Rate Constants for O2 and CO Binding to the α and β Subunits within the R and T States of Human Hemoglobin*

Despite a large amount of work over the past 30 years, there is still no universal agreement on the differential reactivities of the individual α and β subunits in human hemoglobin. To address this question systematically, we prepared a series of hybrid hemoglobins in which heme was replaced by chromium(III), manganese(III), nickel(II), and magnesium(II) protoporphyrin IXs in either the α or β subunits to produce α2(M)β2(Fe)1and α2(Fe)β2(M) tetramers. None of the abnormal metal complexes react with dioxygen or carbon monoxide. The O2 affinities of the resultant hemoglobins vary from 3 μm −1 (Cr(III)/Fe(II) hybrids) to 0.003 μm −1 (Mg(II)/Fe(II) hybrids), covering the full range expected for the various high (R) and low (T) affinity quaternary conformations, respectively, of human hemoglobin A0. The α and β subunits in hemoglobin have similar O2 affinities in both quaternary states, despite the fact that the R to T transition causes significantly different structural changes in the α and β heme pockets. This functional equivalence almost certainly evolved to maintain high n values for efficient O2 transport.

In 1970, Perutz (1) published a detailed mechanistic interpretation of cooperative oxygen binding to hemoglobin (Hb).
Two key structural features of the protein molecule were stressed. First, in deoxy-Hb, the ferrous iron atom was high spin and out of the plane of the porphyrin ring toward the proximal histidine (F8). In the low affinity or T state quaternary conformation, movement back into the plane of the heme was restricted. This restriction was postulated to be the major cause of reduced affinity in the T quaternary state (1). Over the past 30 years, various spectral and structural studies have shown that the R to T conformational transition causes ruffling and strain on the ␣ heme group that results in large changes in its visible spectrum and can result in disruption of the ␣Fe-His(F8) bond when NO is bound (2)(3)(4)(5). Although tacitly accepted by most workers, there is less direct spectral or structural evidence for proximal strain in ␤ subunits.
In the original paper, Perutz (1) also suggested that ligand binding to T state ␤ subunits was sterically restricted by the presence of the His(E7) and Val(E11) side chains almost directly over the iron atom. As a result, Perutz (1) proposed that ligands first bind to ␣ subunits. This binding then causes the switch from the low to the high affinity quaternary state in which the ␤ subunits have a much more open ␤ distal pocket and can readily bind oxygen. Perutz's proposal of an ordered addition of ligands conflicted with results from Gibson's group.
Their experimental data suggested that significant kinetic and equilibrium differences between the Hb subunits occur only for ligands containing three or more non-hydrogen atoms and that the ␤ and not ␣ subunits are more sterically accessible to large ligands such as n-butyl isocyanide, even in the T state (6 -10).
A myriad of experimental approaches were developed to resolve this controversy concerning functional differences between the subunits, including the following: (i) measurements of the ligand binding properties of the isolated ␣ and ␤ chains (3); (ii) discovery or development of spectral signals for ligation of the individual subunits within intact tetramers (11); (iii) selective chemical modification or mutation of key residues in the ␣ and ␤ chains (12,13); (iv) separation of kinetic intermediates by cryogenic electrophoresis (14); (v) x-ray diffraction analysis of partially liganded Hb crystals (15); and (vi) construction of valency and metal hybrid Hbs in which one pair of subunits has an inert metal-porphyrin group and the other O 2and CO-reactive heme groups (16 -24). The latter approach is the most definitive with respect to assigning observed rate and equilibrium constants since only one type of subunit is capable of reacting with ligands.
Despite a large number of experiments and reports over the past 30 years, there is still no universal agreement on the differential reactivities of the individual subunits. Part of the problem is that the two-state model is an oversimplification. It is clear that multiple forms of the low affinity quaternary conformation occur, depending on pH and organic phosphate concentration (25,26), and that there are alternative crystal forms of liganded Hb A 0 (27)(28)(29). In addition, Ackers and coworkers (30 -32) have presented evidence for unique intermediate quaternary states, although some of the work with cyanomet hybrids is being challenged (33,34). The other key problem is that the rate of interconversion of the R and T states is not always rapid with respect to oxygen and carbon monoxide binding. As a result, time courses for ligand binding to ␣(Fe)␤(inert) and ␣(inert)␤(Fe) hybrids are often biphasic, with rapid and slow phases representing very slowly interconverting R and T conformations, respectively.
heterogeneous. The fast and slow phases were assigned to CO binding to R and T state Hb, respectively, and the quaternary conformational transition between the fast and slow binding components was estimated to be extremely slow (less than 1 s Ϫ1 ). Similar complex results were obtained for CO binding to the symmetrical Co(II)/Fe(II) and Mn(II)/Fe(II) hybrids (18 -21). What was needed were metal substitutions that would lock the hybrid Hb tetramers into primarily R or T conformations, not mixtures. Such hybrids would allow unambiguous assignment of rate constants to the iron-containing subunit in one or the other of the quaternary states.
