Proc. Nat. Acad. Sci. USA
Vol. 73, No. 4, pp. 990-994, April 1976
Chemistry
Thermodynamic studies of polymerization of deoxygenated sickle cell hemoglobin* (hemoglobin S solubility/saturation concentration/enthalpy of polymerization/deoxyhemoglobin S microtubules)
BEATRICE MAGDOFF-FAIRCHILD, WILLIAM N. POILLON, TING-I LI, AND JOHN F. BERTLES Department of Medicine, Columbia University College of Physicians and Surgeons; and Hematology Division, Medical Service, St. Luke's Hospital Center, New York, N.Y. 10025
Communicated by John T. Edsall, February 4, 1976
ABSTRACT Solubilities of deoxygenated sickle cell hemoglobin (deoxy-Hb S), at varying pH and temperature over a range of concentrations encompassing those found in erythrocytes, were measured. The technique involved ultracentrifugation, which gave values of the supernatant concentration and the mass of the sedimented material. The data establish that the solubility of deoxy-Hb S is the saturation concentration and is independent of initial concentration. The mass of the pellet phase increases linearly with initial concentration. Moreover, the saturation concentration represents the critical concentration above which monomers are in equilibrium with polymers. These polymers are the putative cause of erythrocyte deformation associated with sickle cell anemia. The solubility-pH profiles of deoxy-Hb S at various temperatures, unlike those of other proteins, show no minima at the isoelectric pH, but instead snow a marked decrease in solubility below pH 7.0, indicating the predominance of polymerization over the expected increase in solubility. Deoxy-Hb S, within specified ranges of temperature and pH, possesses a negative temperature coefficient of solubility, a property characteristic of hydrophobic interactions. The saturation concentration is, however, temperature independent at conditions close to physiological. The enthalpy of polymerization (3.5 kcal/mol) is temperature independent from 60 to 220 for all pH values between 6.45 and 7.40. In the range of 220 to 38°, this parameter becomes less endothermic, having a value of 2.5 kcal/mol at pH 6.45 and a value of zero at pH 7.20. Such behavior of the system suggests a phase transition near 220. Within the range of.conditions examined the polymerization is entropically driven.
terference (7) or schlieren (8) optics. In these cases the minimum gelling concentration was taken to be the concentration of deoxy-Hb S at which the solution becomes optically opaque.
Although determinations of minimum gelling concentration have proved useful in quantitating the "gelation" properties of deoxy-Hb S, the definition of the minimum gelling concentration is an operational one. Values of this concentration so determined are not necessarily solubilities, since solubilities are defined as concentrations at saturation, where a solute is in equilibrium with a solid phase. In the experiments reported here, measurements of solubilities under varying conditions of temperature, pH, and initial concentration have been made. In these studies, however, the deoxy-Hb S monomers are in equilibrium with a phase containing polymers, some or all of which align into paracrystalline arrays.
MATERIALS AND METHODS Venous blood, anticoagulated with ethylenediaminetetraacetate (EDTA), was obtained from patients with sickle cell anemia, and the erythrocytes were washed three times with 0.15 M NaCl. The packed erythrocytes were lysed with toluene according to the procedure of Drabkin (9). Hb S was purified on columns (3 X 10 cm) of CM-Sephadex, each column having -a capacity of 3-4 g of Hb, by the methods of Zade-Oppen (10), as modified for batch separations. Eluates containing Hb S were concentrated overnight to approximately 0.30 g/ml by vacuum ultrafiltration. Electrophoresis or isoelectric focusing of such preparations on polyacrylamide gels showed the absence of fetal Hb and the presence of Hb A2 as a minor contaminant ( 1.24 (11), was not always attained. To insure that the oxygen saturation was zero, about 0.25 mol of dithionite per mole of heme was added. No pH change occurred. The solubilities were independent of the method used to deoxygenate solutions of Hb S. After deoxygenation by either procedure, 4 ml of deoxyHb S were placed in a centrifuge tube and overlaid with
Sickle cell hemoglobin (Hb S) is a variant of normal adult hemoglobin (Hb A) in which a substitution of valine for glutamic acid occurs at position 6 in both ,3 chains. Deoxygenated solutions of Hb S, at concentrations comparable to those within erythrocytes, form liquid crystals or tactoids. These nematic crystals of deoxy-Hb S, the putative cause of erythrocyte sickling, have been characterized optically by their birefringence and polarization dichroism (1, 2). Structural information derived from studies of both x-ray diffraction and optical diffraction of electron micrographs has provided evidence that these paracrystalline arrays are composed of helical microtubules packed into square lattices (3, 4). The term lowest gelling point has been used (5) to denote the concentration at which a solution of deoxy-Hb S loses its fluidity. Binary mixtures of Hb S with Hb A, and with mutant hemoglobins, have been characterized by their "lowest gelling point" as well. More recent experiments, using somewhat different techniques, have evaluated the effect of a diverse population of hemoglobins, both liganded and unliganded, on what has been termed minimum gelling concentration (6). Gelation of deoxy-Hb S has also been studied by sedimentation equilibrium experiments using either in*
This work was presented at the Biophysical Society, 19th annual meeting, Philadelphia, Pa., February 18-21, 1975.
