Aggregation of deoxyhemoglobin subunits.

The formation of deoxyhemoglobin was examined by measuring the heme spectral change that accompanies the aggregation of isolated alpha and beta chains. At low hemeconcentrations (less than 10(-5) M), tetramer formation can be described by two consecutive, second order reactions representing the aggregation of monomers followed by the association of alphabeta dimers. At neutral pH, the rates of monomer and dimer aggregation are roughly the same, approximately 5 X 10(5) M(-1) X(-1) at 20 degrees. Raising or lowering the pH results in a uniform decrease of both aggregation rates due presumably to repulsion of positively charged subunits at acid pH and repulsion of negatively charged subunits at alkaline pH. Addition of p-hydroxymercuribenzoate to alpha chains lowers the rate of monomer aggregation whereas addition of mercurials to the beta subunits appears to lower both the rate of monomer and the rate of dimer aggregation. At high heme concentrations (greater than 10(-5) M) or in the presence of organic phosphates, the rate of chain aggregation becomes limited, in part, by the slow dissociation of beta chain tetramers. In the case of inositol hexaphosphate, the rate of hemoglobin formation exhibits a bell-shaped dependence on phosphate concentration. When intermediate concentrations of inositol hexaphosphate (approximately 10(-4 M) are preincubated with beta subunits, a slow first order time course is observed and exhibits a half-time of about 8 min. As more inositol hexaphosphate is added, the chain aggregation reaction begins to occur more rapidly. Eventually at about 10(-2) M inositol hexaphospate, the time course becomes almost identical to that observed in the absence of phosphates. The increase in the velocity of the chain aggregation reaction at high phosphate concentrations suggests strongly that inositol hexaphosphate binds to beta monomers and, if added in sufficiently large amounts, promotes beta4 dissociation. A quantitative analysis of these results showed that the affinity of beta monomers for inositol hexaphosphate is the same as that of alphabeta dimers. Only when tetramers are formed, either alpha2beta2 or beta4, is a marked increase in affinity for inositol hexaphosphate observed.

The formation of deoxyhemoglobin was examined by measuring the heme spectral change that accompanies the aggregation of isolated (Y and p chains. At low heme concentrations (<lo-" M), tetramer formation can be described by two consecutive, second order reactions representing the aggregation of monomers followed by the association of LYP dimers. At neutral pH, the rates of monomer and dimer aggregation are roughly the same, =5 x 1e5 Mm' s-l at 20". Raising or lowering the pH results in a uniform decrease of both aggregation rates due presumably to repulsion of positively charged subunits at acid pH and repulsion of negatively charged subunits at alkaline pH. Addition ofp-hydroxymercuribenzoate to (Y chains lowers the rate of monomer aggregation whereas addition of mercurials to the p subunits appears to lower both the rate of monomer and the rate of dimer aggregation. At high heme concentrations (>lO-" M) or in the presence of organic phosphates, the rate of chain aggregation becomes limited, in part, by the slow dissociation of /3 chain tetramers. In the case of inositol hexaphosphate, the rate of hemoglobin formation exhibits a bell-shaped dependence on phosphate concentration.
When intermediate concentrations of inositol hexaphosphate (-10e4 M) are preincubated with p subunits, a slow first order time course is observed and exhibits a half-time of about 8 min. As more inositol hexaphosphate is added, the chain aggregation reaction begins to occur more rapidly. Eventually at about 1OV M inositol hexaphosphate, the time course becomes almost identical to that observed in the absence of phosphates. The increase in the velocity of the chain aggregation reaction at high phosphate concentrations suggests strongly that inositol hexaphosphate binds to p monomers and, if added in sufficiently large amounts, promotes p4 dissociation. A quantitative analysis of these results showed that the affinity of /3 monomers for inositol hexaphosphate is the same as that of (u/3 dimers. Only when tetramers are formed, either (Y& or &, is a marked increase in affinity for inositol hexaphosphate observed. In 1965 Bucci and Fronticelli (1) reported a procedure for isolating the (Y and p subunits of human hemoglobin in a functionally intact form (i.e. capable of reversible combinations with heme ligands). Subsequently, Antonini and coworkers (2, 3) showed that the separated chains react rapidly with CO and bind oxygen 30 to 40 times more tightly than hemoglobin.
