Carbon dioxide and oxygen linkage in human hemoglobin tetramers

J. Mol. Hiol. (1987) 196, 917-931

Carbon Dioxide and Oxygen Linkage in Human Hemoglobin Tetramers Michael L. Doyle, Enrico Di Cera, Charles H. Robert and Stanley J. Gill Department

of Chemistry and Biochemistr?y University of Colorado Boulder, CO 80309-0215, U.S. A. (Received 3 April

1987)

Differential binding curve measurements for oxygen in the presence of fixed carbon dioxide activities have allowed a detailed determination of the linkage between carbon dioxide and the oxygenated intermediates of human hemoglobin. Model-independent analysis of the data shows that at pH 7.4: (1) the oxygen binding curves are asymmetrical, the population of the triply oxygenated species being negligible; (2) the shape of the oxygen binding curve is invariant with carbon dioxide activity; (3) the maximum linkage is -0.32 moles carbon dioxide per mole oxygen: and (4) the overall carbon dioxide-dependent shift in the oxygen binding curve cannot be explained in terms of carbamino formation alone, the additional influence of bicarbonate being required. An allosteric model that’ accounts for the low population of triply oxygenated hemoglobin species is employed here as a framework from which to explore the carbon dioxide linkage mechanism at the intermediate stages of oxygenation. Carbon dioxide binding constants are found to be 780 Me1 and 580 Mm* for carbon dioxide binding to the deoxygenated alpha and beta chains, respectively, and 150 M-I for carbon dioxide binding to the oxygenated form of both chains, as determined by simultaneous fitt,ing of the oxygen binding curves with the model. Finally, by use of the det,ermined binding polynomial for the carbon dioxide-oxygen linkage scheme, we have c*onstruct,ed a series of linkage graphs.

1. Introduction The reciprocal linkage between CO, and O2 binding to human hemoglobin has been recognized in a qualitat~ive sense for many years (Margaria & Green, 1933). A review on the subject has been given by Kilmartin & Rossi-Bernardi (1973). The gaseous nature of CO* and the pH-sensitivity of its aqueous species present non-trivial experimental problems. Nevertheless, a detailed understanding of the molecular mechanism of the effect of CO, on the O2 binding curve requires detailed experimental knowledge of the shape of the O2 binding curve, under well-defined solution conditions. Poyart et al. (1978) succeeded in measuring the CO, dependence of the first Adair 0, binding constant of hemoglobin, and Imaizumi et al. (1982) investigated oxygen binding curves over a range of solution conditions. However, a quantitative molecular picture of these physiologically important linkage processes in hemoglobin remains unclear. In studies of identical linkage between two gaseous ligands (Zolla et al., 1985; Richey et al., 1985; Bishop & Gill, 1986), special methods (Dolman

& Gill?

1978) have

been used to control

precisely the activities of the ligands. Such techniques also allow binding curve measurements to be made on samples of respiratory solutions at high concentration, where the complicatSing effects of ligand-linked dissociation are minimized. An extension of these methods is made here to explore the heterotropic linkage in human hemoglobin between the gaseous ligands CO, and 0,. Tn order to investigate this linkage scheme, we have given special attention to controlling solution conditions precisely. Particularly, the pH has been controlled by a gas-tight titration technique (Spokane et a,l., 1980), the hemoglobin samples were highly concentrated, where

and

the

experiments

were

run

at

3O”C,

independently measured values for carbamino formation constants (Mat’thew et al., 1977) could be exploited.

2. Experimental Procedures (a) Di,ffuwntial

0, binding

curve measurrnwnts

Oxygen binding curves were obtained spectrophotometrically by a differential technique in which changes in 0, fractional saturation are measured upon precistl

928

M. L. Doyle et al.

logarithmic changes in the 0, partial pressure (Dolman CLr Gill. 1978). The sample is held vertically as a thin layer bet~wren a gas-permeable membrane and a glass window in a gas-tight cell. Highly concentrated hemoglobin samples can be studied with this technique, minimizing tetramer-dimer the complicating effect’s of the dissociation (*Johnson 8r Arkers. 1977). The technique allows verification of equilibrat,ion of the sample with the gaseous ligands as an unchanging optical signal. ,4 Gary PI9 spertrophotometer was used to make optical density measurements. A unique advantage of the thin-layer rell in measuring linkages between gaseous ligands is precise control of the part’ial pressures (and hence the solution activities) of the ligands.