990
Chemistry: Magdoff-Fairchild et al.
Proc. Nat. Acad. Sci. USA 73 (1976)
991
o1.4E C,
.0
0.10
fl1i.2
E
0.05
-
1.0
-
/
0.16
0.24
0.32
CE (9/ml) FIG. 1. The mass of the pellet per initial volume, mp, as a' function of initial concentration (ci) for the following conditions: pH 6.45, 38°, centrifuged for 1 hr (O); and pH 7.20, 25°, centrifuged for 3 hr (0). In both cases centrifugation was at 270,000 X g.
mineral oil to prevent any reoxygenation. After the hemo-
globin solutions were removed from the anaerobic atmosphere, they were equilibrated for 1 hr in a water bath at the ,desired temperature (+O.1'). Centrifuge tubes were loaded in an SW 50.1 rotor, and an additional 1 hr was allowed for equilibration in the evacuated chamber of a Spinco L3-50 ultracentrifuge that was equipped with a high-temperature accessory (0 ,50°). During the course of any experiment precautions were taken never to exceed the equilibration te'mperature, insuring that no additional polymerization occurred at an elevated temperature. The samples were then centrifuged for 1 hr at 270,000 X g (mnaximum radius), except where otherwise indicated. After centrifugation, the supernatant solution was decanted anaerobically from the sedimented material. The upper limit of the pellet was marked on the centrifuge tube, and the pH of each supernatant was measured through the mineral oil with an IL com-. bination microelectrode on a Radiometer pH meter (model 26), while the equilibration temperature was maintained. The spectrum of the supernatant was recorded after all ma-
nipulations, and in all cases the oxygen saturation was zero as judged by the absorbance ratio noted above. Supernatant concentrations were determined spectrophotometrically after conversion to cyanmet-Hb, using the millimolar extinction coefficient of 11. 0 cm- I (per heme) at 540 nm (I12). The mass of hemoglobin in the well-demarcated pellet was measured by dissolving the pellet in a known volume and determining the hemoglobin concentration. The measured amount of water, when the centrifuge tube was filled to the previously marked limit, was taken to be the pellet volume. Thus, the following parameters were determined: initial and supernatant concentrations, mass and volume of pellet, and pH. From these values, the total amount of hemoglobin in the pellet and the supernatant was calculated and the recovery was found to be within 5% of the initial amount of hemoglobin. If the recovery did not fall within this range, the data were not included in the final results presented. Spectra were recorded on a Cary 14 spectrophotometer. Within the range of 520-600 nm, a cuvette of 0. 1 mm path length with an appropriate attenuator, where necessary, was used. Measurements of absorbance of initial deoxy-Hb S solutions at several concentrations and of supernatants were also recorded on a Cary 14 through the use- of a cuvette of 2 mm path length at a wavelength of 736 nm, where the millimolar extinction coefficient of deoxy-Hb is a minimum (12).
0.22
0.26
cj, (g/mI) FIG. 2. Absorbance of deoxy-Hb S at 736 nm as a function of concentration (solid line). At saturation concentration (cat = 0.22 g/ml) the absorbance corresponds to that calculated for deoxy-Hb A (broken line). Data were obtained at pH 7.20, 250.
RESULTS
Establishment of equilibrium conditions It was necessary to establish that hemoglobin monomers remaining in solution were in equilibrium with the sedimentable phase prior to solubility measurements at varying temperatures and pH. The concentration of supernatants after centrifugation for 1 hr at 380, pH 6.45, was 0.171 I 0.002 g/ml for four different values of initial concentration, ci. Under different conditions, 250, pH 7.20, and centrifugation for 3 hr, the saturation concentration was 0.221 i 0.004 g/ml for seven different values of ci. The mass of the pellet per initial volume (mp) is plotted as a function of cj for the two sets of conditions described above (Fig. 1). The intercepts on the abscissa corresponding to saturation concentration (cat) occur at 0.165 g/ml and 0.217 g/ml, respectively. The differences between these values and those cited above are indicative of the overall experimental errors. The lines are parallel within a divergence of 20. When the lines are superposed and both sets of data points are used, the correlation coefficient is 0.964. To ascertain whether polymers were present in the supernatant after an equilibration period of 2 hr following ultracentrifugation, absorbance measurements -of the starting solutions and supernatants were made. Solutions of deoxy-Hb S, pH 7.20, varying in concentration between 0.24 and 0.29 g/ml, were warmed from 0° to 250 to initiate nucleation and polymer growth. As a result of polymerization, the measured absorbances (Fig. 2, solid line) were higher than those calculated for solutions of deoxy-Hb A at equivalent concentrations (Fig. 2, broken line). The absorbance increment is a measure of turbidity and is proportional to c1, as is mp (Fig. 1). By contrast, no increment in absorbance of the supernatant was observed. Additional absorbance measurements of the supernatant, maintained anaerobically at 250, were made at 3, 5, 18, and 24 hr after centrifugation, to allow for delay time in nucleation (14-16). No increase in absorbance occurred over this time interval. Further evaluation of attainment of equilibrium is obtained by measuring the mass of the pellets per initial volume as a function of the difference between cj and csat for various temperatures over a pH range between 6.45 and 7.40 (Fig. 3). The abscissa was expressed in this manner so as
992
Proc. Nat. Acad. Sci. USA 73 (1976)
Chemistry: Magdoff-Fairchild et al.
