Sickle Hemoglobin Polymer Stability Probed by Triple and Quadruple Mutant Hybrids*

As part of an effort to understand the interactions in HbS polymerization, we have produced and studied a recombinant triple mutant, D6A( (cid:1) )/D75Y( (cid:1) )/E121R( (cid:2) ), and a quadruple mutant comprising the preceding mutation plus the natural genetic mutation of sickle hemoglobin, E6V( (cid:2) ). These recombinant hemoglobins expressed in yeast were extensively characterized, and their structure and oxygen binding cooperativity were found to be normal. Their tetramer-dimer dissociation constants were within a factor of 2 of HbA and HbS. Polymerization of these mutants mixed with HbS was investigated by a micromethod based on volume exclusion by dextran. The elevated solubility of mixtures of HbS with HbA and HbF in dextran could be accurately predicted without any variable parameters. Relative to HbS, the copolymerization probability of the quadruple mutant/HbS hybrid was found to be 6.2, and the copolymerization probability for the triple mutant/HbS hybrid was 0.52.

Sickle cell disease is due to a single DNA base change encoding for the amino acid at the 6th position of the two ␤-globin chains of the hemoglobin tetramer. This surface mutation of glutamic acid to valine does not affect the oxygen carrying ability of hemoglobin. However, either one of the valines resulting from this mutation can dock in a strong hydrophobic pocket in the region of Phe-85/Leu-88(␤) of an adjacent tetramer. Additional interactions from many other contact sites lead to aggregation of deoxy-Hb tetramers and to eventual sickling of the red cells in the circulation. The aggregates responsible for this pathology are long 14-stranded helical polymers whose structure has been deduced from electron microscopy coupled with model building. These models are based on the linear double strands whose x-ray structure has been determined (1)(2)(3) and that have been shown to be constituents of the 14-stranded polymers (4,5).
Interactions of molecules within the 14-stranded structure are complex in many ways. First of all, the existence of two ␤ and two ␣ subunits means that there are two possible regions of interaction for each ␣ or ␤ amino acid when polymers form. Such differences are known as cis-trans differences and were first proposed to explain the unusual behavior of HbC-Harlem (6). Second, because there are so many different interactions possible within a 14-stranded polymer it is also possible that the interactions are different for the same amino acid in different strands. A proposal utilizing both of the above features has recently been put forward as a way to explain quantitatively the polymerization of HbS/HbA mixtures by having four molecules use the second ␤6 in a favorable contact (7). Third, even when an interaction is identified, the effect of a given amino acid on polymer stability may depend not only on its identity but also on the local environment. For example, it has recently been proposed that the mutation of ␤88 Leu 3 Ala increases solubility because of the tightness of fit of the mutation rather than the intrinsic hydrophobicity of the group (8). Finally, interactions at separate sites may not provide additive stability, even when the sites are physically well separated, as has been seen in a triple mutant involving the ␤6 sickle mutation plus ␤88 Leu 3 Ala and ␤95 Lys 3 Ile (9). In short, the interactions within the fiber are sufficiently subtle that it is of paramount importance to learn how different sites are able to contribute to polymer stability to have any hope of a rational approach to designing drugs for the treatment of this disease.
In disentangling such issues many strategies are possible, and no single approach is assured of success. In addition to pursuing the known contact sites within the double strand, another fruitful avenue is to expand upon previously known mutants to develop further the detailed knowledge of regions in which some understanding already exists.
Recently the systematic study of a series of recombinant sickle hemoglobin tetramers with substitution at one to three sites in addition to ␤6 has been reported (10). These three mutations (E121R(␤), D75Y(␣), and D6A(␣)) were all chosen because they are known to enhance polymerization (10 -12), and yet the locations of the mutations were well separated to attempt to avoid concerted interaction among the sites.
Given the enhanced polymer stability brought about by the three mutation sites (E121R(␤)/D75Y(␣)/D6A(␣)), the immediate question was whether the enhancement could overcome the resistance to assembly posed by the presence of Glu at ␤6. The study of these mutants is all the more interesting because the structural basis of their enhancement is somewhat obscure, using presently accepted models for the HbS polymer (13,14), despite the fact that some of the mutants have been previously studied.
