Inhibition of the gelation of extracellular and intracellular hemoglobin S by selective acetylation with methyl acetyl phosphate

Methyl acetyl phosphate binds to the 2,3-diphosphoglycerate (2,3-DPG) binding site of hemoglobin and selectively acetylates three amino groups at or near that site. The subsequent binding of 2,3-DPG is thus impeded. When intact sickle cells are exposed to methyl acetyl phosphate, their abnormally high density under anaerobic conditions is reduced to the density range of oxygenated, nonsickling erythrocytes. This change is probably due to a combination of direct and indirect effects induced by the specific acetylation. The direct effect is on the solubility of deoxyhemoglobin S, which is increased from 17 g/dL for unmodified hemoglobin S to 22 g/dL for acetylated hemoglobin S at pH 6.8. Acetylated hemoglobin S does not gel at pH 7.4, up to a concentration of 32 g/dL. The indirect effect could be due to the decreased binding of 2,3-DPG to deoxyhemoglobin S within the sickle erythrocyte, thus hindering the conversion of oxyhemoglobin S to the gelling form, deoxyhemoglobin S.     

Ligand binding and the gelation of sickle cell hemoglobin.

The solubility equilibrium between monomer and polymer which has been shown to exist in deoxyhemoglobin S solutions is examined in solutions partially saturated with carbon monoxide. The total solubility is found to increase monotonically with increasing fractional saturation. At low fractional saturations the increase is nearly linear, amounting roughly to an increase of 0.01 g cm^?3 in solubility for each 10% increase in fractional saturation. Linear dichroism measurements on the spontaneously aligned polymer phase are used to examine the composition of the polymer as a function of the fractional saturation of the corresponding solution phase. The dichroism experiments show that the polymer phase contains less than 5% of CO-liganded hemes even at supernatant fractional saturations in excess of 70%. The polymer selects against totally liganded hemoglobin molecules by a minimum factor of 65 and against singly liganded molecules by a factor of at least 2.5. Consequently, polymerized hemoglobin S has a ligand affinity which is significantly lower than that of monomeric hemoglobin S in the deoxy quaternary structure.The kinetics of the polymerization reaction in the presence of CO are similar to those observed in pure deoxyhemoglobin S solutions. The polymerization is preceded by a pronounced delay, the duration of which, t_d, is proportional roughly to the 30th power of the solubility. At low fractional saturations, this amounts to a tenfold increase in t_d for each 10% increase in the fractional saturation.These results show that the polymerization reaction is nearly specific for deoxyhemoglobin. Models for the dependence of the solubility and the polymer saturation on ligand partial pressure demonstrate the importance of solution phase non-ideality in determining the solubility of mixtures. The results require selection against partially liganded species which is significantly greater than is predicted by the two-state allosteric model. The data are compatible with either sequential or allosteric models in which the major polymerized component is the unliganded hemoglobin molecule.     

Gelation of sickle cell hemoglobin in mixtures with normal adult and fetal hemoglobins.

We report the results of thermodynamic and kinetic studies on the gelation of mixtures of sickle cell (S) deoxyhemoglobin with normal human adult (A) and fetal (F) deoxyhemoglobins. The delay time of thermally induced gelation was monitored by the increase in turbidity. At the completion of gelation the solubility was determined by sedimenting the polymers and measuring the supernatant concentration spectrophotometrically. Addition of hemoglobins A or F, at mole fractions from 0 to 0.6, resulted in large increases in both the solubility and the delay time. For a 50:50 mixture of deoxyhemoglobin F with deoxyhemoglobin S, the solubility increased by a factor of 1.8 and the delay time by a factor of 10⁷ relative to pure deoxyhemoglobin S at the same total concentration, while for a 50:50 mixture of deoxyhemoglobins A and S the solubility increased by a factor of 1.4 and the delay time by a factor of 10⁴. The relative delay times were independent of both temperature and total hemoglobin concentration. The data have been analyzed according to theoretical models which treat the effects of temperature, concentration, non-ideality and solution composition on the thermodynamics and kinetics of gelation. The increased solubility in mixtures with deoxyhemoglobin F is fully explained by a model in which only deoxyhemoglobin S molecules polymerize. The effect of fetal hemoglobin (α₂γ₂) and hybrid α₂γβ^S molecules is to increase the solution non-ideality through the contribution of their excluded volume. The smaller increase in the solubility observed in comparable mixtures with deoxyhemoglobin A requires that the hybrid α₂β^Aβ^S molecules copolymerize with the deoxyhemoglobin S. The kinetic results for the mixtures can be quantitatively accounted for using a nucleation model in which the equilibrium properties of the polymer are used to describe the critical nucleus. The very large increases in delay time observed for the $\text{S}\text{F}$ mixtures can be explained by assuming that only α₂β₂^S molecules participate in the formation of a nucleus containing about 25 monomers. As in the thermodynamic analysis, the smaller effect of adding deoxyhemoglobin A can be attributed to the contribution of the hybrid molecules in forming the critical nucleus. Thus the difference between the polymerization properties of mixtures of deoxyhemoglobin S with deoxyhemoglobins A and F can be attributed solely to the copolymerization of the α₂β^Aβ^S hybrid molecule and the absence of any significant copolymerization of the α₂γβ^S hybrid.     