6.5
0.23
7.0
7r.5
380 (2)
0.21 0.19 0.17
0.23
Ci Csot (g/ml) -
FIG. 3. The mass of the pellet per initial volume, mp, as a function of (ci - cut). The subscripts, i and sat, denote initial and saturation concentrations, respectively. The mole fraction of the sedimentable hemoglobin ranges between 0.20 and 0.68. Measurements were made at 60(v), 140(Q), 22°(0), 30°(-), and 38°(0) for various pH values. The linear correlation coefficient is 0.864, and the probability that uncorrelated data points would yield such a linear correlation is Csat
E 0-
a
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(3)
(4)
300
(2)0(2)
0.21I
(2)
0.191 0.23
22
0.21
0
0.27
140
(2
0
(2)
0
to
Solubility measurements Solubilities, measured at five temperatures as a function of pH, are shown in Fig. 4. The saturation concentration becomes progressively more pH dependent as the temperature increases from 220 to 380. The values obtained from independent experiments under identical conditions agreed within 1%. The relationship between In csat and the reciprocal of the absolute temperature is shown in Fig. 5 for two pH values, 6.45 and 7.20. At the lower pH, the relationship can be described by two straight lines of slightly differing slope intersecting at a point corresponding to 220. At pH 7.20, the solubility is independent of temperature between 220 and 380; below 220 the solubility decreases similarly to that observed at lower pH. For clarity, the curves are shown only for pH 6.45 and 7.20, particularly since below 220 values of In csat as a function of reciprocal temperature are almost superposable over the entire pH range investigated. Between 220 and 380, the curves in the intermediate pH range (6.45-7.20) fall between those shown in Fig. 5. The values of the enthalpy of solution, AH, (Fig. 6) are derived by evaluating the slopes of the curves in Fig. 5 at small intervals of reciprocal temperature. The heats of solution at lower temperatures are the same over the entire pH range (-3.5 kcal/molt). Above 220 the heat of solution at pH 6.45 increases to a value of -2.5 kcal/mol. This change in enthalpy at about 220 appears abnormally sharp in Fig. 6 (solid line) because the data were taken at relatively large temperature increments in comparison to the range of temperature within which the transition occurs. At pH 7.20 the enthalpy increases to a value of zero (broken line). t 1 cal = 4.184 J.
(2) 0
0.25
I~~~~~(2)
0.30 .
a
6.5
7.0
pH
7.5
FIG. 4. Solubility, csat, of deoxy-Hb S as a function of pH at 380, 300, 220, 140, and 60. The numbers in parentheses adjacent to the experimental points indicate the number of independent experiments, where more than one was performed. DISCUSSION
The fact that measured solubilities represent saturation concentrations, when ci > Csat, is shown by the linear increase of mp with increasing ci under two sets of conditions (Fig. 1). Further evidence for this conclusion is that the values of Csat, 0.171 g/ml and 0.221 g/ml, for the two conditions are independent of initial concentrations. Moreover, the saturation concentration for a particular experimental condition can be considered a critical concentration where monomers are in equilibrium with polymers. Below such critical concentrations, if polymers are present, their concentration is small. Support for equating saturation with critical concentration arises from the fact that absorbance of the supernatant, after centrifugation, was that expected for a solution of deoxy-Hb A at the same concentration. The increment of absorbance, the difference between that observed and that calculated for deoxy-Hb A, reflects turbidity (Fig. 2), and increases with the excess of initial concentration above critical concentration. Such linear dependence of turbidity indicates an increase in polymer mass with increasing ci, analoous to the increase in mp depicted in Figs. 1 and 3. The data of Fig. 1 present evidence that the 2 hr equilibration time routinely used was sufficient for attainment of equilibrium. Had this not been the case, csat would not be independent of Ci, and the data points for two different sets of
Proc. Nat. Acad. Sci. USA 73 (1976)
Chemistry: Magdoff-Fairchild et al. 35 30
20
25
10
15
5
E
I I
Ca
I
0
-2.01
I
U..
0
-5.6
I1
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-5.4
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I
I
T (0C)
993
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_
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_~.