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To probe gelation strength in these experiments, solubility was measured in a newly developed assay that replaces an amount of scarce mutant Hb with dextran, thereby crowding the solution and promoting assembly using only small quantities of the hemoglobin mutant (15). With 12 g/dl dextran, HbS has a solubility of 35.3 mg/ml, the mutant HbS/E121R(␤) gels at 24.3 mg/ml, the mutant HbS/E121R(␤)/D75Y(␣) gels at 11.8 mg/ml, and the quadruple mutant HbS/E121R(␤)/D75Y(␣)/ D6A(␣) gels at a mere 7.0 mg/ml. This enhancement of polymerization is consonant with the behavior of these sites in the SAD mouse construct in which the combination of HbS, Hb-Antilles (E23I(␤)), and HbD Punjab (E121Q(␤)) are expressed to produce an important research tool, i.e. a sickling mouse model (16). In previous studies it was found that the solubility of the above quadruple mutant was quite close to the solubility of HbSAD, which is 6.1 mg/ml.
A fruitful approach in understanding the behavior of natural mutants has been to study their polymerization when mixed with HbS. This permits their hybridization by the spontaneous dissociation of the hemoglobin tetramer into its constituent dimers (4). This approach is applicable here since, as we show, the tetramer-dimer dissociation constants of the recombinant mutants are close to that of HbS. Particularly when the hybrids can be compared with the simultaneous presence of all the sites, the important cis-trans issues can be explored. In this work we report the polymerization of a triple mutant (␣6, ␣75, and ␤121) in hybrids with HbS. We contrast this with the polymerization of a quadruple mutant (the triple mutant plus the ␤6 mutation of HbS) mixed with HbS. By determining solubilities at a variety of fractional mixtures, the adequacy of the description of the mixtures can be tested, and the relative probability of copolymerization can be determined. The latter is directly related to the free energy difference of the hybrid relative to HbS.

EXPERIMENTAL PROCEDURES
Reagents and Plasmids-The restriction endonucleases, alkaline phosphate, and DNA ligase were from Roche Molecular Biochemicals or New England Biolabs. The DNA sequencing kit and the PCR reagent kit were obtained from United States Biochemical Corp. The Geneclean kit was from BIO 101, Inc. The plasmid kit was from Qiagen. The 35 S-labeled dATP was from Amersham Biosciences. Dextran and DPG 1 were purchased from Sigma. The nucleotides used to make the mutations were synthesized by the protein sequencing facility at Rockefeller University. The construction of pGS189 and pGS389 plasmids has been described elsewhere (30,31). All other reagents were of the highest purity available.
Yeast Expression System and Purification of Hemoglobin Mutants-Recombinant pGS389 D6A(␣)/D75Y(␣)/E121R(␤) was transformed into Saccharomyces cerevisiae GSY112 cir o strain using the lithium acetate method described previously (17). The transformants were selected using a complete medium first without uracil and then without uracil and leucine. To express the D6A(␣)/D75Y(␣)/E121R(␤) triple mutant, the yeast strain was grown in 12 liters of yeast extract plus peptone medium in a New Brunswick Fermentor Bioflo IV for 3 days using ethanol as a carbon source. The promoter controlling the transcription of the globin genes was induced for 20 h by adding galactose (Pfanstiehl or United States Biochemical Corp., containing Ͻ0.1% glucose) to a final concentration of 3%. The collection and breakage of the cells after bubbling with CO gas and purification have been described previously (17).
Analytical Methods-SDS-PAGE of the recombinant mutants was performed on the Phast System from Amersham Biosciences. The protein bands were stained with Coomassie Brilliant Blue R-250. Isoelectric focusing was performed on the pH 7-10 Hb-Resolve system from Isolab. The ␣and ␤-globin chains from recombinant hemoglobins were separated by reverse phase HPLC on a Vydac C 4 column with a gradient of 20 -60% acetonitrile containing 0.1% trifluoroacetic acid. Amino acid analysis of globin chains isolated by this procedure was performed on a Beckman 6300 instrument with a System Gold data handling system. The spectrum of each mutant was recorded on a Shimadzu 1601 UV-visible spectrophotometer.
Mass Spectrometry Analysis-Electrospray mass spectrometric analysis of the purified recombinant mutant Hb tetramers was performed with a Finnigan-MAT TSQ-700 triple quadruple mass spectrometer as described previously (10).