where P(r) is the binding polynomial employed to describe the binding reaction (see eqn (3) or eqn (4)). All binding parameters were estimated by least-squares optimization of the appropriate fitting equations to the data. The Gauss-Newton method was used, as modified by Marquardt and others (Frazier & Suzuki, 1973). Confidence intervals, within one standard deviation. on critical parameters were determined by K-tests (Magar, 1972). A Hewlett Packard 9816 computer was used for all the data analysis.

3. Results (a) Adair

(b) Gas nLixt7Lrf!s The total pressure of the gases in the thin-layer cell is atmospheric pressure. as measured directly from a barometer. Precise mixtures of C02/0, and CO,/IS, gases were made gravimetrirally by a procedure in which evacuated 2-I gas cylinders were tared on a Mettler toploading balance followed by addition of accurately measured weights of the desired gas components. The weighing error of the procedure was +O.OZ g, leading to a maximum of 20/b error in the percentage of CO, for the lowrst (1.76:/b, w/w) CO, gas mixtures, and proportionately less error for the mixt,ures of higher CO, composition. (c) Sample preparation Hemoglobin samples, isolat,ed by the standard procedures of Williams & Tsay (1973), were reduced overnight at 4°C with the enzymic reducing system of Hayashi et al. (1973). The sample was then dialyzed at 4’C for 20 h against 250 mm-bis-Tris (pH 7.4). 10 PMEDTA. 0.1 M-sodium chloride. A critically important experimental step has been the precise control of pH and CO, activity. A special gastight pH titration apparatus (Spokane et al., 1980) was used for this purpose. Prior to measuring 0, binding curves. a predetermined amount of sodium bicarbonate was added to the hemoglobin samples, followed by equilibration with known mixtures of CO,/OZ inside the gas-tight, pH titration apparatus. The final concentrations of CO,(aq.) and bicarbonate were calculated from the mol fraction of CO, in water at 3O”f (5373x 10m4 (Wilhelm ef al.. 1977)) and the pK for the reaction CO,(aqueous) + Hz0 + HCO, + H+ which is equal to 6.089 at pH 7.4 and 0.1 M-sodium chloride (Edsall & Wyman. 1958).

The data were t,aken as changes in optical density upon st,epwise dilution of the 0, partial pressure. The fitting equat,ion takes on the general form AOQ = AOD,[B(ri)

-O(ri-

r)].

where AOD, is a parameter representing the change at 577 nm on taking the macromolecule to infinite oxygen activity. .ri is the oxygen StPJ, i. and Audi is the calculated absorbance step i. The function 0 is the fractional oxygen of the macromolecule. given by:

1 a In P(X) “7

d In 5 I pco2 [ ___

Figure 1 shows t’he differential 0, binding data for HbA,t, in the absence of CO, and at a constant pressure of ,510 Torr partial co2 (1 Torr z 133.322 Pa), as changes in absorbance upon changes in the 0, activity. Initially, the 0, binding curves were analyzed individually with a general four-site Adair equation (Adair, 1925): P(2) = 1 +plr+&S2+p323+&X4,

(1) absorbance from zero activity at change at saturation

(3)

where overall Adair constants for the reactions are designated by pi, and x is Hh + i0, -P Hb(O,)i the partial pressure (or activity) of 0,. In this representation, the 0, binding constant#s pi are themselves functions of the COZ partial pressure. The best-fit estimat’es for the overall Adair constants are listed in Table 1, along with the confidence intervals for one standard deviation (67 Oio). The standard errors of the fits approach the spectrophotometer limits of the precision (Cary 219). about 04002 optical density units for the absorbance scale range of 0.05 absorbance units used. A striking feat)ure evident from Table 1 is our inability to resolve the third Adair constant fi3; a result that has recently been reported for a wide range of experimental conditions (Gill et al.. 1987). Since the overall constants directly reflect the concentrations of different oxygenated species, they provide a direct measure of the intermediate oxygenation species of the system. Thus. the unresolvable value of p3 indicates the negligible contribution of the triply ligated species at current levels of precision. (1)) Allosteric