280
-5.8
w
290
300
310
T (OK) 3.2
3.3
3.4
3.5
3.6
T x103 (OK)-I FIG. 5. Relationship between in crat and 1T (OK)-' for two pH values: 6.45 (0), and 7.20 (v). The values of solubility, cst, are taken as numerically equal to moles/liter.
conditions (Fig. 1) would not be superposable. Additional evidence that equilibrium conditions were satisfied is provided by consideration of mechanisms of macromolecular polymerization. The rate-limiting step is usually that of nucleation (13). In the case of deoxy-Hb S, delay times have been demonstrated by a variety of experimental techniques (14-16). An empirical equation (16) relating delay time, td, to supersaturation ratio S, which in our notation is c/C~at, is expressed as 1/td
TS"
where n is about 30, the number of hemoglobin monomers forming a nucleus for polymerization, and the constant y = 10-6/sec. With this equation, calculations from our data over the range of Ci/Csat between 1.2 and 1.9 at pH 6.45 and 380 give delay times that span a large interval, between 1.2 hr and several milliseconds, well within the equilibration time of 2 hr routinely used. Where the minimum value of cil csat was 1.06 at pH 7.20, 250, the delay time would be about 48 hr. The apparent discrepancy between the calculated delay time of 48 hr and the attainment of equilibrium suggests that the empirical equation is not obeyed at low ratios of Ci/Cat. Although delay time is sharply temperature dependent (16), the data presented in Fig. 3, where the values of mp are temperature independent, show that equilibrium had indeed been attained at all temperatures studied. Solubility-pH profiles (Fig. 4) cannot be interpreted as for other proteins because of the polymerization of deoxy-Hb S above a critical concentration. Similar work on deoxy-Hb S evaluating the minimum gelling concentration, at a fixed temperature (8), gave results in general agreement with our data. It might, however, be expected that some minimum in solubility of deoxy-Hb S would occur at or near its isoelectric pH, as it does for other proteins. For example, insulin (17) has a minimum solubility at its isoelectric pH, and the solubility increases rapidly with increasing net charge on the molecule above and below its isoelectric pH. The pH-solubility profile of horse carboxyhemoglobin (18) is more complex in that it displays two minima, one at pH 5.5 and the other at pH 6.6. A different crystalline phase is associated with each pH. Although a minimum solubility of deoxy-Hb S at its isoelectric pH has been predicted theoretically (19), it is not observed. On the contrary, a marked decrease in satu-
FIG. 6. The enthalpy of solution, AH, (0) and pH 7.20 (v).
as a
function of temper-
ature for pH 6.45
ration concentration occurs below pH 7.0, whereas, above pH 7.0 the solubility-pH profiles resemble those for other proteins, as indicated by an increase in solubility with pH. Thus, from examination of the profiles in Fig. 4, particularly
higher temperatures, it becomes apparent that polymerization is enhanced by a net positive charge on the deoxy-Hb at
S molecule. Aligned polymers are present throughout this whole range of pH, as evidenced by birefringence when "gels" are examined between crossed linear polarizers. This does not necessarily imply, however, that the pellet is composed exclusively of aligned polymers. Isotropically dispersed polymers and amorphous aggregates may occur as
well. The temperature coefficient of solubility of deoxy-Hb S is negative between 6° and 220 for all values of pH investigated (Fig. 5), and agrees with that obtained by analytical centrifugation (8). Such a relationship has been associated with hydrophobic interactions, since increasing temperature promotes the stability of these interactions (20). It has also been shown that sickled erythrocytes assume their normal biconcave form when the temperature is lowered to 00 (21). Interpretation of viscosity studies (22) shows that polymers form when the temperature is raised and disaggregate into monomers when it is lowered. One of the salient features of the data presented in Fig. 5 is that at pH 7.20, over a range of temperature between 220 and 380, the saturation concentration is temperature independent. The resultant zero enthalpy of polymerization (Fig. 6) does not necessarily mean that the mechanism of polymer formation is different near physiological pH and temperature than under other conditions, but rather may indicate that exothermic interactions accompany and balance the endothermic polymerization process. Similar temperature independence was observed for the critical concentration of porcine brain tubulin (23), and it was suggested that, within this range, differences in the heat capacities of polymeric and monomeric forms of tubulin may occur. A similar rationale may account for the temperature-independent solubility of deoxy-Hb S at pH 7.20 between 220 and 380. The alternative possibility invoked for the tubulin polymer is that of a conformational change. Such a change, however, does not appear to occur with deoxy-Hb S polymers, since x-ray diffraction patterns, albeit at low resolution (B. Magdoff-Fairchild, unpublished results), are similar for pH values where the temperature coefficient of solubility is zero and where it is negative. Fig. 5 is essentially a phase diagram of the monomerpolymer system of deoxy-Hb S. The parameter cst is used in the phase diagram inasmuch as the fractional pellet vol-
994
Chemistry: Magdoff-Fairchild et al.
