of O2 was mediated

by

an intracellular Hb present in the cells of the gas gland. WITTENBERG (1959) then measured the steady state penetration of 0, through Hb-containing agar membranes with a Teflon-covered 0, electrode and found that the rate of penetration of 0, through membranes

containing

HbO,

was in many cases about 1.6 times as great as through

the

4oc

50

C I

% 53 AIR PRESSURE IN ATM

L

AZ0

Fig. 1. Diffusion of air through hemoglobin solutions of three concentrations. Curve l/l represents oxygen capacity of 22.9 volumes percent; the other curves represent oxygen capacity of l/2 and l/4 this amount, respectively. Horizontal line, Oz/Nz ratio through plasma; lower diagonal line, rate of oxygen diffusion through plasma; three dashed parallel lines, relative rates of oxygen transport calculated from the corresponding Oz/Na data; shaded area, water-vapor tension (with permission from: SCHOLANDER, P. F., 1960a).

4 same membranes

F. KREUZER containing

was proposed for Mb. The work of Scholander this field and initiated

all the Hb in the form of HbCO. and his group became

an animated

discussion

A similar enhancement

the standard

concerning

type of approach

the influence

in

of Hb or M.b

on the transfer of 0,. Since most of the subsequent studies were based on their methods and results, their papers have to be reviewed in detail. SCHOLANDER(1960a) studied the steady-state diffusion of air at various pressures through a Millipore membrane (grade HA with mean pore size of 0.45 f 0.02 p and thickness 0.15 mm containing 800/{, liquid space) charged with a human Hb solution; on the other side of the membrane a moist vacuum was maintained. When a steady state was reached, the amounts of 0, and N, gas coming through the membrane in a measured time interval were analyzed. The results are shown in fig. 1. The 0,/N, ratios in ‘);, are plotted against the air pressure in atm (lower abscissa) or the Paz in mm Hg (upper abscissa), both decreasing from left to right from atmospheric values (one atm or 160 mm Hg, resp.) to l/12 atm or 13 mm Hg, resp.. The 0,/N, ratio in plasma remains unchanged whereas that of various Hb solutions starts from higher values (on the left) and rises with increasing steepness as the Pol decreases. Three curves are presented here for l/l = 0, capacity of 22.9 vol “:, as well as l/2 and l/4 this value. The rate of N, diffusion is always proportional to the pressure. It follows that the increased 0,/N, ratio is exclusively caused by the increased rate of 0, transport, and that the 0, transport is proportional to the product of 0,/N, and the diffusion pressure. The lower diagonal line shows the rate of 0, diffusion through plasma, and the three dashed parallel lines represent the relative rates of 0, transport. The vertical distance between the solid straight line and the respective dashed lines is interpreted as enhancement of the 0, transport by Hb. It may be seen that this effect gradually increases from very low pressures and reaches a constant value independent of PoI up to the highest pressure. The contribution of this enhancement relative to the simple diffusion

in plasma

varies with Po,, being a constant

addition

to the simple

diffusion with PO1 above a critical pressure (here around 20 mm Hg). The relative increase of the 0, transport by the Hb is interpreted as an enhancement of so many times, but it should be noted that this figure may not be generalized since it only holds for a particular Paz, showing the highest value at low P,, ; indeed, expressing the enhancement relative to plain diffusion may even be confusing for an attempt at explaining its mechanism. Thus the total 0, transport is the result of two additive processes, plain diffusion through the water and specific transport mediated by Hb. Decrease of pH from 8.0 to 7.3 caused the critical PO2 above which the specific effect becomes constant to move to higher values of Po,. When washed red cells were smeared on either the upper or lower side of the Millipore filter there was also some enhancement although considerably less than in hemolyzed blood. This important result is, however, open to criticism since there was some hemolysis due to rupturing of the blood cells by the capillary forces in the filter, particularly with the regular HA filter but less so with a VF grade filter (mean pore size 10 +2 ,LL).More recently CAHN (1967) has demonstrated the presence of detergents in membrane filters including Millipore.

FACILITATED DIFFUSIOH OF

PRESSURE

DIFF

-

OXYttN

w---

tllTROGEN

20

OXYGEN

5

MM Hg

Fig. 2. Flux of oxygen and nitrogen through hemoglobin solution at constant pressure gradients by varying absolute pressures. Oxygen capacity of solutions, 20 to 21 volumes percent. (Right) Two membranes at pH 7.2; (left) four membranes at pH 7.2,7.3,8.2, and 8.5, respectively (with permission from: HEMMINGSEN, E., and P. F. SCHOLANDER, 1960).

Substantial O2 enhancement was also found in Mb solutions and in the blood of a marine sanddwelling worm (Thoracophelia) as well as in hemolyzed red cells from fish blood (mackerel and yellowtail Seriola dorsalis). Scholander suggested that when a PO, gradient is imposed upon a Hb solution, O2 molecules are handed down from one Hb molecule to the next in a chain or “bucket brigade” fashion. Provided the “buckets” are emptied at one end and filled at the other (the O2 binding sites remaining fixed in space), a steady state system is set up which results in facilitation of 0, transport through the chain. The maximum rate at which the chain can keep the O2 moving evidently depends upon the constant kinetic motion of the Hb molecules, for the rate of 0, transport via this route is constant and independent of PO,. HEMMINGSEN and SCHOLANDER (1960) varied the total gas pressure while the pressure difference was maintained constant at either 20 or 80 mm Hg (Fig. 2) and found that the specific transport by Hb was abolished when it was opposed by a slight back pressure of 0, of more than 10 mm Hg. It was concluded that a maximally accelerated 0, transport requires full saturation pressure (or more) on one side and full reduction pressure on the other side of the membrane and that the enhancement is impaired by decrease of the saturation difference between the two sides of the membrane (HEMMINGSEN,1963). There was full saturation of the membrane down to PO, values of about 30 mm Hg and the blocking pressure of 10 mm Hg corresponded to about half saturation of the lower surface. The authors pointed out that neither the “bucket-

6 brigade”

F. KREUZER system nor the concept of HbO,

sure of 0, could completely for the mechanism of HbO,

diffusion

can explain why a slight back pres-

block further unloading; this statement seems doubtful diffusion. HEMMINGSEN(1962), however, discounted the

dependency of specific transport on a Hb saturation gradient since 0, pressures surpassing the saturation value by as much as five times did not diminish the enhancement and full steady-state 0, transport took place through a saturated layer of Hb. He tried to prove this point by investigating the passage of 018-labeled 0, through membranes containing fully 0, saturated Hb solution throughout. Tt was found that the unidirectional transport was again enhanced and that this transport (i.e., the fluxes of 0” and Hb0,18 scaled up by the 0 16/O’8 ratio) was equal to the net transport obtained previously when one side of the membrane was kept at zero 0, tension (see also WANG, 1963). Hemmingsen’s conclusion that there was enhancement in the absence of an 0, gradient must be erroneous, however, because there was a gradient for 0” and for HbO 2 I8 resulting in a flux of HbO, I8 and thus in enhanced transport of o18. SCHOLANDER (1965) pointed out, indeed, that maximal enhancement was maintained when the Po, was considerably beyond saturation at the input side, even when some 953:, of the membrane was fully saturated (at a Paz of 450 mm Hg on the input side), but that enhancement vanished when full saturation was reached by raising the back pressure. These experiments clearly show that the Hb does not aid the net transport of 0, unless there is a Hb-bound 0, gradient through the membrane, and that the enhancement in the fully oxygenated part of the membrane is carried by an increased Paz gradient through the solvent due to the enhanced flux through the HbO, gradient at the outlet. The problem of the gradients, which will be taken up in detail below, led ENNS (1964) to suggest an alternative treatment based on the theory of heat transfer. He postulated that the 0, transfer by Hb results from exchange between binding sites of colliding Hb molecules, the rate-limiting factors of this collision theory being the frequency of collisions (proportional to the diffusion coefficient) and the completeness of exchange on collision.

Basic characteristics A number

of facilitated diffusion of 0,

of experimental

diffusion of 0, paragraphs.

findings

is of a diffusive

strongly

nature

suggest that the process

in many respects

as outlined

of facilitated

in the following

1. INFLUENCEOF MEMBRANETHICKNESS ENNS (1964) and WITTENBERG (1966) found that the transport attributed to Hb is inversely proportional to membrane thickness which points to a diffusion process and seems incompatible with a “bucket-brigade” mechanism. This relationship also proves (WITTENBERG, 1966) that the flux is limited by processes occurring in the body of the solution and not at the boundaries (with adequate stirring) and thus supports the view that surface phenomena (as suggested by FATT, 1960, but contradicted by SCHOLANDER,