In the deoxygenated, ferro state, the subunits exhibit a modified Soret absorption spectrum (4, 5) which is analogous to that of the Hb* ' species first observed by Gibson (7) Antonini's (8) belief at that time that deoxyhemoglobin dimers exhibit cooperative ligand binding. Since the sedimentation coefficient for isolated p chains was observed to be around 4 S (4) and that for a chains around 1.9 S, the p subunits were postulated to exist as tetramers until recombined with monomeric a chains. The dissociation of p chain oligomers (Equation la) was thought to account for the majority of the lag phase seen in the stopped flow traces. The second order nature of the remaining portion of the time course was assigned to the aggregation of monomeric units (Equation lb).
Since the original studies of Antonini et al. (41, have shown that unliganded dimers exhibit Hb* spectral and functional characteristics and do not bind ligands in a cooperative manner. Consequently most, if not all, of the subunit aggregation absorbance change is associated with tetramer formation, the last step in Equation 1. In addition, the contention of Antonini et al. (4) that p4 dissociation accounts for the lag phase is inconsistent with the heme concentration dependence of their observed time courses. At micromolar concentrations, the half-time of the absorbance change was proportional to the reciprocal of the initial heme concentration. This relationship would not be observed if a first order dissociation reaction were limiting the overall aggregation rate. As Gibson (6) has suggested, the lag phase is more likely to be due to the lack of absorbance change associated with dimer formation.
In view of these more recent results and interpretations, we have attempted to describe the formation of deoxyhemoglobin at low heme concentrations, using only Equations lb and Id. Quantitative analysis of the absorbance time courses required the assignment of only a single rate constant since the rate of dimer aggregation could be obtained independently from pH drop experiments (10, 12). Further, within this framework, we have attempted to quantitate the effects of protons, mercurials, and organic phosphates on the various rates involved in the aggregation of hemoglobin subunits.

MATERIALS AND METHODS
Human hemoglobin was prepared as described by Wiedermann and Olson (12). Isolated OL and p chains were prepared by the method of Geraci et al. (13) with the following exception: p-mercuribenzoate was removed from the p chains by passage through a Sephadex G-25 column equilibrated with 0.1 M 2-mercaptoethanol (14). Regeneration of the sulfhydryl groups by the DEAE-cellulose procedure of Geraci et al. (13) consistently yielded large populations of fi chains (up to 50%) that were inactive with respect to hemoglobin formation. Although they exhibited normal heme spectra and reacted rapidly with heme ligands, a large portion of these p chain preparations were incapable of recombining with (Y chains, even after several hours of incubation. In contrast, the Sephadex column procedure of Sugita et al. (14) consistently yielded fully active p chain preparations as judged by electrophoresis and the magnitude of the absorbance change accompanying tetramer formation. The isolated chains were judged to be free of mercury by titration with p-hydroxymercuribenzoate.
Chain preparations were stored under 1 atm of CO at 4" to prevent oxidation. were added to the anaerobic chain solutions to scavenge any residual 0, bound to the isolated subunits.
Whenp-hydroxymercuribenzoate was added to the chains, this was always done prior to dithionite addition.

RESULTS
In agreement with the work of Antonini et al. (41, the absorbance change which accompanies the aggregation of unliganded a and /3 chains exhibits an initial lag followed by a decelerating time course indicative of second order behavior (Fig. 1). The Soret difference spectrum observed in these experiments agreed well with the chain aggregation difference spectrum reported by Brunori et al. (5) and with previously reported spectra for the association of deoxyhemoglobin dimers (9-11). We chose to follow subunit aggregation at the 445 nm difference minimum rather than at the 430 nm maximum, even though the latter change is roughly 2-fold larger. The lower background absorbance at 445 nm improved significantly the signal to noise ratio of the traces and reduced nonlinearity between absorbance changes and concentration due to deviations from Beer's law (i.e. optical artifacts due to polychromatic light).
