- Email: [email protected]
Diffusion-limited exchange of 18O between CO2 and water in red cell suspensions
Rcv~iration Physiology ( 1981) 44, 285 298 Elsevier/North-Holland Biomedical Press
D I F F U S I O N - L I M I T E D E X C H A N G E OF 180 B E T W E E N CO s A N D W A T E R IN RED CELL S U S P E N S I O N S
D . N . S I L V E R M A N , C . K . T U and N. R O E S S L E R Department of Pharmacology, University of Florida College of Medicine, Gainesville, FL 32610, U.S.A.
Abstract. The loss of 180 from labeled CO2 caused by the exchange of oxygen with water, a process catalyzed by carbonic anhydrase, has been measured in suspensions of rat erythrocytes at p H 7.4 and and 25 °C. The rate of loss of 180 from all C02 and the rate of loss of 180 from doubly-labeled CO2 are shown to be related to the rate constant for the catalyzed hydration o f CO 2 inside the cell and a rate constant for the diffusion of CO 2 oul of the cell. The results show that°the diffusion of CO2 out of the cell with a haff-time near 2 msec is a slower process than the intracellular, catalytic conversion of CO 2 to H C O f which has a half-time near 0.3 mscc. F r o m this information we estimate the gradient of 180 content in CO 2 in the red cell during an 180-exchange experiment. The rate constant for the entry of CO2 into red cells, also obtained from 180-exchange data, has a value of the same magnitude as that anticipated for the diffusion-controlled rate of encounter between CO 2 and red ,ells. This indication of diffusion-controlled depletion of lsO from CO 2 is supported by experiments with a carbonic anhydrase inhibitor which show that carbonic anhydrase does not have a rate-limiting role in the 180 exchange until greater than 80~,i of the enzyme is inhibited. Carbon dioxyde Carbonic acid Carbonic anhydrase
Diffusion Red cell Water
The loss o f JsO from labeled CO 2 in aqueous solution is caused by the hydrationdehydration cycle and is catalyzed by carbonic anhydrase CO180 + H20 ~ HCOOJSO- + H +_-~ COO + H 2180
(1)
This depletion o f JsO from CO z provides an opportunity to investigate CO 2 kinetics in suspensions of cells that contain carbonic anhydrase since zso loss to water is catalyzed inside the cells but not in the external fluid. The rate of ~80 depletion from CO2 measured in the external solution is, in general, dependent both on the rate of diffusion of CO 2 and HCO 3 from external solution to intracellular sites of Accepted for publication 20 March 1981 0034-5687/81/0000-0000/$02.50 © Elsevier/North-Holland Biomedical Press 285
286
D.N. SILVERMAN et al.
carbonic anhydrase and on the rate of the catalyzed, intracellular loss of ~O from CO2 and H C O / . The two extreme cases are (1) 180 depletion entirely diffusion controlled and (2) 180 depletion entirely controlled by the chemical reaction of equation (1). For suspensions of red cells, Itada and Forster (1977) have interpreted 1SO-exchange experiments using human red cells in terms of the chemical-reaction controlled extreme for CO2 and diffusion control for H C O 3 , whereas Tu et al. (1978) and Silverman et al. (1976) found that the ~80 depletion in suspensions of rat red cells is a diffusion-controlled process for both species. In this report we present an alternative view of the ~80-exchange process using a solution of the kinetic equations which is based on the rate of change of the distribution of ~80 in CO 2 rather than on the rate of depletion of ~O from CO 2. This approach is shown to be equivalent to those previously reported from this laboratory, and provides a further means of interpretation of the data. Furthermore, we have calculated the gradient in ~O content of CO 2 in a red cell during an l~O-exchange experiment and have provided a quantitative explanation of the concentration of carbonic anhydrase inhibitor required to inhibit z~O-exchange in suspensions of erythrocytes. Moreover, the effective permeability observed in studies of ~80-labeled CO 2 in red cell suspensions is interpreted using the Smoluchowski equation for diffusion-controlled encounters between CO, and red cells.
Materials and methods Oxygen-18 labeled bicarbonate was prepared by dissolving K H C O 3 in ~SO-enriched water (up to 80 atom ~o 1sO) and then, after at least a 24-h period, distilling the water off in a vacuum line. Red cells were obtained from freshly-drawn, heparinized blood of rats. The red cells were washed twice at room temperature; for isotope depletion experiments red cells were placed in a solution containing 15 m M total concentration of all species o f CO,, 4.5 m M glucose, 27 m M glycylglycine and 121 mM NaC1. The pH of this solution was 7.40 + 0.02 during all experiments and the temperature was maintained at 25 ° + 0.2 °C. The experimental procedure for performing the isotope depletion experiments has been described previously (Silverman et al., 1976; Tu et al., 1978). The measurements of the isotopic content of CO,_ were made with a mass spectrometer (Finnigan 3000) using a CO s inlet vessel based on a design by Hoch and Kok (1963) or a continuous-flow CO 2 inlet designed by Tu et al. (1978). The first inlet vessel has as its bottom a membrane which is permeable to CO2 and is supported by a stainless steel disc. CO 2 passing across the membrane enters a mass spectrometer to provide a continuous measure of JsO content of CO2 in solution. The time lag from the inlet vessel to the mass spectrometer is less than 2 sec. The continuous-flow inlet is a 2-mm gap in a tube through which red cell suspension flows after mixing; the gap is covered by a Silastic tube permeable to CO2. In this manner, ~80 contents of CO 2 can be determined as soon as 2 sec after mixing.
EXCHANGE OF ~80 BETWEEN CO2 AND WATER IN RED CELLS
287
The ~80 content of CO 2 was expressed as z, the fraction of all oxygens in CO 2 that are JsO: 12 (CO'SO) + (C'80'80) 1/2(46) + (48) z - (COO) + (CO~80) + (C'80~80) = (44) + (46) + (48) The ~80 content of CO 2 was expressed in another manner, as c, fraction of J80 in doubly-labeled CO 2 : (C'80'80) (48) c = (COO) + (CO'80) + (C~80~80) = (44) + (46) + (48) The ~80 content of bicarbonate was determined from the CO 2 generated by rapid acidification o f aliquots o f the reaction mixture. This procedure was described by Mills and Urey (1940). In homogeneous solutions the decrease with time of both z and c follow first-order kinetics with rate constants 0 and 7 respectively (Gerster, 1971; Silverman, 1974) "c -- % = Ae -°t c ~ = Be-~
c -
Each o f these rate constants can be expressed as the sum of its catalyzed and uncatalyzed components: 0 = 0 . . . . t -'1- 0 c a t ; • = ? . . . . t + ~Ycat
Results
The biphasic depletion of ~80 from CO 2 in external fluid after the addition of intact rat erythrocytes is shown in fig. 1. Initially, before addition of red cells the ~sO content of CO 2 was very close to the ~80 content of bicarbonate. After addition of cells the ~O content o f C O 2 decreased more rapidly than that of bicarbonate in the region immediately following addition of cells, labeled B in fig. 1. The second phase o f the biphasic depletion is labeled C in fig. 1. Such a biphasic depletion is not observed when a solution of lysed cells is used (Silverman et al., 1976; Itada and Forster, 1977); rather, the depletion is described by a single exponential. The values o f the ratio c/C were obtained directly from the masses for CO2 detected by the mass spectrometer. This ratio is equal to 1.0 when the JSO-labels in all CO 2 are distributed among singly- and doubly-labelled species in a manner that obeys the binomial probability distribution (see Discussion). The ratio is different from 1.0 when the binomial distribution does not apply. Figure 2 shows the change in c/C during the course of an experiment in whole cell suspensions and at varying concentrations o f the inhibitor o f carbonic anhydrase methazolamide. These data were measured using the CO 2 inlet vessel (Hoch and Kok, 1963). Values of 7 and 0 in Region B were measured from the slopes o f plots such as
288
D . N . S1LVERMAN et aL ' 'RATRInDCEL~LS jO_oo_oc)~~ pH 7.4, 25°C
0.4
W 0.2 Z -1"
0.1
rY z w 0.06 E. w o
&
o
~ o..~. O
o.04
T-T~
0 (,o
t OCO~ • HCO;
A\
c"~ 0-.. c
&
C -C,. IZ~C02 •HCO;
0.02
i
i
5 MINUTES
Fig. 1. The atom fractions r - z~ for ISO in extracellular CO 2 (O) and in CO 2 derived from extracellular H C O f by rapid acidification (O), and the atom fractions c -c~,~ for 180 in CO2(~ ) and in HCO~ (A) before and after the addition of intact rat erythrocytes. The arrows indicate the time at which red cells were added. V1/V 2 = 1430. The pH was 7.4 at 25 °C with a total concentration of all CO 2 species at 15 mM,
Io0 60 4c A B
2O
C
E g
,
,,,,
o
,
Ioo
,
2oo
,
3oo
4oo
SECONDS
Fig. 2. The ratio (c - c J / ( r - ~ ) 2 as a function of time following the addition, at time zero, of rat erythrocytes to an isotonic solution containing 15 mM total concentration of all species of CO 2. The pH was 7.4 at 25 °C. V J V 2 = 4700. The concentration of methazolamide, an inhibitor of carbonic anhydrase, was: (A) 0, (B) 2.4 × 10 -7 M, (C) 4.0 x 10 -7 M, (O) 5.2 x 10 .7 M, (E) 6.4 x 10 .7 M, (F) 7.6 x 10 .7 M, (G) 5 x 10-6M.