(d) Data analysLs

scheme

model jar 0, bindiny

The observed low population of the triply oxygenated species of H bA (Gill et al., 1987) can be interpreted with a sharp conformational t’ransition at the third oxygenation step. subsequently enabling t,he molecule to become fully oxygenated 1987). From structural con (IX Cera et al., siderations an essentially identical mechanism for 0, binding to HbA was proposed by Perutz (1970). Details of the allosteric model that accounts for the low population of triply oxygenated species are 7 Abbreviations used: Hb. hemoglobin: magnetic resonance.

n.m.r., nuclear

CO,-0,

Linkage in Human Hrmoglobin

929

species as a function of the 0, activity. is give11 for hemoglobin ac*t*ordiny to the model iis:

;> -I

2

0

where L is the allostjeric conxta,nt. definrtl as [‘I’]][ Rj in the absence of 0,. The intrinsic. 0, affnity constants in the two quaternary stat.rs arc tiTa ati(l Q, where the subscript cxon ~~~ indicates that oni? the LYchains bind 0, in the T state. The factor 7 is the interaction constant for binding in the 7‘ state. allowing for positively co-operative (; > I ) or negatively co-operative (11 < 1 ) iJlirrilCtio~1 brtwecw the a subunits.

3

tog (pOn/torr) Figure 1. Oxygen binding data for human hemoglobin shown as changes in absorbance as a function of st,epwisr dilution of the oxygen partial pressure. Experimental ronditions \verr 30”(‘, 0.25 w-bis-Tris buffer (pH 7.38), 0.1 M-sodium chloride and the rnzymic reducing system of Hayashi ut al. (I 973). The binding data on the left were obt,ained in the absence of (‘0, and the data on the right show the shift in the binding csurve in the presence of a fixed partial pressure of (‘0, ryual to 510 Torr. The curves were drawn from the Adair equation given in t,hr test.

To explore the mechanism of the (‘0, --0, linkage at the intermediate stages of oxygenation. we have employed the allost,eric model outlined above and have analyzed all the 0, binding curves simultaneously, with the minimum number of terms allowable by the model. A single site for the linkage of CO, in each (*hain was assumed. since covalent blockage of all four amino terminus groups abolishes the (‘0, dependence of the 0, binding curve (Kilmart’in & Rossi- Rernardi. 197 I ). and crystallographic information indicat,es (‘0, adducts bound only at the LXamino-termina,l groups (Arnonr et al.. 1980). Since the interaction parameter y was found to be close to unity and independent of (‘0, activity, it has been dropped from the tittirlg equat’ion for simplification, while four (‘( I2 ilsso(*iJltion constants have been introducled: zR for (‘0, binding to the R state (equal for hot h LXant1 fi chains): zTP for the fi chains in thr ‘l’ state: antI ~~~~

elsewhere (IX C’era it nl.. 1987), but will he summarized helow. The model assumes the existence of two alternat ire quat,ernary st’ructures. the T (lowafinity). and the R (high-affinity) state. In the T state. only the tl cdhains can bind oxygen: binding at t.he p chains is negligible. Interactions between the x (*hains in the T state are allowed, while the R state is assumed to he Ilon-coo-operative, with identical and independent oxygen binding at both the a and p chains. The binding polynomial, which represents a summation of the various equilibrium

given

Owrall Adoir cowtnnts p(‘Oz (Torr)

Table 1

.forjiffing

0, binding curves, at various the Adair equa,tion 83

B2

PI

(‘l’orr - ’ )

(Torf’)

(Torf3)

j&d

pnrfinl prrssure.s oj’ ( Yj2.

P4

(TorF4)

wifh

a AOI),

( x IO- 4)

04li7,5 04i’,O. .* 04VH~ .

I.1

0

0.18 WI 1 0~30

04~1I oa22, 0415

0 04015

IO.6

0. IO 0. I I 0.30 0.13 0478. 0.21

0.010 04~017. 041 I om38

0 04~009 0

0+0068 04~006 1. 0woX5 040032

0.0709

"4

04695. WOi"'~ -. OWH:!

2.x

04~005

0~00029,

04K66.