umes, as measured directly or calculated from other parameters (mp, cj, and c,,t), are independent of temperature in the same manner as that depicted for mP in Fig. 3. Above and to the left of each of the curves shown in Fig. 5, polymers are in equilibrium with monomers; below these curves only monomers are present. Moreover, the trend of the curves at lower temperatures shows no indication that CSat increases independently of temperature at any critical value, as predicted theoretically (Fig. 6, ref. 24). Rather the monomer-polymer equilibrium appears to maintain temperature dependence as the temperature approaches the freezing point of solutions of monomeric hemoglobin. The enthalpy of polymerization is about 3 kcal/ruol at about 220 or below, a value similar to that found by calorimetry (25) and predicted theoretically (24). Examination of Figs. 5 and'6, however, shows that a transition in the enthalpy of about 1-3 kcal/mol occurs near 220. No such transition occurs when enthalpies are measured calorimetrically (25). This discrepancy may arise because each technique could be examining different aspects of polymerization. The transition (Fig. 6) involving energies of a few kcal/Mol may be associated with a change in crystalline phase. At temperatures above 220 it has been shown that microtubules of deoxy-Hb S pack into a square lattice (4). It may be that at lower temperatures the lattice is hexagonal, as is the case for tobacco mosaic virus (26). From our data, it is apparent that the polymerization of deoxy-Hb S is entropically controlled; e.g., at 200 the ipcrease in entropy is about 25 cal/degree-mol. The polymerizations of tubulin and tobacco mosaic virus protein are also entropically controlled. By comparison, the entropy increase for the former system is about 100 cal/degree.mol (23), and for the latter over 700 cal/degree-mol (27). The negative free energy change upon polymerization of deoxy-Hb S is thus four times smaller than that of tubulin and 30 times smaller than that of tobacco mosaic virus protein. Because of the large free energy change associated with the polymerization of tobacco mosaic virus protein, it is not surprising that stable intermediates have been identified and characterized (28). In the case of tubulin, although the free energy change is smaller, intermediates have also been observed (29). The much smaller free energy change of about 7 kcal/ mol associated with the polymerization of deoxy-Hb S does not preclude the existence of stable intermediates. Suggestive evidence for the existence of intermediates is provided by the presence of a transition zone between solute and polymer (8). Should it be possible to"stabilize such intermediates, their thermodynamic parameters could be evaluated
Proc. Nat. Acad. Sci. USA 73 (1976)
and an understanding of the overall mechanism of the polymerization of deoxy-Hb S would emerge. This research was supported by NIH Grant HL 15293 and by NHLI Contract 72-2925-B.
1. Perutz, M. F. & Mitchison, J. M. (1950) Nature 166,677-679. 2. Hofrichter, J., Hendricker, D. G. & Eaton, W. A. (1973) Proc. Nat. Acad. Sci. USA 70,3604-3608. 3. Magdoff-Fairchild, B., Swerdlow, P. H. & Bertles, J. F. (1972)
Nature 239,'217-219.
4. Finch, J. T., Perutz, M. F., Bertles, J. F. & Dobler, J. (1973) Proc. Nat. Acad. Sci. USA 70,718-722. 5. Singer, K. & Singer, L. (1953) Blood 8, 1008-1023. 6. Bookchin, R. M. & Nagel, R. L. (1971) J. Mol. Biol. 60, 263270. 7. Williams, R. C., Jr. (1973) Proc. Nat. Acad. Sci. USA 70,
1506-1508, 8. Briehl, R. & Ewert, S. (1974) J. Mol. Biol. 80, 445-458. 9. Drabkin, D. L. (1946) J. Biol. Chem. 164,703-723. 10. Zade-Oppen, A.M.M. (1963) Scand. J. Clin. Lab. Invest. 15,
4917496.
11. Benesch, R., MacDuff, G. & Benesch, R. E. (1965) Anal. Bio-
chem. 11, 81-87. 12. van Assendelft, 0. W. (1970) Spectrophotometry of Hemoglobin Derivatives (Charles C Thomas, Springfield, Ill.) 13. Oosawa, F. & Higashi, S. (1968) Prog. Theor. Biol. 1, 79-164. 14. Malfa, R. & Steinhardt, J. (1974) Biochem. Biophys. Res. Commun. 59,887-893. 15. Moffat, K. & Gibson, Q. H. (1974) Biochem. Biophys. Res. Commun. 61, 237-242. 16. Hofrichter, J., Ross, P. D. & Eaton, W. A. (1974) Proc. Nat. Acad. Sci. USA 71, 4864-4868. 17. Fredericq, E. & Neurath, H. (1950) J. Am. Chem. Soc. 72, 2684-2691. 18. Rupley, J. A. (1968) J. Mol. Biol. 35,455-476. 19. Minton, A. P. (1975) J. Mol. Biol. 95,289-307. 20. Kauzmann, W. (1959) Adv. Protein Chem. 14,1-63. 21. Murayama, M. (1966) Science 153, 145-149. 22. Allison, A. C. (1957) Biochem. J. 65,212-219. 23. Gaskin, F., Cantor, C. R. & Shelansky, M. L. (1974) J. Mol. Biol. 89,737-758. 24. Minton, A. P. (1974) J. Mol. Biol. 82,483-498. 25. Ross, P. D., Hofrichter, J. & Eaton, W. A. (1975) J. Mol. Biol. 96,239-256. 26. Bernal, J. D. & Fankuchen, I. (1941) J. Gen. Physiol. 25, 111-165. 27. Lauffer, M. A. & Stevens, C. L. (1968) Adv. Virus Res. 13, 1-63.