FACILITATED DIFFUSION OF OXYGEN

7

1960b) are not likely to be limiting, as also discussed by SNELL(1965) and HAMMEL (1966). 2. INFLUENCE OF TEMPERATURE The relative insensitivity to temperature above saturation point was taken as evidence that the transfer process is of diffusive rather than of chemical nature (SCHOLANDER, 1960a; HEMMINGSEN and SCHOLANDER, 1960; HEMMINGSEN, 1965). The effect of temperature may be implied through the dependence of D,, and of the dissociation curve on it (COLLINS,1961a and b). 3. INFLUENCE OF Hb CONCENTRATION ANDVISCOSITY SCHOLANDER (1960a) and HEMMINGSEN (1965) found that the enhancing effect is increased with higher 0, capacity or Hb concentration in the range between 5.7 and 22.9 vol 1;) O2 capacity though not in linear fashion. The increase per unit Hb concentration (slope of this relationship) decreased with increasing Hb concentration in the same way as that of the rate of N, diffusion, this relative slow-down being due to increasing viscosity in both cases. When the original O2 capacity of 22.9 vol3:, was doubled there was a marked increase in viscosity and a decrease in the rate of 0, transport. Support for the viscosity as the cause of this decrease was also provided by experiments which showed almost halving of the specific rate of 0, transport by the Hb in the presence of 10% gelatine in the Hb solution which was enough to make it solidify (SCHOLANDER,1960a). The enhancement became proportional to the Hb concentration in the range between 5.7 and 33 vol o$ 0, capacity when corrected for viscosity alone (HEMMINGSEN, 1966). Since the 0, flux enhancement was reduced in proportion to the diffusion by viscosity, it must be assumed that this was a result of a decreased molecular motion of the Hb (COLLINS,1961a and b). WITTENBERG(1966) showed the dependency of the facilitated flux on the protein concentration for both Hb and Mb with a maximum at 9 mM heme concentration (= about 15 g %) and the same augmentation per mole of heme in Hb and Mb, not per mole of protein. The diffusion coefficient of Mb is greater than that of Hb but the rate of O2 dissociation is less, and possibly the opposing effects of these two rate-limiting parameters may balance each other (WITTENBERG, 1966). 4. INFLUENCE OF MOLECULAR SIZEANDMOBILITY OF THEPIGMENT Experiments with Mb are important for the mechanism because Mb is smaller and therefore more mobile, has only one 0, site, and shows much higher 0, affinity. In experiments with 0 l8 HEMMINGSEN (1965) found that a full enhancing effect still occurred at a Paz of 8.5 mm Hg with Mb rather than of 40 mm Hg with Hb, and that Mb was more sensitive to back pressure, both these properties being due to the higher 0, affinity of Mb, furthermore that the enhancement was almost the same with Mb as with Hb of double 0, capacity, i.e., the effects with Mb against Hb were indirectly proportional to the root of the molecular weights. HEMMINGSEN (1965) found the linear velocities of 0, for the enhancements to relate to the diffusion coef-

8

F. KREUZER

ficients of the pigments flux to the diffusion

(from POLSON, 1939) as does the linear velocity for the diffusive

coefficient

of the gas; this strongly

indicates

cess is rate-limited by the spatial movement of the HbO, flux being proportional to the diffusion coefficient.

that the transfer

and MbO,

molecules,

prothe

WITTENBERG (1965, 1966) presented a table on the relation between molecular size and Hb-facilitated flux in various individual pigments. There is an inverse relationship between flux augmentation and mobility size, and it was concluded again that pigment diffusion of 0,.

of the pigment molecule or molecular molecules must move to facilitate the

Evaluation of mechanism The characteristics and relationships pointing to a diffusive nature of enhanced transport of 0, strongly suggest a “carrier” type mechanism, virtually excluding any interface or orientation phenomena, as possible cause of the effect. Two versions compatible with this concept have been proposed: I. Dijiision of HbO, or MbO,. The spatial diffusion of the pigment molecule would enter here as a rate-limiting factor. 2. “Bucket-brigade” (Scholander, 1960a) and collision theory (Ems, 1964). The ratelimiting factors here would be the frequency of collisions (which is proportional to the diffusion coefficient) and the completeness of exchange on collision. The trivial possibility that Hb may augment the diffusion of 0, merely by increasing the 0, capacity of the solution may be rejected a priori since the rate of diffusion is proportional to the gradient of the diffusing species, which is HbO, and not total O,, and on the basis of experiments with annelid hemoglobins which show no enhancement in spite of a considerable O2 capacity (WITTENBERG, 1966). Two lines of evidence identify the diffusing species as HbO, (WITTENBERG, 1966): 1) The Hb-augmented flux of O2 attains its maximum value at a Po, sufficient to saturate the Hb on the side of the layer of solution exposed to 0, and it is constant with greater of Hb0,16, and P 02, and 2) a gradient of HbO, ’ ’ diffusing into an environment of Hb0,18, must be conversely a gradient of HbO, ’ 6 diffusing into an environment present in the isotope experiments of HEMMINGSEN(1962). WITTENBERC (1966) as well as KELLER and FRIEDLANDER(1966a) mentioned against the collision theory of ENNS (1964) that, if the diffusion of HbO, occurs by a collisional mechanism rather than by Brownian movement of the Hb molecules (i.e., by ligand transfer according to SCHOLANDER, 1960a, and ENNS, 1964), DHt,oL would increase with increasing Hb concentration because of the increased collision rate, and the rate should be proportional to the square of the Hb concentration, which is contrary to the experimental facts where the rate is proportional to the concentration. Since the Hb molecules can rotate freely about any axis even at the red celiconcentration, restricted rotation by increased Hb concentration cannot be invoked to explain a decreased collision rate at high Hb concentration. PERUTZ (1948) has shown that the Hb molecules in the red cell are arranged in a closely packed lattice, in which the intermolecular distance (75 A) is the same as the

FACILITATED DIFFUSION OF OXYGEN

9

effective diameter of the freely moving molecules. Translational movement at this concentration (about 35 gq/,) might be very limited, but the molecules are in true solution and retain freedom of rotation. The flux mediated per unit of heme concentration by these very concentrated solutions of Hb or Mb is about 10% of the flux mediated per unit of heme in dilute solutions (WITTENBERG,1966; see also MOLL, 1962), which might suggest that about lo?:, of the facilitated flux is brought about by molecular rotation. This conclusion is contradicted by diffusion theory (WYMAN,1966) which indicates that molecular rotation contributes only a negligible proportion to the facilitated flux (see also HEMMINGSEN, 1965 ; WITTENBERG,1965 ; KELLERand FRIEDL~NDER, 1966a), since the relaxation time of the Hb molecule (of the order of 10e6 set) is small and the dissociation rate of O2 from the protein is relatively slow (half-life of an O2 molecule attached to the protein of the order of 0.1 set). Perhaps the translational diffusion of protein molecules in concentrated solutions is greater than anticipated (see below). Translational diffusion of the protein might at first glance seem unlikely since the protein molecules diffuse so much more slowly than the free 0, molecules. WYMAN (1966) asked: “How could a fly hope to increase his rate of progress by alighting on the back of a tortoise?” The problem however assumes a new complexion when we take account of the fact that under the experimental conditions the amount of 0, present in combination with Hb is many times that present in free solution (WYMAN, 1966; MOLL, 1966). WITTENBERG (1965) mentioned that the diffusion coefficient of Hb is much less than that of 0, (some 100 times), but the difference in flux becomes smaller when the respective concentrations are considered (concentration of HbO, about 100 times larger than that of O,), since the flux is proportional to diffusion coefficient times concentration difference; the difference in the diffusion coefficient is thus compensated by the difference in concentration so that the two fluxes are about equal. This led WYMAN(1966) to conclude: “A swarm of flies whose forward progress through the air was limited by the necessity of passing through a narrow orifice in a barrier might well improve their situation by riding on the backs of an army of tortoises which could pass under the barrier along the ground.” WITTENBERG(1966) concluded that reversible 0, binding with the carrier itself moving is a sufficient condition for facilitation and no special property of Hb is required, since hemerythrin, which is not a heme protein but binds 0, reversibly at the site containing two ferrous iron atoms, facilitates 0, diffusion too (WITTENBERG, 1963). HAMMEL(1966) specified that this reversible binding is sufficient if 1) all three molecules (O,, Hb, and HbOz) are free to diffuse down their respective concentration gradient, and 2) the velocity constants for combination and dissociation, particularly the latter, are such as to provide less than full saturation over some portion of the diffusion pathway for the ligand molecules. The second requirement is true in general whether the velocity constants (but not their ratio) are increased by enzymatic activity and thereby reduce the time to achieve steady state fluxes or whether the velocity constants are already large enough without enzyme assistance (as in enhanced diffusion of O2 and CO through a Hb solution).

10

F. KREUZEH

The first alternative concerning enzymatic acceleration has been demonstrated recently in the case of enhanced diffusion of CO2 through a water solution of bicarbonate and carbonic anhydrase (ENNs, 19651967a and b; ENNS,SHAMand ANDERSON,i966; LONGMUIR,FORSTERand CHI-YUANWoo, 1966; WARD and ROBB, 1967).