EXCHANGE OF )80 BETWEEN CO 2 AND WATER IN RED CELLS
289
fig. 1 in the i n t e r v a l f r o m 2 to 20 sec after a d d i t i o n o f r e d cells. T h e s e slopes, as m e a s u r e d with the C O 2 inlet o f H o c h a n d K o k (1963), a r e d e t e r m i n e d by the )SO-exchange c a u s e d b y the r e d cells a n d b y the r e l a t i v e l y slow r e s p o n s e time o f the a p p a r a t u s . T h e a v e r a g e a n d s t a n d a r d d e v i a t i o n o f 6 e x p e r i m e n t s each using r e d cells f r o m a different r a t was 7/0 = 1.22 + 0.07 m e a s u r e d at p H 7.4 a n d 25 °C with the r a t i o o f the v o l u m e o f red cells to v o l u m e o f external fluid, V2/V ~, e q u a l to 3.0 × 10 ~. Using the c o n t i n u o u s - f l o w inlet (Tu et al., 1978) in which the values o f Y a n d 0 in the B region are not limited b y the response time o f the a p p a r a t u s , a n d t a k i n g d a t a in the interval f r o m 2 to 10 sec after mixing gave y/0 = 1.23 +_ 0.06 for 5 e x p e r i m e n t s using r a t red cells. T h e a g r e e m e n t between the values o f 7/0 m e a s u r e d b y the two m e t h o d s is o b t a i n e d b e c a u s e y/0 m e a s u r e s the rate at which 180 labels in C O 2 d e p a r t f r o m a b i n o m i a l d i s t r i b u t i o n (see Discussion), a process which is c a u s e d in these e x p e r i m e n t s by the p r e s e n c e o f r e d cells. T h e a p p a r a t u s itself d o e s n o t f r a c t i o n a t e i s o t o p e s to a n y a p p r e c i a b l e extent. T h e value o f 7/0 was i n d i s t i n g u i s h a b l e f r o m 2.0 ( + 0 . 0 5 s t a n d a r d d e v i a t i o n for 9 e x p e r i m e n t s ) for c a r b o n i c a n h y d r a s e h o m o g e n e o u s in solution, o b t a i n e d f r o m h e m o l y s a t e . This result was i n d e p e n d e n t o f the c o n c e n t r a t i o n o f c a r b o n i c a n h y d r a s e in the solution. T h e r a t i o s y/0 o b t a i n e d using intact r a t e r y t h r o c y t e s e x h i b i t e d i n h i b i t i o n at c o n c e n t r a t i o n s o f m e t h a z o l a m i d e g r e a t e r t h a n o r e q u a l to a p p r o x i m a t e l y 5 × 10-7 M, s h o w n in table I. R e d cell s u s p e n s i o n s were i n c u b a t e d for at least two h o u r s with
TABLE 1 The inhibition by methazolarnide of the exchange of )80 from CO2 to water in red cell suspensions a Methazolamide x 10 7 M
×
71~ 103 sec 1
71/01 Observed
yl/01 Calculated from equation 6c
0
19
1.2
1.1
1.3
19
1.2
1.3
19 14 11 4.1 2.6 1.4
1.3 1.5 1,6 1,7 2.0 2.0
1.5 1.6 1.7 1.8 2.0 2.0
3.2 5.6 10.0 20.0 50.0 100.0
Inhibition of carbonic anhydrasea (',/'o) 0 74 87 92 96 98 99 99.5
for rat erythrocytes was 4700. Temperature was 25 °C at pH 7.4. The total concentration of all species of CO z was 15 raM. The values for the uncatalyzed exchanges 0unca t and "~uncatwere 7.0 × 10 - 4 see - I and 1.4 x 10 -3 sec -I respectively. b These values are rate constants for the region B of 1SO-exchange described in the text and shown in fig. 1. c The ratio of equation (6) calculated using k i = 216 sec-1 and KJ = 5 × 10 _8 M with kc = (2500 sec-~)/ (1 + (I)/KI). K) ) x 100%' a Calculated from ( 1 K{+-(I) a VI/V 2
290
D . N . S I L V E R M A N et al.
TABLE 2 The inhibition by methazolamide of the exchange of JSo from CO 2 to water in solutions of lysed red cells a Methazolamide xl08 M
~ ×103 sec -t
0 ×103 sec - I
7/0
0 2 4 7 10 15
11.8 8.38 6.65 4.94 3.93 2.95
5.92 4.35 3.40 2.56 1.97 1.44
1,99 1.93 1.96 1.93 2.00 2.05
a V1/V 2 for rat erythrocytes was 23,300 before lysis. Temperature was 25 °C at pH 7.4. The total concentration of all species of CO 2 was 15 raM.
the concentrations of methazolamide reported in table 1 before experiments were begun. In separate experiments, not shown here, the fractional inhibition of y and 0, were measured after incubations varying from 2 min to 3 h in the presence of 1 × 10 -6 M methazolamide. An incubation time of 5 min was sufficient to produce maximum inhibition of ~so exchange. This is consistent with the results o f Holder and Hayes (1965) who found a half-time of approximately 30 sec for the diffusion o f methazolamide from whole plasma into human and dog red cells. The rate of diffusion of methazolamide is not a factor in determining the degree of inhibition in our experiments. An inhibition constant Kl for the interaction of methazolamide with carbonic anhydrase from rat erythrocytes was determined by measuring the fractional inhibition i of 0ca t a t 12 different concentrations of methazolamide (1 to 35 × 10 -s M) in the presence o f cell lysate. Typical results are given in table 2. The experimental conditions were identical to those given in table 1 and Materials and Methods except cells were lysed. The value of KI = 4.6 × 10 -~ M + 15~o was obtained from the least squares slope of a plot of I/i versus 1/(1 - i) in which I is the methazolamide concentration (Maren et al., 1960).
Discussion
The change in 180 content of CO z in red cell suspensions at chemical and diffusion equilibrium is a biphasic curve as illustrated in regions B and C in fig. 1, a pattern that was observed by Itada and Forster (1973, 1977) for total ~80 content T, and for both x and c by Tu et al. (1978) (see also Silverman et al., 1976). It has been explained in the following manner: Initially, before addition o f red cells, the 780 content of CO 2 is very close to the 180 content of bicarbonate. Upon addition of cells the labeled CO 2 enters red cells rapidly and is depleted o f 780 by the catalytic
E X C H A N G E OF lsO B E T W E E N CO 2 A N D W A T E R IN R E D CELLS
291
action of carbonic anhydrase (region B of fig. 1). After approximately 40 sec to one minute, another region (region C of fig. 1) is reached in which the loss of LsO content of CO2 by passage of CO2 into cells and rapid catalysis therein is balanced by the production of labeled CO2 outside the cells by the dehydration of labeled HCO£ which proceeds at a rate close to the uncatalyzed rate. This explanation is supported by the rapid decrease in ~O content of CO2 compared to the much slower decrease of ~sO content of HCOf in region B, shown in fig. 1, and by the rapid change in the distribution of ~80 in CO2 during region B (Silverman and Tu, 1980). In the biphasic depletion, region B is most informative for our purposes since the major component of the LSO-exchange depends on the diffusion and kinetic properties of CO2, whereas the major component for region C depends on the diffusion and kinetic properties of HCO 3 . To account for ~sO loss from CO2 in region B we consider the diffusion of labeled CO 2 into the cell and the subsequent catalytic hydration-dehydration by which rsO is lost to solvent. The arguments for the loss ol~SO from all CO2, measured as a decrease in 3, and from doubly-labeled CO:, measured as a decrease in c, are analogous. The complete kinetic equations are given by Tu et al. (1978), based on a method originally developed by Gerster (1971). For clarity of discussion we will use a simplified model which disregards the bicarbonate diffusion into the cell. This can be justified by fig. I, in which the depletion in region B is very rapid for CO2 compared with HCO3; this is due mostly to the much greater permeability of the red cell membrane to CO~ compared to the permeability to HCO 3. (COt80)~ @
(COJ80)2 kc/~ (C0160)2 q_ H2~80
(2)
Here subscript 2 refers to a concentration or rate constant inside the red cell and subscript 1 refers to outside, kc is the pseudo first-order rate constant for the hydration of CO: inside the cell, * for which the catalyzed reaction is by far more rapid than the uncatalyzed. The stoichiometric factor 1/3 is used because one out of three of the intermediate bicarbonate ions formed dehydrate to produce '80-labeled water (see equation 1 and Mills and Urey, 1940). The rate constants k~ and k~ describe the rate of diffusion of CO: into and out of the cells. Due to the requirement of mass balance in these equilibrium experiments, they are related by Vik e =
V2ki
where V~ represents the volume of extracellular solution and V2 represents the total intracellular volume. Applying the steady-state assumption to the above reaction, the rate of change of ~, which is accessible to measurement, is given by: kJ3 ] - d ~l = ke ~r dt k~ + kc/3
(3)
292
D.N. SILVERMAN et al.