Functional Studies-The oxygen binding curves of the hemoglobins were determined at 37°C on a modified Hem-O-Scan instrument (Aminco). Before the measurements, the purified Hb sample was dialyzed in 50 mM bis-Tris, pH 7. 5, and converted to the oxy form. These samples were concentrated using CentriPrep, Centricon, and MicroCon ultrafiltration devices (10,000 molecular weight cut-off, Amicon) to a final concentration of 0.6 mM. To measure the effect of anions on the oxygen affinity of these hemoglobin mutants, an aliquot of a solution of 5.6 mM DPG or 2.5 M NaCl in 50 mM bis-Tris, pH 7.5, was added to the Hb sample to achieve the desired final concentration.
Measurement of Gelation Concentration (C sat )-The gelation concentration of the hemoglobin mutants or hemoglobin mixtures was determined by the "Dextran-Csat" micromethod as described previously (15). The concentrated hemoglobin sample in the oxy form in 50 mM potassium phosphate buffer, pH 7.5, was mixed with dextran at a final concentration of 120 mg/ml. Mineral oil was layered on top, and fresh sodium dithionite solution (50 mM final concentration) was added anaerobically below the Hb/dextran mixture using a gas-tight syringe. After stirring and incubation for 30 min in a 37°C water bath, the resulting gel under the oil layer was disrupted with a narrow wire loop, and the tubes were centrifuged in a microcentrifuge for 30 min. The clear supernatant was carefully separated from the aggregated Hb, and the hemoglobin concentration was measured spectrophotometrically and verified by amino acid analysis after acid hydrolysis of an aliquot.
Copolymerization Theory-The analysis uses a small modification of the extensively used copolymerization theory (5,18). The solubility observed, c s , is related to the solubility of pure HbS, denoted c s o . Because of reproportionation among the subunits, if the additive species is a fraction X of total molecules, then, (1 Ϫ X) 2 are pure HbS molecules, 2X(1 Ϫ X) are hybrids, and X 2 are pure tetramers of the additive species. These fractions are denoted X 1 , X 2 , and X 3 , respectively. Each of these species copolymerizes with a probability denoted e i , which is related to the free energy difference between having HbS polymerized and the ith species polymerized. By this definition, copolymerization probability e 2 is identically 1 for the case of hypothetical "hybrids" of HbS with HbS, i.e. HbS mixed with itself. Then using Equations 22-25 of Eaton and Hofrichter (5) it is straightforward to show that if c o is the initial concentration, c p is the concentration of the pure polymer, v is the specific volume of the monomer, c x is the concentration of the dextran, and v x is the specific volume of the dextran, then in which ⌫ is an activity coefficient ratio given by where ␥ s is the activity coefficient of the monomers at solubility, and ␥ s o is the activity coefficient of monomers at c s o . The expression for ⌫ has been modified from that used in the footnote to Table III.2 of Eaton and Hofrichter (5) to include the volume exclusion due to the dextran in which the solubility is measured. The volume of the dextran molecules has been taken here as 0.664 ml/mg as measured directly by Bookchin et al. (15). This is almost equal to the Hb molar specific volume v.
Activity coefficients are calculated based on scaled particle theory, described by Minton (19), using the volumes described above and assuming spherical particles. Because the first equation cannot be simply inverted to give an expression of c s , it is solved numerically.
Circular Dichroism Measurements-The CD spectra of HbA and recombinant mutants were measured on a Jasco J-715 spectropolarimeter at 25°C as described previously (10).
Measurement of Tetramer-Dimer Dissociations-This measurement was performed on the CO-liganded recombinant hemoglobins on a Superose-12:HR 10/30 column using an Amersham Biosciences FPLC system (20). The absorbance of the eluent was measured at 405 nm with the Amersham Biosciences on-line mercury lamp detection system with a 5-mm flow cell. For the double mutant E6V(␤)/E121R(␤), K d was calculated as described previously using the parameters (V d and V t ) that were determined from the standard dimeric Hb Rothschild and tetrameric cross-linked Hb (20). For recombinant mutants , the elution volume (V) at low or high concentrations was not within the standards presumably due to the interaction of their strong positive charges with Superose-12 column. Thus, their K d values were calculated by curve fitting the experimental volume data allowing V d /V t to vary (10).

