Permeability of human erythrocytes to ammonia …...tant mixture flowed through a 1.7-mm-diam glass...

AMERICAN JOURNAL OF PHYSIOLOGY Vol. 222, No. 4, April 1 972. Prtnted in u.s.n

Permeability of human erythrocytes to

ammonia and weak acids

ROBERT A. KLOCKE, KAJSA K. ANDERSSON, HAROLD H. ROTMAN, AND ROBERT E. FORSTER Department of Physiology, Univer-sity of Pennsylvania, School of Medicine, Philadelphia, Pennsylvania, 19104

KLOCKE, ROBERT A., KAJSA K. ANDERRSON.HAROLD H. ROT- . MAN, AND ROBERT E. FORSTER. Permeability of human ery throcy tes to ammonia and weak acids. Am. J. Physiol. 222(3): 1004-1013. 1972.- We have developed a continuous-flow rapid-reaction apparatus, using a glass pH electrode, capable of measuring changes in pH of ho.01 unit as early as 0.01 set after mixing. With this apparatus

we have measured the change of extracellular pH with time following mixture of a suspension of about 2570 fresh human red cells in saline with solutions of NH3 or of one of seven weak acids in saline. From these data we calculated the permeability of the red cell membrane for the unionized NH3 or acid. The average permeability of the human red cell at 37 C in centimeters per second for NH3 , was 1.08 X 10S2; for acetic acid, 1.44 X 1w3; for barbituric acid, 8.75 X 1 Oe4; for butyric acid, 1.10 X 10e2; for formic acid, 1.52 X 10V3; for lactic acid, 1.13 X le3; for propionic acid, 4.93 X 10B3; and for valeric acid, 2.70 X 10m2. The rate of NH3 and formic acid movement into the red cells was not altered by the simultaneous flux of water into or out of the cell produced by osmotic gradients as great as -88 and + 1,100 mOsm/liter, respectively. We present theoretical arguments that any effect of experimentally achievable fluid fluxes through the red cell membrane upon simultaneous solute flux (“solvent drag”) would be so small as to be difficult to detect.

solvent drag: rapid-reaction pH apparatus

AT PRESENT, MEASUREMENT OF erythrocyte membrane permeability is limited to substances whose half-time for equilibration is greater than 0.003 set, the practical limit of reaction velocity which can be observed in existing rapid- mixing apparatus. The rapidity of equilibration between extracellular and intracellular concentration is dependent upon the ratio of the size of the intracellular reservoir or sink for the diffusing substance to the membrane permeability. Equilibration time decreases as either the effective sink size decreases or permeability increases.

In the case of nitrogen, a chemically inert gas, diffusion equilibrium across the cell membrane is complete in less than 0.001 set (14), and the exchange process cannot be studied with available techniques because it permeates the membrane rapidly and can be stored in the cell interior only in physical solution. 02 and CO have a large intracellular sink since they combine with hemoglobin, and therefore reach equilibration more slowly, permitting obser- vation of the rate of the process ( 15). However, the rate of exchange is limited to a large degree by intracellular gas diffusion and probably not by the diffusion resistance of the

membrane, so the latter’s permeability cannot be computed. Intracellular gradients of bound 02 and CO result from the slow diffusion of the large ligand-hemoglobin complex in the concentrated solution present inside the cell (26). The rate of chemical reaction between the ligand and hemoglobin is actually less important in determining the speed of gas uptake than the rate of diffusion. Therefore, we cannot measure membrane permeability with greater accuracy by using a gas which reacts more rapidly with hemoglobin in solution.

Weak acids with pK considerably below intracellular pH or weak bases with an acidic pK above intracellular pH are ideal for studying membrane permeability because: a) on entering the cell the uncharged molecules are ionized almost instantly ( 13) and completely; b) the strong buffering capacity of hemoglobin neutralizes the H+ or OH- produced, thus providing a large sink; and c) the ionized reaction product is small and diffuses as readily as the unionized molecule. Therefore, intracellular gradients of the ionized and unionized molecules should be negligible. The exchange is rate limited by diffusion across the red cell membrane, permitting calculation of the membrane permeability.

We have measured the rate of extracellular pH change of human erythrocyte suspensions in a continuous-flow rapid-reaction apparatus as either ammonia or one of seven weak acids penetrated the cells. The time course of intracellular and extracellular concentrations of these compounds was calculated from measurement of extracellular pH, enabling us to compute membrane permeability.

MATERIALS AND METHODS

The continuous-flow rapid-reaction apparatus modified for pH measurements is shown in Fig. 1. The cell suspension and a permeant solution were propelled into a mixing chamber in a volume ratio of either 1: 1 or 1: 2.5, respectively, by the two 130-ml motor-driven syringes. The reactant mixture flowed through a 1.7-mm-diam glass tube of variable length at a linear velocity of about 280 cm/set and impinged on the tip of a glass pH electrode. The time which the cells in the mixture reaching the pH electrode had been exposed to the permeant molecule was linearly related to the length of the glass tube. A correction of -t-O.005 set was made to compensate for the effect of a stagnant layer of reactant mixture present on the electrode surface (unpublished observations). Initially only two syringes were used, but the apparatus was later modified to accept four syringes so that

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1’ERMEABILl’I’Y OF HUMAN ERYTHROCYTES 1005

,--0 AMPLIFIER

PLASTIC ELECTRODb- HOLDER 7

WICK I

FIG.

changes in Diagram of continuous-flow apparatus for following rapid pH. Apparatus within dotted line was maintained at 37 c.

&ervations on several compounds could be made in the salne experiment. The temperature of the reagents and electrode was maintained at 37 C.