A series of time courses in which one or both of the chain concentrations was varied are shown in Fig. 1. The total absorbance change was directly proportional to the a-heme concentration when the p subunits were present in excess ( Fig. 1A) and to P-heme concentration when the (Y subunits were in excess (Fig. 1B). These results show that both chain preparations are fully reactive with respect to hemoglobin formation and that there are no significant deviations from Beer's law over the heme concentration range used (2 to 15 x 10m6 M). As shown in Fig. lC, the halftime of the overall reaction increases 4-fold, from 1.4 to 5.6 s, in going from 8.0 to 2.0 x lo-" M total heme concentration after mixing. This heme concentration dependence agrees well with that reported by Antonini et al. (4) and indicates little contribution from a first order p4 dissociation rate.
The time courses in Fig. 1 were analyzed in terms of the following scheme: (2) a6 + a6 -CT 6 2 2 (b) All of the heme absorbance change was attributed to the dimer association step, Equation 2b. The rate of this reaction, k2, was fixed at 5.2 x lo5 M-' s-l, the value reported by Wiedermann and Olson (12) for the rate of dimer aggregation in 0.1 M bis-Tris, 0.1 M NaCl at pH 7.0, 200.' As shown by the correspondence between the experimental points and the calculated lines in Fig. 1, Equation 2 provides a good quantitative description of the time course of tetramer formation. It is particularly satisfying that the dimer association rate measured independently by pH drop experiments (12) applies quantitatively to the overall subunit aggregation process. The average value of k, obtained from 24 separate fits using four different chain preparations was 5.0 -C 1.0 x lo5 Mm' s-' for the reaction in 0.1 M bis-Tris, 0.1 M NaCl at pH 7.0, 20". An analysis of a number of experiments similar to those reported in Fig. 1 indicated that the optimum condition for determining the value of k, was to mix equimolar concentration of (Y and /3 chains at approximately 8 x 10eg M total heme. Under these conditions, the absorbance change is relatively large, 0.06 to 0.08, whereas deviations from Beer's law and contributions from the dissociation of /3 oligomers are still negligible (see "Discussion").

Effects of Protons and p-Hydroxymercuribenzoate-
In the range pH 7 to 8, there is little dependence of the time course of chain aggregation on proton concentration ( Fig. 2, Table II, and Ref. 4). However, at either low or high pH, there is a definite decrease in the velocity of the reaction which results from a relatively uniform lowering of both k, and k, (Table II). This decrease in rate is probably due to unfavorable electrostatic interactions between positively charged subunits at acid pH and the negatively charged subunits at alkaline pH.
In agreement with the results of Antonini et al. (41, the addition ofp-hydroxymercuribenzoate to either one or both of the chains causes a marked decrease in the velocity of the aggregation reaction. The addition of 1 eq of mercurial to /3 chains appears to cause a decrease in both the rate of monomer and the rate of dimer aggregation (Table II and Fig. 3A). In contrast, the addition of mercurial to (~104 cysteine appears to affect only the rate of dimer formation (Table II and Fig. 3B), These results are consistent with the currently accepted idea that the CX& interface is formed during monomer association and the c& interface during dimer association (9-11, 18-24).
Since ~~104 cysteine is located at the c& interface, modification of this residue would be expected to affect the rate of monomer association, but a priori, there is no reason to expect an effect on the rate of dimer aggregation (i.e. DL& interface formation). McDonald and Noble (25) have shown that cysteines 93 and 112 of isolated p chains react at equivalent rates with p-hydroxymercuribenzoate.
Therefore, when one p-hydroxymercuribenzoate per heme is added to p chains, 50% of the subunits should be modified at p93 cysteine and 50% at /3112 cysteine.