Purification and Characterization of D6A(␣)/D75Y(␣)/ E121R(␤)-The
recombinant mutant D6A(␣)/D75Y(␣)/ E121R(␤) lacking the sickle mutation was expressed in yeast and purified by CM-cellulose 52 chromatography (9,10,17,21). Its purity was verified by chromatography on an Amersham Biosciences FPLC Mono S column. It showed one band upon isoelectric focusing in the pH 6 -8 Hb-Resolve system from Isolab, and its migration was consistent with the loss of four negative charges per ␣␤ subunit compared with HbA (Asp 3 Ala and Asp 3 Tyr) and a substitution equivalent to the loss of two negative charges (Glu 3 Arg) (Fig. 1). By SDS-polyacrylamide gel electrophoresis, it showed a single band at 16 kDa in the same position as the denatured subunits of HbA and HbS.
HPLC Analysis and Amino Acid Analysis-The purified recombinant HbS mutants were analyzed by reverse phase HPLC using a denaturing solvent to separate the globin chains (Fig. 2). The ␤-chain containing a substitution of Arg for Glu at ␤121 eluted at 30.5 min ahead of the normal ␤-chain from HbA (35.0 min). The elution position of the ␣-chain from D6A(␣)/ D75Y(␣)/E121R(␤) coincided with the ␣-chain from natural HbA (43.2 and 42.7 min, respectively), indicating that the replacement of the hydrophilic residue Asp at the ␣-chain by nonpolar amino acids Ala and Tyr does not alter their chromatographic behavior significantly on the reverse phase C 4 column. Amino acid analysis of each isolated subunit gave the expected composition (Table I). For the mutated ␤-chain containing Glu-121(␤) 3 Arg and mutated ␣-chain containing Asp-6(␣) 3 Ala and Asp-75(␣) 3 Tyr, the values for Arg, Glu, Asp, and Ala were in reasonable accord with theoretical values. The values for the other amino acids were also in good agreement with the known composition of this mutant.
Mass Spectrometry-Mass spectrometric analysis of the mutant D6A(␣)/D75Y(␣)/E121R(␤) by the electrospray ionization mass spectrometry method gave the expected mass for both ␣ and ␤ subunits. The molecular mass of the ␤-chain containing    pared with that of HbA (Fig. 3). In the far ultraviolet region from 200 to 250 nm, comparison of all five spectra indicated that their CD profiles were practically identical showing that no change occurred in helical content and showing that there were no adverse effects of the mutations on their secondary structures. In the Soret region, the maximum ellipticity at 414 nm was identical to that of HbA. The minor differences at 412 nm observed between the individual Hbs were no greater than the differences between the natural HbA and HbS. Thus, the overall features of these CD curves are identical to those of native HbA, indicating no adverse effects on the heme pocket by the amino acid replacements.
Tetramer-Dimer Dissociations-Since these recombinant hemoglobin mutants have quite different surface charges than HbA and HbS, their tetramer-dimer dissociation was investigated. The two other previously reported recombinant HbS hemoglobins, E6V(␤)/E121R(␤) and D75Y(␣)/E6V(␤)/E121R(␤), were also included for comparison. For the double mutant E6V(␤)/ E121R(␤), K d was calculated using the GraFit program as described previously (20) using the parameters (V d and V t ) that were determined from the standard dimeric Hb Rothschild and tetrameric cross-linked Hb (Fig. 4A). The K d values of the double and triple mutants were calculated by curve fitting the experimental volume data, allowing V d /V t to vary (Fig. 4, B-D) (20).
As shown in Table II, the tetramer-dimer dissociation constants for the liganded recombinants were in the range of 0.3-1.0 m, which are the same within experimental error for native HbS (K d ϭ 0.4 M) (Table II). These results show that the amino acid replacements in all these recombinants have no significant effect on the dissociation behaviors at the ␣1␤2 interfaces in the liganded hemoglobins.