0 04004

040022 0w020, 040028

0 0~00009 0 040003

04~00068 0~000061, 0woo85 04wO019 04~00017. 04Hw2:3

19.2 27.2

71 .B 192 510

0.1 I 04b7, 0.18 0.10 0.06. 0.17 I I.076 ti.046. 0. I2 0~070 0.042,

0.1 1

040076,

0405

1

0.0053

0401 I. 04071 0.0018 0~00036. 0.0024 oal14 0~00029, 0.0019 wlom7

040017, (MO12

D = standard error of’s point (absorbance units). Confidenw intervals within one standard deviation

0

0~0000 1

(6704) were determined

0w13 04012. 04M~16

0~00040

04~oooO69

0~000006, 0+00009

byf-testing

0479X

0~0730

2.x

0.7 1.5. 04)71.i 0~0735 0~0720. 0~0750

I4i

04~71-4 0~0700. 0472x WJ744

2.1

04~i2!~. 04)7.‘,9

2.2

M. L. Doyle et al.

930

and rTorl corresponding to the unligated and ligated states of the a chains in the T state. The (“0, association constants include the combined effects of hicarbonate and CO,(aqueous). Linkage at the fi chains in the T state requires only one term, since the fl chains are assumed not t*o bind oxygen in this stat#e. Similarly. one t,erm represents CO, linkage in t,he R state, since independent measurements of carhamino formation to the R state gave nearly the same values for the c( and /l chains (Perrella et al., 1975a,h; 1977; Morrow et al., 1976: Matthew et al.. 1977). The binding polynomial in equation (4) is therefore modified to include the effect, of CO, as:

+

&

(1+TRYJ4[1 +w:14, (5)

where L, urn and ~~ are the model parameters in t,he absence of CO,, and y is the CO, activity. A schematic representation of t)his model is given in Figure 8. All the experimental data were simultaneously fitted by equation (5). and are shown in Figure 3. This procedure is a critical test of the model, since the data are fitted along two ligand activity “coordinates”. It’ can be seen that CO, has little, if any, influence on the shape of the 0, binding curve. The fitted values of the model parameters, given in t,he Figure legend, can be used to calculate the dependence of the Adair 0, binding constants as a function of CO,. Figure 4 shows the calculated theoretical curves generated from the model parameters, compared to t,he actual modelindependent values for the Adair constants

O-6 m 0.4

Figure 3. Oxygen binding curve of human hemoglobin at increasing fixed partial pressures of carbon dioxide, Data were obtained as in Fig. 1 and represented in this Figure as binding curves. The CO, parGal pressures (in Torr)‘are: zero (I). 10.6 (a). 27.2 (A). 71.6 (A). 191 (+). and 510 (0). The theoretical curves were drawn from rqn (5), and the model parameters determined as K T3L= 0.0974 ( k 0.0034) Tot-r - ’ . L = 1% ( + 0.33) x 10s. ~ca= 11.21 (+ 1.13) Torr-‘. T&= 780 (*go) x1. 29, = 220 (530) M-l. r$ = 586 (270) M-‘, and ~~ = 153 (+6) x-l. The standard error of a point was equal to 0.0003 absorbance unit. The absorbance changes of all the data set)s were scaled to allow visual comparison. 0. fractional oxygen saturation.

obtained by individual fitting of the Oz binding curves. The good agreement indicates the appropriateness of the allosteric model. In Figure 5, the logarithm of the median oxygen pressure of t’he binding curve (p,) is drawn as a function of t’he logarit,hm of the activity of CO,. The slope of this curve gives the moles of CO,

“-

bit--l -

r-Ii--ww ‘\0 6,’ R

6-m

-2f

b T

Figure 2. Schematic representation of’ the allosteric model described in the text for the heterot,ropic linkage of CO2 and O2 binding to human hemoglobin. The 4 subunits of hemoglobin in the high-afIinit,y, or R state. are shown to the left as squares. All 0, binding sites hare identical 0, affinity. Identical low-affinity CO, binding sites are shown as circles. The 4 subunits of hemoglobin shown to the right are in the T state. Sterir hindrance at the b subunits prevents O2 binding and is depicted as an enclosed circle around the binding site. Heterogeneous high affinity COz binding sites are shown as squares for the a chains and triangles for the p chains. Continuous lines connecting CO, to 0, binding sites (a chains in the T state) indicate the heterotropic interactions allowed within that quaternary &ate. Broken lines indicate the absence of such interactions.