Over the past 12 years, Morimoto and co-workers (24,(35)(36)(37)(38)(39) have prepared and characterized metal-substituted hybrid Hbs using first transition metal ions. Some of the hybrid Hbs can be used as T or R state models. The definition of conformational state behavior is based historically and experimentally on O 2 binding properties. Low O 2 affinity comparable to that of the first oxygenation step of deoxy-Hb A 0 (K O 2 Ϸ0.003 Ϫ 0.01 M Ϫ1 ) refers to the T state, and high O 2 affinity comparable to that of the last oxygenation step of Hb A 0 (K O 2 Ϸ1 Ϫ 3 M Ϫ1 ) refers to the R state. In 1986 Shibayama et al. (35,36) showed that, at neutral or low pH, Ni(II)/Fe(II) hybrids of human Hb show T state behavior with respect to oxygen binding and spectral properties. Luisi and Shibayama (37) and Luisi and co-workers (38) showed that these proteins crystallize in the deoxy form of Hb A 0 and have the structural features characteristic of the T quaternary state. The Ni(II) atom forms only 5-and 4-coordinate complexes which are characteristic of the deoxy T state. More recently, Park and co-workers (39) 2 prepared Mg(II)/ Fe(II) hybrid Hbs that also show functional and structural characteristics of the low affinity T state. In this case, the Mg(II) atom forms only 5-coordinate complexes with porphyrin and globin, and as a result, Mg(II)/Fe(II) Hb crystallizes in the T quaternary conformation, even the presence of bound CO.
In contrast, Cr(III)/Fe(II) hybrids of human Hb show very high affinities for O 2 and the chemical and spectral characteristics of the R state (24). In this case, the Cr(III) atom has an ionic radius (0.62 Å) approximately equal to that of low spin Fe(II), forms strong hexacoordinate complexes with water or OH Ϫ as an axial ligand, and is expected to fit in the flat plane of the porphyrin ring, and have a proximal His-Cr(III) bond as short as that in oxy-Hb (40 -43). Similar arguments apply to Mn(III)-porphyrin complexes (21). However, the Cr(III)/Fe(II) hybrids are much more convenient to examine kinetically since this metal is inert to sodium dithionite.
In this work, we have used all four hybrids in an attempt to assign unambiguously rate and equilibrium constants for O 2 and CO binding to ␣ and ␤ subunits within T and R state-like conformations of Hb A 0 . R state parameters were assigned based on measurements with Cr(III) and Mn(III) hybrids and T state parameters based on results for the Ni(II) and Mg(II) hybrids. Our goal was to determine association and dissociation rate constants for O 2 and CO binding to all four types of metal hybrids under identical conditions. The results have provided two sets of kinetic parameters for ␣ and ␤ subunits thought to be in mostly T conformations, i.e. the Ni(II) and Mg(II) hybrids, and two sets of parameters for subunits in mostly R conformations, i.e. the Cr(III) and Mn(III) hybrids. These results have been compared with previous estimates of O 2 and CO ligand binding constants to provide a final resolution of the problem of differential reactivities of the ␣ and ␤ subunits. The absolute values of the kinetic parameters are very important for two other reasons. (i) They show that the addition of O 2 and CO to the ␣ and ␤ subunits is not ordered to any great extent, either at equilibrium or kinetically, and thus, the stereochemical mechanisms for cooperative ligand binding to each subunit need to be re-examined. (ii) These parameters also provide the starting points for evaluating the effects of mutagenesis on the ligand binding properties of recombinant Hbs and for designing more efficient Hb-based, O 2 delivery pharmaceuticals (45,46).