The glass electrode (type 403-GAZ, Ingold, Inc.) pro- truded into the flowing stream through a rubber gasket in the electrode holder. Both the silver-silver chloride reference electrode and the holder were filled with 2.5 M KC1 and (>onnected by a porous ceramic plug. A thin cotton wick ~XI from the KC1 through the rubber gasket to the tip of tile pH electrode to complete the circuit. The output of the conlbination electrode was amplified by a vibrating capaci- tance electrometer (model 3 1, Applied Physics Corp.) and recorded on a potentiometric strip chart (model SR, E. H. Sargent 8z Co.). The response time of the entire system to a change in pH in the flowing stream was lo-15 sec. Stable readings (kO.01 pH unit) were recorded during flow with hfTers having concentrations as low as 0.001 M. Static pH ~lleasurements in the apparatus were the same (=tO.Ol pH unit) as those made during reagent flow. The glass electrode hid no measurable sodium error at 37 C in 0.150 M NaCl at pH less than 8.7. KC1 was substituted for NaCl in experi- ;~~nts conducted at higher pH or in more concentrated salt solutions. Cation error was absent in KC1 solutions at pH less than 9.3, the upper limit of pH attained in our experi- relents.

Erythrocytes were separated from freshly drawn hep- arinized human blood by centrifugation at room temperature. Cells were washed 3 times with isotonic NaCl or KC1 and resuspended in the same medium. Solutions of ammonia ore prepared from reagent grade NH&l or (NH&SO4 . Acid solutions were standardized by titration. The pH of ycrmeant solutions was adjusted with NaOH or HCl to the tfesired value. The acidic dissociation constant for ammonia ;j t 0.15 ionic strength at 37 C was taken from Banks and Schwartz (2); the other values were determined by titration at 37 C (Table 1).

The pH of the reactant solutions was determined anaero- bically at 37 C with a glass electrode (type 130, Ingold, Inc.) using a saturated calomel reference electrode. The pH Illeasurements with this electrode were identical with those obtained in the reaction apparatus during flow. Intracellu- Ix pH was assumed equal to the pH of a lysate of erythrocytes separated from the cell suspension by centrifugation for 30 min at 2,750 X g and frozen in an acetone-Dry Ice

TABLE 1. Acidic dissociation constants I

Substance Ionic Strength, M

Acetic acid Ammonium Barbituric acid Butyric acid Formic acid Formic acid Lactic acid Propionic acid Valerie acid

0.15 0.15 0.15 0.15 0.15 0.86 0.15 0.15 0.15

* Obtained from Banks and Schwartz (2).

Acidic Dissociation Constant, M

2.51 X 1O-5 9.32 x lo-lo* 8.50 X 1O-5 2.04 X 1O-5 2.24 X 1O-4 3.31 x 1o-4 2.29 x 1o-4 1.86 x 1o-5 1.99 x 1o-5

bath ( 19). Extracellular pH at the start of the reaction was obtained by measuring the pH of a solution composed of the permeant solution and the supernatant of the cell suspension, mixed in the same proportion that was present in the reactant mixture.

Hemoglobin present in the supernatant of the cell suspension was measured by the method of Crosby and Furth (9). Total hemoglobin in the cell suspension was measured as cyanmethemoglobin. Osmolalities were determined by freezing-point depression (Osmette, Precision Systems, Inc.). Partition coefficients between olive oil and water of permeant molecules were determined by equilibrating 0.1 M

aqueous solutions with the oil at 37 C. The permeant concentration in the aqueous phase was measured; the concentration in the oil was assumed equal to the difference in concentration in the aqueous phase before and after equilibration. Concentration of acid was determined by titration. Ammonia concentrations were measured by the Conway microdiffusion technique (7). Values of 1.6 X 10-e cm2 and 8.7 X 10-r’ cm3 were used for red cell surface area and volume, respectively (2 7).

RESULTS AND CALCULATIONS

The time course of pH in experiment 4 with NH3 is shown in Fig. 2. In order to obtain a value for permeability from the observed measurements, the extracellular pH change must be related to NH3 concentration. Ln the following de- velopment, concentrations are used and activity coefficients are assumed equal to 1.0. This assumption has little effect on the calculation of permeability, since the diffusing species is uncharged and therefore has an activity coefficient of unity.

Assuming that only NH3 enters the cell as the exchange progresses the equilibrium between NH3 and NHd+ will be disturbed. NH4+ is converted to NH3 , liberating hydrogen ion which either remains free or combines with OH- to form water:

[NH4+];=0 - [NHa]e = ([H+]e - [H+]:=‘) + (K,/[H+l:=” - Kvl[H+leJ (4

where the subscript e indicates extracellular concentrations, the superscript t = 0 indicates the value at the start of the reaction, and K, is the dissociation constant of water equal to 2.4 X lo-14 at 37 C. This relationship permits calculation of [NH4+le at any time from the measured pH, since the initial values of [NH 4f e and [H+le would be known from the ]


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1006 KLOCKE, ANDERSSON, ROTMAN, AND FORSTER

Ttme (set)

TIME (set)

FIG. 2. Change in pH observed in experiment 4 after mixture of ammonia solution and erythrocyte suspension. Smooth continuous curve represents expected time course of pH for an ammonia permeability (PNH~) of 8.75 X 10B3 cm/set. pH changes over entire course of reaction as shown in inset.

composition of the reactant solutions. Equation I assumes that the NHJNH,+ and H+/OH- systems are the only extracellular buffers present. Other buffers which might be present are plasma proteins, bicarbonate, and hemoglobin. The cells were washed 3 times with saline equilibrated with air during preparation which removed all significant amounts of the plasma proteins and bicarbonate. However, hemolysis tends to occur with time, adding hemoglobin to the suspending fluid. He moglobin concentration in the supernatant was measured at the sta rt of all experiments and averaged 0.011 mM with the highest value being 0.020 mM. The ex tracellular hemoglobin concentration in the mixture was half this, providing no significant buffering power in comparison to that of the ammonia or weak acid which was present in millimolar quantities.