('C1 is the a t o m fraction of ~80 in C O 2 measured in the external fluid.) Equation (3) is formally equivalent to the equation describing the formation of enzyme-substrate complex with subsequent reaction. The term in brackets expresses the probability that a molecule of CO z which has entered a cell will react to lose an ~sO label before it passes out again. When k i ,> k c this probability is low, the rate of depletion of mso from CO 2 is determined by the rate of the hydration-dehydration reaction, and CO2 passes through the cell losing very little of its label. Under such circumstances, the initial binominal distribution of ~80 labels a m o n g the species of CO, is undisturbed and c = T2. As a consequence 7 = 2- (i.e. d(ct - c ~)/dt = 2d (z~ - rrD/dt) (Gerster, 1971; Silverman, 1974). When k~ ,~ k~ the rate of depletion of ~sO from CO2 is determined by diffusion properties of CO 2 in the cell suspension and several hydration-dehydration cycles can occur before CO 2 passes out of the cell. Consequently the cascade C180~80 ~ CO~80 ~ C O 0 is shortened when observed outside the cell to become C~80~80--,CO0, the binominal distribution no longer holds, and c ¢ x2. N o w y = 0 since the rate of entry into the cell has become the rate determining step, which is independent o f the label. Under the experimental conditions of these studies y~/0j = 1.22 + 0.07 in suspensions o f rat erythrocytes with the ratio of volume o f external fluid to cell volume OfVl/V 2 --- 3300. Thus, we can infer that k~ > k~. This is consistent with the analysis o f Tu et al. (1978) who have applied the N e w t o n - R a p h s o n iterative procedure to the rate equations describing ~80-exchange in suspensions of rat erythrocytes and, using experimentally determined values of 0~ and y~, have determined that k~ = 1890_+980 sec -t and k~ = 2 1 6 _+38 sec -~ (mean and standard deviation). Boyer et al. (1977) and Hackney and Boyer (1978) have described the kinetic and stoichiometric considerations by which the relationship between the distribution of label a m o n g species and the rate constants k c and ki can be established. In the Appendix we apply a similar approach to ~80 depletion from CO 2 in red cell suspensions; the results are consistent with those o f T u et al. (1978): k c = 2500 _+ 200 s e c t and k~ = 470 _+ 190 sec-~, These values of k~ indicate a half-time of about 2 msec for the residence of CO 2 in a red cell based on consideration of diffusion processes only. This is a measure of the time a CO 2 molecule stays in the red cell before it diffuses out of the cell. Wistrand and W~thlstrand (1977) have reported that rat red cells contain 25 # M of a high activity carbonic anhydrase with values of kc, , and K m similar to those of the human C enzyme. (The low activity or B form of carbonic anhydrase was found to be present at 10/~M.) The kinetic constants describing the catalytic action of human carbonic anhydrase C at chemical equilibrium have been obtained by Simonsson et al, (1979) and can be used to give a confirming value of k~ = 1800 sec -t for the catalyzed hydration of CO2 in the cell at chemical equilibrium*. These values of k~ indicate a half-time near 0.3 msec for CO2 in a red * The velocity of the catalyzed dehydration at chemical equilibrium, which equals the velocity of the catalyzed hydration, is given by Simonsson et al. (1979) v
kceXt (E) ( H C O f ) K0n- + ( H C 0 3 )
E X C H A N G E OF lsO BETWEEN CO2 A N D WATER IN RED CELLS
293
cell before it is catalytically converted to HCO3-. Thus, as inferred from the value of 71/01, the catalytic conversion o f CO: to H C O 3 in a red cell is a faster process than the diffusion of CO, out o f the cell. Through the relationship k e = V2k~/V ~we obtain k c = 0.07 or 0.14 sec -~ depending on whether we use the value of k~ determined by Tu et al. (1978) or determined in the Appendix. These values can be c o m p a r e d to the value of ko expected for a diffusion-controlled contact of CO2 with red cells according to the Smoluchowski (1917) a p p r o a c h to diffusion through a spherical surface. At V ~ / V 2 = 3300 there are about 3.2 x 106 red blood cells per c m 3. The rate constant for the collision of CO, with red cells is then given by k c = 41tNDa where N is the number of red cells per cm 3, and D is the diffusion coefficient o f CO 2 in external solution (D = 2 x 10-Scm 2 .sec -~, Gros and Moll, 1971). We assume a spherical cell with a radius a = 2.6 x 10 -4 cm which reproduces the volume o f a red cell (-'80 /.tm3). kc = 4rt (3.2 x 106
c m -3)
(2 x 10 -s cm 2 -sec -1) (2.6 x I0 4 cm) = 0.21 sec -j
The similarity between observed and calculated ko is consistent with the possibility that the observed value of k~ is nothing more than the barrier to CO 2 diffusion created by the solution including unstirred layers associated with the cell membrane, with the m e m b r a n e itself presenting no barrier to CO 2 diffusion. A similar conclusion was drawn by Gros and Moll 0971). If this hypothesis is true, then to express the diffusion barrier o f a red cell to CO 2 in terms of a single permeability constant P is not meaningful. However, if the red cell m e m b r a n e is a distinct barrier to CO2 diffusion, then the value of P~-10 -2 cm • sec -~ determined by Silverman et al. (1976) is pertinent. The Smoluchowski equation suggests but does not prove that the former explanation is more correct and that k~ measured by the 180 technique is a composite measure of C O 2 permeability from extracellular solution to intracellular carbonic anhydrase. The fact that k c > lq in these experiments implies that a gradient exists for the ~80 content of CO2 in the red cell; CO: near the center of the cell will have been exposed to carbonic anhydrase for a period longer than CO 2 near the surface. The gradient can be calculated from the solutions to the problem of simultaneous diffusion and irreversible chemical reaction (i,e., the loss of ~O to H20) presented by Crank (1969) for various geometries. We assume a spherical model of the red with k~t = 1.6 × 106 sec- I and Keff -~ 0.25 M at pH 7.4 for human C carbonic anhydrase. Then k£ for dehydration is given by the following at ( H C O f ) = 0.014 M which is much less than Keff-
k~ k~, (E) Keff To convert to I% for hydration we multiply by the equilibrium ratio (HCO3/CO2). At a concentration of 2.5 x 10 -5 M enzyme this gives k c = 1800 sec - r . The rate constant k c is related to 0 and ? inside the cell through the relationships k c = 3 02/f and k c = 3 ~2/2f in which f is the fraction of all CO 2 species in solution existing as CO 2. This explains why 02, the rate constant for ~80-exchange between CO 2 and water, is smaller by a factor of f/3 than k c, the rate constant for CO 2 hydration.
294
D.N. S1LVERMAN et al.
cell of radius a and assume a steady state condition (i.e., the J~O content o f CO2 in the cell is constant with time); eq. 4 is obtained from Crank's equations 6.18 and 8.24 __z = l + 2 a [~ ~o rcr
11=]
_(_- 1_ ) " sin C _nr_ n a
1 1+
n2(Pc -I
-
)_] 1
(4)
is the ~80 content of CO 2 at a distance r from the center of the sphere and ~,, is that tsO content of CO 2 at the surface. Pc is the ratio Pc
=
k~/3 D/~2 ko/3 + a2
(5)
with D the diffusion coefficient of CO 2 inside the cell. The solutions for other geometries are similar in form to eq. (4) and hence the choice of model is not so critical in calculations designed to provide qualitative features of the combined diffusion and chemical reaction. Curves for r/~, calculated from eq. (4) at various values of Pc are given in fig. 3. For ~80 depletion in the absence of inhibitors we found kc = 2500 sec-t; using a = 2.6 x 10 -4 cm, a value which reproduces the volume of a red cell (=80 #m3), and D = 8 x 10 -6 cm 2 • s e c - I for CO 2 in internal fluid (Gros and Moll, 1971) gives Pc~-0.42 from eq. (5). Referring to fig. 3 shows that there is a gradient of ~sO content in CO2 at steady state in the cells. When carbonic anhydrase is inhibited in the cell k c is much smaller than lq and LsO exchange is limited in rate only by the chemical reaction, then no significant gradient exists as shown in fig. 3. Equation (3) indicates that, upon increasing concentration of an inhibitor of carbonic anhydrase, the rate of depletion of ~80 from CO2 in the external solution of a red cell suspension will become noticeably inhibited when ~ / 3 is reduced in Pc =.OJ 0.8
T
0.6
% 0.4 0.2
0.2
0.4
0.6
0.8
5
r/a
Fig. 3. The ratio of z, the lSO content of C O 2 a t a distance r from the center of the red cell considered as a sphere of radius a, to %, the 180 content of CO2 at the surface of the sphere in an 180-depletion experiment at chemical equilibrium. Curves were calculated from eq. (4) of the text for various values of Pc.