EXPERIMENTAL PROCEDURES
Preparation of Metal-Fe(II) Hybrid Hemoglobins-Hb A 0 and its isolated chains were prepared in carbon monoxide forms as described by Fujii et al. (47). Cr(III)/Fe(II) hybrid Hbs were prepared as previously reported (24). Mn(III)/Fe(II) hybrid Hbs were prepared as described by Waterman and Yonetani (48). Ni(II)/Fe(II) hybrid Hbs were prepared as described by Shibayama et al. (35). Mg(II)/Fe(II) hybrid Hbs were prepared as described by Park et al. (39).
Measurements of CO Binding-CO binding to the deoxygenated metal/Fe(II) hybrid Hbs were measured using stopped-flow rapid mixing technique as described by Mathews et al. (49). Concentrated Hb samples were diluted in deoxygenated buffer to a concentration of 10 M on a per metal basis. In order to ensure complete anaerobiosis, small amounts of sodium dithionite were added to solutions of Cr(III)/Fe(II) hybrids. Dithionite was not added to solutions of Ni(II)/Fe(II) and Mg(II)/Fe(II) hybrids. The oxygen affinities of the latter Hbs are so low that complete deoxygenation is easily attained without dithionite. The deoxygenated hybrid Hbs were mixed with anaerobic buffer containing 33.4 M CO, and the resultant absorbance changes were measured at 436 nm. CO binding experiments were carried out at the following three pH conditions: 6.5, 7.4, and 8.4. When the hybrids showed monophasic time course, the data were fitted empirically to a single exponential expression as shown in Equation 1, where ⌬A t is the observed absorbance change at time t; ⌬A 0 is the total absorbance change; and k obs was the observed pseudo first-order rate constant. In case of CO binding, k obs ϭ kЈ CO [CO], where kЈ CO is the bimolecular CO association rate constant. When the hybrid Hbs showed biphasic time courses, the data were fitted to a two-exponential expression as shown in Equation 2, where F f is the fraction of fast reacting species, and k f and k s are the observed pseudo first-order rate constants for the fast and slow phases. For each phase, kЈ CO was calculated by dividing of the observed rates, k s and k f , by [CO].
Measurements of CO Dissociation-CO dissociation rate constants were determined by mixing HbCO samples with buffer containing 1 atm of NO in the stopped-flow apparatus and monitoring displacement of bound carbon monoxide at 420 and 406 nm as described by Mathews et al. (50). The Hb samples were diluted to 10 M on a per metal basis into anaerobic buffer containing 100 M CO and then mixed with anaerobic buffer containing NO. Under these conditions, the observed replacement rate constant is equal to the CO dissociation constant, k CO (50).
Measurements of O 2 Association-Oxygen rebinding to the metal-Fe(II) hybrids was measured after flash photolysis using the pulsed dye laser system described by Mathews et al. (50) and Rohlfs et al. (51). The Hb concentration was 200 M on a per metal basis, and 1-mm path length cuvettes were used. Absorbance changes were measured at 436 nm. The observed pseudo first-order rate constant for bimolecular O 2 rebinding is given by Equation 3, where kЈ O  and Mn(III) hybrids, the value of k O 2 is poorly defined in these plots since the absolute value is 10 to 100 times smaller than the observed rate constant at the lowest accessible [O 2 ], usually air-equilibrated buffer. In the case of the Ni(II) and Mg(II) hybrids, the y intercept is defined, with dissociation rate constants on the order of 1000 -2000 s Ϫ1 .
Measurements of O 2 Dissociation-O 2 dissociation rate constants were determined by mixing HbO 2 samples with buffer equilibrated with 1 atm CO in the stopped-flow apparatus, and the ligand replacement reaction was followed at 423 nm as described by Mathews et al. (50). The protein was diluted to 10 M in buffers containing O 2 concentrations ranging from 262 M (air) to 1250 M (1 atm O 2 ). Under these conditions, the observed replacement rate, r obs , is given by Equation 4.

CO Association
Constants-Rapid mixing time courses for the reaction of CO with ␣ 2 (Cr)␤ 2 (Fe) and ␣ 2 (Fe)␤ 2 (Cr) Hbs are biphasic (Fig. 1A). The CO association rate constants (kЈ CO ) and percentages of fast and slow components are listed in Table  I. Under the same buffer conditions, the time courses for CO binding to the Ni(II)/Fe(II) and Mg(II)/Fe(II) hybrids are monophasic, even in the absence of organic phosphates (Fig.  1B). The values of kЈ CO for these low affinity hybrids are also listed in Table I.