attempts

at quantitative treatment of facilitated diffusion of 0,

Several authors have derived equations to account for the experimental results of Scholander and his group (COLLINS,1961a and b; WANG, 1961, 1963; FATT and LA FORCE,1961; LA FORCEand FATT, 1962, 1964; Fox and LANDAHL,1965; ZILVERSMIT, 1965; KELLERand FRIEDL~NDER,1966a; HAMMEL,1965, 1966; WYMAN,1966). They all assumed that the enhancement of 0, transport by Hb was due to Hb diffusion, that chemical equilibrium existed among the Hb species and 0, according to the HbO, dissociation curve (i.e., the reaction rates were neglected), and that Henry’s law equilibrium was present between the liquid and gas phases. They calculated the total 0, flux by applying the first law of Fick for steady state with two additive terms for the diffusion of 0, and that of HbOz, taking the concentration differences of 0, and HbO, between the two boundaries, i.e., assuming linear gradients within the film. However, the authors made, in most cases, no attempt to actually fit their resulting equations to the experimental data, but instead only indicated that they described the experimental data qualitatively (SNELL, 1965), so that the quantitative explanation had not been sufficiently successful hitherto (BRIGHT, 1967). Apart from theoretical difficulties concerning the assumptions (see below), there were uncertainties in assuming the physical parameters, particularly for D,, which was investigated experimentally in realistic conditions only later (see below). HEMMINGSEN( 1965,1966)foundthat the 0, flux enhancement is directly proportional (1: 1) to the equilibrium oxygenation of Hb (Hb oxygenation being uniform through the membrane), and that the curves for enhancement and oxygenation fall on top of each other when plotted as a function of PO,. If the transfer was rate-limited by the reaction rates, there would be a displacement of the flux curve toward higher pressures relative to the dissociation curve, as in the CO experiments of MOCHIZUKI and FORSTER(1962). ~EM~INGSENconcluded that equilibrium, or nearly so, existed between Hb and O2 as well as between solution and gas phase at the entrance surface, i.e.,that the transfer process was not rate-limited by the oxygenation reactions. FRIEDLANDER and KELLER(1965) showed that the augmentation effect is at a nlaximum in systems in which 1ocaI equilibrium can be assumed and decreases as the system departs from equilibrium. Calculations showed that the assumption of local chemical equilibrium is doubtful in the red cells, even more so when one considers that the in uivo system is a nonsteady-state system. Subsequently, however, KELLER and FRIEDLANDER (I 966a) caiculated that the equilibrium approach neglecting chemical reaction rates was indeed justified, at least for their experiments with Hb solutions, where reasonable agreement was found between their calculations and the measured data of HEMMINGSEN and SCHOLANDER (1960) as well as the experimentally determined

FACILITATED DIFFUSION OF OXYGEN

11

values of DNbOz(KELLERand FRIEDLANDER, 1966b). A similar conclusion was reached by SPAETH(1967). SNELL(1965)

pointed out that even in steady-state systems chemical kinetic considerations may be important if the specific reaction times are of the same order of magnitude as the diffusion times. He was th.e first to try a more general development of facilitated diffusion including the kinetics of the chemical reactions of 0, with Hb. Steady-state 0, flux was calculated from a formula incorporating the terms for O2 and HbO, diffusion but adding a reaction kinetics correction for a weighted average chemical reaction velocity function at the two boundaries. A comparison with the data of HEMMINGS~Nand SCHOLANDER (1960) gave good agreement only when taking into consideration this semi-empirical reaction correction; without such correction the equilibrium difference in saturation between the two boundaries was larger than was to be expected in a non-equilibrium kinetic situation, i.e., a true saturation at the entrance was lower and a true saturation at the exit was higher than at equilibrium, so that the total 0, flux became too large when assuming equilibrium. Influence of chemical reaction rates

There should occur an enormous facilitation of CO movement across a film due to the large concentration gradients for HbCO as compared with those for dissolved CO. MOCHIZUKI and FOR~TER(1962) studied the diffusion of CO through Hb solutions

in th.e presence of 0,. They found a facilitation wh.ich was very much greater than that for O,, but was still nowhere near what it should have been theoretically, if one assumed chemical equilibrium in the film. There was an increase in facilitated CO flow when the calculated equilibrated concentration gradient of HbCO across it decreased in the presence of an increased 0, concentration. It was concluded that the reaction velocities of CO and Hb, in particular the rate of dissociation from HbCO which is favored by increased 02, are limiting the overall process and that chemical equilibrium does not exist between Hb and the gases at the film surfaces. LA FORCE(1966), and LA FORCEand FATT (1967) analyzed the steady state diffusion of the system CO+O,

+ Hb, assuming the Haldane relationship to hold at equilibrium. The total flux of CO was calculated from the adaptation of the first law of Fick to the diffusion of CO and HbCO (analogous to the treatment for O2 discussed above). The final equation incorporating the second law of Fick with th.e reaction term for CO, HbCO, and HbOz was numerically solved assuming certain physical parameters and the results were compared to the data of MO~H~ZUKIand FORSTER (3962). The agreement was considered fairly satisfactory but again the need for better physical parameters was felt. WITTENBERG (1966), however, found no augmented diffusion of CO in various pigments including Hb and Mb, not even in the presence of 0,. CO abolished or at least diminished the augmented flux of O2 through Hb solution (WITTENBERG,1959, 1966). WYMAN (1966) tried to explain the Iack of CO facilitation in Wittenberg’s experiments by pointing out that the CO system should be extremely sensitive to even minute back pressures and adequate stirring to prevent back pressure might be barely possible

12

F. KREUZER

experimentally, furthermore that the system may well be far from equilibrium low pressure side due to the slow rate of dissociation of CO from HbCO, would act to reduce enhancement tal conditions (e.g., effectiveness WITTENBERG (1966) as against

on the which

(MITCHELL, 1967). Thus differences in the experimenof stirring) might explain the discrepant findings of those

of MOCHIZUKI and FORSTER (1962), although

WITTENBERG (1966) remarked that stirring of the gas phase was more likely to be limited in the apparatus of MOCHIZUKI and FORSTER (1962) than in his set-up. The 0, probably served to suppress recombination of dissociated CO with Hb at the Millipore surface. As to O,, WITTENBERG (1966) concluded that the rate of dissociation must be ratelimiting since pigments of appropriate molecular size (ascaris body wall Hb and succinyl ascaris perienteric fluid Hb) but with very small rate of O2 dissociation do not facilitate 0, diffusion. The rate of combination is unlikely to be limiting since there is no change in the facilitated 0, flux when the 0, concentration is changed 20-fold and the rate of combination is proportional to the 0, concentration. Since, on the other disequilibrium hand, the rate of association falls with decreasing Paz, an association effect might appear at low 0, concentrations and hence low flow rates (BRIGHT, 1967). The possibility that the rate of ligand dissociation may be rate-limiting suggests that a mathematical description of the phenomenon should take into account not only the diffusion coefficient of Hb but also the mean time during which )-Ib and 0, molecules remain in combination (WITTENBERG, 1966). Fox and LANDAHL (1965) pointed to the possible importance of the Bohr effect on the dissociation curve. The oxygneation of Hb on one side of the filter would result in a net production of H+ (lower pH), while on the other side of the filter the dissociation of HbO, would result in a net consumption of H+ (higher pH), leading to a pH difference. The resulting migration of both H+ and Hb ions each of which have different charges and mobilities, should manifest itself in an electric potential difference across the membrane (< 2mV according to BRIGHT, 1967). Because of this pH shift the dissociation curve at the low pressure side will be steeper than that at the high pressure side, which may account for the steep fall in flow for a relatively small back pressure applied to the low pressure side. Comparison of these calculations with the data of HEMMINGSENand SCHOLANDER(1960) showed much higher gas transport than experimentally found when using the dissociation curve supplied by these authors at pH 7.3 in both cases; better agreement was reached when using a dissociation curve at pH 7.93 for the calculations. BRIGHT (1967) presented a flow equation including electric forces and the kinetics of the Bohr proton exchange, and concluded that the presence of a significant departure from equilibrium would decrease facilitation by depressing the saturation difference; as a net result, the chemical reactions were more rate-limiting than the voltage was facilitating, and it was thought that the Bohr effect kinetics was rate-limiting rather than the gas reaction rates. In order to isolate these effects, BRIGHT (1967) suggested to repeat the experiments with a highly buffered solution to reduce the voltage difference, the H+ net productivity, and hence the pH difference by the increased ionic intensity.

FACILITATED DIFFUSION OF OXYGEN

13

The problem of the gradients Enhancement of O2 flux depends on the maintenance of a difference in pigment oxygenation between the surfaces, but seems independent of the amount of oxygenated pigment in the membrane. It rises with increasing difference in saturation between the surfaces and becomes constant after reaching the ma~munl difference even when the P,, at the high pressure side keeps rising. The increasing P,, at the high pressure side after reaching complete saturation at the entrance causes the dissociation curve to move more and more towards the low pressure side, leaving behind it an increasingly thick layer of completely saturated HbO,, and the dissociation curve becomes steeper. Maximum enhancement was found with low 0, pressures (around 10 mm Hg) where the dissociation curve has maximum slope (SCHOLANDER, 1960a; LA FORCE and FATT, 1962; SNELL,1965; KELLER and FRIEDLWNDER, 1966a), but this was a maximum relative to plain diffusion and the absolute specific transport could not have reached its maximum yet in this range. Changes in temperature and pH shift the curve in the low pressure range, and consequently the pressure at which the slope is maximum will shift the maximum in the flux parameter; increase in pH makes the curve steeper and shifts it to the left so that the maximum in the flux parameter is then higher and occurs at lower pressures (SCHOLANDER, 1960a; LA FORCE and FATT, 1962). However, there is no dependency on pH and temperature beyond the point of complete saturation on the higher side of the membrane and a change in slope of the dissociation curve does not seem to alter the enhancement. But nevertheless the HbO, term will depend, because of the sigmoid shape of the HbO, dissociation curve, not only on the pressure differential but also on the absolute pressure at the cell boundaries (LA FORCE and FATT, 1964). The application of Fick’s first law requires steady state conditions with a linear concentration drop across a homogeneous medium, i.e., dc~dx=constant (JOST, 1952), if the diffusion coefficient is independent of the concentration. This requirement poses a problem in the presence of two interconnected gradients. If the PO, gradient is assumed linear through the whole layer as in the case of plain diffusion of 0, only, the HbO, gradient cannot be linear but must follow the dissociation curve if equilibrium may be assumed. Consequently, the proportionality factor DHboz would have no defined relationship to the molecular velocity of the pigment, as it would be different for various segments of the diffusion path (HEMMINGSEN, 1965). If, on the other hand, the HbO, gradient is assumed linear, the Po, gradient falls precipitously soon after the entrance side of the layer and is close to zero the rest of the way (ENNs, 1964). It should be noted, however, that two of the requirements mentioned above are questionable at least. D,, is not independent of concentration but decreases with increasing concentration in non-linear fashion (see below), certainly above the point (about 8 gy/: Hb concentration) where the Hb solutions are no longer ideal (RIVEROS-MORENO and WITTENBERG,1968). In this case the gradient would be convex against the coordinates in the plot of the concentration difference c against the distance x [f(c) = -a x; JOST, 19521; the dissociation curve, on the other hand, would be concave in the same