Reversible solubility of deoxyhemoglobin S

The solubility of deoxyhemoglobin S in 1.96 M phosphate is sensitive to changes in oxygenation and temperature in a manner similar to the widely used $\text{in vitro}$ gelation assay. In addition, the pH of the phosphate buffer used in the solubility determination has a profound effect on deoxyhemoglobin S solubility. It is suggested that solubility in 1.96 M phosphate may be a sensitive method of monitoring the aggregation phenomenon of deoxyhemoglobin S.     

The solubility of hemoglobin beta 4 S, the mutant subunits of sickle cell hemoglobin

The single subunit hemoglobin β₄^S was found to have a solubility comparable to that of oxygenated rather than deoxygenated Hb S, although it contains twice as many mutant chains as the parent hemoglobin and probably has a quarternary structure similar to deoxyhemoglobin A. This finding supports the assumption that receptor sites in the α chains of sickle hemoglobin are essential for sickling.     

The gelation of deoxyhemoglobin S in erythrocytes as detected by transverse water proton relazation measurements

At 37 °C, when samples of blood, washed erythrocytes, or isolated hemoglobin from individuals with sickle cell disease are deoxygenated, the transverse water proton relaxation time is sharply decreased. In similar samples from normal adults homozygous for hemoglobin A, only a slight decrease in t₂ is observed upon deoxygenation at 37 °C. In samples containing deoxyhemoglobin S the value of t₂ increases as the temperature is decreased from 37 °C to 4 °C, in contrast to samples containing oxyhemoglobin S, oxyhemoglobin A, or deoxyhemoglobin A where t₂ decreases as the temperature decreases. It is suggested that this decrease in t₂ observed in samples of deoxyhemoglobin S at 37 °C is the result of an increase in the amount of preferentially oriented water at macromolecular interfaces which occurs under conditions known to produce deoxyhemoglobin S gelation. Conditions which reverse deoxyhemoglobin S gelation such as lowering the temperature to 4 °C decrease the amount of preferentially oriented water which results in an increase in the value of t₂. Thus, measurement of the transverse water proton relaxation time can be used to monitor the gelation of deoxyhemoglobin S inside the erythrocyte.     

The effect of 2,3-diphosphoglycerate on the solubility of deoxyhemoglobin S

Although highly charged polyanions, such as inositol hexaphosphate, have been clearly shown to decrease the solubility of deoxyhemoglobin S, the effect of 2,3-diphosphoglycerate (DPG), the endogenous allosteric effector within the red cell, has been more controversial. In this work we have compared the effect of DPG on the solubility of native deoxyhemoglobin S and a derivative in which the DPG binding site is blocked by cross-linking the two beta 82 lysine residues. At pH 6.6 and 30 degrees C the solubility of deoxyhemoglobin S was found to be decreased by 15% (i.e., from 18.8 to 16.0 g/dl) in the presence of saturating concentrations of DPG. Under the same conditions DPG had no effect on the solubility of the cross-linked derivative. This result establishes unequivocally that the binding of DPG within the beta cleft directly facilitates the polymerization of deoxyhemoglobin S. Under physiological conditions, the solubility of deoxyhemoglobin S was found to be decreased by 6% in the presence of an equimolar concentration of DPG. A solubility decrease of this magnitude is sufficient to enhance the tendency of SS cells to sickle and may exacerbate the clinical symptoms of sickle cell disease.     