The fast CO-reacting phases for the high affinity Cr(III) hybrids are dominant at pH 7.4 and 8.4 in the absence of IHP. The kЈ CO values for this phase are roughly independent of pH. In the absence of organic phosphates, kЈ CO for the ␤(Fe) containing hybrid is slightly greater than that for the ␣(Fe) hybrid. Addition of IHP increases the fraction of the slow phase and decreases the values of kЈ CO for both the fast and slow phases. However, the changes in the fast rate constants are very small compared with marked increases in the fraction of slow phase produced by decreasing pH and the presence of IHP.
The Cr(III)/Fe(II) hybrids bind oxygen almost non-cooperatively (n max ϭ 1.0 -1.1) with very high affinities. The P 50 values for these proteins at pH 7.4 and 8.4 in the absence of IHP are comparable to those of isolated ␣ or ␤ chains (24). Under these conditions, the deoxygenated Cr(III) hybrids appear to stay in an R state even in the absence of bound ligands. Consequently, we assigned the fast rate constants for the ␣ 2 (Fe)␤ 2 (Cr) hybrid at pH 7.4 or 8.4 to that for CO binding to an ␣(Fe) subunit within an R state-like conformation of tetrameric Hb, and the fast rate constants for ␣ 2 (Cr)␤ 2 (Fe) to those for CO binding to a ␤(Fe) subunit within this high affinity conformational state. These association rate constants, kЈ ␣CO ϭ 6 M Ϫ1 s Ϫ1 and kЈ ␤CO ϭ 7.4 M Ϫ1 s Ϫ1 , are either equal or very close to those reported previously for R state forms of Hb A 0 (12,21,50). We used low heme concentrations in our experiments with the Cr(III) hybrids. As a result, an appreciable fraction of dimers was present. However, dimerization does not appear to affect the measured value of kЈ CO for R state Hb because under most conditions the kinetic parameters for the last step in ligand binding to tetrameric Hb and those for binding to dimeric Hb are almost identical (12,13,52).
The time courses for CO binding to the Ni(II) and Mg(II) hybrids are very similar to each other and show much less dependence on pH and IHP. The association rate constants for CO binding to the ␣ 2 (Ni)␤ 2 (Fe) and ␣ 2 (Mg)␤ 2 (Fe) hybrids (kЈ CO ϭ 0.05 to 0.07 M Ϫ1 s Ϫ1 ) are consistently 2-fold smaller than those for the corresponding ␣(Fe) containing hybrid Hbs (kЈ CO ϭ 0.12 to 0.16 M Ϫ1 s Ϫ1 ; Table I, part B, pH 6.5, 7.4 Ϯ IHP). Our values for the Ni(II) and Mg(II) hybrids agree well with those reported previously for T state forms of cyanomet valency and other metal hybrid Hbs. In the presence of IHP, ␣(Fe) subunits in cyano-Fe(III)/Fe(II), Co(II)/Fe(II), and Mn(II)/Fe(II) hybrids show larger association rate constants for CO binding than those for ␤(Fe) subunits (17)(18)(19)(20). Shibayama et al. (22) obtained a rate constant of 0.15 M Ϫ1 s Ϫ1 for bimolecular CO rebinding to both the ␣(Fe) and ␤(Fe) containing Ni(II) hybrids after flash photolysis in 0. 1 M phosphate at pH 6.6. Their higher value for the ␤(Fe) kЈ CO may be due to incomplete conversion of the hybrid to the T state during the time between

FIG. 1. Normalized time courses for CO binding to Cr(III)/ Fe(II) and Ni(II)/Fe(II) hybrid hemoglobins at pH 7.4, 25°C.
Reactions were carried out in a stopped-flow, rapid mixing apparatus, and absorbance changes were measured at 436 nm. The concentrations after mixing were 5 M Hb on a per metal basis and 16.7 M CO. The solid lines represent fits to a single or two exponential expression. A, time courses for CO binding to ␣ 2 (Cr)␤ 2 (Fe) in the absence and presence of 100 M IHP. B, time courses for CO binding to ␣ 2 (Fe)␤ 2 (Ni) and ␣ 2 (Ni)␤ 2 (Fe) hybrids in the absence of IHP. photolysis and ligand rebinding or to the effects of inorganic phosphate.