Functional Studies-The oxygen binding properties of the mutant D6A(␣)/D75Y(␣)/E121R(␤) were determined at a hemoglobin concentration of 0.6 mM (Table III) Analysis of Polymerization Data-The mixtures of HbS with HbF and HbA provide valuable control experiments for analysis using the dextran assay as employed here. HbF does not polymerize of its own (i.e. e 3 ϭ 0) nor does it copolymerize (i.e. e 2 ϭ 0). This allows the solubility data for the HbS/HbF mixtures to be compared with a prediction from the theory since there are no unknown parameters (5). Fig. 5 shows the comparison of the theory with the solubility data. The HbS/HbF FIG. 4. Percent tetramer as a function of total hemoglobin concentrations for four different hemoglobins. Measurements were make on a Superose-12:HR 10/30 column using an Amersham Biosciences FPLC system. The insets show log-log plots of the data in which representation the curve is linear and from which K d may be determined. For all cases the sample volume injected was 100 l, and the flow rate of the 150 mM Tris acetate, pH 7.5, was 0.4 ml/min. data is reasonably well described. For describing HbA/HbS mixtures, there is also no need to vary parameters. Previous studies have established that HbA has little or no polymerization itself (e 3 ϳ 0), and recent work has proposed on theoretical grounds that e 2 ϭ 0.357 for HbA/HbS mixtures (7), which agrees well with the extensive body of copolymerization data on that mixture system (5). The solubility of HbA/HbS mixtures can thus be predicted as shown in Fig. 5, and the predictions are clearly in excellent agreement with the data. The agreement of the HbF/HbS and HbA/HbS data with the predictions made without variable parameters confirms the validity of the description developed above and its application to the dextran assay, including the use of dextran-specific volumes. Given the consistency of the data and the reasonableness of the assumptions, it is possible to proceed with confidence to the mutant hybrids to determine the copolymerization probability, e 2 for the triple and quadruple mutants. This will determine the free energy changes due to the mutation sites.
Of the two mutants constructed, the triple mutant lacks the ␤6 Glu 3 Val mutation and does not show polymerization (e 3 3 0). Thus the data can be fit varying only e 2 , which is found to be 0.52. As is shown in Fig. 5, the fit to the data is excellent using this copolymerization probability.
For the quadruple mutant, the analysis is now slightly changed because not only does the mutant polymerize by itself, it polymerizes more readily than HbS. From studies on the pure quadruple mutant c s ϭ 7 mg/ml using the dextran assay in which the solubility for HbS is 35.3 mg/ml (10). This gives a polymerization probability of e 3 ϭ 6.01. That is, relative to the polymerization of HbS, this mutant will polymerize at 6 times lower activity. Setting e 3 from the experiments on the pure mutant allows a single parameter to be varied to determine e 2 , the copolymerization of the hybrid HbS and the quadruple mutant. Surprisingly the copolymerization of the mutant is 6.15, i.e. that the hybrid is more favored relative to HbS than is a tetramer of the quadruple mutant itself.

DISCUSSION
Functional Character of the Mutants-Since these recombinant hemoglobins have increased positive charge at the protein surface, circular dichroism and tetramer-dimer dissociation were measured to ensure that the overall conformation and tetramer stability of these recombinant hemoglobins was not compromised. The circular dichroism results indicate that overall structures of these recombinant hemoglobins expressed in yeast were practically the same as those of natural Hb. The tetramer-dimer dissociation studies suggested that the amino acid replacements in all these recombinants have no significant effect on the strength of the interaction at the ␣ 1 ␤ 2 interfaces. Therefore, we conclude the effect of the amino acid substitutions in the recombinant hemoglobin on the polymerization process arises from tetrameric interactions.
Cis-Trans Effects on Polymerization-It is completely unexpected that the hybrid quadruple mutant polymerizes with almost the same probability as the full mutant. One would have expected, given the polymerization of the hybrid, that the addition of sites of favorable interaction in the full quadruple mutant would significantly increase the net strength of interaction. Clearly if the mutant sites on both halves of the molecule interact with their neighbors within the polymer the hybrid should have only half the interaction strength. It might seem that the present result could be achieved if only one-half of the tetramer sites were engaged in favorable interaction much like the ␤6 site itself. However, since the hybrids would have two ways to be positioned within the polymer, the probability would be reduced (just as seen for HbA/HbS hybrids). In

FIG. 5. Solubility of hybrids with HbS as a function of increasing fraction of hybrid (X).