EXCHANGE OF 1~O BETWEEN CO2 AND WATER IN RED CELLS
295
magnitude to a value near k~. Table 1 shows that inhibition o f 0~ in red cell suspensions first becomes apparent at a concentration of methazolamide near 5 x 10 -7 M. This is consistent with the values of k~ and kc given above and with KI = 5 x 10 -8 M for inhibition of carbonic anhydrase in rat red cell lysate: With 5 x 10 _7 M methazolamide in the cells, kc/3 is near 100 sec -j*, a value near in magnitude to k~ determined by Tu et al. (1978) of 216 sec -L. The main l~oint is that inhibition by 50~o of ~80-exchange in red cell suspensions is observed when the ratio i n E q u a t i o n 3, ~ / ( ~
+ k~),is near 0.5, and not when K](K~ + [I]) is near 0.5,
as is the case for noncompetitive inhibition of enzyme alone. These observations are in accord with the explanation that JsO exchange from CO2 in red cell suspensions is diffusion-controlled. More specifically, the decrease in 0~ and 7~ upon addition of inhibitor should be proportional to the decrease in
+ k~ and
3 /\
3 + k~ respectively, in
which k~ is decreased by inhibitor. This consideration indicates that the fractional inhibition of 0~ should be greater than the fractional inhibition of 7~ at any given concentration o f carbonic anhydrase inhibitor, a trend which appears in table 1. Table 1 also gives a calculated value of the ratio 7/0. 2kc//2k~/',
)
7 -
0
=
(6)
k~./(k~ + lq )
3/ ,3 in which kc in the presence of a concentration of methazolamide (I) is given by (2500 sec ~)/(1 + ( I ) / K 0 and lq is 216 sec -~. (Equation 6 is identical to equation 7 derived in the Appendix.) There is a rough quantitative agreement between this calculated value of equation (6) and the observed ratios 7~/0j at each inhibitor concentration as shown in table 1. Another view of the data presented in table 1 is given by fig. 2 which shows the variation in c/~ 2 with time after addition of red cells to a solution containing ~80-labeled CO 2 and HCO 3. This figure demonstrates the change in distribution of '80 labels between singly- and doubly-labeled CO 2 in red cell suspensions caused by compartmentalization o f carbonic anhydrase. In support of the argument for diffusion-controlled loss of ~O from CO2, the pattern for c/~a is unchanged up to 2.4 x I0 -7 M methazolamide. At this concentration of inhibitor KI/(KI + |) is 0.17 indicating about 80% inhibition of carbonic anhydrase. * In the presence of 5 x 10-7 M of an inhibitor with K1 = 5 × 10-8 M: kc
kext (E) Keff 1 + K j ]
(HCO£) = (1.6 x 106)(2.5 x 10-5) (0.0143) = 300 sec-r
(co;)
× 10Z
(0.25) 1 +5 x 10-8](0"0007)
296
D . N . S I L V E R M A N et al.
Acknowledgements
This work thank
was supported
Mr. George
Wynns
by National
Institutes of Health
Grant
HL
18671. W e
for excellent technical assistance.
Appendix
The purpose of this Appendix is to apply the kinetic and stoichiometric considerations for ISO_exchange obtained by Boyer et al. (1977) and Hackney and Boyer (1978) to obtain a relationship between ?l/01, kc, and k i and to use this relationship to obtain numerical values for k i. The term p expresses the probability that CO2, once inside the cell, will go on to form bicarbonate rather than exit from the cell. p = kc/(k c + ki), with rate constants described in the text. The expression (1 - p) (p)i is the probability of CO 2 exiting the cell after i cycles through the hydration-dehydration pathway. If i is the number o f times a CO 2 molecule passes through the hydration-dehydration pathway then the average number of oxygens lost from CO 2 to water is 2 (1 - (2/3)i), and the average number of doubly-labeled CO 2 molecules lost is 1 - (1/3) i. o is the average number of oxygens exchanged before CO 2 exits the cell and is given by a sum of terms, each term representing the product of the probability of i reversals of the hydration-dehydration pathway and the average number o f oxygens lost for i reversals. 6=
~ ( 1 - p) (p)i 2 ( 1 - 2/3) i) i=O
Similarly o is the average number of doubly-labeled CO 2 molecules lost before exit : o=
~ (1-p)(p)i(1-(l/3)
i)
i=0
These equations are simplified in a manner described by Boyer et al. (1977) using the expression: ~
bi=l~bforb
i=l
After this procedure we obtain: 6o=
2p 3 - 2p 2p/3 1 - p/3
For slow reaction in the red cell, that is when k i ~>k c and p -" 0, then 6 = 0 0 = 0. When there is rapid catalysis in the cell, that is when k c ~> k i and p = 1, then 6 = 2 and o = 1. The ratio ~,l/01 is the ratio of the rate constant for the decrease in atom fraction of ~So in CO 2 to the rate constant for the loss of atom fraction of doubly-labeled CO 2 molecules when sampling CO 2 from the extracellular fluid. A ,i = 2 o ~ 2 ( 3 - 2 p ) 01 6 3- p where the factor 2 enters to account for two oxygen atoms per CO 2. Inserting the expression p = kc/(k c + ki) gives: ?L Oj
2(kc + 3ki) 2k c + 3k i
{7)
E X C H A N G E O F 180 B E T W E E N CO 2 A N D W A T E R IN R E D CELLS
297
This expression establishes the relationship between the 180 depletion processes observed in the external solution and the chemical and diffusion processes within the cell. F r o m this expression we obtain the upper and lower limits for yl/01 for slow reaction in the cell when k i ~> kc, then yl/01 = 2.0. For rapid catalysis in the cell when k c ~> k i, then yl/0~ = 1.0. We can use an experimentally determined value o f k c and Eq. (3) to estimate ki, the rate constant for diffusion of CO 2 out o f the cell. Experimental values o f 0cal obtained from lysed rat erythrocytes were multiplied by the dilution factor VI/V 2. This yielded 02 = 83_+6 sec -I for intact cells, if we a s s u m e that the activity of the enzyme does not change. However, if the intracellular p H is lower than the extracellular p H this procedure for obtaining 02 leads to inaccuracy. Based on the published pH-dependence o f the c o m p o n e n t of 0 catalyzed by carbonic anhydrase C (Silverman et aL, 1979), an intracellular ph which is lower than extracellular pH by 0.2 unit would lead to a value o f 02 which is too small by about 2 0 ~ . This possible error has not been included in the following calculations. Using the relationship (Silverman, 1974) k c = 302/f where f is the fraction of all CO 2 species in solution existing as CO 2, the value k c = 2500 + 200 sec - r was obtained. Using 71/01 = 1.22 and k c = 2500 sec - I in equation (7), we obtain k i = 470 sec -1. Small errors in 71/0j lead to large errors in k i calculated from Equation (7): The reported standard deviation of 0.07 in ~,1/01 results in a standard deviation of 40% in the value calculated for k i . This value of k i can be compared to k i = 216 sec - j obtained by Tu et al. (1978) by a numerical solution of the kinetic equations describing 1so-depletion in red cell suspensions.
References Boyer, P. D., L. deMeis, M. Carvalho and D. D. Hackney (1977). D y n a m i c reversal of enzyme carboxyl group phosphorylation as the basis of the oxygen exchange catalyzed by sarcoplasmic reticulum adenosine triphosphatase. Biochem. 16: 136-140. Crank, J. (•969). The Mathematics of Diffusion. Oxford, Clarendon Press, Gerster, R. (1971). Cin6tique de l'6change des atomes d'oxyg~ne en phase h6t6rog~ne entre C~802 et H20. Int. J. Appl. Radiat. Isot. 22: 339-348. Gros, G., and W. Moll (1971). The diffusion of carbon dioxide in erythrocytes and hemoglobin solutions. Pfliigers Archiv. 324: 249-266. Hackney, D . D . and P . D . Boyer (1978). Evaluation o f the partitioning of bound inorganic phosphate during medium and intermediate phosphate-water oxygen exchange reactions of yeast inorganic pyrophosphatase. Proc. Natl. Acad. Sci. U.S.A. 75:3133 3137. Ho'eK G. and B. K o k (1963). A mass spectrometer inlet system for sampling gases dissolved in liquid phases. Arch. Biochem. Biophys. 101: 160-170. Holder, L.B. and S. L. Hayes (1965). Diffusion of sulfonamides in aqueous buffers and into red ceils. Molec. Pharmacol. 1 : 266-279. Itada, N. and R . E . Forster (1973). Continuous measurement of 1SO exchange between CO 2 and water catalyzed by red blood cell carbonic anhydrase. Fed. Proc. 32 : 349. Itada, N. and R.E. Forster (1977). Carbonic anhydrase in intact red blood cells measured with 180 exchange. J. Biol. Chem. 252:3881 3890. Maren, T. H., A. L. Parcell and M. N. Mali k (1960). A kinetic analysis of carbonic anhydrase inhibition. J. Pharm. Exp. Ther. 130: 389-400. Mills, G. A. and H. C. Urey (1940). The kinetics of isotope exchange between carbon dioxide, bicarbonate ion, carbonate ion and water. J. Am. Chem. Soc. 62: 1019-1026. Silverman, D . N . (1974). A new approach to measuring the rate of rapid bicarbonate exchange across membranes. Mol, Pharmacol. 10:820 836. Silverman, D . N , , C . K . Tu and G . C . Wynns (1976). Depletion of JSO from C~SO2 in erythrocyte suspensions. J. Biol, Chem. 251 : 4428-4435. Silverman, D. N., C . K . Tu, S. Lindskog and G . C . W y n n s (1979). Rate of exchange o f water from the active site of h u m a n carbonic anhydrase C. J. Am. Chem. So¢. 101 : 6734-6740.
298
D.N. SILVERMAN et al.
Silverman, D. N. and C. K. Tu (1980). Rate limiting event in the depletion of ISO from C O 2 in red cell suspensions. In: Biophysics and Physiology of Carbon Dioxide, edited by H. Bartels, C, Bauer and G. Gros. Berlin-Heidelberg-New York, Springer Verlag, pp. 291-298. Simonsson, 1., B.-H. Jonsson and S. Lindskog (1979). A 13C-NMR study of CO2-HCO f exchange catalyzed by human carbonic anhydrase C at chemical equilibrium. Eur. J. Biochem. 93: 409-417. Smoluchowski, M. V. (1917). Versuch einer mathematischen Theorie der Koagulationskinetik kolloider L6sungen. Physik. Chem. 92: 129-168. Tu, C.K., G.C. Wynns, R.E. McMurray and D~ N. Silverman (1978). CO 2 kinetics in red cell suspensions measured by 180 exchange. J. Biol. Chem. 253:8178 8184. Wistrand, P. J. and T. W~hlstrand (1977). Rat renal and erythrocyte carbonic anhydrases: purification and properties. Biochim. Biophys. Acta. 481: 712-721.