Since /3112 cysteine is located in the c~,/l, interface and p93 cysteine near the 01& interface, 1 eq of mercurial added to the /3 subunits would be expected and is observed to influence the rate of both steps in the overall chain aggrega-* We also allowed bothk, and k, to vary, and although the program required significantly longer execution time, the fitted values fork, were, in all cases, close to the values reported by Wiedermann and Olson (12). tion process (Table II) Table II. were mixed and the reactions followed at 445 nm. AA/ AA, represents the normalized absorbance change (see Fig. 1). The solid lines represent best fits to Equation 2 and were calculated using the parameters listed in Table II (Fig. 4C). This nonproportionality between half-time and reciprocal heme concentration implies a significant contribution from a slow, first order dissociation process.
AS shown in Fig. 4C, 2,3-diphosphoglycerate exerts an effect on chain aggregation which is similar to that observed with inositol-Ps. Again, when the /3 chains are preincubated with the organic phosphate, a slow first order phase is observed and contributes a majority of the absorbance change. In the case of 2,3-diphosphoglycerate, the half-time of the slow phase is 18 s. The major difference between 2,3-diphosphoglycerate and inositol-P, is the inability of the diphosphate to increase significantly the velocity of the overall chain aggregation process when it is added to the a chains alone.

Acceleration of Tetramer
Formation-At 8 x 10m6 M heme when inositol-P, is present in the a chain and not the /3 chain solution, the time course for chain aggregation exhibits a rate which is a-fold greater than that seen in the absence of phosphates (Fig. 4A). This observation requires that inositol-P, binds to intermediates in the reaction (i.e. monomers or c$l dimers) and increases their rate of aggregation. The velocity of the overall reaction reaches a maximum at about 10m4 M inositol-P, and then decreases back to the original rate at much higher phosphate concentrations (Fig. 5A). This "bellshaped" dependence is analogous to that observed by Wiedermann and Olson (12) for the dependence of the rate of dimer association on inositol-P, concentration. These authors showed that the rate of association of a dimer containing bound phosphate with a phosphate-free dimer is much greater than either the rate of association of two phosphate-free dimers or the rate of association of two dimers, both containing bound phosphate. The resultant dimer aggregation rate, k, in Equation 2, is given by: where K is the equilibrium dissociation constant for the binding of inositol-P, to ap dimers; kn,n, the rate of association of phosphate free dimers; /z","~, the rate of association of unlike dim&s, one with phosphate bound and one without; KDX,DX, the rate of association of phosphate containing dimers; and X represents inositol-PG.
A series of a! (inositol-P,) + p time courses were measured in which the inositol-P, concentration was varied from 0 to 5 x 10M2 M, and the results were analyzed in terms of Equation 2. Only the value of k, was allowed to vary; K2 was fixed at values calculated from Equation 3 using the parameters measured by Wiedermann and Olson (12) in 0.1 M bis-Tris, 0.1 M NaCl at pH 7.0, 20" (k,, = 5.2 X lo5 M-' s-l, k,,, = 149 X lo5 M-' S-l, k DX,DX = 6.8 x lo5 M-I s-l, and K = 2 x 10m4 M). As shown in Fig. 5B, the value of k1 is roughly independent of phosphate concentrations. Evidently, monomer association is little influenced by the presence of inositol-P,. The increase in the velocity of the overall reaction in the presence of inositol-P, appears to be due almost entirely to the large rate of asymmetrical dimer aggregation (i.e. @(inositol-P,) + a/S. Aggregation of p Chains-The polymerization of /3 chains also exhibits a "bell-shaped" dependence on inositol-P, concentration. When the p subunits are titrated wth inositol-P6 prior to mixing with LY chains, the fraction of slowly dissociating /3 tetramers reaches a maximum at about 3 x 1OV M inositol-P,. As the phosphate concentration is raised further, to 2 to 5 x 10m2 M, this fraction decreases back to 0 (Fig. 61. This observation suggests strongly that inositol-P, binds, albeit weakly, to Equimolar concentrations (8 x 1Omg M total heme after mixing) of (Y and 6 chains were