28. Klug, A. & Durham, A. C. H. (1971) Cold Spring Harbor Symp. Quant. Biol. 36,449-460. 29. Kirschner, M. C., Williams, R. C., Weingarten, M. & Gerhart, J. C. (1974) Proc. Nat. Acad. Sci. USA 71, 1159-1163.
Vol. 73, No. 4, pp. 990-994, April 1976
Chemistry
Thermodynamic studies of polymerization of deoxygenated sickle cell hemoglobin* (hemoglobin S solubility/saturation concentration/enthalpy of polymerization/deoxyhemoglobin S microtubules)
BEATRICE MAGDOFF-FAIRCHILD, WILLIAM N. POILLON, TING-I LI, AND JOHN F. BERTLES Department of Medicine, Columbia University College of Physicians and Surgeons; and Hematology Division, Medical Service, St. Luke's Hospital Center, New York, N.Y. 10025
Communicated by John T. Edsall, February 4, 1976
ABSTRACT Solubilities of deoxygenated sickle cell hemoglobin (deoxy-Hb S), at varying pH and temperature over a range of concentrations encompassing those found in erythrocytes, were measured. The technique involved ultracentrifugation, which gave values of the supernatant concentration and the mass of the sedimented material. The data establish that the solubility of deoxy-Hb S is the saturation concentration and is independent of initial concentration. The mass of the pellet phase increases linearly with initial concentration. Moreover, the saturation concentration represents the critical concentration above which monomers are in equilibrium with polymers. These polymers are the putative cause of erythrocyte deformation associated with sickle cell anemia. The solubility-pH profiles of deoxy-Hb S at various temperatures, unlike those of other proteins, show no minima at the isoelectric pH, but instead snow a marked decrease in solubility below pH 7.0, indicating the predominance of polymerization over the expected increase in solubility. Deoxy-Hb S, within specified ranges of temperature and pH, possesses a negative temperature coefficient of solubility, a property characteristic of hydrophobic interactions. The saturation concentration is, however, temperature independent at conditions close to physiological. The enthalpy of polymerization (3.5 kcal/mol) is temperature independent from 60 to 220 for all pH values between 6.45 and 7.40. In the range of 220 to 38°, this parameter becomes less endothermic, having a value of 2.5 kcal/mol at pH 6.45 and a value of zero at pH 7.20. Such behavior of the system suggests a phase transition near 220. Within the range of.conditions examined the polymerization is entropically driven.
terference (7) or schlieren (8) optics. In these cases the minimum gelling concentration was taken to be the concentration of deoxy-Hb S at which the solution becomes optically opaque.
Although determinations of minimum gelling concentration have proved useful in quantitating the "gelation" properties of deoxy-Hb S, the definition of the minimum gelling concentration is an operational one. Values of this concentration so determined are not necessarily solubilities, since solubilities are defined as concentrations at saturation, where a solute is in equilibrium with a solid phase. In the experiments reported here, measurements of solubilities under varying conditions of temperature, pH, and initial concentration have been made. In these studies, however, the deoxy-Hb S monomers are in equilibrium with a phase containing polymers, some or all of which align into paracrystalline arrays.