14

F. KREUZER

plot. Furthermore the assumption of chemical equilibrium may be erroneous as outlined above and shown below. One basic difficulty encountered here is that HbO, is related to the local P,, through the membrane in a rather complicated manner when both O2 and HbOz are moving. The pigment molecules will change their state of oxygenation continuously as they diffuse along the Po, gradient. HbO, molecules will move according to the HbO, gradient into regions with lower P,, and unload their 0,, thus increasing the local Po, and decreasing the PO, gradient as well as decreasing the concentration of HbO, and increasing the HbO, gradient, while Hb molecules will move in opposite direction into regions with higher Po, and be loaded with 0,, thus decreasing the Po, gradient too as well as increasing the lib,, concentration and the HbO, gradient again. Although 0, and HbO, diffuse separately according to their respective local gradients, the two flux components cannot be measured separately and simultaneously and there must be some interaction between the two gradients. In steady state the total flux must be the same through any cross-section of the meInbrane, always being the sum of diffusive flux through the liquid and pigment-mediated flux. it might be considered likely that the Po, gradient as well as the HbO, gradient is non-linear when enhancement prevails. Consequently the ratio between the amount of 0, diffusing through the liquid and that transported by the pigment is not constant but follows a function which has not yet been worked out (HEMMINGSEN, 1965). ZILVERSMIT (1965) pointed out that it is not immediately apparent, in particular, by what force enhanced transport takes place in that portion of the membrane in which no gradient of HbOz exists. Fig. 3 shows an example (by Zilversmit) of the calculated concentrations when the PO, was 200 mm Hg on one side and zero on the other. It is surprising at first sight that enhancement of O2 transport depends on the simultaneous diffusion of free O2 and HbO,, notwithstanding the fact that at Paz of 200 mm Hg at the inlet there is no HbO, gradient in the left half of the membrane. Apparently in this portion of the membrane only the flow of free 0, contributes to the transport. This flow is enhanced when Hb is present in the membrane because the concentration of free O2 decreases from its initial value at the far left to near zero in about half the membrane thickness. In the right portion the Hb transports the 0, the rest of the way by diffusion and continuous unloading. In the middle portion one finds a gradual transition in the nature of the O2 transport from primarily free 0, to HbO,. A similar conclusion was reached by SCHOLANDER (1965) and HAMMEL(1966). WYMAN(1966) plotted the calculated value of Po, against the distance x for each of three values of enhanced flux F chosen from WITTENBERG (1966), assuming equilibrium, and arrived at a similar result as ZILVERSMIT (1965). The slopes at any value of x give the gradients of P,, which are proportional to the flux of dissolved 0, at that point. When the gradient is constant the flux is constant, and in this case it is the same as the total Aux, the saturation gradient being zero, Therefore, in the linear gradient range the total flux of 0, at the high pressure face of the slab must be due entirely to dissolved 0,. Further to the left, where the curve of Po, against x is no longer straight, part of the flux is taken over by the bound 0,. By dividing the flux of bound 0, (= total flux minus

FACILITATEDDIFFUSION OF OXYGEN

15

x Fig. 3. Free and hemoglobin-bound oxygen concentration in Millipore membrane. Oxygen pressure at inlet (x = 0) is 200 mm Hg; at outlet (x = 150 p) zero. Top: Oxygen tensions in presence and absence of hemoglobin. Bottom: Oxygen concentrations and transport in membrane containing 15 % hemoglobin solution: broken - dotted line: free oxygen concentration, ordinate at left gives volume of oxygen (at standard temperature and pressure) per ml of hemoglobin solution; broken line: hemoglobin-bound oxygen concentration, ordinate at left; solid line: free oxygen transport as a percentage of total oxygen transport, ordinate at right (with permission from: ZILVERSMIT,D. B. 1965).

the flux of dissolved 0,) by the product of D,,, m (=4 for Hb), and Hb concentration saturation gradient is obtained. The facilitation is proportional to the difference between the slope of the straight line for dissolved O2 transport alone and the actual slope at the high pressure side of the slab where Po, is linear in x. The enhanced flux is independent of PO, provided PO2 is sufficiently great to have full saturation at the high pressure face of the slab. Approximate numerical analysis showed that the reaction term largely exceeds the diffusion term (about 100 times) so that departure from equilibrium should be small. It would be very much greater for CO. WYMAN (1966) concluded that the problem of the simultaneous gradients for PO, and HbO, remained unsolved, and that a complete description of the two gradients and thus of the enhanced flux of 0, (and CO) was not possible on the basis of chemical equilibrium. HAMMEL(1966) tried to interpret the observation of HEMMINGSENand SCHOLANDER (1960) that there appeared to be no facilitated 0, flux if the Po, on the low pressure side of the membrane was no more than 10 mm Hg with 30 mm Hg on the other side,

16

F. KREUZER

whereas the theory predicts a substantial enhancement of the 0, flux since the Hb would presumably be only 55-65% saturated at this partial pressure on the low side. He assumed that the P,, in the water at the entrance side is less than that in the gas phase, perhaps because the 0, molecules are unable to pass the interface between the gas and the water phase at a sufficient rate to maintain the Po, on the water side of the interface at the same level as in the gas phase when Hb is facilitating the movement of 0, through the film, thus increasing the gradient across the interface. However, since interface phenomena have been shown to be unlikely (see above), another explanation may have to be sought. If one plots the dissociation curve for a pressure difference of 20 mm Hg (between 10 and 30 mm Hg) and for a pressure difference of 80 mm Hg (between 20 and 100 mm Hg) for two types of experiments in HEMMINGSEN and SCHOLANDER(1960) over the same distance (thickness of membrane), it is found that the back pressure point occurs at the place of the same slope in both curves where, in both cases, the dissociation curve becomes much less steep rather suddenly. Furthermore the saturation at a back pressure of 10 mm Hg would be much higher if the pH were around 8 instead of 7.3 as suggested by FOX and LANDAHL (1965). WITTENBERG (1969) offered another explanation. He pointed out that this discrepancy may be due to an experimental artifact. Stirring was minimal in the back-pressure experiments of HEMMINGSENand SCHOLANDER(1960) and there may have been present a thin layer of static or poorly stirred gas at the Millipore surface. Oxygen diffusing into this layer from the Millipore would raise the local 0, tensions above that in the bulk gas phase. The 0, pressure immediately inside the fluid at its interface with the gas phase must be greater than that in the gas phase. It can be seen that this is true, for a flux of 0, occurs when the 0, pressure in the gas phase is zero; and were it also zero immediately inside the fluid phase, there would be no dissolved 0, and therefore no flux. The calculations by MURRAY (1969) show that a small increment in Po, at the boundary corresponds to a large increment in fractional saturation of the Hb. In the back-pressure experiments of HEMMINGSENand SCHOLANDER(1960) the absolute values of the fluxes were substantially less than in the wet-vacuum experiments of SCHOLANDER (1960) which is direct evidence

of inadequate

stirring

of the gas phase (WITTENBERG, 1969).

Important physical parameters One of the most conspicuous deficiencies found in all calculations discussed so far concerned the lack of reliable and realistic data for the physical parameters, particularly the diffusion coefficients of 0, (Do,) and Hb (Dn,,). After sporadic earlier attempts concerning Hb and Mb (POLSON, 1939; ROUGHTON, 1959; FATT and LA FORCE, 1962), this gap has been largely closed by recent experimental work. Figure 4 presents a plot of the available data for Do, in protein solutions against protein concentration and fig. 5 a similar plot of Do2 in Hb solutions against Hb concentration. The agreement between the data of the different authors is quite satisfactory in general. The curves for protein and Hb solutions practically coincide with the possible exception of the concentration range above 30 gyO where the protein values lie somewhat higher than the Hb values. The dependency on concentration

FACILITATED

Do2 x lot5 cn&%sec -

DIFFUSION

17

OF OXYGEN

-

3.0

Plot of Do2 against x Kreuzer (1950) l Pircher (1952) 0 Galdst;ck(1966)

protein concentration

at 25*C

All data reduced to Do* for saline = 2.03x10%18.& (according to Goldstick, 1966)

.

2.0

0. .

o

x.

x

0 l l

.o l

x l

2

1.0

5

10

15

20

2s

30

35

40 ‘Protein

45 (4 %)

Fig. 4.Plot of available data for 0~ diffusjon coefficient DO, in serum protein solutions against protein concentration at 25 “C. Data of PIRCHER (1952) in MetHb solution for comparison.