Thermodynamics of 2,3-diphosphoglycerate association with human oxy- and deoxyhemoglobin

The association of 2,3-diphosphoglycerate with oxy- and deoxyhemoglobin was studied by means of ultrafiltration and microcalorimetry. It was found that in addition to parameters that are known to influence the binding of 2,3-diphosphoglycerate to both species of hemoglobin (such as pH, temperature and concentration of competing anion), the association is also strongly dependent on the hemoglobin concentration. The difference between the apparent association constants for the formation of the complex of the organic phosphate with oxy- and deoxyhemoglobin is relatively small. At pH 7.3, 25° C and 0.154 M chloride this difference is only 0.6 kcal/mole of free energy favoring the Hb·DPG complex. This free energy difference increases with decreasing pH but is not strongly affected by hemoglobin concentration. The enthalpy change for the formation of the 2,3-diphosphoglycerate complex with deoxyhemoglobin is 8–10 kcal/mole more exothermic than the complex with oxyhemoglobin.     

Thermodynamics of gelation of sickle cell deoxyhemoglobin.

This paper describes the thermodynamic behavior of gels of deoxyhemoglobin S. The solubility of the protein with respect to assembled hemoglobin fibers has been measured using a sedimentation technique. The solubility in 0.15 m-potassium phosphate buffer (pH 7.15) is found to decrease with increasing temperature, attain a minimum value of 0.16 g cm^?3 at 37 °C, and then increase at higher temperatures. The amount of polymer present at various hemoglobin concentrations and temperatures is presented as part of a phase diagram that may be useful for the calibration of other measurement techniques. The effects of varying pH and urea concentration upon the solubility have also been studied.The heat absorption accompanying gelation has been measured by scanning calorimetry. Using sedimentation data on the amount of polymer formed, molar enthalpy changes are obtained. There is a large negative heat capacity change of ? 197 cal deg. mol^?1 and ΔH = 0 near 37 °C. Calorimetric molar enthalpy changes are found to agree with those calculated from the temperature dependence of the solubility by the van't Hoff equation.Our previous two-phase, two-component thermodynamic model of gelation is extended to include the effects of solution non-ideality. A large contribution to the activity of the hemoglobin in the solution phase results from the geometric effect of excluded volume. Incorporating solution phase non-ideality permits the calculation of standard state thermodynamic quantities for the gelation process at 37 °C: ΔG^O ? ?3 k cal mol^?1, ΔH^O ~ 0, ΔS^O ~ 10 cal deg.^?1 mol^?1. The excluded volume effect is also capable of explaining observations of the minimum gelling concentrations of hemoglobin mixtures containing deoxyhemoglobin S without requiring copolymerization of the non-S hemoglobin.     

Gelling properties of apohemoglobin S alone and in mixtures with hemoglobin S

Apohemoglobin S formed a gel in the cold (5 degrees C) with a protein concentration in the supernatants after centrifugation of the gels (Csat) near 27 g/dl, in 0.02 M phosphate buffer at pH 7.2. Under the same experimental conditions in mixtures of apohemoglobin S and deoxyhemoglobin S the solubility of hemoglobin S in the cold was decreased from Csat greater than 40 g/dl in the absence to about 18 g/dl in the presence of apohemoglobin S. Conversely, in the same mixture, Csat of apohemoglobin S was decreased to about 5 g/dl. Also, gelling occurred in mixtures of oxyhemoglobin S and its apoderivative. Apohemoglobin A alone did not form gels; however, it induced fiber formation in deoxyhemoglobin S in the cold; unlike apohemoglobin S, it was not included in the precipitate. Gels of apohemoglobin S were not birefringent, and inspection at the electron microscope failed to show the presence of organized structures. Excluded volume effects were probably at the origin of the decreased solubility of hemoglobin S and apohemoglobin S in the presence of each other.     

Effect of oxygen concentration on trasverse water proton relaxation times in erythrocytes homozygous and heterozygous for hemoglonin S.

The transverse water proton relaxation times (T₂) of erythrocytes homozygous and heterozygous for hemoglobin S have been measured as a function of oxyhemoglobin concentration at 37 °C. An immediate decrease in T₂ is observed in S/S erythrocytes as the amount of oxyhemoglobin is decreased and the maximum change is observed at 50% deoxyhemoglobin S. In heterozygous erythrocytes, the T₂ remains unchanged until a critical level of deoxyhemoglobin is attained. The critical level of deoxyhemoglobin is a function of the percentage of hemoglobin S in the heterozygous erythrocytes. A Hill plot of the data obtained from S/S erythrocytes gives an n value of around 2.4. These results suggest that the measurement of T₂ is sensitive to the very early stages of the polymerization process. This suggestion is supported by calculations; our T₂ measurements are sensitive to a range of correlation times expected for hemoglobin monomers at one extreme and linear polymers of seven hemoglobin molecules at the other extreme.     