Our T state kЈ CO values for ␤(Fe) subunits based on results for Ni(II) and Mg(II) hybrids are ϳ2-fold smaller than those based on studies with mutant and native human Hbs. Mathews et al. (49) reported that kЈ CO ϭ 0.12 Ϯ 0.03 and 0.18 Ϯ 0.05 M Ϫ1 s Ϫ1 for T state ␣(Fe) and ␤(Fe) subunits, respectively. These assignments were based on comparisons between Hbs containing one mutated and one native subunit. Perrella et al. (14) reported similar values, kЈ ␣CO ϭ 0.10 Ϯ 0.04 M Ϫ1 s Ϫ1 and kЈ ␤CO ϭ 0.15 Ϯ 0.02 M Ϫ1 s Ϫ1 , based on detailed analysis of the overall CO-binding reaction. In their work, cryogenic isoelectric focusing was used to separate the partially liganded tetrameric intermediates. Both sets of authors concluded that the ␣(Fe) and ␤(Fe) subunits have equivalent rates of CO binding within the T state since the errors in their individual subunit rate constants were greater than or equal to the differences between them.
CO Dissociation Constants-The time courses for NO replacement of bound CO were monophasic for all of the hybrid Hbs examined, regardless of pH and the presence of IHP. CO dissociation rate constants (k CO ) for the Cr(III), Mn(III), Ni(II), and Mg(II) hybrids and native Hb A 0 are listed in Table II. The k CO values for the Mn(III) and Cr(III) hybrids are similar to that for fully liganded Hb A 0 , depend little on reaction conditions, and can be used to assign rate constants for CO dissociation from ␣(Fe) and ␤(Fe) subunits within R quaternary states: k ␣CO ϭ 0.012 Ϯ 0.001 and k ␤CO ϭ 0.007 Ϯ 0.001 s Ϫ1 (Table V).
In contrast, the k CO values for the Ni(II) and Mg(II) hybrids are affected greatly by pH and the addition of inositol hexaphosphate. The presence of two bound CO molecules shifts these hybrids from T toward R quaternary conformations in the absence of organic phosphates, even at pH 6.5. Shibayama et al. (35) have shown that inositol hexaphosphate can shift the CO-liganded Ni(II)/Fe(II) hybrid to the T state at pH 6.5. As shown in Table II, part B, addition of IHP causes dramatic 10 -20-fold increases in the CO dissociation rate constants for both the Ni(II) and Mg(II) hybrids. The k CO values for the ␣(Fe) and ␤(Fe) subunit within these hybrids have been assigned as the rate constants for CO dissociation from T state Hb, i.e. k ␣CO ϭ 0.21 s Ϫ1 and k ␤CO ϭ 0.19 s Ϫ1 (Table VI). Sharma et al. (53,54) and Simolo et al. (55) showed that the rate constant for CO dissociation from native Hb 4 (CO) is in the range 0.1 to 0.2 s Ϫ1 . Samaja et al. (56) reported similar rate constants for the dissociation of CO from mono-liganded Hb A 0 and assigned tentative values for the individual subunits, 0.16 -0.22 s Ϫ1 for ␣(Fe) subunits and 0.10 -0.15 s Ϫ1 for ␤(Fe) subunits.
Photochemical Spectral Changes Associated with Cr(III) and Mg(II) Protoporphyrins-Flash photolysis time courses for the bimolecular O 2 rebinding to all four metal hybrid Hbs were recorded at several different ligand concentrations. In addition to the absorbance changes associated with Fe-ligand bond formation, an "extra" rapid phase was observed for the Cr(III) and Mg(II) hybrids (i.e. Fig. 2 inset and Fig. 6). Since both these hybrids are photosensitive, the extra fast phases probably originate from excited states of the Cr(III) and Mg(II) porphyrins. In the case of the Mg(II) hybrids, the extra absorbance transition appears in the initial microsecond region and overlaps with the fast or R state phase for bimolecular O 2 rebinding. The wavelength dependence of this absorbance change is very similar to the difference spectrum between the triplet state and the ground state of Mg(II)PPIX (57). Both difference spectra show an isosbestic point at 432 Ϯ 1 nm and a broad peak around 475 nm. This correspondence suggests strongly that the extra fast phase for the Mg(II) hybrids is due to decay of the photoexcited triplet state of Mg(II)PPIX and not ligand binding. In the case of the Cr(III) hybrid, there is an initial absorbance change that decays in ϳ2.5 s, shows no dependence on [O 2 ], and is too rapid to interfere with measurements of ligand rebinding. Shibayama et al. (22) observed similar spectral changes associated with Ni(II)PPIX during and after photolysis of deoxygenated Ni(II)/Fe(II) hybrids in the 100-ps time region. In the   (Fig. 4). The y intercepts in these plots are close to zero with respect to the experimental values on the y axis, which range from ϳ10,000 to 100,000 s Ϫ1 . Under these conditions, kЈ O 2 for the ␤(Fe) subunits is roughly 2-fold greater than that for the ␣(Fe) subunits: kЈ ␤O 2 Ϸ80 M Ϫ1 s Ϫ1 versus kЈ ␣O 2 Ϸ40 M Ϫ1 s Ϫ1 , for both the Cr(III) and Mn(III) hybrids (Table III,  part A). These values are in good agreement with previous measurements of R state O 2 association rate constants based on mutant and chemically modified Hbs (12,13,50,52,58).