Do2 Ylot5 cmVsec

1

307

Plot of DO2 against Hb concentration at 25°C x Kreuzer (1950 and 1953) l Pircher (1952) f) Goldstick (1966) o Keller (1964) A DN~ from Lonqmuir and Rouyhton (1952) . calculated by Durrer and Rouqhton (1967). personal communlc(rtIon All data reduced to DoZ for salme = 2 07x 10-5cm2/5,c (accordmq to Goldstick 1966)

J 5

10

15

20

25

30

35

40

45

55 50 c Hb(y%)

Fig. 5. Plot of available data for 02 diffusion coefficient Do2 in Hb solutions against Hb concentration at 25 “C. Solid line = values used for computation, broken line = extrapolation.

18

F. KREUZER PLOT OF DHb AGAINST D,,,

CHb. 20.25°C __.-

cm*/sec

1O-6, - .\

>---%Keller

and Friedlhnder. 1966 . Mall. 1966 *_ M Adam6 and Fatt. 1967 b--n Riveroa-Moreno and Wittenberg.1968 .

Cd

&lld

curve

with sharp

kneezcurve

to these authors .see text I ,o_8-.- - compromise curveused for colculatmns here / 0 5 10 15 20 25 30 accordmg

35

CHb.g/lOOml

Fig. 6. Plot of available data for Hb diffusion coefficient DH~ in Hb solutions against Hb conccntration at 20-25 “C.

in Hb soIutions

can be described

by a linear function

up to concentrations

of 35-40

gT<,. The data recently reported by WISE and ~~UGHTON (1969), covering the range from 0 to 20 gyd) Hb only, are somewhat lower than the points in fig. 5 in the range of 10 to 20 gli, Hb (not shown in fig. 5). The available values of D,, are summarized in fig. 6. The discrepancies between the values of the different authors, the considerable scatter of the points, and the manner of drawing the regression line are of considerable consequence for an attempt at accurate quantitative computations, as discussed in detail by KREUZER and HOOFD (1970) and mentioned below, but need not concern us here. The available data of D,, are plotted in fig. 7. MOLL (1966b) calculated the minimum D,, necessary to produce the specific 0, transport observed by SCHOLANDER (1960a) and concluded that the directly determined values are sufficiently high. Quantitative matkemati~al desc~~tion of faci~tat~ of chemical kinetics KREUZER and HOOFD (1970) have recently

0,

developed

diffusion including the influence

general

mathematical

solutions

FACILITATED

DIFFUSION

OF

19

OXYGEN

PLOTOFDlvlbAGAINST Crrb.20-25'C DM,b,’ d/set 10-l

5

2

10.;

5 -

Experimental

data

of

RiverosMoreno and -.-.--__

from Hb - - -regression from Hb-

- -regress,on

Wittenberg, 1968 11ne. ‘V13V7 I~ne, V-,/VT-

2

IO.’ 5

10

15

20

25 30 C,,b,g/l00mI

35

Fig. 7. Plot of available data for Mb diffusion coefficient DMb in Mb solutions against Mb concentration at 20-25 “C.

and applied them to numerical evaluation of the system 0, and Hb. Their line of approach will be reviewed here only very briefly and the reader is referred to the original paper for details. It was assumed that the diffusion of 0, occurs through a layer of thickness L = 180 p (WYMAN, 1966) containing an aqueous solution of Hb and being exposed to a constant 0, pressure on both sides, x = 0 and x = L, at steady state. The total gas flux was supposed to be caused by simultaneous free diffusion of 0, and by diffusion of HbO,, taking into account the combination and dissociation reactions between 0, and Hb. The basic equations were the second law of Fick together with the reaction terms for O,, HbO,, and Hb, and then passing to steady state. The boundary conditions were Henry’s law at the interfaces for 0, and the assumption of impermeability of the interfaces for HbO,, both applied to the two interfaces at x=0 and x=L. The resulting formula was solved for two marginal regions, one region between x=0 and x=x0, the other for x near L. Then an analogous solution was developed for the rest of the layer for 0, and HbO,. Thus five equations evolved with five unknown quantities, one of which being the flux F ; by an approximate solution neglecting two of these five quantities the authors arrived at an approximate formula for

20

F. KREUZER

F in terms of 0, pressure and saturation,

F being the sum of diffusion

of 0, and HbO,.

Eventually two expressions for the course of 0, and HbO, in the layer were obtained. It was interesting to note that for 0, this was equivalent to an equilibrium solution

between

a raised low pressure

and a lowered

high pressure

as already

sug-

gested by SNELL (1965). The most interesting results may be summarized as follows. The PO2 gradient does not gradually approach zero at the low pressure side as suggested hitherto, but there is rather, in the thin layer of the slab close to x=0, a step in the gradient exhibiting a slope equal to that of the line originating at the high pressure side, i.e., 0, is transported through the two surfaces by plain diffusion only and at equal rates since the surfaces are impermeable to HbO, and there is steady state present. The computed curves for the relationship between Po, and HbO, saturation at non-equilibrium were notably different from the standard dissociation curves always presumed in all previous work; the saturation at P,, = 0 was greater than zero and that at the high pressure side was always lower than at equilibrium and never reached full lOOo/:, saturation. The presence of any back pressure on the low pressure side raises the saturation there more than was to be expected at equilibrium. The computed facilitated fluxes agreed very well with the experimental data of WITTENBERC(1966) as shown, e.g., in fig. 8, although

FACIUTATED

FLUX

(lO”‘M

Icm2/sec)

1.:

1.C

0.:

HEMOGLOBIN

(g % 1

Fig. 8. Comparison between computed curve and experimentalidata of WITTENBERC (1966) for the dependency of the facilitated flux on Hb concentration. Solid line = computed, points according to WITTENBERG (1966). Values of DHb from compromise regression line in fig. 6.

FACILITATED DIFFUSION OF OXYGEN

21

it should be noted that this agreement depended very much on the choice of the numerical values of D,, in particular (see fig. 6). Since excellent agreement was obtained when choosing well-founded mean values of D,, from the scatter of experimental points (fig. 6) it may be concluded that the mathematical treatment of facilitated diffusion of O2 based on simultaneous diffusion of 0, and HbOz provides a quantitative description of the experimental results if the chemical reaction rates are also taken into account. MURRAY(1969) also studied the equation suggested by WYMAN(1966) to explain the facilitated diffusion of 0, in a Hb solution. He used a singular perturbation approach which in this particular situation reduced the problem from that of solving a nonlinear second order differential equation to that of solving an algebraic quadratic one. The method also suggested functional forms for the dependence of the fractional saturation of Hb on the O2 concentrations at the surfaces of the membrane through which the 0, diffuses. Comparison between the theoretically calculated facilitated flux with that found experimentally by WITTENBERG(1966) showed a good agreement for Hb and O,, but the computed facilitated flux was almost double the experimental value for Mb and 02, as also found by KREUZERand HOOFD(unpublished results). Physiological

significance

Most experiments discussed here were performed at steady state in order to exclude the capacitive factor of Hb and Mb, but the gas exchange processes in the body are nonsteady-state phenomena where the capacitive function is definitely important, In spite of this an attempt may be made to estimate the possible role of enhanced transport in the O2 exchange of lungs and tissues. This possible role will depend on the conditions of the natural environment for Hb and Mb. 1. PHYSIOLOGICAL IMPORTANCE OF DIFFUSION OF Hb IN REDCELLS Fair evidence is available for the belief that the interior of the red cells is equivalent to a highly concentrated (about 35 g?:,) but true watery solution of Hb (BATEMAN et al., 1953) although this solution is no longer ideal (osmotic pressure independent of concentration) above a concentration of 8 g% (RIVEROS-MORENO and WIT~E~~G, 1968). An interna structure with possible interaction with the Hb molecules and thus an effect on the condition of the Hb cannot be excluded but there is no convincing evidence or any agreement between the various authors concerning such a structure. PERUTZ(1948) pointed out that the Hb molecules in the interior of the red cell are almost touching each other and probably can only rotate but barely show any translational movement. However, the experimental determinations of Dnb in very concentrated Hb solutions (fig. 6) have shown that there is still some spatial diffusion present with Dub= 3 -7 x lo- a cm’/sec at 35 9% Hb. There remains some scatter of the results between various investigators and the value of DNb may become rather sensitive to even slight deviations of Hb concentration and, therefore, viscosity (ADAMSand FATT, 1967). The establishment of an accurate value of Dub for highly concentrated Hb solutions

22

F. KREUZER PLOTOF DHbin

DHbAGAlNSTDOzlN35g%Hb

10~8cm2/sec

~

i 0.2

0.3

0.5 04 Do,in10-5 cm2/sec

Fig. 9. Plot of DH~ against DO, in 35 g% Hb solution.

as present in the red cell is important since the values of D,, are connected to concomitant values of Do, in the presence of a particular total 0, transport (fig. 9). KLUC et al. (1956a) found a value of D,,=0.4 x lo-’ cm*/sec for D,,=O whereas most other authors arrived at higher values (fig. 5). However, if D,, should really be greater than zero as concluded above from experimental determinations, Do, would become even smaller, for instance, Do, =0.27 x lo-’ cm’/sec for D,,=7 x lo- * cm*/sec. Thus the possible role of Hb diffusion for O2 diffusion inside the red cells remains unclear. According to MOLL (1966b), on the other hand, D,, is about l”C, of Do, at this high Hb concentration. At physiological gas pressures the molar concentration of Hb is, however, about 50 times higher than the molar concentration of O,, and the diffusion rate of Hb may thus have a quarter of the intensity of the 0, diffusion, i.e., just as many 0, binding groups of Hb as O2 molecules may pass a given area. According to MOLL (1966b) the diffusion of 0, at 1 atm gas partial pressure difference should be enhanced at the most by about lo?/, which would not be far from the conclusion by LONCMUIR and ROUGH-CON(1952) as well as KLUG et al. (1956a) that Hb diffusion may be neglected in the red cell. SCHROEDERand HOLMQUIST(1968) calculated that facilitated transport may contribute about 60/o to the total flux of 0, into the erythrocyte. The most obvious attempts at an answer is of course to perform experiments with intact red cells. The early trials by SCHOLANDER(1960a) and HEMMINGSEN(1965) may