Reactivity of Glu-22(beta) of hemoglobin S for amidation with glucosamine

X-ray diffraction analysis of deoxyhemoglobin S crystals has implicated that a number of carboxyl groups of the protein are present at or near the intermolecular contact regions. The reactivity of these or other carboxyl groups of hemoglobin S for the amidation with an amino sugar, i.e., glucosamine, and the influence of amidation on the oxygen affinity and polymerization have been investigated. Reaction of oxyhemoglobin S at pH 6.0 and 23 degrees C with 20 mM 1-ethyl-3-[3-(dimethylamino)propyl]carbodiimide (EDC) and 100 mM [3H]glucosamine for 1 h resulted in an incorporation of nearly two residues of glucosamine per tetramer. The amidation was very specific for the carboxyl groups of globin; the glucosamine was not incorporated into the heme carboxyls. Derivatization of hemoglobin S by glucosamine increased the O2 affinity of the protein but had no influence on either the Hill coefficient or the Bohr effect. Amidation by glucosamine also increased the solubility of deoxyhemoglobin S by about 55%. Tryptic peptide mapping of the modified hemoglobin S indicated that the peptides beta-T3 and beta-T5 contained the glucosamine incorporated into the protein. Sequence analysis of glucosamine-modified beta-T3 and beta-T5 demonstrated that the gamma-carboxyl groups of Glu-22 and Glu-43, respectively, had been derivatized with glucosamine. The residue Glu-43(beta) shows a high selectivity toward glycine ethyl ester also, whereas Glu-22(beta) is not reactive toward this amine.(ABSTRACT TRUNCATED AT 250 WORDS)     

Ligand-dependent aggregation of chicken hemoglobin AI

The hemoglobin A_I component of the white leghorn chicken may potentially provide an animal model for the $\text{in vitro}$ aggregation behavior of human hemoglobin S. In solutions of low ionic strength, it has been found to undergo a striking loss of solubility upon deoxygenation, leading to the formation of macromolecular aggregates. This property is not shared by the other major chicken hemoglobin component, designated A_II. Compositional and NH₂-terminal sequence analysis indicate that extensive primary structural differences reside in the alpha chains of these two hemoglobins. The beta chains appear to be identical. Examination by electron microscopy suggests that the deoxyhemoglobin A_I forms microcrystalline arrays. The A_I component shows diminished reactivity with ¹³CO₂, as judged from ¹³C NMR measurements.     

The reversible titration of tyrosyl residues in human deoxyhemoglobin

The reaction of hemoglobin with N-acetyl imidazole at neutral pH indicated that in carboxyhemoglobin 1.80 residues per heme were acetylated while in deoxyhemoglobin only 1.15 residues were available to the reagent. The reversible titration of these residues in alkali was followed by difference spectrophotometry at 245 nm. Hill plots of the titration data, assuming 2 residues titrable per heme an3 Δε = 10500 per tyrosyi residue upon ionization, showed a slope of 1.5 and a pH near 11. The average pK of these groups in carboxyhemoglobin was previously found to be near 10.5. Also. by difference spectrophotometry it was shown that exposure of deoxyhemoglobin to alkaline pH was accompanied by a modification of the Soret region of the absorption spectrum, which might indicate the appearance of liganded conformation in the deoxyhemoglobin system. The sedimentation velocity of deoxyhemoglobin demonstrated that at alkaline pH dissociation into duners occurred at pH's lower than 10, where no ionization of tyrosines was detectable. The titration of tyrosines was independent from protein concentration.The low availability of tyrosyl residues to acetylation in deoxyhemoglobin, the cooperativity of proton binling of these residues and the change in conformation of hemoglobin concomitant with their titration are all consistent with results of Simon et al., Moffat, and Moffat et al., and with the model proposed by Perutz for explaining the heme-heme interaction. The free energy of the pK shift of the tyrosyl residues in carboxy and deoxyhemoglobin can be included in the free energy of the heme-heme interaction.     

Inhibitory effect of deoxyhemoglobin A2 on the rate of deoxyhemoglobin S polymerization.