Solubility is measured using a dextran assay as described in the text. Filled symbols show data points, while open symbols show predictions or fits. As an aid to the eye, the theoretical points are connected by dashed lines. Because the prediction depends on initial concentration, which varied between some experiments, the theoretical curve is not smooth. The hybrids of HbS/HbF and HbS/HbA have had their solubility predicted from known data and the theory of mixed polymerization adapted to the dextran assay as described in the text. The agreement of the predictions and the data validates the use of this theory for the assay used. The hybrids of triple and quadruple mutants are described by least squares fitting Equation 1 by variation of the copolymerization probability e 2 . For the triple mutant e 2 ϭ 0.66, while for the quadruple mutant e 2 ϭ 5.8. In fitting the quadruple mutant, the copolymerization probability of the pure mutant was taken as 6.0 based on previous experiments. S/F, HbS/HbF; S/A, HbS/HbA. short, having only half the mutation sites potent does not solve the dilemma.
The preceding example in which one-half of the sites are ineffectual is a special case of the situation where the site interactions are asymmetric. Such an idea was first proposed to describe the polymerization of HbC-Harlem (6). It is possible to treat the asymmetric (cis-trans) case in general. Suppose that in the full quadruple mutant, although both sets of mutation sites interact with the polymer, they do so with different strength, labeled ⌬G ϩ and ⌬G Ϫ . In the full mutant since both sites are involved in the net stability, the net change in free energy is ⌬G ϩ ϩ ⌬G Ϫ . In the hybrid, either one configuration (⌬G ϩ ) or the other (⌬G Ϫ ) is active; the net probability is the average of the two possible configurations. In this explanation, it is a coincidence that the net probability for copolymerizing the hybrid, {exp(⌬G ϩ /RT) ϩ exp(⌬G Ϫ /RT)}/2, is about the same as that for the copolymerization of full mutant, exp{(⌬G ϩ ϩ ⌬G Ϫ )}/RT. Following this approach, a consistent set of values can be found with probabilities of 11.8 and 0.51 implying a favorable interaction energy of 1.47 kcal/mol and an unfavorable energy (penalty) of Ϫ0.40 kcal/mol (The details are described under "Appendix."). The structural implication of this view is that one set of contacts stabilizes the polymer, while the same mutation sites on the other side of the molecule make a second set of contacts that weakly destabilize the polymer.
These conclusions then have implications for analysis of the triple mutant. The diminished likelihood for polymerization of the triple mutant hybrid is the result of competition between the repulsive effects of burial of ␤6 Glu and the attractive strength of the three other mutation sites. Since the strength of the attraction is known from the quadruple mutant analysis above, the strength of the repulsion can be determined (as discussed in detail under "Appendix"). This analysis directly gives the probability of positioning Hb so that ␤6 Glu is in the receptor pocket as 0.045. Although this probability is small, it translates into an effective solubility of 42.5 g/dl for HbA, which is an accessible concentration and one found in some erythrocytes. Very few experiments have directly probed the possibility that HbA can polymerize in low phosphate buffers. In one study, using the Benesch oxygen equilibrium method, no effects on P 50 were seen on HbA to concentrations around 50 g/dl (21). However, it might be argued that if the kinetics are sufficiently slow, such a scanning method might miss the effect of polymerization. On the other hand, there are reports of the assembly of HbA in high phosphate buffers (22). In this case it should also be noted that these aggregates do not show polymers in differential interference contrast microscopy. 2 In short, the evidence is inconclusive as to whether polymers form in HbA at such concentrations as required by the cis-trans analysis.