FACILITATED DIFFUSION OF OXYGEN

23

have been invalidated by considerable hemolysis (ROUGHTON,1963), probably caused by the presence of detergents in his Millipore filters (CAHN, 1967). Nevertheless these results seemed to be confirmed by MOLL (1969) who showed experimentally that the 0, transfer was enhanced by 640%)in red cells at a PoZ difference of 110 mm Hg at 37 “C; the maximum of facilitation was equal to the free diffusion at 100 mm Hg PoZ, and the rate of facilitation corresponded to a D,, of 5 - 6 x lo-’ cm’/sec. KU~CHAI and STAUB(1969) have repeated the experiment of SCHOLANDER (1960a) and found, indeed, extensive hemolysis on Millipore filters. However, when using fine stainless steel wire screen on which hemolysis averaged less than 1“&they still could demonstrate considerable Hb-facilitated 0, transport in packed human red cell layers at 21-23 “C. The enhancement of O2 diffusion in these packed red cells was the same as that in concentrated Hb solutions of equal Hb concentration (29.5 and 29.7 go{,, resp.). They concluded from this observation that the net steady-state 0, diffusion resistance of the red cell membrane is small relative to that of the red cell interior (thus confirming the previous finding by KREUZERand YAHR, 1960) and that the interior of the red cell has no special structure or organization affecting the mobility of Hb molecules (in agreement with PERUTZ,1948). The enhancement found by these authors, interpreted by simultaneous diffusion of 0, and HbO,, was compatible with an 0, diffusion coefficient of 0.9 x lo- ’ cm’lsec, and a Hb02 diffusion coefficient of 5.4 x lo-’ cm’/sec in their media having a Hb concentration of about 30 god,; this value of the 0, diffusion coefficient agrees very well with that in fig. 5 and the value of the HbO, diffusion coefficient corresponds to that reported by MOLL (1966b, see fig. 6, and 1969, see above). However, these considerations and experiments in vitro in steady-state conditions do not provide any answer yet to the question of the role of facilitated 0, diffusion under truly physiological circumstances. Facilitation is proportional to the difference in oxygenation along the path of the 0,. However, on the basis of observed arteriovenous differences, the oxygenation differentials rarely exceed 50%, which would give correspondingly lower enhancements (HEMMINGSEN, 1966). According to COLLINS(1961), facilitation might accelerate 0, and CO, transport particularly with lowered gas concentration differences at hypoxia, and might also mediate an equitable distribution of gases to tissues, i.e., as concentration of 0, falls in a given area of tissue the transport of 0, to that region is spontaneously increased by this mechanism. In nonsteady-state systems as present in the body both the P,, and the HbO, gradients change continuously with time during oxygenation and deoxygenation. In the beginning the speed of O2 loading und unloading, respectively, is determined largely by the rate of chemical reaction, and an 0, transport by HbO, diffusion should be of minor importance, also because the HbO, concentration gradient needs time to be built up. On the other hand, both P,, and HbO, gradients decrease gradually as equilibration is approached. Thus there might be a maximum for Hb02 diffusion in the middle of the time of exchange. SIRSand ROUGHTON(1963) indeed found no hint of an acceleration by Hb02 diffu-

24

F. KREUZER

ZEIT

(msec)

-

Fig. 10. Oxygenation velocity with fixed and mobile hemoglobin. Results from calculations by computer IBM 7090 (with permission from: MOLL,1966a). sionwhentheycompared the initial speed of oxygenation at different ambient PO, values. Recently MOLL (1968/69) has shown by numerical computer calculations that Hb diffusion did not accelerate the initial rate of O2 uptake and release but speeded up the last two thirds of saturation change by about 30°i:, of the time (fig. 10); the acceleration of the 0, uptake by Hb diffusion was more pronounced in the presence of lower 0, pressures. 2. PHYSIOLOGICALIMPORTANCEOF DIFFUSION OF Mb IN MUSCLE The situation is even more complicated in the case of Mb since not only the Mb concentration in the tissues but also the characteristics of the cellular medium (protein concentration and viscosity in particular) and the condition of the Mb in relation to the environment are important. The protein content of mammalian muscle is 16-21 g per 100 g fresh tissue (HEILBRUNN, 1949). The viscosity of the protoplasm of various cells is around 2-4 centipoise (HEILBRUNN, 1949), whereas the viscosity of an 18 go/, serum protein solution is about 6 centipoise (KREUZER, 1953), and that of a 34 g”/:, Hb solution about 10 centipoise (KREUZER, 1953). Not all of the muscular volume is occupied by muscle cells, and the muscle cell is highly structured and in particular contains fibrous proteins and intracellular membranes. The Mb, which is assumed to be in solution in the cell juice, is quite possibly excluded from mitochondria and other organelles, and is certainly excluded from the volume occupied by the contractile proteins (WITTENBERG, 1965). Nothing is known concerning the actual protein concentration and the viscosity of the remaining cell juice supposedly containing the Mb dissolved in free solution, and in regard to the mobility (diffusion coefficient) or the distribution of Mb in the cells. There is urgent need for quantitative histochemical studies of Mb in muscle. Recent studies have shown that Mb may be preferentially located near the cell membrane and at fibrillar structures possibly related to an internal cell membrane system (fluorescent antibody technique; KAGEN and GUREVICH,

FACILITATED DIFFUSION OF OXYGEN

25

1967), or at the myofibrils mainly in the A band (except in the H zone) and also at the Z line (benzidine-peroxidase reaction; GOLDFISCHER,196?), but these findings are not easily reconciled and depend much on the method; JAMES(1968) formulated some criticism but seemed to agree that the histochemical evidence rather suggests that the Mb is immobile. The amount of Mb present in muscles varies from one animal to another as it does among muscles of the same animal, and may change with the functional condition of the muscle (e.g., chronic hypoxia and physical training). The concentration of Mb in human heart muscle is about 1.5-2.5 g :‘, dry weight (or 0.3-0.5 gy/o wet weight) (HEMMINGSEN, 1966; WYMAN,1966; BLESSING,1967). In human skeletal muscle it is about 2-5 g y/o dry weight (or 0.4-1.0 g?Jj wet weight) (WITTENBERG,1965; WYMAN, 1966). The concentration of Mb in that part of the muscle volume in which it is sequestered cannot be estimated with certainty, but probably exceeds 1.7 g’$$of lo- 3 M which is within the range required for significant facilitated diffusion (required minimum probably 1O-3 M) (WITTENBERG,1965), but the Mb concentration taken alone does not take into account the influence of the other proteins on Mb mobility. HEMMINGSEN (1966) estimated that the true, local concentration of Mb must be substantially higher, say twice or more the value given above, depending on the distribution which is unknown. In solution this would more than double the rate of 0, diffusion under optimal conditions (HEMMINGSEN,1966). An even larger transport enhancement could prevail in muscles of diving animals, the muscles of seals commonly having an O2 capacity of 5 vol?{,. ~IVE~OS-MO~ENOand WI~TENBERG(1968) measured D,, as a function of the Mb concentration (fig. 7). MOLL (1968) determined D,, by measuring the diffusion of Mb from a muscle homogenate rich in Mb (heart muscle of the rat) into a homogenate poor in Mb (skeletal muscle of the rat). He found a value of 1.5 x lo-’ cm’/sec at 20 “C and 2.7 x lo- ’ cm”/sec at 37 “C. The total protein concentration of these homogenates was 20-22 g”i. The values of D Mbfound here were about 8 times lower than the value found by POLSON(1939) for a 0.4 gq I Mb solution. Since a homogenate may be supposed to offer less resistance to diffusion than intact muscle tissue, these values should be maximal values possibly occurring in the intact cell. MOLL(1967) also investigated the facilitated 0, diffusion in muscle itself by measuring the steady-state passage of O2 across thin muscle layers of the rat interposed between a streaming gas phase and a streaming fluid phase. Facilitated diffusion of O2 was found in most preparations although there was considerable scatter in the results and no quantitative data were reported. The total O2 capacity of Mb is sufficient for lo-15 set muscle metabolism at rest and for 2-3 set during activity according to MILLKAN (1937, 1939), whereas WYMAN (1966) estimated 5.5 set at rest. Millikan thought that Mb acts as a short time 0, store to tide the muscle over from one contraption to the next, particularly in hypoxia, whereas Wyman considered the function of Mb as a significant 0, storage reservoir as dubious, also in view of the slowness of Mb deoxygenation. CROTE, HUHMANNand NIESEL(1967) pointed out that Mb can act as a short time 0, store and as an O2 car-

26

F. KREUZER

rier only in tissue regions with critical 0, supply, due to the steep dissociation

curve.

Thus MbO, diffusion might play a role at the venous end of the capillaries, particularly with higher Mb concentrations in this region which, however, have not been shown to exist experimentally.