@i OI 9

I

:. ,I, _

-4 -

-5-

--6,

’

-4

-3

-2

-I

Log [co* (aq 11

Figure 4. Effect of carbon dioxide on the overall Adair constants fli (m), /Iz (*) and fi4 (A). The data points were obt,ained by individual titting of 0, binding (urvcs according t,o the Adair equation. The theoretical curves were drawn according to the values of the bs predicted by the allosteric- model paramet,ers, obtained independently by a simultaneous fit of all the binding curves (shown in Fig. 3). aq., aqueous.

CO,-0,

Linkage in Human Hemoglobin

931 -

saturation values, where hemoglobin vie0 (Di Cera et al.. 1987). (b) ? 3 (r s

I.1

Y

0.9

/ /

/ -/ e

-07~:

-4

-3

-2

-I

log [co, (OS)I

Figure 5. Linkage between CO, and O2 binding to human hemoglobin shown as the logarithm of the median pressure of 0, saturation (p,,,) OCTRUS the logarithm of the activity of (‘02. The continuous curve was calculated with the best-fit model parameters reported in the legend to Fig. 3. The broken line is generated by the predicted linkage due only to carbamino linkage. Carbamino association constants have been determined previously by n.m.r. methods (Matthew et aZ., 1977) and are equal to 1: = 1IO M - ’ and 1.; = 435 Me1 for the a and /? chains in the deoxy T state. and 2,” = 50 M-~ and 1; = 60 M-l for the R state.

released per mole of O2 bound at a particular partial pressure of COZ. The maximum slope 0.32. agrees wit.h previous work observed, (Tma,izumi et al., 1982). The current study has been done at 30°C in order to exploit the 0,.linked of human association constants carbamino hemoglobin. det,ermined by nuclear magnetic resonance (n.m.r.) methods (Matthew et al., 1977). Thus one (*an use the c*arbamino constants to predict the portion of the CO,-0, linkage that arises from cqa,rbamino formatsion. The broken curve in Figure 5 is the predicted linkage based on carbamino formation at the amino terminus groups of oxy and deoxy hemoglobin. The inability of cxarbamino formation a.lone to account for the ent,ire (‘0,-O, linkage suggests bicarbonate may be involved.

4. Discussion (a) Oqgenation

reaction

The model-independent, Adair scheme used to analvze the 0, binding curves at various fixed CO, activities yielded the result that t,he population of triply oxygenatetl species of HbA is negligible, This result has been regardless of CO2 activity. observed over a range of experimental conditions (Gill et IL/., 1987) and appears to be an intrinsic property of human hemoglobin in its reaction with oxygen. The physiological relevance of this property is seen in the high degree of co-operat,ivity in the binding curve that is attained at high 0,