MATERIALS AND METHODS Venous blood, anticoagulated with ethylenediaminetetraacetate (EDTA), was obtained from patients with sickle cell anemia, and the erythrocytes were washed three times with 0.15 M NaCl. The packed erythrocytes were lysed with toluene according to the procedure of Drabkin (9). Hb S was purified on columns (3 X 10 cm) of CM-Sephadex, each column having -a capacity of 3-4 g of Hb, by the methods of Zade-Oppen (10), as modified for batch separations. Eluates containing Hb S were concentrated overnight to approximately 0.30 g/ml by vacuum ultrafiltration. Electrophoresis or isoelectric focusing of such preparations on polyacrylamide gels showed the absence of fetal Hb and the presence of Hb A2 as a minor contaminant ( 1.24 (11), was not always attained. To insure that the oxygen saturation was zero, about 0.25 mol of dithionite per mole of heme was added. No pH change occurred. The solubilities were independent of the method used to deoxygenate solutions of Hb S. After deoxygenation by either procedure, 4 ml of deoxyHb S were placed in a centrifuge tube and overlaid with
Sickle cell hemoglobin (Hb S) is a variant of normal adult hemoglobin (Hb A) in which a substitution of valine for glutamic acid occurs at position 6 in both ,3 chains. Deoxygenated solutions of Hb S, at concentrations comparable to those within erythrocytes, form liquid crystals or tactoids. These nematic crystals of deoxy-Hb S, the putative cause of erythrocyte sickling, have been characterized optically by their birefringence and polarization dichroism (1, 2). Structural information derived from studies of both x-ray diffraction and optical diffraction of electron micrographs has provided evidence that these paracrystalline arrays are composed of helical microtubules packed into square lattices (3, 4). The term lowest gelling point has been used (5) to denote the concentration at which a solution of deoxy-Hb S loses its fluidity. Binary mixtures of Hb S with Hb A, and with mutant hemoglobins, have been characterized by their "lowest gelling point" as well. More recent experiments, using somewhat different techniques, have evaluated the effect of a diverse population of hemoglobins, both liganded and unliganded, on what has been termed minimum gelling concentration (6). Gelation of deoxy-Hb S has also been studied by sedimentation equilibrium experiments using either in*
This work was presented at the Biophysical Society, 19th annual meeting, Philadelphia, Pa., February 18-21, 1975.
990
Chemistry: Magdoff-Fairchild et al.
Proc. Nat. Acad. Sci. USA 73 (1976)
991
o1.4E C,
.0
0.10
fl1i.2
E
0.05
-
1.0
-
/
0.16
0.24
0.32
CE (9/ml) FIG. 1. The mass of the pellet per initial volume, mp, as a' function of initial concentration (ci) for the following conditions: pH 6.45, 38°, centrifuged for 1 hr (O); and pH 7.20, 25°, centrifuged for 3 hr (0). In both cases centrifugation was at 270,000 X g.
mineral oil to prevent any reoxygenation. After the hemo-
globin solutions were removed from the anaerobic atmosphere, they were equilibrated for 1 hr in a water bath at the ,desired temperature (+O.1'). Centrifuge tubes were loaded in an SW 50.1 rotor, and an additional 1 hr was allowed for equilibration in the evacuated chamber of a Spinco L3-50 ultracentrifuge that was equipped with a high-temperature accessory (0 ,50°). During the course of any experiment precautions were taken never to exceed the equilibration te'mperature, insuring that no additional polymerization occurred at an elevated temperature. The samples were then centrifuged for 1 hr at 270,000 X g (mnaximum radius), except where otherwise indicated. After centrifugation, the supernatant solution was decanted anaerobically from the sedimented material. The upper limit of the pellet was marked on the centrifuge tube, and the pH of each supernatant was measured through the mineral oil with an IL com-. bination microelectrode on a Radiometer pH meter (model 26), while the equilibration temperature was maintained. The spectrum of the supernatant was recorded after all ma-
nipulations, and in all cases the oxygen saturation was zero as judged by the absorbance ratio noted above. Supernatant concentrations were determined spectrophotometrically after conversion to cyanmet-Hb, using the millimolar extinction coefficient of 11. 0 cm- I (per heme) at 540 nm (I12). The mass of hemoglobin in the well-demarcated pellet was measured by dissolving the pellet in a known volume and determining the hemoglobin concentration. The measured amount of water, when the centrifuge tube was filled to the previously marked limit, was taken to be the pellet volume. Thus, the following parameters were determined: initial and supernatant concentrations, mass and volume of pellet, and pH. From these values, the total amount of hemoglobin in the pellet and the supernatant was calculated and the recovery was found to be within 5% of the initial amount of hemoglobin. If the recovery did not fall within this range, the data were not included in the final results presented. Spectra were recorded on a Cary 14 spectrophotometer. Within the range of 520-600 nm, a cuvette of 0. 1 mm path length with an appropriate attenuator, where necessary, was used. Measurements of absorbance of initial deoxy-Hb S solutions at several concentrations and of supernatants were also recorded on a Cary 14 through the use- of a cuvette of 2 mm path length at a wavelength of 736 nm, where the millimolar extinction coefficient of deoxy-Hb is a minimum (12).
0.22
0.26
cj, (g/mI) FIG. 2. Absorbance of deoxy-Hb S at 736 nm as a function of concentration (solid line). At saturation concentration (cat = 0.22 g/ml) the absorbance corresponds to that calculated for deoxy-Hb A (broken line). Data were obtained at pH 7.20, 250.