Once the extracellular [NHd+] is known, [NH& is calculated from the equilibrium relationship :

lBH31e = fmH4fle

rH+l P (2)

where K, is the acidic dissociation constant at the ionic strength of the reactant mixture. Equilibrium is assumed to exist at all times because the velocity of the ionization reac- tions is great in comparison to the velocity of NH3 movement (13).

Q,, the amount of NH3 , in moles, that has left the extracellular fluid at any time is:

Q = v~i[NH4+]:=~ - [N&+]e + [NH$=O - [NH3],) (3)

where V, is the extracellular fluid volume. Assuming conservation of mass and a negligible amount

of ammonia present in the cell membrane, Q is also equal to the total amount of ammon ia in the intracellular fluid :

Q = Vi([NHd+]i + [NH3]i) (a> where the subscript i refers to intracellular concentrations and Vi is the effective volume of intracellular fluid, taken to be 0.7 17 of the total cell volume (32). Because the buffering curve of hemoglobin, that is the H+bound plotted against pH, is approximately linear (11) we can relate the intracellular [H+] to Q as follows : where B = moles H-tbound/ (moles Hb X ApH), taken to be 2.54 ( 1 l), and it is assumed that all NH3 entering the red cell is ionized.

rH 1 +t= i [H 1 + ix0 exp ( - 2.303Q/B[Hb] ivi) (3;)

[Hb] i is the intracellular hemoglobin concentration calculated from the total hemoglobin concentration and hematocrit. Intracellular pH is about 7.2, 2 pH units less than the pK, of NH3 , 9.03 (2) so that all but about 1% of the intracellular ammonia is in the ionized form, leading to a maximum error in computed intracellular pH of 0.02 units.

Finally, instantaneous intracellular NH3 concentration can be calculated from ‘the equilibrium equation, since CH 1 + i and ([NH31 + [NHA+])i = Q/Vi are known. The extracellular and intracellular NH 3 concentrations calculated from the observed pH values in Fig. 2 are plotted in Fig. 3. In both figures the smooth lines represent the expected changes for a permeability of 8.75 X 10m3 cm/set. As noted in these figures, [NH& and PH, decrease markedly during the experiment. Intracellular NH 3 concentration remains relatively low since most of the NH3 entering the cell is ionized. [H+]i decreases during the experiment, the exact change depending upon the amount of NH3 entering the cell. Extremely large pH changes are pre- vented due to the strong buffering power of hemoglobin. [NH,+], decreases relatively little during the experiment, but [NH +] 4 i rises to a level greater than that in the extracellular fluid since NH4+ follows a Donnan distribution in the same manner as H+.

If no water movements occurred during the experiment, PNH~ , the NH3 permeability in centimeters per second, is equal to total flux divided by the mean gradient and cell surface area. Equations 1-5 can be combined into one equation to give the permeability as a function of extracellular hydrogen ion concentration and the initial conditions, but the relation is unwieldly and it proved more convenient to solve the equations serially. In early experiments the [NH31 gradient was obtained by graphical integration of the area between the [NH31 curves. In later experiments fitting of permeability values to the data was done by computer.

The experimental conditions and permeabilities obtained for the ammonia experiments are given in Table 2. PNH~ averaged 1.10 X low2 cm/set, 3 times as great as that of water under a diffusion gradient (0.33 X 10v2 cm/set) (3).

This method can be adapted to measure permeability to weak acids, as illustrated in Fig. 4 where the change in extracellular pH with time following mixture of butyric acid and a red cell suspension is plotted. In the acid experiments the sign of the exponent in equation 5 becomes positive, since intracellular hydrogen ion concentration increases with penetration of acid, the opposite of that seen with

FIG. 3. Extracellular and intracellular ammonia concentrations calculated from pH measurements of experiment 4. Smooth curves are calculated changes permeability of 8.75

in X

concentrations 1 OW3 cm/set.

OSXI 0.02 0.04 0.06 0608 0.10 TIME (set) *

expected with an ammonia


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PERMEABILITY OF HUMAN ERYTHROCYTES

TABLE 2. Permeability of human red cells to NH3

1007

Exp No.

1 0.197 2 0.125 3 1.108 4 2.951 5 2.845 6 2.750 7 2.602 8 2.514 9 1.436

10 1.300

Experimental Conditions

[NH& , mu [NHa+l, , mu PHe pH: Hematocrit, y0

0.996 8.34 7.02 14.0 0.955 8.13 7.02 10.7 4.623 8.41 7.03 16.5 2.887 9.04 7.06 14.4 2.655 9.05 7.07 11.0 2.750 9.05 7.07 11.0 2.932 8.98 7.03 11.5 3.020 8.95 7.03 11.5 3.373 8.66 7.08 13.4 3.400 8.69 7.08 14.5

t=o

Ext. osmolality - int. osmolality,

mOsm /liter

5 0 6

11 -88

122 4

157 -9

1,143

t=oo

7.25 1.16 X 1O-2 7.23 1.01 x 1o-2 7.30 9.25 x 1o-3 7.63 8.75 X lo-” 7.59 1.32 X 1O-2 7.96 1.40 x 1o-2 7.53 1 .Ol x 1o-2 7.43 9.38 X 1O-3 7.37 1.12 x 10-Z 7.63 1.19 x 1o-2

P, cm /set

Avg 1.08 X 1O-2

[NH& is the concentration of ammonia and [NH,+], is that of ammonium in the extracellular fluid. pH, is the pH in the extracellular !1uid, pHi is that inside the cells. Ext. osmolality - int. osmolality is the difference in osmolality between the intra- and extracellular tluid.