mixed and the reactions followed at 445 nm. For these experiments inositol-P, UP,) was added to the 01 chain solutions only to prevent the formation of p chain tetramers. As mentioned in the text a small slow phase (tliZ -10 to 20 min) is observed in the (Y (inositol-P,) + p experiments but comprises only 5 to 10% of the total absorbance change. This slow phase was subtracted from the total changes, and the resultant fast phase was analyzed in terms of Equation 2. A, normalized time courses for a (inositol-PJ + p. The concentration of inositol-P, after mixing is shown beside each curve. The solid lines represent fits to Equation 2. kz was fixed as described in the text and k, allowed to vary. Values of k, and k,, respectively; were: 5.0 x lo5 M-' s-l, 5.2 x lo5 M-' s-' for no inositol-P,; 11.0 x lo5 M-' s-l, 27.4 x IO5 M-' SK' for 7.5 x 10m5 M inositol-P,; 5.9 X lo5 M-' s-l, 10.6 X lo5 M-' s-l for 1 X 10m2 M inositol-Pg. B, dependence of the rates of monomer, k,, and dimer, k,, aggregation on inositol-P, concentrations. Values of It, were calculated from Equation 3 as described in the text. Values fork, were obtained from fits to Equation 2. The concentration of inositol-P, is given as that after mixing. p monomers. Consequently, at very high concentrations inosi-M-P, causes the dissociation of p tetramers. When this dissociation is substantial, the chain aggregation reaction exhibits a "normal," rapid time course (the 50,000 pM curve in Fig. 6).
When the p chains are preincubated with 3 x 10-j M inositol-P,, the total aggregation absorbance change decreases roughly 30% (the 30 FM curve in Fig. 6). However, as the inositol-P, concentration is raised further, the aggregation absorbance change begins to increase and eventually approaches and surpasses slightly the magnitude of the changes observed in the absence of phosphates. A direct demonstration of the effect of inositol-P, on the p-heme spectrum is shown in Fig. 7. A large difference spectrum is observed when /3 chains are mixed with 0.5 to 1.5 x 10m4 M inositol-P,. However, little absorbance change is seen when the experiment is repeated using a thousand-fold higher phosphate concentration. The p chain difference spectrum at intermediate phosphate concentrations is different from the overall difference spectrum produced by mixing unliganded a! and p chains. The /3 chain spectrum is smaller in magnitude and appears to represent a were mixed and the reaction followed at 445 nm through a 1.5~cm cuvette.
Only the 6 chain solution contained inositol-P,. The concentration of inositol-P, before mixing is listed beside each curve. The inset shows a log plot of the time course at lo+ M inositol-Pg; note the time scale is in minutes.
The lines were drawn through the points and do not represent theoretical fits.
blue shift of the Soret absorption peak. As shown in the inset of Fig. I, the reaction of p chains with inositol-P, can be followed in the stopped flow apparatus. At 8 x 1OmB M heme almost all of the absorbance change occurs slowly and exhibits a higher order kinetic pattern indicative of monomer aggregation.
The following equilibria, where X represents inositol-Ps, were used to analyze the results in Figs. 6 to 8. This scheme assumes that /3 dimers are thermodynamically unstable; that is, K, is the product of a very small number representing dimer formation and a very large number representing tetramer formation from dimers (see "Discussion" and Footnote 3). The fraction of slowly dissociating (with a rate =10m3 s-l) or spectrally altered /3 chains is given by: The fraction of p4 (inositol-P,) was calculated from: 0, the fractional spectral change at 440 nm produced by inositol-P, binding in static spectral titrations (data were collected in the Cary 118C and normalized to a maximum of 85% p4 (inositol-P,) at 50 PM inositol Pg; A, difference between the total absorbance change observed for the aggregation of phosphate-free 01 and p chains and that observed when the 6 chains were preincubated with inositol-P, (data were collected in the stopped flow apparatus and normalized to a maximum of 85% p4 (inositol-PJ at 50 wrn phosphate); 0, fraction of slow spectral change obtained from the stopped flow experiment given in Fig. 6. The solid line represents a theoretical lit to the data using Equation 5 and the parameters listed in the text.