Addition of IHP and lowering the pH cause complex changes in the time course for O 2 rebinding to the Cr(III) and Mn(III) hybrids ( Fig. 3 and Table III, part A). Both conditions promote formation of low affinity conformations. As result, slow ligand association phases are observed and become dominant at pH 6.5 in presence of inositol hexaphosphate. The observed rate constants for these slow phases are similar to those observed for O 2 binding to Ni(II) and Mg(II) hybrids in the absence of organic phosphates (see Ref. 22; Table III, part B).
Rate constants for O 2 dissociation from the high affinity forms of Cr(III) and Mn(III) hybrids were obtained by analyzing time courses for the displacement of bound oxygen by carbon monoxide using Equation 4. The resultant values of k O 2 are given in Table IV, part A. At pH 7.4 and 8.4, these hybrids remain completely in the high affinity quaternary conformation, and the rate parameters can be assigned unambiguously to the R state. There is good agreement between the Cr(III) and Mn(III) hybrids, with k ␣O 2 Ϸ16 s Ϫ1 and k ␤O 2 Ϸ32 s Ϫ1 for both types of proteins. These values are consistent with the low values of the y intercept in plots of k obs versus [O 2 ] obtained from the flash photolysis experiments (Fig. 4). They also agree with previously reported values of k O 2 for the R state subunits (7,12,13,50,52,58) Rates  Table III, part B. Similar behavior was observed for the two Mg(II) hybrids, but in this case the fast phase for O 2 rebinding to the Fe(II) subunits is obscured by the spectral changes associated with photoexcited Mg(II)PPIX (Fig. 6). Plots of k obs for the slow phases of this protein versus [O 2 ] are also linear (Fig. 7), and the bimolecular rate constants in the absence and presence of IHP at pH 7.4 are given in Table III,  part B. With one exception, the fraction of slow O 2 rebinding does not show much dependence on ligand concentration for the Ni(II) and Mg(II) hybrids. In the case of ␣ 2 (FeO 2 )␤ 2 (Mg) the magnitude of the slow phase decreased significantly as [O 2 ] was increased in the absence of IHP at pH 7.4. This result suggests that a significant fraction of the initial ␣ 2 (FeO 2 )␤ 2 (Mg) complex is in a high affinity, R state-like conformation and that the rate of the R to T transition after photolysis is on the same order as that due to ligand recombi-    Table IV (Fig. 7). One mm pathlength cells were used, and the time courses were followed at 436 nm. ϩIHP indicates that 100 M inositol hexaphosphate was added to the protein solution. When two phases were observed, two rates are reported, and the percentage of the fast and slow absorbance changes are shown in parentheses (see Figs. [3][4][5]. Rate constants for O 2 dissociation from the Ni(II) and Mg(II) hybrids were estimated from the y intercepts of plots of k obs for the slow phases observed after flash photolysis (see Fig. 7). The resultant values are listed in Table IV, part B. In the absence of IHP, k O 2 is estimated to be roughly 400 s Ϫ1 for ␣(Fe) subunits and 650 s Ϫ1 for ␤(Fe) subunits. Addition of IHP increases the dissociation rate constant for both subunits, but the largest effect is on k O 2 for ␣(Fe) subunits, which increases to a value approaching 5,000 s Ϫ1 (Fig. 7B; Table IV, part B). IHP also selectively increases the association rate constants for O 2 binding to T state ␣(Fe) subunits as shown in Fig. 7 and Table IV, part B. When IHP is added to ␣ 2 (Fe)␤ 2 (Ni), O 2 rebinding becomes monophasic and shows an observed rate that is significantly greater than that observed for the slow phase in the absence of the organic phosphate. This marked increase is  observed to be due to ϳ2 and ϳ10-fold increases in kЈ O 2 and k O 2 , respectively (see Equation 3).