D I F F U S I O N - L I M I T E D E X C H A N G E OF 180 B E T W E E N CO s A N D W A T E R IN RED CELL S U S P E N S I O N S
D . N . S I L V E R M A N , C . K . T U and N. R O E S S L E R Department of Pharmacology, University of Florida College of Medicine, Gainesville, FL 32610, U.S.A.
Abstract. The loss of 180 from labeled CO2 caused by the exchange of oxygen with water, a process catalyzed by carbonic anhydrase, has been measured in suspensions of rat erythrocytes at p H 7.4 and and 25 °C. The rate of loss of 180 from all C02 and the rate of loss of 180 from doubly-labeled CO2 are shown to be related to the rate constant for the catalyzed hydration o f CO 2 inside the cell and a rate constant for the diffusion of CO 2 oul of the cell. The results show that°the diffusion of CO2 out of the cell with a haff-time near 2 msec is a slower process than the intracellular, catalytic conversion of CO 2 to H C O f which has a half-time near 0.3 mscc. F r o m this information we estimate the gradient of 180 content in CO 2 in the red cell during an 180-exchange experiment. The rate constant for the entry of CO2 into red cells, also obtained from 180-exchange data, has a value of the same magnitude as that anticipated for the diffusion-controlled rate of encounter between CO 2 and red ,ells. This indication of diffusion-controlled depletion of lsO from CO 2 is supported by experiments with a carbonic anhydrase inhibitor which show that carbonic anhydrase does not have a rate-limiting role in the 180 exchange until greater than 80~,i of the enzyme is inhibited. Carbon dioxyde Carbonic acid Carbonic anhydrase
Diffusion Red cell Water
The loss o f JsO from labeled CO 2 in aqueous solution is caused by the hydrationdehydration cycle and is catalyzed by carbonic anhydrase CO180 + H20 ~ HCOOJSO- + H +_-~ COO + H 2180
(1)
This depletion o f JsO from CO z provides an opportunity to investigate CO 2 kinetics in suspensions of cells that contain carbonic anhydrase since zso loss to water is catalyzed inside the cells but not in the external fluid. The rate of ~80 depletion from CO2 measured in the external solution is, in general, dependent both on the rate of diffusion of CO 2 and HCO 3 from external solution to intracellular sites of Accepted for publication 20 March 1981 0034-5687/81/0000-0000/$02.50 © Elsevier/North-Holland Biomedical Press 285
286
D.N. SILVERMAN et al.
carbonic anhydrase and on the rate of the catalyzed, intracellular loss of ~O from CO2 and H C O / . The two extreme cases are (1) 180 depletion entirely diffusion controlled and (2) 180 depletion entirely controlled by the chemical reaction of equation (1). For suspensions of red cells, Itada and Forster (1977) have interpreted 1SO-exchange experiments using human red cells in terms of the chemical-reaction controlled extreme for CO2 and diffusion control for H C O 3 , whereas Tu et al. (1978) and Silverman et al. (1976) found that the ~80 depletion in suspensions of rat red cells is a diffusion-controlled process for both species. In this report we present an alternative view of the ~80-exchange process using a solution of the kinetic equations which is based on the rate of change of the distribution of ~80 in CO 2 rather than on the rate of depletion of ~O from CO 2. This approach is shown to be equivalent to those previously reported from this laboratory, and provides a further means of interpretation of the data. Furthermore, we have calculated the gradient in ~O content of CO 2 in a red cell during an l~O-exchange experiment and have provided a quantitative explanation of the concentration of carbonic anhydrase inhibitor required to inhibit z~O-exchange in suspensions of erythrocytes. Moreover, the effective permeability observed in studies of ~80-labeled CO 2 in red cell suspensions is interpreted using the Smoluchowski equation for diffusion-controlled encounters between CO, and red cells.
Materials and methods Oxygen-18 labeled bicarbonate was prepared by dissolving K H C O 3 in ~SO-enriched water (up to 80 atom ~o 1sO) and then, after at least a 24-h period, distilling the water off in a vacuum line. Red cells were obtained from freshly-drawn, heparinized blood of rats. The red cells were washed twice at room temperature; for isotope depletion experiments red cells were placed in a solution containing 15 m M total concentration of all species o f CO,, 4.5 m M glucose, 27 m M glycylglycine and 121 mM NaC1. The pH of this solution was 7.40 + 0.02 during all experiments and the temperature was maintained at 25 ° + 0.2 °C. The experimental procedure for performing the isotope depletion experiments has been described previously (Silverman et al., 1976; Tu et al., 1978). The measurements of the isotopic content of CO,_ were made with a mass spectrometer (Finnigan 3000) using a CO s inlet vessel based on a design by Hoch and Kok (1963) or a continuous-flow CO 2 inlet designed by Tu et al. (1978). The first inlet vessel has as its bottom a membrane which is permeable to CO2 and is supported by a stainless steel disc. CO 2 passing across the membrane enters a mass spectrometer to provide a continuous measure of JsO content of CO2 in solution. The time lag from the inlet vessel to the mass spectrometer is less than 2 sec. The continuous-flow inlet is a 2-mm gap in a tube through which red cell suspension flows after mixing; the gap is covered by a Silastic tube permeable to CO2. In this manner, ~80 contents of CO 2 can be determined as soon as 2 sec after mixing.
EXCHANGE OF ~80 BETWEEN CO2 AND WATER IN RED CELLS
287
The ~80 content of CO 2 was expressed as z, the fraction of all oxygens in CO 2 that are JsO: 12 (CO'SO) + (C'80'80) 1/2(46) + (48) z - (COO) + (CO~80) + (C'80~80) = (44) + (46) + (48) The ~80 content of CO 2 was expressed in another manner, as c, fraction of J80 in doubly-labeled CO 2 : (C'80'80) (48) c = (COO) + (CO'80) + (C~80~80) = (44) + (46) + (48) The ~80 content of bicarbonate was determined from the CO 2 generated by rapid acidification o f aliquots o f the reaction mixture. This procedure was described by Mills and Urey (1940). In homogeneous solutions the decrease with time of both z and c follow first-order kinetics with rate constants 0 and 7 respectively (Gerster, 1971; Silverman, 1974) "c -- % = Ae -°t c ~ = Be-~
c -
Each o f these rate constants can be expressed as the sum of its catalyzed and uncatalyzed components: 0 = 0 . . . . t -'1- 0 c a t ; • = ? . . . . t + ~Ycat
Results
The biphasic depletion of ~80 from CO 2 in external fluid after the addition of intact rat erythrocytes is shown in fig. 1. Initially, before addition of red cells the ~sO content of CO 2 was very close to the ~80 content of bicarbonate. After addition of cells the ~O content o f C O 2 decreased more rapidly than that of bicarbonate in the region immediately following addition of cells, labeled B in fig. 1. The second phase o f the biphasic depletion is labeled C in fig. 1. Such a biphasic depletion is not observed when a solution of lysed cells is used (Silverman et al., 1976; Itada and Forster, 1977); rather, the depletion is described by a single exponential. The values o f the ratio c/C were obtained directly from the masses for CO2 detected by the mass spectrometer. This ratio is equal to 1.0 when the JSO-labels in all CO 2 are distributed among singly- and doubly-labelled species in a manner that obeys the binomial probability distribution (see Discussion). The ratio is different from 1.0 when the binomial distribution does not apply. Figure 2 shows the change in c/C during the course of an experiment in whole cell suspensions and at varying concentrations o f the inhibitor o f carbonic anhydrase methazolamide. These data were measured using the CO 2 inlet vessel (Hoch and Kok, 1963). Values of 7 and 0 in Region B were measured from the slopes o f plots such as
288
D . N . S1LVERMAN et aL ' 'RATRInDCEL~LS jO_oo_oc)~~ pH 7.4, 25°C
0.4
W 0.2 Z -1"
0.1
rY z w 0.06 E. w o
&
o
~ o..~. O
o.04
T-T~
0 (,o
t OCO~ • HCO;
A\
c"~ 0-.. c
&
C -C,. IZ~C02 •HCO;
0.02
i
i
5 MINUTES
Fig. 1. The atom fractions r - z~ for ISO in extracellular CO 2 (O) and in CO 2 derived from extracellular H C O f by rapid acidification (O), and the atom fractions c -c~,~ for 180 in CO2(~ ) and in HCO~ (A) before and after the addition of intact rat erythrocytes. The arrows indicate the time at which red cells were added. V1/V 2 = 1430. The pH was 7.4 at 25 °C with a total concentration of all CO 2 species at 15 mM,
Io0 60 4c A B
2O
C
E g
,
,,,,
o
,
Ioo
,
2oo
,
3oo
4oo
SECONDS
Fig. 2. The ratio (c - c J / ( r - ~ ) 2 as a function of time following the addition, at time zero, of rat erythrocytes to an isotonic solution containing 15 mM total concentration of all species of CO 2. The pH was 7.4 at 25 °C. V J V 2 = 4700. The concentration of methazolamide, an inhibitor of carbonic anhydrase, was: (A) 0, (B) 2.4 × 10 -7 M, (C) 4.0 x 10 -7 M, (O) 5.2 x 10 .7 M, (E) 6.4 x 10 .7 M, (F) 7.6 x 10 .7 M, (G) 5 x 10-6M.