The occurrence

of MbO,

gradients

between well and critically

supplied tissue regions in beginning hypoxia could lead to decrease of the mean 0, saturation of Mb without simultaneous decrease of 0, consumption. WYMAN (1966), however, feels that Mb probably rather performs its function when in the oxygenated state in the sense of facilitation of diffusion. Provided the Mb maintains a certain mobility in the cells, again the oxygenation at the points of entry and demand would be decisive (HEMMINGSEN, 1966). MILLIKAN (1937, 1939) observed spectrometrically a considerable or even complete deoxygenation of Mb during contraction, and a complete reoxygenation during relaxation. Thus there would be intermittently a condition where a transport increase could be obtained. In many cases the PO, in the cell might be sufficiently low so that there is no inhibition by back pressure, and the Po, outside muscle cells might be sufficiently high to fully utilize the transport capabilities of the small amount of Mb present. However, it might well be that convection by stirring and/or cytoplasmic streaming may be more important in the cells than this effect (LONGMUIR and BOURKE, 1960). MOLL (1968) calculated that the facilitated 0, diffusion amounts to a free 0, diffusion equivalent to about 2 mm Hg Po, difference for rat skeletal muscle, 6 mm Hg for human skeletal muscle with three times higher Mb concentration, 4 mm Hg for rat heart muscle, and 3 mm Hg for human heart muscle. This means that, if facilitated diffusion of 0, is present amounting to a free diffusion at 3 mm Hg Po, difference, the Po, in the blood needed for sufficient 0, supply to the tissue is 3 mm Hg lower than without facilitation; thus, according to the HbO, dissociation curve of the blood, the venous blood can release about 1.2 ml O,/lOO ml blood more 0, with an 0, capacity of 20 vol O{,0,. WYMAN (1966) calculated, assuming steady state and equilibrium and rather arbitrary values for DoI and D,,, that Mb is capable of taking over a substantial part of the 0, transport in th.e cells whenever the Po, drops to about 10 mm Hg or less. A cyclic change of Mb saturation in rhythmically contracting muscle is not inconsistent with this view, although, if during a certain part of the cycle the Mb were completely deoxygenated throughout the muscle, its role as a mechanism of transport would be temporarily suspended, the muscle passing through a phase of 0, debt. The contributions from ordinary and facilitated diffusion are about equal at a Po, of 15 mm Hg, and the relative contribution from facilitated
27

FACILITATEDDIFFUSION OF OXYGEN at such low PO, values, the two contributions

thus again being about

equal in this PO,

range. FORSTER (1967) computed that the facilitation in muscle (Mb concentration = 1.2. mg/g, D,,= l/25 of Do,) would be 12’3; for a PO, gradient from 10 to 1 mm Hg, and 20% for a gradient from 5 to close to zero mm Hg, the Mb being about halfsaturated at the higher 0, pressures. It may be interesting to note that, according to WHALEN (1968), red muscle appears to have a considerably higher PO, than white muscle, an approach which might be worth being further pursued. In conclusion, the physiological importance of facilitated diffusion of O2 by Hb and Mb remains at the speculative level as long as the exact physiological conditions are largely unknown and cogent experiments under really physiological conditions are lacking.

References ADAMS, L. R. and I. FAD

(1967). The diffusion coefficient of human hemoglobin at high concentrations. Respir. Physiol. 2: 293-301. BATEMAN,J. B., S. S. Hsu, J. P. KNUDSENand K. L. YUDOWITCH(1953). Hemoglobin spacing in erythrocytes. Arch. Biochem. Biophys. 45: 411-422. BLESSING,M. H. (1967). Ueber den Myoglobingehalt des Herzmuskels

des Menschen. Arch. Kreis-

lauff. 52: 236-278.

BRIGHT, P. B. (1967). The basic flow equations of electrophysiology in the presence of chemical reactions: II. A practical application concerning the pH and voltage effects accompanying the diffusion of 02 through hemoglobin solution. Bull. Math. Biophys. 29: 123-138. CAHN, R. D. (1967). Detergents in membrane filters. Science 155: 195-196. COLLINS,R. E. (1961a). Transport of gases through hemoglobin solution. Science 133: 1593-1594. COLLINS,R. E. (1961b). Transport of gases through hemoglobin solution. BUN. Math. Biophys. 23: 223-232.

DAVSON,H. (1959). A Textbook of General Physiology. Second edition. London, Churchill, p. 234. DDRRER, E. by F. J. W. ROUGHTON(1967). Personal communication. Letter of May 18, 1967. ENNS, T. (1964). Molecular collision-exchange transportjof oxygen by hemoglobin. Proc. Nat. Acad. Sci. 51: 247-252. ENNS, T. (1965). Carbonic anhydrase facilitated transport of COZ. Federation Proc. 24, nr. 1485, p. 397. ENNS, T., G. B. SHAMand S. ANDERSON(1966). Carbonic anhydrase diffusion of CO2 in whole blood. Physiologist 9: 176. ENNS, T. (1967a). Facilitation by carbonic anhydrase of carbon dioxide transport. Science 155: 44-47. ENNS, T. (1967b). Gas transport and the red cell. Federafion Proc. 26: 1802-1804. FATT, I. (1960). Oxygen diffusion. Letter to the Editor. Science 132: 368. FATT, I. and R. C. LA FORCE (1961). Theory of oxygen transport through hemoglobin solutions. Science 133: 1919-1921. FATT, I. and R. C. LA FORCE(1962). Diffusion coefficient of oxyhaemoglobin. Nature 195: 505. FORSTER,R. E. (1967). Oxygenation of the muscle cell. Circulation Res. 20, Suppl. 1, I 115-121. Fox, M. A. and H. D. LANDAHL(1965). Theory of hemoglobin facilitated oxygen Itransport. Bull. Math. Biophys. 27: 183-190.

FRIEDL~NDER,S. K. and K. H. KELLER(1965). Mass transfer in reacting systems near equilibrium. Use of the affinity function. Chem. Eng. Sci. 20: 121-129.

28

F.

KREUZER

GOLDFISCHER,S. (1967). The cytochemical localization of myoglobin in striated muscle of man and walrus. J. Cell. Biol. 34: 398403. GOLDSTICK,T. K. (1966). Diffusion of oxygen in protein solutions. Ph. D. Thesis, University of California, Berkeley, Calif. GROTE, J., W. HUHMANNand W. NIESEL (1967). Untersuchungen iiber die Bedingungen fir die Sauerstoffversorgung des Myokards an perfundierten Rattenherzen. II. Zur Funktion des Myoglobins. Pligers Arch. ges. Physiol. 294: 256-264. HAMMEL,H. T. (1965). Oxygen transport through hemoglobin solutions. Scientific results of marine biological research, nr. 48. Essays in marine physiology. Presented to P. F. Scholander in honour of his sixtieth birthday. Oslo, Universitetsforlaget, 164-177. HAMMEL,H. T. (1966). Oxygen transport through hemoglobin solutions. AMRL-TR 66-19, WrightPatterson Air Force Base, Ohio. HEILBRUNN,L. V. (1949). An Outline of General Physiology. Second edition. Philadelphia, Saunders. HEMMINGSEN,E. and P. F. SCHOLANDER(1960). Specific transport of oxygen through hemoglobin solutions. Science 132: 1379-1381. HEMMINGSEN, E. (1963). Accelerated exchange of oxygen-l 8 through a membrane containing oxygensaturated hemoglobin. Science 135: 733-734. HEMMINGSEN,E. A. (1963). Enhancement of oxygen transport by myoglobin. Camp. Biochem. Physiol. 10: 239-244. HEMMINGSEN, E. A. (1965). Transfer of oxygen through solutions of heme pigments. Acfa Physiol. Stand., Suppl. 246, 53 pp. HEMMINGSEN, E. A. (1966). Enhanced transport of oxygen by hemoglobin and myoglobin. Proc. Int. Symp. Cardiovasc. Effects Hypoxia, Kingston, Ontario, Canada, 1965. Basel/New York, Karger, pp. 41-54. JAMES,N. T. (1968). Histochemical demonstration of myoglobin in skeletal muscle fibres and muscle spindles. Nature 219: 1174-1175. JOST, W. (1952). Diffusion in Solids, Liquids, Gases. New York, Academic Press. KAGEN, L. J. and R. GUREVICH(1967). Localization of myoglobin in human skeletal muscle using fluorescent antibody technique. J. Histochem. Cytochem. 15: 436-441. KELLER, K. H. (1964). The steady state transport of oxygen through hemoglobin solutions. Ph. D. Thesis, Johns Hopkins University, Baltimore, Md. KELLER, K. H. and S. K. FRIEDL~NDER(1966a). The steady-state transport of oxygen through hemoglobin solutions. J. Gen. Physiol. 49: 663-769. KELLER,K. H. and S. K. FRIEDL~NDER(1966b). Diffusivity measurements of human methemoglobin. J. Gen Physiol. 49: 681-687.