Rate and Equilibrium Constants for Ligand
Binding to R State Hemoglobin Subunits-Summaries of our new and previous assignments of rate and equilibrium constants for CO and O 2 binding to the individual ␣(Fe) and ␤(Fe) subunits within R or T state-like Hb conformations are given in Tables V-VIII. When corrected for differences in temperatures, the largest discrepancies for a given subunit and quaternary structure are Յ2-fold. The assignment of rate constants to the individual ␣(Fe) and ␤(Fe) subunits is unambiguous in the case of the Cr(III), Mn(III), Ni(II), and Mg(II) hybrid Hbs since the partner subunit is incapable of binding ligands. The assignments for mutant and chemically modified Hbs are based on the assumption that only the rate constants of the modified subunit are affected and often require detailed analyses and comparisons between several modified proteins to obtain rate constants for the native subunits (13). In our view, the agreement among the values reported in Tables V-VIII is remarkably good. We have used the Cr(III) and Mn(III) hybrids at pH 7.4 and 8.4 in the absence of phosphates as models for R state Hb. The assignment of rate parameters to these proteins is straightforward since at neutral or high pH in the absence of IHP the time courses are predominantly one phase (Figs. 1A, 2, and 3; Tables I, part A, to IV, part A). The ␣(Fe) and ␤(Fe) subunits in R state Hb bind CO with roughly equal association rate constants, kЈ ␣CO Ϸ kЈ ␤CO Ϸ7 M Ϫ1 s Ϫ1 , and only slightly different dissociation rate constants, k ␣CO ϭ 0.012 versus k ␤CO ϭ 0.007 s Ϫ1 . In the case of O 2 binding, the ␤(Fe) subunits exhibit 2-fold higher association and dissociation rate constants than those for the ␣(Fe) subunits as follows: kЈ ␤O 2 ϭ 76 M Ϫ1 s Ϫ1 versus kЈ ␣O 2 ϭ 36 M Ϫ1 s Ϫ1 and k ␤O 2 ϭ 32 s Ϫ1 versus k ␣O 2 ϭ 16 s Ϫ1 . However, the association equilibrium constants for O 2 binding to R state ␣(Fe) and ␤(Fe) subunits are identical: at 25°C in the absence of phosphates.
Rate Parameters for T State Hemoglobin Subunits-The Ni(II) and Mg(II) hybrids serve as models for T state Hb at pH 7.4 in the presence and absence of IHP. Assignment of association rate constants for CO binding is straightforward and unambiguous in stopped-flow experiments. When the deoxygenated forms of the Ni(II) and Mg(II) hybrids are mixed with CO, simple monophasic time courses are observed and can be assigned to reactions with T state subunits (Fig. 1B). These data show that T state ␣(Fe) subunits react about 2 times more rapidly with carbon monoxide than T state ␤(Fe) subunits, kЈ ␣CO ϭ 0.16 M Ϫ1 s Ϫ1 versus kЈ ␤CO ϭ 0.07 M Ϫ1 s Ϫ1 , and that this difference persists in the presence of IHP. These values do differ significantly from previous ones derived from studies with mutant and native Hbs. Experiments with the latter proteins suggested either equal rate constants for CO binding or slightly greater values for T state ␤(Fe) subunits (13,14,49). In our view, the assignments based on the metal hybrids are the least ambiguous since the differences between the ferrous subunits can be seen directly in the observed time courses (Fig. 1B).
In contrast, it proved difficult to assign rate constants for CO dissociation from T state subunits. The observed rate constant is a weighted sum of the R and T rates since these conformations interconvert more rapidly that CO dissociation. In the absence of IHP, only the ␣ 2 (Fe)␤ 2 (Mg) hybrid at pH 6.5 showed a dissociation constant, ϳ0.1 s Ϫ1 , high enough to be due to a predominance of T state protein (Table II, part B). However, in the presence of IHP at pH 6.5, the observed rates for all four Ni(II) and Mg(II) hybrids do appear to be due exclusively to T state conformations. Under these conditions, the ␣(Fe) and ␤(Fe) subunits show roughly equal rates of CO dissociation, ϳ0.2 s Ϫ1 (Table VI).