EXCHANGE OF )80 BETWEEN CO 2 AND WATER IN RED CELLS
289
fig. 1 in the i n t e r v a l f r o m 2 to 20 sec after a d d i t i o n o f r e d cells. T h e s e slopes, as m e a s u r e d with the C O 2 inlet o f H o c h a n d K o k (1963), a r e d e t e r m i n e d by the )SO-exchange c a u s e d b y the r e d cells a n d b y the r e l a t i v e l y slow r e s p o n s e time o f the a p p a r a t u s . T h e a v e r a g e a n d s t a n d a r d d e v i a t i o n o f 6 e x p e r i m e n t s each using r e d cells f r o m a different r a t was 7/0 = 1.22 + 0.07 m e a s u r e d at p H 7.4 a n d 25 °C with the r a t i o o f the v o l u m e o f red cells to v o l u m e o f external fluid, V2/V ~, e q u a l to 3.0 × 10 ~. Using the c o n t i n u o u s - f l o w inlet (Tu et al., 1978) in which the values o f Y a n d 0 in the B region are not limited b y the response time o f the a p p a r a t u s , a n d t a k i n g d a t a in the interval f r o m 2 to 10 sec after mixing gave y/0 = 1.23 +_ 0.06 for 5 e x p e r i m e n t s using r a t red cells. T h e a g r e e m e n t between the values o f 7/0 m e a s u r e d b y the two m e t h o d s is o b t a i n e d b e c a u s e y/0 m e a s u r e s the rate at which 180 labels in C O 2 d e p a r t f r o m a b i n o m i a l d i s t r i b u t i o n (see Discussion), a process which is c a u s e d in these e x p e r i m e n t s by the p r e s e n c e o f r e d cells. T h e a p p a r a t u s itself d o e s n o t f r a c t i o n a t e i s o t o p e s to a n y a p p r e c i a b l e extent. T h e value o f 7/0 was i n d i s t i n g u i s h a b l e f r o m 2.0 ( + 0 . 0 5 s t a n d a r d d e v i a t i o n for 9 e x p e r i m e n t s ) for c a r b o n i c a n h y d r a s e h o m o g e n e o u s in solution, o b t a i n e d f r o m h e m o l y s a t e . This result was i n d e p e n d e n t o f the c o n c e n t r a t i o n o f c a r b o n i c a n h y d r a s e in the solution. T h e r a t i o s y/0 o b t a i n e d using intact r a t e r y t h r o c y t e s e x h i b i t e d i n h i b i t i o n at c o n c e n t r a t i o n s o f m e t h a z o l a m i d e g r e a t e r t h a n o r e q u a l to a p p r o x i m a t e l y 5 × 10-7 M, s h o w n in table I. R e d cell s u s p e n s i o n s were i n c u b a t e d for at least two h o u r s with
TABLE 1 The inhibition by methazolarnide of the exchange of )80 from CO2 to water in red cell suspensions a Methazolamide x 10 7 M
×
71~ 103 sec 1
71/01 Observed
yl/01 Calculated from equation 6c
0
19
1.2
1.1
1.3
19
1.2
1.3
19 14 11 4.1 2.6 1.4
1.3 1.5 1,6 1,7 2.0 2.0
1.5 1.6 1.7 1.8 2.0 2.0
3.2 5.6 10.0 20.0 50.0 100.0
Inhibition of carbonic anhydrasea (',/'o) 0 74 87 92 96 98 99 99.5
for rat erythrocytes was 4700. Temperature was 25 °C at pH 7.4. The total concentration of all species of CO z was 15 raM. The values for the uncatalyzed exchanges 0unca t and "~uncatwere 7.0 × 10 - 4 see - I and 1.4 x 10 -3 sec -I respectively. b These values are rate constants for the region B of 1SO-exchange described in the text and shown in fig. 1. c The ratio of equation (6) calculated using k i = 216 sec-1 and KJ = 5 × 10 _8 M with kc = (2500 sec-~)/ (1 + (I)/KI). K) ) x 100%' a Calculated from ( 1 K{+-(I) a VI/V 2
290
D . N . S I L V E R M A N et al.
TABLE 2 The inhibition by methazolamide of the exchange of JSo from CO 2 to water in solutions of lysed red cells a Methazolamide xl08 M
~ ×103 sec -t
0 ×103 sec - I
7/0
0 2 4 7 10 15
11.8 8.38 6.65 4.94 3.93 2.95
5.92 4.35 3.40 2.56 1.97 1.44
1,99 1.93 1.96 1.93 2.00 2.05
a V1/V 2 for rat erythrocytes was 23,300 before lysis. Temperature was 25 °C at pH 7.4. The total concentration of all species of CO 2 was 15 raM.
the concentrations of methazolamide reported in table 1 before experiments were begun. In separate experiments, not shown here, the fractional inhibition of y and 0, were measured after incubations varying from 2 min to 3 h in the presence of 1 × 10 -6 M methazolamide. An incubation time of 5 min was sufficient to produce maximum inhibition of ~so exchange. This is consistent with the results o f Holder and Hayes (1965) who found a half-time of approximately 30 sec for the diffusion o f methazolamide from whole plasma into human and dog red cells. The rate of diffusion of methazolamide is not a factor in determining the degree of inhibition in our experiments. An inhibition constant Kl for the interaction of methazolamide with carbonic anhydrase from rat erythrocytes was determined by measuring the fractional inhibition i of 0ca t a t 12 different concentrations of methazolamide (1 to 35 × 10 -s M) in the presence o f cell lysate. Typical results are given in table 2. The experimental conditions were identical to those given in table 1 and Materials and Methods except cells were lysed. The value of KI = 4.6 × 10 -~ M + 15~o was obtained from the least squares slope of a plot of I/i versus 1/(1 - i) in which I is the methazolamide concentration (Maren et al., 1960).
Discussion
The change in 180 content of CO z in red cell suspensions at chemical and diffusion equilibrium is a biphasic curve as illustrated in regions B and C in fig. 1, a pattern that was observed by Itada and Forster (1973, 1977) for total ~80 content T, and for both x and c by Tu et al. (1978) (see also Silverman et al., 1976). It has been explained in the following manner: Initially, before addition o f red cells, the 780 content of CO 2 is very close to the 180 content of bicarbonate. Upon addition of cells the labeled CO 2 enters red cells rapidly and is depleted o f 780 by the catalytic
E X C H A N G E OF lsO B E T W E E N CO 2 A N D W A T E R IN R E D CELLS
291
action of carbonic anhydrase (region B of fig. 1). After approximately 40 sec to one minute, another region (region C of fig. 1) is reached in which the loss of LsO content of CO2 by passage of CO2 into cells and rapid catalysis therein is balanced by the production of labeled CO2 outside the cells by the dehydration of labeled HCO£ which proceeds at a rate close to the uncatalyzed rate. This explanation is supported by the rapid decrease in ~O content of CO2 compared to the much slower decrease of ~sO content of HCOf in region B, shown in fig. 1, and by the rapid change in the distribution of ~80 in CO2 during region B (Silverman and Tu, 1980). In the biphasic depletion, region B is most informative for our purposes since the major component of the LSO-exchange depends on the diffusion and kinetic properties of CO2, whereas the major component for region C depends on the diffusion and kinetic properties of HCO 3 . To account for ~sO loss from CO2 in region B we consider the diffusion of labeled CO 2 into the cell and the subsequent catalytic hydration-dehydration by which rsO is lost to solvent. The arguments for the loss ol~SO from all CO2, measured as a decrease in 3, and from doubly-labeled CO:, measured as a decrease in c, are analogous. The complete kinetic equations are given by Tu et al. (1978), based on a method originally developed by Gerster (1971). For clarity of discussion we will use a simplified model which disregards the bicarbonate diffusion into the cell. This can be justified by fig. I, in which the depletion in region B is very rapid for CO2 compared with HCO3; this is due mostly to the much greater permeability of the red cell membrane to CO~ compared to the permeability to HCO 3. (COt80)~ @
(COJ80)2 kc/~ (C0160)2 q_ H2~80
(2)
Here subscript 2 refers to a concentration or rate constant inside the red cell and subscript 1 refers to outside, kc is the pseudo first-order rate constant for the hydration of CO: inside the cell, * for which the catalyzed reaction is by far more rapid than the uncatalyzed. The stoichiometric factor 1/3 is used because one out of three of the intermediate bicarbonate ions formed dehydrate to produce '80-labeled water (see equation 1 and Mills and Urey, 1940). The rate constants k~ and k~ describe the rate of diffusion of CO: into and out of the cells. Due to the requirement of mass balance in these equilibrium experiments, they are related by Vik e =
V2ki
where V~ represents the volume of extracellular solution and V2 represents the total intracellular volume. Applying the steady-state assumption to the above reaction, the rate of change of ~, which is accessible to measurement, is given by: kJ3 ] - d ~l = ke ~r dt k~ + kc/3
(3)
292
D.N. SILVERMAN et al.