where C, is the total heme concentration; (X), the concentration of unbound inositol-P,; andf,, the fraction of p monomers. The fraction of /3 monomers is given by the appropriate root (0 < f0 < 1) of the following polynomial: f", (4Kl$l + K,(X))-4) + fg(Co(l + K3(X))-') -Co(l + K3(X))-' = 0 (5b) where the K values are defined in Equation 4. A summary of /3 chain polymerization data is shown in Fig.  1878 Formation of Deoxyhemoglobin 8, where the fractional P-heme spectral change or the fraction of slowly dissociating @ tetramers is plotted versus the logarithm of the total inositol-P, concentration.
The solid line represents a best fit to the experimental data and was calculated from Equation 5 using the following parameters: K, = 8 x 10':' M ', K, = 10" M-', K:, = 10" M I, and C,, = 8 x 10mfi M.
The fitted value of K, predicts 10% tetramers on a per heme basis at 8 x 1OV M p chains and 74%> tetramers at 8 x lo-" M. These percentages of p tetramers agree well with those calculated from the ofinositol-P,) + ,6 experiments shown in Fig. 4, A and B.
The results in Fig. 8  Similarly, the equilibrium constant for tetramer to dimer dissociation of deoxyhemoglobin is of the order of 10. lo to lo-" M at neutral pH (26,27). At pH 7.0, 20", the rates of monomer and dimer aggregation are approximately the same, =5 x lo" Mm' s'. Thus, the rate of formation of the thermodynamically more stable o,/XI interface is essentially identical to the rate of formation of the less stable aIpp interface. Consequently, the kinetic expression of the difference in stabilities of the two sets of intersubunit bonds must reside in the dissociation rate constants: the velocity of tetramer to dimer dissociation must be greater than the velocity of dimer to monomer dissociation.
At higher heme concentrations, evidence is observed for the presence of p chain oligomers. For example, the half-times of the chain aggregation reactions at 8 x lo-" and 80 x lo--" M heme are the same but the characteristics of the time courses are markedly different (Fig. 4) In the case of inositol-P,, as the phosphate concentration is raised, binding to p monomers occurs and eventually promotes complete dissociation of all /$ molecules (Equation 5 and Fig. 8).
Quantitative analysis of the data in Fig. 8 (Fig. 4B). The relatively sharp rise in the fraction of p? in going from 8 x 10m6 to 8 x lo-" M heme reflects the fourth order nature of the p chain aggregation reaction (Equation 5). In the past, most workers have assumed that p chains are tetramers at all heme concentrations (4,18,28). This idea was based on sedimentation velocity studies which indicated 4.0 to 4.5 s~,,~ values for isolated /3 chains. However, all of these studies used schlieren optics and, therefore, heme concentrations >lO@' M. Consequently, these high s~,),~~ values do not conflict with our observations. In fact, the value ofK, obtained from the data in Fig. 8 predicts .sP,,,,< values greater than 4.0 S at lo--' M heme:' :'It is unrealistic to assume that p tetramer formation is a concerted process requiring the simultaneous collision of 4 subunits. Similarly, the dissociation process probably occurs in two steps: pd -WP -4p. The fit of the data in Fig. 4B to a scheme using Equation 2 and a pJ -4p step exhibited a systematic pattern of deviations between observed and calculated points. We interpret this to mean that at least two steps are involved in the dissociation of p chain polymers.
Similar evidence for pt intermediates is shown in the inset of Fig. 7. The time course observed when p chains are reacted with inositol-P, cannot be analyzed in terms of a concerted 4/3 -pG reaction (i.e. a plot of the reciprocal of the absorbance cubed versus time is not linear). On the other hand, the limited data available on the molecular weight of deoxygenated p chains as a function of heme concentration precludes any serious attempt at assigning individual rate and equilibrium constants to the association and dissociation of p dimers. Furthermore, as shown in Fig. 8