PH

I , I r I

0.00 0.02 0.04 0.06 0.08 0.10 TIME (sect:)

FIG. 4. Change in pH observed in experiment 1.3 following mixture of butyric acid solution and erythrocyte suspension. Smooth curve napresents expected time course of pH for a butyric acid permeability of 1.19 X 10D2 cm/set. Shaded area represents values expected with (i &5y0 deviation in permeability.

BUTYRIC i 1 ACID

mM I EXTRACELLULAR

TIME bed

FIG. 5. Extracellular and intracellular butyric acid concentrations calculated from pH measurements of experiment 13. Smooth curves are &culated changes in concentrations expected with a butyric acid permeability of 1.19 X 10B2 cm/set. Shaded area represents values cspected with a &5a/, deviation in permeability.

NH3 entrance. In addition, equation I becomes: - LO

LA 1 -

e - LA 1 e = ([H+]6” - [H+]e> + (fLI[H+le - Kw/[H+]:=O) (6)

where A- is the acidic anion. The concentrations of extracellular and intracellular

butyric acid calculated from the data of Fig. 4 are shown in Fig. 5. The continuous lines in both figures are the expected changes computed for a permeability of 1.19 X 10m2 cm/set. The shaded areas represent deviation of &5 % from this permeability. Although by 0.04 set the change in pH is half completed, the exchange of acid is half completed in a much shorter time, 0.02 sec.

Conditions of the experiments with acids and the calculated permeabilities are summarized in Table 3. The permeabilities to the monocarboxylic saturated fatty acids increase 20-fold from formic through valeric acid.

Ammonia and formic acid movements were measured during both water influx and efflux in an effort to demonstrate solvent drag. Osmolality in the ammonia and formic acid solutions was varied by changing the concentration of impermeant solute, KC1 in experiments 5, 6, 10, 21 and 23, and sucrose in experiment 6. Since water flux per se was not measured, it was calculated using osmotic permeability data from the literature (5). The instantaneous change in intracellular water volume, dVi , was evaluated by the Runge- Kutta method of numerical approximation,

dVi = P,A Osm~=“V~co

- v Osm,t=“V~=o dt

i v

> (7)

e

where P, is the value of water permeability under an osmotic gradient, chosen to be 0.3 cm4/(Osm X set), OsmE=O the initial intracellular osmolality, and Osmi=O the original extracellular osmolality. The fraction of osmotically active water was considered constant in this calculation. Calculated water volumes were used to correct permeant concentrations for changes in concentration produced by water flow.

The results of two experiments on NH3 movement during


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1008 KLOCKE, ANDERSSON, ROTMAN, AND FORSTEK

TABLE 3. Permeabilities of human red ceils to unionized acids

Ace tic

Barbi turic

Bu tyric

Formic

Lactic

Propionic

Valerie

Exp No.

17 1.949 3.470 4.87 6.97 11.8 18 2.124 1.166 4.34 7.12 11.4

26 0.469 2.459 4.72 7.07 9.5

13 2.467 3.032 4.78 7.03 11.8 14 0.385 5.070 5.81 7.04 11.6

19 0.078 5.411 5.20 7.00 11.6 20 0.841 4.123 4.38 7.12 14.6 21 0.805 4.075 4.19 7.12 15.0 22 1.036 3.853 4.22 7.03 10.3 23 0.720 4.140 4.24 7.03 10.1

24 0.185 5.230 5.02 7.00 11.6 25 0.352 2.487 4.49 7.12 11.4

15 0.800 3.492 5.37 6.97 11.8 16 1.848 1.307 4.58 7.07 9.5

11 2.331 3.072 4.82 7.03 11.8 12 0.372 4.999 5.83 7.04 11.6

ce [HAle is the concentra

llular and intracellular cellular fluid.

-

H&J- &-, n-l&t PHe PHi Hematocrit, y0

P . . ,tion or unlonlzed acid fluid, respectively. Ex

and [A-]8 that of acid anion t. osmolali tY - int. osmolality

in extracellular fluid. pHe and pHi are the pH in extra- the difference in osmolality between intra- and extra- iS

water flux into (experiment 5) and out of (experiment 6) the cell are plotted in Fig. 6. Permeabilities for the two experiments were essentially the same, 1.32 X low2 cm/set with water flux in and 1.40 X 10D2 cm/set with water flux out. The slightly higher value was obtained when water was flowing against the direction of NH3 flux, the opposite of the expected effect of solvent drag. Permeabilities measured during no water movement (experiment 7) and during water efflux in experiment 6 were also the same. Even when the osmotic gradient was increased to 1,100 mOsm/liter (experiment IO), no change in PNH~ was noted as compared to the control experiment (experiment 9).

Similar experiments comparing the flux of formic acid, a more slowly penetrating solute, into red cells with (experiments 20 and 22) and against (experiments 21 and 23) water flux were conducted, but no consistent effect of solvent movement on solute flux was seen. The major water flux was complete long before the formic acid equilibrium was attained. Therefore only the initial portion of the curve of formic acid concentration versus time was used in the calculations of permeability in Table 3 in order to make the comparisons during the period of greatest water movement.