(‘02-O2

linkage

functions

in

n~echnt~i~sttr

The mechanism of CO,-0, linkage in human hemoglobin is known to involve the reversible formation of carbamino adduc:t,s at the amino termini of the c( and /3 chains (I’errella et al.. 1975a,b), and the carbamino formation constants to deoxy and carbonmonoxy hemoglobin have been determined by n.m.r. techniques at, 30°C (Morrow PI al., 1976; Matthew et al., 1977). Our results, also obtained at 30”(1. can be interpreted in caonjunction with the n.m.r. results. Thus the next question we can ask is whether t,he magnitude of the (10,--O, linkage is due primarily to carbamino linkage! or whether bicarbonate also makes an important contribution. The inability of t hr carbamino formation to explain the observed overall shift in 0, affinity (Fig. 5) suggests that. t.hwe is an additional heterotropic effect of bic:arbonat,ta. Supporting this notion is work showing that bicarbonate decreases the 0, affinity of hcrnoglobin (Kernohan et nZ., 1966; Kreuzer et al.. 1972). The present study suggests t,hat. the effect of bicarbonat,e is significant even in t.hfh prrasenc*c’of dissolved CO,. of the bicarbonate and The partitioning carbamino linkage effects on 0, binding to t,he x and /3 chains can be evaluated in the framework of the allosteric model described in Results. along with the known values for the carbamino formation constants. The CO, binding constants reported in the legend to Figure 3 indicate a larger (‘0, IinkagcL effect to O2 binding at the CI chains than at tho /? chains. However. it is known that the> carbamino contribution to the CO&), linkagch is much larp at the /I chains than at the a chains (Perrella ef ol., 1977; Morrow et al.. 1976; Matthew rt ol., 1977). This leads one to conclude that the incnreasetl linkage effect observed at the N c,hains is due to thcb effect of bicarbonat,e. This is consisitent with t hr known anion binding sites at the amino terminus of the c( chains (Arnonr et al., 1976: O’l~onnrll vl rrl.. 1979), as well as work demonst.rating that chloridr (a planar structural analog of and nitrate bicarbonate) effectively inhibit c*arbamylation of the amino terminus groups of the c( chains (Nigw rt nl.. 1976). An esbimate of the bicarbonate binding afinity in 0.1 M-sodium chloride and pH 7.4 can be mde 13~ subtracting the overall CO, binding c*onstatlts in the present stud?. from i he det,ermined carbamino formation constants dc~termincd bj n.m.r. This lea’ds to a bicarbonate binding c+onstanf to the CL cahains of the deoxy stat<, qua1 t,o Jx = 33( *5) &fI-‘. Tn (*ontrast, the afinitirs of both ccand p chains. which are assumcd to hv tquivalcnt ox)in thrt state. an’ found qua1 IO J4 = 7( +4) M-I. The determined 02-linkccl af!finitJ of bicarbonate at the dcoxy form of t hv /I chains ih equal to 5(&l) Y-l. approximatel!. the SilIll(‘ as

M. L. Doyle et al.

932

I* 2-

5 I

0

3

2

I 4 ’

x Figure 6. Number of CO, molecules bound (F)/hemoglobin molecule at various fixed CO, partial pressu_es,as a function of the number of O2 molecules bound (X). The curves were drawn with the binding polynomial for O2 and CO, binding to hemoglobin described in the text. The fixed CO2 partial

pressures of the curves are labeled (in

Torr) in the Figure. that for the oxy state fl chains, so that the bicarbonate linkage is seen to be localized primarily at the CIchains. (c) CO,-0,

linkage

graphs

It should be pointed out that, although the 0, by their binding sites are well-characterized location in the heme pocket, the number of CO, binding sites can not be specified as unequivocally. However, there appear to be essentially four __ 02-linked binding sites for COZ (Kilmartin & Rossi-

Rernardi, 1971) and these observations have been incorporated into the allosteric model used in the present study. There is of course the possibility of other CO, binding sites that are not O,-linked, but these would not be revealed by the present study. An attractive feature of representing the data by this model is that it enables determination of the binding polynomial for 0, and COZ binding to hemoglobin, from which a series of linkage graphs (Wyman, 1984) can be constructed. These graphs can be used to evaluate the COZ-O2 linkage in great detail. For instance, Figure 6 shows the number of COZ molecules bound per hemoglobin molecule as a function of the number of oxygens bound, at several fixed CO2 activities. A linkage relation can be written to describe the relationship between the plots in Figures 6 and 3 (Wyman, 1984):