('C1 is the a t o m fraction of ~80 in C O 2 measured in the external fluid.) Equation (3) is formally equivalent to the equation describing the formation of enzyme-substrate complex with subsequent reaction. The term in brackets expresses the probability that a molecule of CO z which has entered a cell will react to lose an ~sO label before it passes out again. When k i ,> k c this probability is low, the rate of depletion of mso from CO 2 is determined by the rate of the hydration-dehydration reaction, and CO2 passes through the cell losing very little of its label. Under such circumstances, the initial binominal distribution of ~80 labels a m o n g the species of CO, is undisturbed and c = T2. As a consequence 7 = 2- (i.e. d(ct - c ~)/dt = 2d (z~ - rrD/dt) (Gerster, 1971; Silverman, 1974). When k~ ,~ k~ the rate of depletion of ~sO from CO2 is determined by diffusion properties of CO 2 in the cell suspension and several hydration-dehydration cycles can occur before CO 2 passes out of the cell. Consequently the cascade C180~80 ~ CO~80 ~ C O 0 is shortened when observed outside the cell to become C~80~80--,CO0, the binominal distribution no longer holds, and c ¢ x2. N o w y = 0 since the rate of entry into the cell has become the rate determining step, which is independent o f the label. Under the experimental conditions of these studies y~/0j = 1.22 + 0.07 in suspensions o f rat erythrocytes with the ratio of volume o f external fluid to cell volume OfVl/V 2 --- 3300. Thus, we can infer that k~ > k~. This is consistent with the analysis o f Tu et al. (1978) who have applied the N e w t o n - R a p h s o n iterative procedure to the rate equations describing ~80-exchange in suspensions of rat erythrocytes and, using experimentally determined values of 0~ and y~, have determined that k~ = 1890_+980 sec -t and k~ = 2 1 6 _+38 sec -~ (mean and standard deviation). Boyer et al. (1977) and Hackney and Boyer (1978) have described the kinetic and stoichiometric considerations by which the relationship between the distribution of label a m o n g species and the rate constants k c and ki can be established. In the Appendix we apply a similar approach to ~80 depletion from CO 2 in red cell suspensions; the results are consistent with those o f T u et al. (1978): k c = 2500 _+ 200 s e c t and k~ = 470 _+ 190 sec-~, These values of k~ indicate a half-time of about 2 msec for the residence of CO 2 in a red cell based on consideration of diffusion processes only. This is a measure of the time a CO 2 molecule stays in the red cell before it diffuses out of the cell. Wistrand and W~thlstrand (1977) have reported that rat red cells contain 25 # M of a high activity carbonic anhydrase with values of kc, , and K m similar to those of the human C enzyme. (The low activity or B form of carbonic anhydrase was found to be present at 10/~M.) The kinetic constants describing the catalytic action of human carbonic anhydrase C at chemical equilibrium have been obtained by Simonsson et al, (1979) and can be used to give a confirming value of k~ = 1800 sec -t for the catalyzed hydration of CO2 in the cell at chemical equilibrium*. These values of k~ indicate a half-time near 0.3 msec for CO2 in a red * The velocity of the catalyzed dehydration at chemical equilibrium, which equals the velocity of the catalyzed hydration, is given by Simonsson et al. (1979) v
kceXt (E) ( H C O f ) K0n- + ( H C 0 3 )
E X C H A N G E OF lsO BETWEEN CO2 A N D WATER IN RED CELLS
293
cell before it is catalytically converted to HCO3-. Thus, as inferred from the value of 71/01, the catalytic conversion o f CO: to H C O 3 in a red cell is a faster process than the diffusion of CO, out o f the cell. Through the relationship k e = V2k~/V ~we obtain k c = 0.07 or 0.14 sec -~ depending on whether we use the value of k~ determined by Tu et al. (1978) or determined in the Appendix. These values can be c o m p a r e d to the value of ko expected for a diffusion-controlled contact of CO2 with red cells according to the Smoluchowski (1917) a p p r o a c h to diffusion through a spherical surface. At V ~ / V 2 = 3300 there are about 3.2 x 106 red blood cells per c m 3. The rate constant for the collision of CO, with red cells is then given by k c = 41tNDa where N is the number of red cells per cm 3, and D is the diffusion coefficient o f CO 2 in external solution (D = 2 x 10-Scm 2 .sec -~, Gros and Moll, 1971). We assume a spherical cell with a radius a = 2.6 x 10 -4 cm which reproduces the volume o f a red cell (-'80 /.tm3). kc = 4rt (3.2 x 106
c m -3)
(2 x 10 -s cm 2 -sec -1) (2.6 x I0 4 cm) = 0.21 sec -j
The similarity between observed and calculated ko is consistent with the possibility that the observed value of k~ is nothing more than the barrier to CO 2 diffusion created by the solution including unstirred layers associated with the cell membrane, with the m e m b r a n e itself presenting no barrier to CO 2 diffusion. A similar conclusion was drawn by Gros and Moll 0971). If this hypothesis is true, then to express the diffusion barrier o f a red cell to CO 2 in terms of a single permeability constant P is not meaningful. However, if the red cell m e m b r a n e is a distinct barrier to CO2 diffusion, then the value of P~-10 -2 cm • sec -~ determined by Silverman et al. (1976) is pertinent. The Smoluchowski equation suggests but does not prove that the former explanation is more correct and that k~ measured by the 180 technique is a composite measure of C O 2 permeability from extracellular solution to intracellular carbonic anhydrase. The fact that k c > lq in these experiments implies that a gradient exists for the ~80 content of CO2 in the red cell; CO: near the center of the cell will have been exposed to carbonic anhydrase for a period longer than CO 2 near the surface. The gradient can be calculated from the solutions to the problem of simultaneous diffusion and irreversible chemical reaction (i,e., the loss of ~O to H20) presented by Crank (1969) for various geometries. We assume a spherical model of the red with k~t = 1.6 × 106 sec- I and Keff -~ 0.25 M at pH 7.4 for human C carbonic anhydrase. Then k£ for dehydration is given by the following at ( H C O f ) = 0.014 M which is much less than Keff-
k~ k~, (E) Keff To convert to I% for hydration we multiply by the equilibrium ratio (HCO3/CO2). At a concentration of 2.5 x 10 -5 M enzyme this gives k c = 1800 sec - r . The rate constant k c is related to 0 and ? inside the cell through the relationships k c = 3 02/f and k c = 3 ~2/2f in which f is the fraction of all CO 2 species in solution existing as CO 2. This explains why 02, the rate constant for ~80-exchange between CO 2 and water, is smaller by a factor of f/3 than k c, the rate constant for CO 2 hydration.
294
D.N. S1LVERMAN et al.
cell of radius a and assume a steady state condition (i.e., the J~O content o f CO2 in the cell is constant with time); eq. 4 is obtained from Crank's equations 6.18 and 8.24 __z = l + 2 a [~ ~o rcr
11=]
_(_- 1_ ) " sin C _nr_ n a
1 1+
n2(Pc -I
-
)_] 1
(4)
is the ~80 content of CO 2 at a distance r from the center of the sphere and ~,, is that tsO content of CO 2 at the surface. Pc is the ratio Pc
=
k~/3 D/~2 ko/3 + a2
(5)
with D the diffusion coefficient of CO 2 inside the cell. The solutions for other geometries are similar in form to eq. (4) and hence the choice of model is not so critical in calculations designed to provide qualitative features of the combined diffusion and chemical reaction. Curves for r/~, calculated from eq. (4) at various values of Pc are given in fig. 3. For ~80 depletion in the absence of inhibitors we found kc = 2500 sec-t; using a = 2.6 x 10 -4 cm, a value which reproduces the volume of a red cell (=80 #m3), and D = 8 x 10 -6 cm 2 • s e c - I for CO 2 in internal fluid (Gros and Moll, 1971) gives Pc~-0.42 from eq. (5). Referring to fig. 3 shows that there is a gradient of ~sO content in CO2 at steady state in the cells. When carbonic anhydrase is inhibited in the cell k c is much smaller than lq and LsO exchange is limited in rate only by the chemical reaction, then no significant gradient exists as shown in fig. 3. Equation (3) indicates that, upon increasing concentration of an inhibitor of carbonic anhydrase, the rate of depletion of ~80 from CO2 in the external solution of a red cell suspension will become noticeably inhibited when ~ / 3 is reduced in Pc =.OJ 0.8
T
0.6
% 0.4 0.2
0.2
0.4
0.6
0.8
5
r/a
Fig. 3. The ratio of z, the lSO content of C O 2 a t a distance r from the center of the red cell considered as a sphere of radius a, to %, the 180 content of CO2 at the surface of the sphere in an 180-depletion experiment at chemical equilibrium. Curves were calculated from eq. (4) of the text for various values of Pc.