DISCUSSION

The permeability calculations contain the implicit assumption that both the intracellular and extracellular fluid spaces are well-stirred compartments without any diffusion gradients and that ammonia undergoes no chemical reaction save protonation. The intracellular volume of the red cell is small, resulting in maximum diffusion distances for exchange of less than 1 Small molecules have relatively

Ext. osmolality - Int. osmolality,

mOsm/liter

5 -10

1,215 -4

1,206

t =oO

PHe

' 6.75 6.94

7.08

6.82 7.07

6.95 7.09 7.21 6.88 6.97

6.95 7.18

6.90 6.85

6.85 7.09

P, cm /set

1.17 x 1o-3 1.70 x 1o-3

8.75 X 1O-4

1.19 x 1o-2 1.06 X 1O-2

4.69 x lo-4 1.35 x 10-a 1.07 X 1o-3 2.35 X 1O-3 2.35 X 1O-3

5.61 X 1O-4 1.70 X 10-S

4.63 X 1O-3 5.23 X 1O-3

3.06 X 10-S 2.35 X 10-Z

large diffusion coefficients even in concentrated hemoglobin solutions (25), and diffusion equilibrium inside the cell should be attained within 1 msec as long as the diffusing molecules do not bind to protein. Jacquez et al. (21) have postulated that ammonia binds to plasma proteins because they found that ammonia solubility in plasma was greater than that calculated for ammonia in water. However, in their calculations they extrapolated to an ammonia pressure of 1 mm Hg from published data obtained at 1 atm pressure. Henry’s law does not apply to ammonia at this high pressure and the extrapolation is not valid. Other published solubility data obtained at low ammonia tensions (4) are identical to those measured in plasma, making it unlikely that ammonia binds to proteins.

The assumption of a well-mixed extracellular compart- ment is more critical since that space in our experiments is considerably larger than the intracellular volume, and, con- sequently, diffusion distances are greater. However, extracellular convective motion is present since turbulent flow is maintained in the reacting mixture at all times. This is in contrast to a stopped-flow apparatus in which turbulent flow exists only at the beginning of the reaction.

Theoretically, a stagnant layer of fluid is present on the cell surface even when turbulent flow prevails in the apparatus, and Dainty ( 10) has raised the possibility that this may result in an underestimate of the true permeability. However, from geometric c’onsiderations alone, the extracellular fluid in the NH3 experiments could provide an average stagnant layer surrounding each cell less than 2 p thick. It is also possible to calculate a maximal value for this layer from comparisons of the measured rate of HbOz formation in red cell suspensions as compared to that in


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PERMEABILITY OF HUMAN ERYTHROCYTES 1009

0.0 0.00 0.01 0.02 0.03 0,04 0.05

TIME (sod

FIG. 6. Changes in extracellular ammonia concentration (upper Ijoints) and intracellular ammonia concentration (lower points) calculated from observed pH’s in experiments 5 and 6. In experiment 5 with ammonia movement in same direction as water flows, initial transmembrane gradient was - 88 mOsm/liter and calculated permeability was 1.32 X 10m2 cm/set. In experiment 6 water flow in opposition to ammonia movement was produced by an initial osmotic gradient OE 122 mOsm/liter; calculated permeability was 1.40 X lOa cm/set.

ilernoglobin solutions, obtained in a continuous-flow rapid- reaction apparatus. This estimate for comparable conditions in the same instrument was 1.4 p (5, 15). Choosing the tiiffusion coefficient of NH3 in saline as approximately that of water, 2 X low5 cm2/sec (35), this represents only 1% of the total resistance to NH3 uptake by red cells. We there- tore believe this is not significant error in our estimates of c+ell permeability.

In our experiments a single value of permeability can be iitted to the experimental curve with little discrepancy, <upporting the validity of the theoretical calculations. In Figs. 4 and 5 the permeability is constant within =t5 % throughout the entire experiment, but in some experiments \&en equilibrium was reached, as indicated by cessation of t)H change, the calculated intracellular and extracellular c*oncentrations, although constant, were not equal. This discrepancy most likely represents an error in one of the assumed values in the computations, e.g., the distribution \ olume of intracellular water, the buffering power of hemo- qlobin, or the effect of intracellular contents on the acid tiissociation constant. The algebraic mean difference be- 111 een the extracellular and intracellular NH 3 concentrations at 0.1 set after the start of the experiment was less than 1% of the initial difference between the two concentrations; the average absolute difference, neglecting sign, was 9 %. Even though this concentration difference was rel- ;ttively small, it would significantly alter the calculated per- rtleability in the later portions of the experiment where the wtal gradient across the membrane is small. For this reason, \\-e used only the first two-thirds to three-fourths of an ex- {Jeriment to calculate a permeability value.

&An intracellular water volume obtained by drying red ct’lls, equal to 7 1.7 % of the total cell volume (32), was used 111 the calculation of intracellular concentrations. The fraction of intracellular water which is available for distribution (:,f the diffusing substance is unkn .own. In osmotic exchanges the fraction of participating water can appear to be less t Ilan 1 .O, possibly due to water binding to proteins, but is not critical because the permeant intracellular concen- rrations were ,3 and 5).

so low for the early parts of the process (F g i s.

JYIovement of ions during the time in which the uncharged SH 3 or weak acid is eq uilibrating across the erythrocyte ttlembrane would invalidate the measurements of perme-

ability. It is unlikely that cations, including NH& would rapidly exchange across the membrane. The constancy of PNH~ in spite of large variation in extracellular [NHd+] sub- stantiates this. For example, in experiments 2 and 3, PNH~ is essentially constant despite a fivefold variation in [NH4+], .