KLUG, A., F. KREUZERand F. J. W. ROUGHTON(1956a). The diffusion of oxygen in concentrated hemoglobin solutions. Helv. Physiol. Pharm. Acta 14: 121-128. KLUG, A., F. KREUZERand F. J. W. ROUGHTON(1956b). Simultaneous diffusion and chemical reaction in thin layers of hemoglobin solution. Proc. Roy. Sot. B 145: 452-472. KREUZER,F. (1950). Ueber die Diffusion von Sauerstoff in SerumeiweisslGsungen verschiedener Konzentration. Helv. Physiol. Pharm. Acta 8: 505-516. KREUZER, F. and A. BETTICHER(1951). Eine Apparatur hoher Empfindlichkeit und Stabilitlt zur Messung der Oxydationszeiten des HLmoglobins. Helv. Physiol. Pharm. Acta 9: 244-253. KREUZER, F. (1953). Modellversuche zum Problem der Sauerstoffdiffusion in den Lungen. He/v. Physiol. Pharm. Acta 11, Suppl. 9, 99 pp. KREUZER,F. and W. Z. YAHR (1960). Influence of red cell membrane on diffusion of oxygen. J. Appl. Physiol. 15: 1117-1122.

KREUZER,F. and L. J. C. HOOFD(1970). Facilitated diffusion of oxygen in the presence of hemoglobin. Respir. Physiol. 8 : 280-302.

KUTCHAI, H. and N. C. STAUB(1969). Steady-state, erythrocytes. J. Gen. Physiol. 53: 576-589.

hemoglobin-facilitated

02 transport

in human

FACILITATED

DIFFUSION

OF OXYGEN

29

LA FORCE, R. C. and I. FATT (1962). Steady-state diffusion of oxygen through whole blood. Trans. Faraday Sot. 58: 1451-1464. LA FORCE, R. C. and I. FATT (1964). Steady-state gas transport through hemoglobin solutions. Biopolymers, Symposia No. 1: 555-562. LA FORCE R. C. (1966). Steady-state diffusion in the carbon monoxide + oxygen + haemoglobin system. Trans. Faraday Sot. 62: 1458-1468. LA FORCE, R. C. and I. FATT (1967). Conditions for countergradient diffusion of oxygen through a hemoglobin barrier. In: Chemical Engineering in Medicine and Biology, edited by D. Hershey. New York, Plenum Press, pp. 107-l 15. LONGMUIR,I. S. and F. J. W. ROUGHTON(1952). The diffusion coefficients of carbon monoxide and nitrogen in haemoglobin solutions. J. Physiol. (London) 118: 264275. LONGMUIR,I. S. and A. BOURKE(1960). The measurement of the diffusion of oxygen through respiring tissue. Biochem. J. 76: 225-229. LONGMUIR,I. S., R. E. FORSTERand CHI-YUANWoo (1966). Diffusion of carbon dioxide through thin layers of solution. Nature 209: 393-394. MILLIKAN, G. A. (1937). Experiments on muscle haemoglobin in vivo; the instantaneous measurement of muscle metabolism. Proc. Roy. Sac. B 123: 218-241. MILLIKAN,G. A. (1939). Muscle haemoglobin. Physiol. Reu. 19: 503-523. MITCHELL, P. (1967). Translocations through natural membranes. Adu. Enzymology 29: 33-87. MOCHIZUKI, M. and R. E. FORSTER(1962). Diffusion of carbon monoxide through thin layers of hemoglobin solution. Science 138: 897-898. MOLL, W. (1962). Die Carrier-Funktion des Hamoglobins beim Sauerstoff-Transport in Erythrocyten. Ppiigers

Arch. ges. Physiol.

275: 412419.

MOLL, W. (1966a). Der Prozess der gleichzeitigen Diffusion und ReaktionvonHLmoglobin undsauerstoff bei der Sauerstoff-Aufnahme und- Abgabe des Blutes. Habilitationsschrift, Tubingen, 67 pp. MOLL, W. (1966b). The diffusion coefficient of haemoglobin. Respir. Physiol. 1: 357-365. MOLL, W. (1967). Untersuchungen zur Oa-Transportfunktion des Myoglobins im Muskel. Pfligers Arch. ges. Physiol. 297: R 93-94. MOLL, W. (1968). The diffusion coefficient of myoglobin in muscle homogenate. Ppigers Arch. ges. Physiol.

299: 247-251.

MOLL, W. (1968/69). The influence of hemoglobin diffusion on oxygen uptake and release by red cells. Respir. Physiol. 6: l-15. MOLL, W. (1969). Measurements of facilitated diffusion of oxygen in red blood cells at 37 “C. Pfliigers Arch. ges. Physiol.

305: 269-278.

MURRAY,J. D. (1969). On Wyman’s facilitated diffusion equation. Manuscript. PERUTZ, M. F. (1948). Submicroscopic structure of the red cell. Nature 161: 204-205. PIRCHER,L. (1952). Die Diffusionskonstante des Sauerstoffs in Methamoglobinlosungen verschiedener Konzentrationen. Helv. Physiol. Pharm. Acru 10: 110-l 12. POLSON,A. (1939). Untersuchungen tiber die Diffusionskonstanten der Proteine. KoN. Z. 87: 149-181. RIVEROS-MORENO, V. and J. B. WITTENBERG (1968). The self-diffusion coefficient of hemoglobin and myoglobin in concentrated solutions. Manuscript. ROUGHTON,F. J. W. (1932). Diffusion and chemical reaction velocity as joint factors in determining the rate of uptake of oxygen and carbon monoxide by the red blood corpuscle. Proc. Roy. Sot. B 111: l-36. ROUGHTON,F. J. W. (1959). Diffusion and simultaneous chemical reaction velocity in haemoglobin solutions and red cell suspensions. Progr. Biophys. Biophys. Chem. 9: 55-104. ROUGHTON,F. J. W. (1963). Kinetics of gas transport in the blood. Brit. Med. Bull. 19: 80-89. SCHOLANDER, P. F. (1960a). Oxygen transport through hemoglobin solutions. Science 131: 585-590. SCHOLANDER,P. F. (1960b). Oxygen diffusion. Letter to the Editor. Science 132: 368. SCHOLANDER, P. F. (1965). Tension gradients accompanying accelerated oxygen transport in a membrane. Science 149: 876-877.

F.

30

KREUZER

SCHROEDER,W. A. and W. R. HOLMQUIST(1968). A function for hemoglobin AIM?In: Structural Chemistry and Molecular Biology, eds. A. Rich and N. Davidson. San Francisco and London, Freeman, 238-255. SIRS, J. A. and F. J. W. ROUGHTON(1963). Stopped-flow measurements of CO and 02 uptake by hemoglobin in sheep erythrocytes. J. Appl. Physiol. 18 : 158-l 65. SNELL, F. M. (1965). Facilitated transport of oxygen through solutions of hemoglobin. J. Z’heoret. Biol. 8: 469419.

SPAETH, E. E. (1967). The convective diffusion of oxygen, carbon dioxide and inert gas in blood. Report from W. M. Keck Laboratory of Environmental Health Engineering, California Institute of Technology, Pasadena, California. SPAETH,E. E. and S. K. FRIEDL~NDER(1967). The diffusion of oxygen, carbon dioxide, and inert gas in flowing blood. Biophys. J. 7: 827-851. WANG, J. H. (1961). Transport of oxygen through hemoglobin solutions. Science 133: 1770-1771. WANG, J. H. (1963). Chemical reaction accelerated transport of molecules through membranes. J. Theoret.

Biol. 4: 175-178.

WARD,

W. J. and W. L. ROBB (1967). Carbon dioxide - oxygen separation: Facilitated transport of carbon dioxide across a liquid film. Science 156: 1481-1484. WHALEN,W. J. (1968). Personal communication. WISE, D. L. and G. HOUGHTON(1969). Solubilities and diffusivities of oxygen in hemolyzed human blood solutions. Biophys. .I. 9: 36-53. WITTENBERG, J. B. (1958). Active transport of oxygen. Biol. BUN. 115: 372-373. WITTENBERG,J. B. (1959). Oxygen transport - a new function proposed for myoglobin. Biol. BUN. 117: 402403. WITTENBERG,J. B. (1963). Facilitated diffusion of oxygen through haemerythrin solutions. Nature 199: 816817. WI~TENBERG,J. B. (1965). Myoglobin-facilitated diffusion of oxygen. J. Gen. Physiol. 49: 57-74. WITTENBERG,J. B. (1966). The molecular mechanism of hemoglobin-facilitated oxygen diffusion. J. Biol. Chem. 241: 104-l 14. WITTENBERG,J. B. (1969). Personal communication. Letter of May 7, 1969. WYMAN, J. (1966). Facilitated diffusion and the possible role of myoglobin as a transport mechanism. J. Biol. Chem. 241: 115-121. ZILVERSMIT, D. B. (1965). Oxygen-hemoglobin system: a model for facilitated membranous transport. Science 149 : 874-876.

Note

added

in proof

In the chapter “Basic characteristics of facilitated diffusion of Oz”, section “4. Influence of molecular (1965) found . furthermore that size and mobility of the pigment” I have stated: “. . . HEMMINGSEN the enhancement was almost the same with Mb as with Hb of double 02 capacity, i.e., the effects with Mb against Hb were indirectly proportional to the root of the molecular weights”. WITTENBERG (1970, private communication by letter of February 19, 1970) has reported to me that he has recalculated Hemmingsen’s published values and does not concur in his conclusion from his data, The Hb and Mb concentrations in solutions on which Hemmingsen bases this conclusion were different, one fell on the steeply rising portion of the curve (fig. 8 of this paper), the other was near the maximum of the curve. Of course the enhancement per unit heme was different, but the cogent point is that both fell on the same curve relating facilitated flux to protein concentration. This is consonant with Wittenberg’s conclusion that Hb and Mb enhance oxygen diffusion to the same extent at any given heme concentration.