Vibrational Entropy-The nonadditivity of the interactions can be explained in another way that does not invoke asymmetry. In the assembly of HbS to form fibers, a significant entropic penalty (ϳ35.5 kcal/mol) is incurred by the removal of hemoglobin monomers from solution in which they could freely rotate and translate (23). The stabilization from the various intermolecular contacts is nowhere near this great, and assembly would be thermodynamically forbidden without the reclamation of lost entropy by vibrations of the molecules about their equilibrium positions in the polymer structure. Such reclaimed entropy is thought to account for about 26.5 kcal/mol (24). Polymer stability thus arises from the additive contributions of contact energy and the free energy due to recovered vibrational motion. These can be competitive with a stronger bond resulting in greater localization of the molecule within the aggregate, leading to lessened vibrations. Such an effect is believed to be operative in HbC-Harlem (29). Thus the similarity of the copolymerization probability for the quadruple mutant and its hybrids with HbS may be the consequence of such an interplay. The strengthened contacts in the quadruple mutant in this explanation have been offset by a somewhat diminished vibrational entropy because of the multiplicity of contact points. In the case of the mutant hybrids, the molecules are somewhat freer, albeit less strongly held. If this explanation is correct, it should make a noticeable effect on the kinetics of polymerization of the quadruple mutant. In fact there is preliminary evidence for such a kinetic effect. 3 Nonadditivity has been seen previously in the triple mutant E6V(␤)/L88A(␤)/K95I(␤) relative to the constituents E6V(␤)/ L88A(␤) and E6V(␤)/K95I(␤) (9). In that case, both double mutants significantly increased the solubility of HbS, but the triple mutant had the same elevated solubility as E6V(␤)/ K95I(␤). An analysis of the mutant E6V(␤)/L88A(␤) revealed that the enhancement of the solubility was due to vibrational restriction since the contact energy was the same as that of pure HbS as determined by kinetics and by modeling of the structure (8). On the other hand, the mutation of K95I replaces a charged group, and the result is expected to involve changed contact energy as well as vibrational entropy. Given that, it is plausible that the restriction of molecular motion that occurs in the K95I mutation involves the same restriction as that of the L88A mutation. Hence there would be no added effect of the L88A site since, in effect, its mode of action has already been preempted by the K95I mutant.
Structural Interpretation-Finally we turn to the question of how to understand the enhancements observed in terms of fiber structure. The ␣6 mutation known as HbSarawa (␣6 Asp 3 Ala) is found to create a lower solubility tetramer (12.0 versus 14.7 g/dl) when combined with ␤ S subunits (11) in addition to its enhancement as a part of the mutants discussed here (10). Nevertheless, the ␣6 site has no nearby polymer contacts within 5Å on adjacent tetramers. This mutation may engender some small changes internal to the tetramer (25). This is borne out by the observation that this mutation raises oxygen affinity (P 50 decreases by about 40%), although its cooperativity, as measured by the Hill n value, is essentially unchanged (10,11,26).
The ␣75 mutation (␣75 Asp 3 Tyr), known as Hb Winnipeg, decreases solubility even more than the ␣6 mutation (again when combined with ␤ S subunits) in addition to the effects seen here. For this site the solubility drops to 7.8 versus 14.7 g/dl (11). ␣75 has an extensive set of contacts in the polymer. The naturally occurring Asp contacts attractive positive charged groups (Lys at ␤66, ␤144, and ␣60) as well as repulsive groups (Asp at ␤21, ␤73, and ␣64). Hence it is plausible that placement of a Tyr at ␣75 would not sacrifice much, if any, charge-charge stability, whereas it would gain stability from contact with several hydrophobic groups (␤70 Ala, ␤88 Leu, ␤91 Leu, and ␤145 Tyr) as well as its contact with ␤19 Asn and ␤87 Thr.
Mutations at ␤121 are the most well known of the three sites studied. Hybrids of HbS with HbD Punjab (HbD Los Angeles) (␤121 Glu 3 Gln) or HbO Arab (␤121 Glu 3 Lys) enhance polymerization (with an effect trans to the ␤6 in the contact site). The double mutant HbS plus ␤121 Glu 3 Arg also favors polymerization (10). At first sight the effects of the mutation on polymerization might seem plausible since ␤121 is involved in several contacts along the double strand axis (3). However, the details prove to be problematic. The native, negatively charged Glu is close to the positive charge of Lys-17 in both cis and trans position. The replacement Arg or Lys ␤121 thus makes an unfavorable contact with these Lys amino acids. ␤121 is also close to ␤116 and 117 in the trans position from which repulsion would be expected between His (116 and 117) and Lys or Arg. On the other hand, no negative charges are found in contacts near ␤121 that might interact favorably with Lys or Arg. The remaining residues within 5 Å of the Arg at ␤121 are ␤16 Gly, ␤13 Ala, and ␤114 Pro. Thus it is difficult to understand in simple structural terms the origin of the enhanced polymerization brought about by the substitution at ␤121. (In passing it should be noted that ␤23 is also thought to have interactions with ␤116 and 117 (27). The possibility that a mutant containing both ␤23 and ␤121 would exhibit mutual interactions through the intermediary of ␤116-117 made it less desirable for the present study to combine both ␤23 and ␤121 in the same mutant.) In sum, while there is no question that these mutations enhance polymerization, only changes at ␣75 are readily reconciled with the established polymer structures.