From a consideration of the primary sequence of hemoglobin A₂ and the reported 5 å molecular contacts between deoxyhemoglobin S molecules in a crystal, it is predicted that hemoglobin A₂ might act as an inhibitor of the polymerization of deoxyhemoglobin S in a manner similar to hemoglobin. F. This has been tested experimentally by measuring the rate of change of the transverse water proton relaxation times (T₂) in equimolar mixtures of hemoglobin S and one of the non-gelling hemoglobins A, F or A₂. Hemoglobins A₂ and F have far more pronounced inhibitory effects on the rate of polymerization than does hemoglobin A. These molecules contain several amino acid differences from hemoglobin A beta chains which are located in the 5 Å molecular crystal contacts and these altered crystal contacts result in a much stronger inhibition of the rate of polymerization. Since hemoglobin A₂ is a normal hemoglobin found in small amounts in all adult red cells, increased delta chain synthesis may have potential importance in therapy for sickle cell disease.     

Calorimetric and optical characterization of sickle cell hemoglobin gelation.

We have used two techniques to characterize the gelation of deoxyhemoglobin S, a high sensitivity heat-flow calorimeter to measure the heat of gelation and a simple light-transmission method to measure the optical birefringence resulting from the alignment of deoxyhemoglobin S fibers in the gel. A theory for the interpretation of the birefringence measurements is presented. We combine the results of the calorimetric and optical measurements with those of sedimentation experiments to obtain enthalpy changes for gelation. The enthalpy change obtained from scanning and isothermal calorimetric measurements (0.25 m-potassium phosphate, 0.05 m-sodium dithionite, pH 6.9) varies from 4000 to 2200 cal mol⁻¹ hemoglobin between 16 and 25 °C. There is a large apparent heat capacity change of −130 to −190 cal deg.⁻¹ mol⁻¹. The apparent enthalpy change estimated from solubility measurements and birefringence melting experiments is 2200 ± 500 cal mol⁻¹ in qualitative agreement with the calorimetric results. Analysis of the time dependence of the calorimetric and optical progress curves at 20 °C leads to a rough estimate of 1800 to 4000 and −800 to 1500 cal mol⁻¹ hemoglobin for the enthalpies of polymerization and alignment of fibers, respectively. The small magnitude of the observed enthalpy change is in accord with the view that no large conformational change takes place in the deoxyhemoglobin S molecule upon gelation.     

Structural features required for the reactivity and intracellular transport of bis(3,5-dibromosalicyl)fumarate and related anti-sickling compounds that modify hemoglobin S at the 2,3-diphosphoglycerate binding site

Bis(3,5-dibromosalicyl)fumarate (I) reacts preferentially with oxyhemoglobin to cross-link the two beta 82 lysine residues within the 2,3-diphosphoglycerate (DPG) binding site and as a result markedly increases the solubility of deoxyhemoglobin S. The cross-link acts by perturbing the acceptor site for Val 6 within the sickle cell fiber (Chatterjee, R., Walder, R. Y., Arnone, A., and Walder, J. A. (1982) Biochemistry 21, 5901-5909). In the present studies we have compared a large number of analogs of I to determine the structural features of the reagent required for specificity and for transport into the red cell. Both electrostatic and hydrophobic interactions contribute to the binding of these compounds at the DPG site. The optimal position for the negatively charged groups on the cross-linking agent for productive binding is adjacent to the ester as in the original salicylic acid derivatives. There is a direct correlation between the reactivity toward hemoglobin and the hydrophobicity of the substituent attached at the para position. Phenyl and substituted phenyl derivatives as in the analgesic, antiinflammatory drug diflunisal are particularly effective. These groups probably interact with hydrophobic residues of the amino-terminal tripeptide and the EF corner of the beta chains adjacent to the DPG binding site. Although bis(3,5-dibromosalicyl)fumarate is very reactive toward hemoglobin in solution, it is much less effective in modifying hemoglobin within the red cell. The reaction with intracellular hemoglobin was shown to be limited by competing hydrolysis of the reagent catalyzed at the outer surface of the erythrocyte membrane. Inactivation of the red cell membrane acetylcholinesterase with phenylmethylsulfonyl fluoride did not inhibit this reaction. Introduction of a single methyl group onto the carbon-carbon double bond of the fumaryl moiety decreases the lability of the ester 10-fold, due to steric effects, and allows the reagent to be taken up by the red cell and modify intracellular hemoglobin. The kinetics of transport of the methylfumarate derivative, bis(3,5-dibromosalicyl)mesaconate, are first-order, consistent with passive diffusion. The attachment of larger alkyl groups onto the cross-link bridge further enhances the transport of the reagent into the red cell. The solubility of deoxyhemoglobin S cross-linked with the butylfumarate derivative was found to be increased by almost 10% compared to the original fumarate diester.(ABSTRACT TRUNCATED AT 400 WORDS)     

X-ray and functional studies of hemoglobins Nancy and Cochin-Port-Royal.