Movement of anions rather than cations is more likely tot- complicate the experiments. Giebel and Passow ( 17) have measured permeabilities of organic anions in horse erythrocytes by observing their exchange with chloride ion, the movement of the acidic anion being rate-limiting. Valerate and butyrate ions achieved 90 % of their equilibrium distribution in 1 min; lactate movement was more than 45 times slower. Since our experiments were completed in less than 1 set, usually 0.1-0.2 set, anion exchange should not inter- fere with the measurements. Variations in the concentration of the organic anion had no effect on the permeabilities which were calculated, assuming movement of only the uncharged acid (Table 3). /--

In the ammonia experiments the extracellular [OH-] was large and the exchange of Cl- for OH- across the membrane could possibly invalidate the interpretation of the extracellular pH change. In those experiments in which the pH started at a relatively high value, pH decreased rapidly to a plateau in 0.2 set, as shown in the insert in Fig. 2. At this point there was no NH3 gradient across the membrane (Fig. 3). Al- though the final equilibrium pH was much lower (7.63 in the experiment shown in Figs. 2 and 3) the plateau re- mained almost constant to 1.4 set, the longest reaction time that can be observed in our apparatus. After the initial rapid pH decrement due to NH3 movement, pH was 8.22 at 0.243 set, and 8.19 at 1.33 set, a drop of only 0.03 pH in about 1 sec. It is likely that this slow pH change represents exchange of Cl- for OH- across the membrane (37). Using these figures, we have computed an approximate value for OH- permeability of 2.6 X 10m5 cm/set at pH 8.2. Considering the small change in [OH-] and the errors involved in measurement of such a small difference, this agrees quite well with investigations of OH- permeability in our laboratory, which indicates that the permeability at this pH is 1.1 X 10m5 cm/set (8).

The permeabilities listed in Tables 2 and 3 are greater for compounds with higher lipid solubilities. Penetration of a lipid membrane is dependent upon two factors, the diffusion coefficient of the permeant in the lipid and the partition coefficient between the membrane and the surrounding aqueous phase ( 12). The square root of molecular weight provides a practical index of the relative diffusion coefficients of small molecules. Since determination of the membrane- water partition coefficient is not feasible, the olive oil-water coefficient was substituted (Table 4). The product of permeability and square root of molecular weight is plotted as a function of the olive oil-water partition coefficient in Fig. 7. The linear relationship indicates the data are compatible with penetration through a lipid diffusion barrier. However, we cannot conclude from the data that transfer through “pores” was not a factor in the movement of these molecules. The use of the olive oil-water partition coefficient is at best a crude approximation, and the solubility of a substance may vary widely from one lipid to another. For example, we found that the olive oil partition coefficient of ammonia (0.02) is more than 6 times that of mineral oil


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TABLE 4. Ohe d-water partition COefiCientS of permeant molecules at 37 C

Substance

Acetic acid 0.020 Ammonia 0.018 Butyric acid 0.486 Formic acid 0.0058 Oxygen 5* Propionic acid 0.109 Valerie acid 2.24

Solubility in Olive Oil Solubility in Water

* For cottonseed oil rather than olive oil. (From: J. H. Law- rence, W. F. Loomis, C. A. Tobias, and F. H. Turpin. Preliminary observations on the narcotic effect of xenon with a review of values for solubilities of gases in water and oils. J. Physiol., London 105: 197-204, 1946.)

FOFIMK: AMMONIA PRCMOMC BUIYRIC WLERIC

Lo%0

[ 11 P (MW)h

X X

-2*o’ -2.0 -1.0 0.0

LOG SOLUBILITY in OLJVE Ok

10 SOLUBILITY in WATER 1 FIG. 7. Plot of logarithm of product of permeability and square root

of molecular weight of experimental substance as a function of logarithm of olive oil-water partition coefficient of substances all at 37 C. A value of 0.004 was assumed for olive oil-water partition coefficient of lactic acid as best estimate from our experimental observations. However, there was a large experimental error in our measurements at this low a solubility.

(0.003), so that if we used the latter value in Fig. 7, the data for NH3 would be displaced further from that of the larger molecular weight acids.

Green ( 18) has measured the rate of penetration of saturated monocarboxylic acids into human erythrocytes and his results are qualitatively similar to ours. He also found increasing rates of penetration with increasing length of the carbon chain from one to five atoms. Above five carbon atoms the rates began to decrease. In his experiments Green measured changes in intracellular oxyhemoglobin concentration, inferring that these gave a reliable indication of increasing intracellular hydrogen ion concentration as the acid entered the cells. In support of this method he noted that the dissociation of oxygen from a hemoglobin solution was essentially complete in 0.02 set (20). However, in cell suspensions, as opposed to hemoglobin solutions, the rate of Bohr shift is more than an order of magnitude slower; the half-time at room temperature is 0.190-0.3 10 set ( 16). In the case of rapidly permeating acids, the change in oxyhemoglobin concentration should be limited both by acid penetration and the rate of the Bohr shift. As a result, Green’s ingenious experiments yield only semiquantitative

KLOCKE, ANDERSSON, ROTMAN, AND FORSTER

data and cannot be used to calculate true permeabilities. While our experimental data are compatible with diffusion through a lipid membrane, they cannot be completely reconciled with a membrane model which postulates penetration only through water-filled pores. The pore concept assumes that a molecule confined in a narrow aqueous channel has an “effective” diffusion coefficient much smaller than its free diffusion coefficient in bulk solution. Based on geometric considerations, Renkin (29) derived an expression which corrects for this restriction of diffusion in a pore by estimating A,/A, , the fraction of total pore area which is effective for diffusion :