Vibrational entropy might provide a way to reconcile structural data and the unambiguous stabilization of the polymer. The ionic interactions that appear to be present in the native forms at ␣75 and ␤121 in HbS could serve more to limit flexibility (by specificity of contacts) rather than to add much sta-bility by the strength of the contacts. The latter is especially pertinent if internal water can substitute for the ion pair lost in the mutation. On the other hand, in the mutant, the repulsive interactions add flexibility in positioning the molecules within the polymer and thus paradoxically make an entropic contribution to stability. The most interesting case would be that of ␣6 since the native Asp is thought to form hydrogen bonds with two Ser residues, ␣1 and ␣7. The loss of these hydrogen bonds is thus thought to loosen the Hb structure (25).
Summary-It is of course possible that part of the stability gain is vibrational and part arises from, e.g. the successful burial of Tyr ␣75. If vibrational entropy is indeed a cause of the nonadditivity seen, it points to the necessity of probing the details of the thermodynamics of assembly by other means than solubility alone since a single measurement is incapable of separating the contact energy terms from the vibrational terms. Kinetic measurements are one way of doing this since equilibrium nucleation theory is successfully used to describe the nucleation process, and the nuclei have a different balance of energetic terms than does the infinite polymer. It may also be possible to discern such entropic effects by the direct observation of polymer motion; such studies are presently underway. Regardless of whether an unexpected assembly of HbA or the vibrational motion of Hb polymers proves to be the correct explanation, the value of performing such hybrid experiments is clear in exposing the intricacies of the assembly process in HbS. APPENDIX We denote by subscript each unique configuration of the mutant relative to receptor. Then for the mutant there is an energy difference ⌬G relative to having HbS in the same configuration. Hence for each the microscopic copolymerization probability ẽ may be defined as The copolymerization probability e i is the quantity directly inferred from the observation of copolymerization. This differs from the microscopic probability ẽ that was encountered by the molecular species. Typically ⌺n is the total number of sites (14 strands) times the number of alternatives, 2, for a total denominator of 28. To illustrate, consider the copolymerization of HbA first in a fiber in which all sites are equivalent. There are two possible orientations of an HbA/HbS hybrid. In one orientation the ␤6 Val contacts its receptor site, and the ␤6 Glu remains solvated. Labeling that case as 1, ẽ 1 ϭ 1 so that the probability of that microstate is the same as in HbS. The reverse case, in which the Glu is placed into the hydrophobic pocket, will have a large energetic penalty. Labeling that configuration as 2, with a large penalty it follows that ẽ 2 3 0, and the probability of that microstate is very small. Therefore the net observed copolymerization probability for the hybrid is e 2 ϭ (14 ϫ 1 ϩ 14 ϫ 0)/(14 ϩ 14) ϭ 0.5. Recently it has been proposed that four outer strands involve both ␤6 sites, which causes a different weighting (7). For that case, the energetic penalties give microprobabilities of 1 or 0 again (since if one bad contact makes the probability almost 0, two such contacts will be indistinguishable). Of the 28 ␤6 sites, 18 have effectively 0 probability, FIG. 6. Schematic of possible states of hybrids. The hemoglobin molecule is shown as a circle divided into its constituent dimers by a vertical line. The three mutation sites are denoted schematically by small dots; the ␤6 site is denoted by a large dot. The receptor pocket for the ␤6 in the polymer is denoted by an asterisk. The native HbA ␤6 is shown as an open circle, whereas the ␤6 Val of HbS is shown as filled circle. The new mutation sites may interact with two distinct regions, denoted by ϩ or Ϫ. It is unknown whether the stronger (ϩ) sites are cis or trans to the ␤6 that meets with the receptor, hence there are two ways the experiment may be interpreted as denoted by I and II. The hybrids are made with HbS, so the three added mutant sites are absent. Calculation of the copolymerization of hybrids must include both possibilities denoted 1 and 2; i.e. if case I is that which occurs in nature, the copolymerization of the quadruple mutant must include the possibility of IA1 and IA2, and the copolymerization of the triple mutant must include IB1 and IB2.