The assignment of T state O 2 binding parameters was made easier by previous analyses of oxygen equilibrium curves for both the Ni(II) and Mg(II) hybrids (35,36). 2 Association rate constants for the T state subunits were taken from analyses of the concentration dependence of the slow phases recorded after laser photolysis of the oxygenated forms of the Ni(II) and Mg(II) hybrids.  Fig. 7). In our view, combining the equilibrium and kinetic measurements provides a more accurate estimate of the T state dissociation rate constants since the y intercepts are more poorly defined than either K O 2 or kЈ O 2 . This analysis suggests that the T state ␣(Fe) and ␤(Fe) subunits have roughly equal rate and equilibrium constants for O 2 binding in the absence of IHP at pH 7.4: Shibayama et al. (22) came to the same conclusions. Their assignments were based on kinetic data for Ni(II) hybrids measured in 0.1 M phosphate, pH 6.6, 20°C. The ␣(Fe)and ␤(Fe)-containing hybrids showed very similar association and dissociation rate constants with kЈ O 2 Ϸ6 M Ϫ1 and k O 2 Ϸ2000 s Ϫ1 . The higher dissociation rate constant is probably due to the presence of inorganic phosphate and the lower pH value.  (Table II, part A). The equilibrium constants for CO binding to the subunits within R state hemoglobin were calculated from the ratio of the rate constants, K RCO ϭ kЈ RCO /k RCO . The parameters based on the metal hybrids are compared with those obtained from analyzing mutant hybrids (50) and native human hemoglobin using p-hydroxybenzoate modification of ␤Cys-93 to enhance the differences between the subunits (12 (Table III, part A). The k RO2 values were computed from the average of those observed for the Fe(II)/Cr(III) and Fe(II)/Mn(III) hybrids at pH 6.5, 7.4, and 8.4 (Table IV, part A). The equilibrium constants for O 2 binding to the subunits within R state hemoglobin were calculated from the ratio of the rate constants, K RO2 ϭ kЈ RO2 /k RO2 . The parameters based on the metal hybrids are compared to those obtained from analyzing mutant hybrids (50) and native human hemoglobin using p-hydroxybenzoate modification of ␤Cys93 to enhance the differences between the subunits (12). binding to the individual subunits are very similar to each other in the low affinity and high affinity hybrids, both in the absence and presence of inositol hexaphosphate. Thus, Perutz's original mechanism that proposed an ordered addition of ligands is not correct. The equilibrium functional equivalence is still surprising since the structural mechanisms that cause the 500 -1000-fold decrease in affinity in going from the R to T state are still thought to be quite different for the two subunits. Based on recent sitedirected mutagenesis studies, steric hindrance by distal residues does appear to play a key role in regulating oxygen affinity in ␤ subunits, whereas proximal constraints on iron reactivity are thought to be more important in ␣ subunits (1, 49, 60 -63).
The absence of chain differences does enhance the physiological activity of Hb by maximizing the Hill coefficient or n value for the native tetramer. The extent of O 2 transport is directly related to the slope of the oxygen equilibrium curve as follows: the higher the n value, the greater the amount of O 2 transported per iron atom. Large intrinsic differences between the O 2 affinities of the ␣ and ␤ subunits in both the high and low affinity quaternary states would decrease the extent of cooperativity, causing a marked reduction in transport. Instead, the subunits in Hb A 0 have evolved to have similar affinities giving rise to high n values and efficient O 2 transport.  (Table III, part B). The equilibrium constants for O 2 binding to the subunits within T state hemoglobin, K TO2 , were computed as the average of the first constant (K 1 ) determined in oxygen equilibrium curve measurements for Fe(II)/Ni(II) and Fe(II)/Mg(II) hybrids at pH 7.4 in the presence and absence of IHP (35,36). 2 The k TO2 values were computed as kЈ TO2 /K TO2 . The values in parentheses for k TO2 are the average of the values listed in Table IV, part B which were obtained from the y intercepts in Fig. 7. The values in parentheses for K TO2 were computed from the rate constants in Tables III, part B and IV,