As/A, = [I - ;I{1 - 2.lO[;]+ 2.09 [;1”

5

[ 11 (8)

- 0.95 5 rP

where rs is the radius of the solute molecule, and rp is pore radius. Using this equation, the observed sevenfold difference in ammonia and formic acid permeabilities, which equals their diffusion coefficients in free solution times the effective pore area, would be expected in a 4.0-A pore (27) according to equation 8, if the two molecules had radii of slightly greater than 1.0 and 2.0 A, respectively. Avail- able data on interatomic bond lengths of these two molecules indicate that these radii are fairly reasonable (36). In the pore model very small changes in molecular size have quite large effects on the rate of penetration. How- ever, none of the remaining data can be fitted to this pore size. Observed permeabilities of lactic and barbituric acids are only slightly less than formic acid, even though they are much larger molecules. The other aliphatic acids have greater permeabilities than formic acid, even though they should be less able to diffuse through an aqueous channel. For example, valeric acid, a molecule much larger than formic acid, has a permeability 17 times greater than the former. It is reasonable to expect that a molecule such as this, with a significant lipid solubility, would pass through the membrane substance itself. Stein (34) has pointed out that permeabilities calculated on the basis of equation 8 differ from measured permeabilities by a factor as large as 10,000.

If ammonia and formic acid movement occurs through pores, then their rate of entry into the cell might be affected by solvent flow. However, in neither of our experiments with these substances were we able to demonstrate any solvent drag. Transport of a solute particle through a large water-filled pore during solvent flow is the result of two processes, diffusion and convection. Total flux of solute, Js , is described by the differential equation (22) :

J ‘S

S = -D, g + vcs (9)

X

where D, is the solute diffusion coefficient in bulk solution, dcs/dx the solute concentration gradient, v is the linear velocity of the solution (flow into the cell considered as positive), and cs is the solute concentration.

Integrating equation 9 under conditions of steady-state flux and evaluating with boundary conditions at the ex- ternal surface of the membrane, cs = C, at x = 0, and


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PERMEABILITY OF HUMAN ERYTHROCYTES 1011

at the internal surface, cs = Ci at x = Ax: where L, is the hydraulic coefficient in centimeters per

J -V [C, exp(vAx/D,) - Ci]

second, VW is the partial molal volume of water, AC,,, is

S = 1 - exp(vAx/D,)

(10) the osmolal difference of the impermeable solute causing the water flow, and F, is the fraction of the total red cell

This equation is similar to the treatment of diffusion and , convection (22) and to an equation used to estimate the effect of solvent drag in the red cell (33). The equation differs from those expressions which Landis and Pappen- heimer (24) and Kedem and Katchalsky (23) used to describe simultaneous diffusion and convection in that it does not assume a linear concentration gradient across the membrane. As VAX/D, increases, the linear transmembrane gradient becomes distorted. When flow is zero, equation 10 becomes equal to the Fick diffusion equation. The mathematical statement in equation 9 implicitly assumes that there is no friction between the permeant solute and the membrane, that is the wall of the pore. If there is, D, must include the additional resistance and would be decreased. In addition, vC, would no longer equal the convected solute, because v is the linear velocity of the solvent (precisely the velocity of the solution as a whole), and the solute would travel at a lesser velocity because of friction with the wall (“sieving” (24)). Frictional resistance between solute and wall will therefore decrease both terms on the R.H.S. equation 9, and moreover it can be shown (and is intuitively reasonable) that the proportional decrease will be the same. Therefore VAX/D, will be the same even if there is friction between the solute and the membrane. Note that we are considering only friction within a pore and not that at the entrance.

The effect of solvent drag on solute transfer can be determined by comparing solute flux under conditions of solvent flow ( Js, flow) to diffusive flux (Js, diff):

J Stflow =

J Stdiff

11, , the diffusion coefficient of the formic acid in bulk solution, is 1.5 X 10d5 cm?/sec at 18 C? The linear velocity of the solution, v, equals volume flow rate per cross- sectional area available for water flow, but is difficult to assess because the pore area is unknown. However, we can obtain a minimal value for the pore area from the experi- Inental measurement of the diffusion permeability of the red cell for water, P, :

where D, is the free self-diffusion coefficient of water; F,, r is the fraction of the total red cell surface area repre- sented by the restricted pore area for water (24) and Ax is the path length. This restricted pore area for water is less than the actual geometric pore area. Thus, a maximal estimate of the average linear velocity (v,,) of the stream becomes :

surface made up of water. Substituting vmax from equation 13 into the exponent of equation II:

exponent = LpVwACosm D&v Ds W)

L, for human red cells at 37 C is 0.0 15 cm/set (5), V, is 18 ml/mole, D, is 2.3 X 10D5 cm2/sec (35), AC,,, was a maximum of 1.2 mOsm/ml and P, is 0.0033 cm/set (3). Therefore :

0.015 X 18 X 2.3 X 1O-5 X 1.2 X 1O-3 = 0.0033 x 1.5 X 10-S o . l5

Substituting this maximal value for the exponent into equation II, we find that the solvent drag would be less than 9 % of the total flux, and this great only for the earliest part of the solute movement. This would be too small to be measured reliably. Therefore, our attempts to produce solvent drag are neither evidence for nor against the exist- ence of pores in the erythrocyte membrane. Even if pores exist, rates of volume flow which would measurably alter the concentration profile through the membrane cannot be attained. By the same token, experimental solvent fluxes should not affect permeability- measurements or diffusion transfer across the red cell membrane significantly.