/a F\

/aln2\

\E),“y=- \r?lny),-

(6)

where 7 and x are the number of carbon dioxide and oxygen molecules bound per molecule of hemoglobin. The linearity observed in the plots of Figure 6 shows that the derivative on the left of equation (6) is equal to a constant throughout the entire range of X. Thus, the derivative shown on the right is equal to a constant for all values of X as well, and indicates that the CO, linkage on the 0, binding curve is constant throughout the entire range of oxygenation. Figure 3 demonstrates this by the observed invariant shape of the O2 binding curve as a function of the CO* activity, and is consistent wit’h other observations (Tmaizumi et al.. 1982). Another set of linkage graphs derivable from the binding polynomial is shown in Figure 7. Tn each of

log x

Figure 7. Right: number of 0, molecules bound (X)/hemoglobin molecule ?s a function of the logarithm of the partial pressure of CO2 (indicated, in Torr). Left: number of CO, molecules bound ( Y)/h emoglobin molecule as a function’ of the logarithm of the O2 partial pressure (indicated, in Torr). Both Figures were generated with the binding polynomial for 0, and CO, binding to hemoglobin described in the text. The tangent line drawn in each Figure shows the expected equal slopes of the curves according to the following linkage relation (Wyman, 1984): (&))., for given activities

of CO2 and 0,.

= (~),.,

(6)

CO,--0, Linkage in Human Hem&bin

Figure 8. Left: number of O2 molecules bound (indicated. in TOW), as a function of the number of binding sites at, various fixed 0, partial pressures discussed in t,he text. The 0, part,ial pressures of the

933

(X)/hemoglobin molecule at various fixrd 0, I)artiiLl pressure CO, molecules bound (7). Right: titration of’ thr (),-linked (‘0, (indicated, in Tort-), as calculated from t)hr binding I)olynomial intermediate curves are A. 10 and 20 Torr. from the I&.

linkage between 0, of molecules of the designated ligand bound per molecule of hemoglobin as a function of the logarithm of t,he partial pressure of the effector ligand. Linkage relations (see the legend to Fig. 7 for the equation) show that the slopes of these curves at specific activities of 0, and CO, will be equal. For example, a tangent line drawn in each plot at IO Tot-r 0, and 100 Tot-r CO, demonstrates this point. Figure 8 (left) displays the relationship between the number of oxygen atoms bound and the number of carbon dioxide molecules bound, at several fixed O2 activities. Clearly the plots are not linear, in contrast to the converse effect plotted in Figure 6. Consequently the shape of the COZ binding curve changes at different activit’ies of 0, as shown in Figure 8 (right). In the absence of O,, the CO, binding curve shows independent binding, wit,h slight heterogeneity between the Q and /? chains. However. in contrast to 0,. COZ has a higher affinity for the T state and at certain 0, activities (where the I1 state is significantly populated) the (XJ, binding reaction then converts the R state to the T state. leading t,o co-operativity in the CO, binding curve. One sees this situation in Figure 8 (right) when the 0, partial pressure is equal t.o 10 Torr.

Arnone.

The use of’ linkage graphs has been inspired bq’ stimulating discussions with tJeffries Wyman. We thank Ho Hedlund for his assistance in the hemoglot)iIl preparations. This work was supported by Kational Institutes of Health grant HL2232fi.

Kreuzer. F.. Roughton. F. ,J. W.. Rossi-Brrnwrdi. I,. & Kernohan, .J. (‘. (1972). In Osygrn ilfiffinity ~4

these

plots.

the

heterotropic

and CO, is shown as the number

References Adair. G. S. (1925). ,I. Hiol. C’hem. 63, 529-545. Arnonr. A.. O’Donnell, S. 8 Schuster, T. (1976). E$d. I’m. FP~. Amer. Xoc. h’xp Hiol. 35. 1604.

A., Rogers. P. H. & Brilry. 1’. I). (1980). In and Physiology of C’arbon Dioxide (Bauer. C!., Cros, G. & Bart’els. H.. eds). pp. 67 71, SpringrrVerlag, Sew York. 25. I381 Bishop, G. & Gill. S. (1986). Hiopolymers. 1384. TX (>era, E.. Robert. (‘. H. 8r (iill. S. .I. (1987). Hiochemi~try, 26, 4003-4008. Dolman. D. & Gill. 8. ,J. (1978). Anal. Riochrnr. 87. I%7 134. Edsall, ,J. T. & N’yman. J. (1968). In I~iophysicvi Chemistry, vol. I. p. ,558. Academic Press, Sew York. Frazier. R. D. 13. $ Suzuki. E. (1973). III I'hyskol Biophysics

Principles

und

Tech,niques

of

Protein

( ‘hevn ist ry

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by G. A. Gilbert