The mutations in hemoglobin Nancy beta145(HC2) Tyr leads to Asp and hemoglobin Cochin-Portal-Royal beta146(HC3) His leads to Arg involve residues which are thought to be essential for the full expression of allosteric action in hemoglobin. Relative to the structure of deoxyhemoglobin A, our x-ray study of deoxyhemoglobin Nancy shows severe disordering of the beta chain COOH-terminal tetrapeptide and a possible movement of the beta heme iron atom toward the plane of the porphyrin ring. These structural perturbations result in a high oxygen affinity, reduced Bohr effect, and lack of cooperatively in hemoglobin Nancy. In the presence of inositol hexaphosphate (IHP), the Hill constant for hemoglobin Nancy increases from 1.1 to 2.0. But relative to its action on hemoglobin A, IHP is much less effective in reducing the oxygen affinity and in increasing the Bohr effect of hemoglobin Nancy. This indicates that IHP does not influence the R in equilibrium T equilibrium as much in hemoglobin Nancy as in hemoglobin A, and this probably is due to the disordering of His 143beta which is known to be part of the IHP binding site. IHP is also known to produce large changes in the absorption spectrum of methemoglobin A, but we find that it has no effect on the spectrum of methemoglobin Nancy. In contrast to the large structural changes in deoxyhemoglobin Nancy, the structure of deoxyhemoglobin Cochin-Port-Royal differs from deoxyhemoglobin A only in the position of the side chain of residue 146beta. The intrasubunit salt bridge between His 146beta and Asp 94beta in deoxyhemoglobin A is lost in deoxyhemoglobin Cochin-Portal-Royal with the guanidinium ion of Arg 146beta floating freely in solution. This small difference in structure results in a reduced Bohr effect, but does not cause a change in the Hill coefficient, the response to 2,3-diphosphoglycerate, or the oxygen affinity at physiological pH.     

Kinetics of the polymerization of hemoglobin S: studies below normal erythrocyte hemoglobin concentration.

The kinetics of polymerization of deoxyhemoglobin S have been studied by measuring transverse water proton relaxation times (T₂) in hemoglobin solutions. As seen by other techniques, the kinetic profile consists of a delay time followed by a decrease in T₂ during polymerization. The length of the delay time can be decreased and the rate of change of T₂ can be increased by increasing the concentration of hemoglobin S or non-gelling hemoglobin or ovalbumin. At a total protein concentration of about 210 mg/ml the kinetic profiles in all three cases are indistinguishable suggesting that a non-specific protein-protein interaction may be involved in the kinetics of polymerization. In addition, it is suggested that no polymer formation occurs during the delay period.     

Chemical potential measurements of deoxyhemoglobin S polymerization. Determination of the phase diagram of an assembling protein

We have used the "osmotic stress" method to determine the phase diagram of deoxyhemoglobin S polymerization. This method involves equilibration, through a semipermeable membrane, of the protein with solutions of inert polymers of known osmotic pressure. With deoxyhemoglobin A and S solutions, in which we have demonstrated achievement of equilibrium, plots of osmotic pressure versus concentration initially agree closely with the results of other methods of measurement of colligative properties. However, once the known solubility value is exceeded for the deoxyhemoglobin S solutions at various temperatures, there is a rapid rise in hemoglobin concentration over a narrow osmotic pressure range and then a more gradual increase in concentration. We believe that these two regions correspond, respectively, to the onset of the polymerization process, and of subsequent continuing growth and compression or alignment of polymer. We derive the thermodynamic values for these processes and show that the behavior of the deoxyhemoglobin S system is analogous to the phase transition for a simple chemical system. These results are relevant to understanding the intracellular polymerization of deoxyhemoglobin S in sickle cell disease, and these concepts are applicable to other protein assembly systems.