Recently Sha’afi et al. (33) have reported measurements of urea permeability obtained during volume flow into the erythrocyte. During water movement into the cell, calculated solute permeability ( Ps) decreased instead of increasing as predicted by pore theory. To reconcile this discrepancy with theory, they postulated a nonuniform pore comprised of two resistive components in series with the relative values of these resistances different for water and for solute. However, the data presented are not completely consistent with this conclusion. According to the postulated theory, as flow into the cell approaches zero and reverses direction, the calculated permeability should go through a minimum and then increase. The calculated P, for urea presented in Fig. 5 of their paper shows no such minimum value; permeability decreases throughout the experiment despite changes in sign of volume flow. It seems more likely, as they suggest, that changes in permeability may be due to an incorrect estimation of mean solute concentration in the membrane.

Our conclusion concerning the importance of solvent drag differs from that of Sha’afi et al. (33). The principal difference between the two treatments, which are in gen- eral similar, is the choice of the local solute diffusion coefficient in the membrane. Pore theory assumes that the flux of hydrophilic nonelectrolytes is governed only by geometric considerations. Hence, the restriction of diffusion of any substance in the pore can be calculated from its free diffusion coefficient in bulk solution provided molecular and pore dimensions are known (24). Sha’afi

Vm ax = &,VwACosm/Fw = &.%ACosm D,lR& (13) et al. (33) obtain their estimate of the diffusion coefficient of solute in the water of the pore from measured permea-

l The diffusion coefficient for formic acid was calculated from that bilities of the red cell for the solute. This necessarily in- of water: 2.3 X 10-S cm2/sec (35) on the assumption that it was creases their estimate of VAX/D, and of the relative mag- proportional to 1 /(molecular weight% nitude of Js, flow . However, they do not appear to have


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1012 KLOCKE, ANDERSSON, ROTMAN, AND FORSTER

allowed for the fact that the same friction that, in their approach, reduces D, in the pore from its value in free solution would also make the linear velocity of the solute produced by convection less than the linear velocitv of the solvent, v. Returning to our experimental results, if the calculations of Sha’afi et al. (33) are correct, and the value of D, in equation 11 should be several orders of magnitude less than its value in free solution, one can calculate that the measured P, for formic acid during the early portion of the experiments in which there was a large water flow out of the cell should have been reduced to one-fifth of the control value in the absence of significant water movement. A change of this magnitude should have been easily detectable, but no effect of osmotic flow was seen.

Solvent drag has been demonstrated in other biological membranes. Using toad skin treated with antidiuretic hormone, Andersen and Ussing (1) found that acetamide permeability in the direction of solvent flow was twice the permeability measured in the direction opposite to volume flow. However, this well known finding is not inconsistent with our failure to find evidence of solvent drag in red cells. Although the average flux per square centimeter of total surface area in our experiments was about 2.5 times that in the experiments of Andersen and Ussing, the overall thickness of the toad skin is about four orders of magnitude greater than that of the red cell. Thus it is not unreasonable to expect VAX/D, to be several orders of magnitude greater for the toad skin experiments, making the predicted importance of solvent drag flux relative to diffusion flux correspondingly larger.

The permeability to a lipid soluble molecule such as valeric acid can provide insight into the mechanism of oxygen uptake by the red cell. Both oxygen and valeric acid have high permeabilities that cannot be reconciled with transport through pores alone. Since both are quite lipid soluble, presumably transport takes place by solution in and diffusion through the lipid membrane. The oxygen permeability of the cell membrane cannot be measured experimentally, since oxygen uptake is rate limited in part by simultaneous diffusion and chemical reaction inside the

REFERENCES

cell. We can extrapolate oxygen permeability from valeric acid permeability, since presumably the mechanism of entry is the same:

P P

oxy = Val aoxY d”x = 0 089 cm/set . ,P (15’; ,’ aVa1 Z/MW,,y

where P is permeability, a is the membrane-water partition coefficient (assumed equal to the olive oil-water coefficient), MW is molecular weight, and the subscripts ox) and Val represent oxygen and valeric acid respectively’* The values of a are taken from Table 4, and that of Pvai from Table 3. Another approach to an estimate of POX! is through X, which is the ratio of the permeability of the red cell wall to that of the cell interior; in other words : CD oxy of the wall/wall thickness)/(D,,, of the cell interior cell thickness). The diffusion coefficient of 0 2 at 37 C in 18 mM hemoglobin solution is taken as 7.6 X 10-G cm2/sec and the best estimate of average cell thickness as 0.8 p (15), making the permeability of the cell interior equal to 0.095 cm/set. Therefore X = 0.089/0.095 = 0.94. Probably the best direct experimental estimate of X is 1.5, obtained from comparisons of the rates of red cell gas uptake and calculations of the expected rates of gas uptake of a comparable layer of hemoglobin ( 15). In view of the numerous approximations involved, the agree- ment between these two estimates of X is gratifying.

We are indebted to Dr. Herbert W. Wallace for analyses of hemoglobin solutions.

This study was supported by Training Grant 2TOl-HE-05430 from the National Institutes of Health.

R. A. Klocke and H. H. Rotman were Postdoctoral Trainees of the Public Health Service.

R. A. Klocke’s present address is: Dept. of Medicine, State Univer- ity of New York at Buffalo, 462 Grider- St., Buffalo, N. Y., 14215.

H. H. Rotman’s present address is: Albert Einstein Medical Center, Northern Division, Philadelphia, Pa., 19141.

K. J. Andersson’s presentaddress is : Vapengatan 13, 12652 Hager- sten, Sweden.

Address requests for reprints to R. E. Forster, Dept. of Physiology, School of Medicine, University of Pennsylvania, Philadelphia, Pa. 19104.

Received for publication 26 April 1971.

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