EXCHANGE OF 1~O BETWEEN CO2 AND WATER IN RED CELLS
295
magnitude to a value near k~. Table 1 shows that inhibition o f 0~ in red cell suspensions first becomes apparent at a concentration of methazolamide near 5 x 10 -7 M. This is consistent with the values of k~ and kc given above and with KI = 5 x 10 -8 M for inhibition of carbonic anhydrase in rat red cell lysate: With 5 x 10 _7 M methazolamide in the cells, kc/3 is near 100 sec -j*, a value near in magnitude to k~ determined by Tu et al. (1978) of 216 sec -L. The main l~oint is that inhibition by 50~o of ~80-exchange in red cell suspensions is observed when the ratio i n E q u a t i o n 3, ~ / ( ~
+ k~),is near 0.5, and not when K](K~ + [I]) is near 0.5,
as is the case for noncompetitive inhibition of enzyme alone. These observations are in accord with the explanation that JsO exchange from CO2 in red cell suspensions is diffusion-controlled. More specifically, the decrease in 0~ and 7~ upon addition of inhibitor should be proportional to the decrease in
+ k~ and
3 /\
3 + k~ respectively, in
which k~ is decreased by inhibitor. This consideration indicates that the fractional inhibition of 0~ should be greater than the fractional inhibition of 7~ at any given concentration o f carbonic anhydrase inhibitor, a trend which appears in table 1. Table 1 also gives a calculated value of the ratio 7/0. 2kc//2k~/',
)
7 -
0
=
(6)
k~./(k~ + lq )
3/ ,3 in which kc in the presence of a concentration of methazolamide (I) is given by (2500 sec ~)/(1 + ( I ) / K 0 and lq is 216 sec -~. (Equation 6 is identical to equation 7 derived in the Appendix.) There is a rough quantitative agreement between this calculated value of equation (6) and the observed ratios 7~/0j at each inhibitor concentration as shown in table 1. Another view of the data presented in table 1 is given by fig. 2 which shows the variation in c/~ 2 with time after addition of red cells to a solution containing ~80-labeled CO 2 and HCO 3. This figure demonstrates the change in distribution of '80 labels between singly- and doubly-labeled CO 2 in red cell suspensions caused by compartmentalization o f carbonic anhydrase. In support of the argument for diffusion-controlled loss of ~O from CO2, the pattern for c/~a is unchanged up to 2.4 x I0 -7 M methazolamide. At this concentration of inhibitor KI/(KI + |) is 0.17 indicating about 80% inhibition of carbonic anhydrase. * In the presence of 5 x 10-7 M of an inhibitor with K1 = 5 × 10-8 M: kc
kext (E) Keff 1 + K j ]
(HCO£) = (1.6 x 106)(2.5 x 10-5) (0.0143) = 300 sec-r
(co;)
× 10Z
(0.25) 1 +5 x 10-8](0"0007)
296
D . N . S I L V E R M A N et al.
Acknowledgements
This work thank
was supported
Mr. George
Wynns
by National
Institutes of Health
Grant
HL
18671. W e
for excellent technical assistance.
Appendix
The purpose of this Appendix is to apply the kinetic and stoichiometric considerations for ISO_exchange obtained by Boyer et al. (1977) and Hackney and Boyer (1978) to obtain a relationship between ?l/01, kc, and k i and to use this relationship to obtain numerical values for k i. The term p expresses the probability that CO2, once inside the cell, will go on to form bicarbonate rather than exit from the cell. p = kc/(k c + ki), with rate constants described in the text. The expression (1 - p) (p)i is the probability of CO 2 exiting the cell after i cycles through the hydration-dehydration pathway. If i is the number o f times a CO 2 molecule passes through the hydration-dehydration pathway then the average number of oxygens lost from CO 2 to water is 2 (1 - (2/3)i), and the average number of doubly-labeled CO 2 molecules lost is 1 - (1/3) i. o is the average number of oxygens exchanged before CO 2 exits the cell and is given by a sum of terms, each term representing the product of the probability of i reversals of the hydration-dehydration pathway and the average number o f oxygens lost for i reversals. 6=
~ ( 1 - p) (p)i 2 ( 1 - 2/3) i) i=O
Similarly o is the average number of doubly-labeled CO 2 molecules lost before exit : o=
~ (1-p)(p)i(1-(l/3)
i)
i=0
These equations are simplified in a manner described by Boyer et al. (1977) using the expression: ~
bi=l~bforb
i=l
After this procedure we obtain: 6o=
2p 3 - 2p 2p/3 1 - p/3
For slow reaction in the red cell, that is when k i ~>k c and p -" 0, then 6 = 0 0 = 0. When there is rapid catalysis in the cell, that is when k c ~> k i and p = 1, then 6 = 2 and o = 1. The ratio ~,l/01 is the ratio of the rate constant for the decrease in atom fraction of ~So in CO 2 to the rate constant for the loss of atom fraction of doubly-labeled CO 2 molecules when sampling CO 2 from the extracellular fluid. A ,i = 2 o ~ 2 ( 3 - 2 p ) 01 6 3- p where the factor 2 enters to account for two oxygen atoms per CO 2. Inserting the expression p = kc/(k c + ki) gives: ?L Oj
2(kc + 3ki) 2k c + 3k i
{7)
E X C H A N G E O F 180 B E T W E E N CO 2 A N D W A T E R IN R E D CELLS
297
This expression establishes the relationship between the 180 depletion processes observed in the external solution and the chemical and diffusion processes within the cell. F r o m this expression we obtain the upper and lower limits for yl/01 for slow reaction in the cell when k i ~> kc, then yl/01 = 2.0. For rapid catalysis in the cell when k c ~> k i, then yl/0~ = 1.0. We can use an experimentally determined value o f k c and Eq. (3) to estimate ki, the rate constant for diffusion of CO 2 out o f the cell. Experimental values o f 0cal obtained from lysed rat erythrocytes were multiplied by the dilution factor VI/V 2. This yielded 02 = 83_+6 sec -I for intact cells, if we a s s u m e that the activity of the enzyme does not change. However, if the intracellular p H is lower than the extracellular p H this procedure for obtaining 02 leads to inaccuracy. Based on the published pH-dependence o f the c o m p o n e n t of 0 catalyzed by carbonic anhydrase C (Silverman et aL, 1979), an intracellular ph which is lower than extracellular pH by 0.2 unit would lead to a value o f 02 which is too small by about 2 0 ~ . This possible error has not been included in the following calculations. Using the relationship (Silverman, 1974) k c = 302/f where f is the fraction of all CO 2 species in solution existing as CO 2, the value k c = 2500 + 200 sec - r was obtained. Using 71/01 = 1.22 and k c = 2500 sec - I in equation (7), we obtain k i = 470 sec -1. Small errors in 71/0j lead to large errors in k i calculated from Equation (7): The reported standard deviation of 0.07 in ~,1/01 results in a standard deviation of 40% in the value calculated for k i . This value of k i can be compared to k i = 216 sec - j obtained by Tu et al. (1978) by a numerical solution of the kinetic equations describing 1so-depletion in red cell suspensions.
References Boyer, P. D., L. deMeis, M. Carvalho and D. D. Hackney (1977). D y n a m i c reversal of enzyme carboxyl group phosphorylation as the basis of the oxygen exchange catalyzed by sarcoplasmic reticulum adenosine triphosphatase. Biochem. 16: 136-140. Crank, J. (•969). The Mathematics of Diffusion. Oxford, Clarendon Press, Gerster, R. (1971). Cin6tique de l'6change des atomes d'oxyg~ne en phase h6t6rog~ne entre C~802 et H20. Int. J. Appl. Radiat. Isot. 22: 339-348. Gros, G., and W. Moll (1971). The diffusion of carbon dioxide in erythrocytes and hemoglobin solutions. Pfliigers Archiv. 324: 249-266. Hackney, D . D . and P . D . Boyer (1978). Evaluation o f the partitioning of bound inorganic phosphate during medium and intermediate phosphate-water oxygen exchange reactions of yeast inorganic pyrophosphatase. Proc. Natl. Acad. Sci. U.S.A. 75:3133 3137. Ho'eK G. and B. K o k (1963). A mass spectrometer inlet system for sampling gases dissolved in liquid phases. Arch. Biochem. Biophys. 101: 160-170. Holder, L.B. and S. L. Hayes (1965). Diffusion of sulfonamides in aqueous buffers and into red ceils. Molec. Pharmacol. 1 : 266-279. Itada, N. and R . E . Forster (1973). Continuous measurement of 1SO exchange between CO 2 and water catalyzed by red blood cell carbonic anhydrase. Fed. Proc. 32 : 349. Itada, N. and R.E. Forster (1977). Carbonic anhydrase in intact red blood cells measured with 180 exchange. J. Biol. Chem. 252:3881 3890. Maren, T. H., A. L. Parcell and M. N. Mali k (1960). A kinetic analysis of carbonic anhydrase inhibition. J. Pharm. Exp. Ther. 130: 389-400. Mills, G. A. and H. C. Urey (1940). The kinetics of isotope exchange between carbon dioxide, bicarbonate ion, carbonate ion and water. J. Am. Chem. Soc. 62: 1019-1026. Silverman, D . N . (1974). A new approach to measuring the rate of rapid bicarbonate exchange across membranes. Mol, Pharmacol. 10:820 836. Silverman, D . N , , C . K . Tu and G . C . Wynns (1976). Depletion of JSO from C~SO2 in erythrocyte suspensions. J. Biol, Chem. 251 : 4428-4435. Silverman, D. N., C . K . Tu, S. Lindskog and G . C . W y n n s (1979). Rate of exchange o f water from the active site of h u m a n carbonic anhydrase C. J. Am. Chem. So¢. 101 : 6734-6740.
298
D.N. SILVERMAN et al.
Silverman, D. N. and C. K. Tu (1980). Rate limiting event in the depletion of ISO from C O 2 in red cell suspensions. In: Biophysics and Physiology of Carbon Dioxide, edited by H. Bartels, C, Bauer and G. Gros. Berlin-Heidelberg-New York, Springer Verlag, pp. 291-298. Simonsson, 1., B.-H. Jonsson and S. Lindskog (1979). A 13C-NMR study of CO2-HCO f exchange catalyzed by human carbonic anhydrase C at chemical equilibrium. Eur. J. Biochem. 93: 409-417. Smoluchowski, M. V. (1917). Versuch einer mathematischen Theorie der Koagulationskinetik kolloider L6sungen. Physik. Chem. 92: 129-168. Tu, C.K., G.C. Wynns, R.E. McMurray and D~ N. Silverman (1978). CO 2 kinetics in red cell suspensions measured by 180 exchange. J. Biol. Chem. 253:8178 8184. Wistrand, P. J. and T. W~hlstrand (1977). Rat renal and erythrocyte carbonic anhydrases: purification and properties. Biochim. Biophys. Acta. 481: 712-721.