RESULTS
Establishment of equilibrium conditions It was necessary to establish that hemoglobin monomers remaining in solution were in equilibrium with the sedimentable phase prior to solubility measurements at varying temperatures and pH. The concentration of supernatants after centrifugation for 1 hr at 380, pH 6.45, was 0.171 I 0.002 g/ml for four different values of initial concentration, ci. Under different conditions, 250, pH 7.20, and centrifugation for 3 hr, the saturation concentration was 0.221 i 0.004 g/ml for seven different values of ci. The mass of the pellet per initial volume (mp) is plotted as a function of cj for the two sets of conditions described above (Fig. 1). The intercepts on the abscissa corresponding to saturation concentration (cat) occur at 0.165 g/ml and 0.217 g/ml, respectively. The differences between these values and those cited above are indicative of the overall experimental errors. The lines are parallel within a divergence of 20. When the lines are superposed and both sets of data points are used, the correlation coefficient is 0.964. To ascertain whether polymers were present in the supernatant after an equilibration period of 2 hr following ultracentrifugation, absorbance measurements -of the starting solutions and supernatants were made. Solutions of deoxy-Hb S, pH 7.20, varying in concentration between 0.24 and 0.29 g/ml, were warmed from 0° to 250 to initiate nucleation and polymer growth. As a result of polymerization, the measured absorbances (Fig. 2, solid line) were higher than those calculated for solutions of deoxy-Hb A at equivalent concentrations (Fig. 2, broken line). The absorbance increment is a measure of turbidity and is proportional to c1, as is mp (Fig. 1). By contrast, no increment in absorbance of the supernatant was observed. Additional absorbance measurements of the supernatant, maintained anaerobically at 250, were made at 3, 5, 18, and 24 hr after centrifugation, to allow for delay time in nucleation (14-16). No increase in absorbance occurred over this time interval. Further evaluation of attainment of equilibrium is obtained by measuring the mass of the pellets per initial volume as a function of the difference between cj and csat for various temperatures over a pH range between 6.45 and 7.40 (Fig. 3). The abscissa was expressed in this manner so as
992
Proc. Nat. Acad. Sci. USA 73 (1976)
Chemistry: Magdoff-Fairchild et al.
6.5
0.23
7.0
7r.5
380 (2)
0.21 0.19 0.17
0.23
Ci Csot (g/ml) -
FIG. 3. The mass of the pellet per initial volume, mp, as a function of (ci - cut). The subscripts, i and sat, denote initial and saturation concentrations, respectively. The mole fraction of the sedimentable hemoglobin ranges between 0.20 and 0.68. Measurements were made at 60(v), 140(Q), 22°(0), 30°(-), and 38°(0) for various pH values. The linear correlation coefficient is 0.864, and the probability that uncorrelated data points would yield such a linear correlation is Csat
E 0-
a
Vf
(3)
(4)
300
(2)0(2)
0.21I
(2)
0.191 0.23
22
0.21
0
0.27
140
(2
0
(2)
0
to
Solubility measurements Solubilities, measured at five temperatures as a function of pH, are shown in Fig. 4. The saturation concentration becomes progressively more pH dependent as the temperature increases from 220 to 380. The values obtained from independent experiments under identical conditions agreed within 1%. The relationship between In csat and the reciprocal of the absolute temperature is shown in Fig. 5 for two pH values, 6.45 and 7.20. At the lower pH, the relationship can be described by two straight lines of slightly differing slope intersecting at a point corresponding to 220. At pH 7.20, the solubility is independent of temperature between 220 and 380; below 220 the solubility decreases similarly to that observed at lower pH. For clarity, the curves are shown only for pH 6.45 and 7.20, particularly since below 220 values of In csat as a function of reciprocal temperature are almost superposable over the entire pH range investigated. Between 220 and 380, the curves in the intermediate pH range (6.45-7.20) fall between those shown in Fig. 5. The values of the enthalpy of solution, AH, (Fig. 6) are derived by evaluating the slopes of the curves in Fig. 5 at small intervals of reciprocal temperature. The heats of solution at lower temperatures are the same over the entire pH range (-3.5 kcal/molt). Above 220 the heat of solution at pH 6.45 increases to a value of -2.5 kcal/mol. This change in enthalpy at about 220 appears abnormally sharp in Fig. 6 (solid line) because the data were taken at relatively large temperature increments in comparison to the range of temperature within which the transition occurs. At pH 7.20 the enthalpy increases to a value of zero (broken line). t 1 cal = 4.184 J.
(2) 0
0.25
I~~~~~(2)
0.30 .
a
6.5
7.0
pH
7.5
FIG. 4. Solubility, csat, of deoxy-Hb S as a function of pH at 380, 300, 220, 140, and 60. The numbers in parentheses adjacent to the experimental points indicate the number of independent experiments, where more than one was performed. DISCUSSION
The fact that measured solubilities represent saturation concentrations, when ci > Csat, is shown by the linear increase of mp with increasing ci under two sets of conditions (Fig. 1). Further evidence for this conclusion is that the values of Csat, 0.171 g/ml and 0.221 g/ml, for the two conditions are independent of initial concentrations. Moreover, the saturation concentration for a particular experimental condition can be considered a critical concentration where monomers are in equilibrium with polymers. Below such critical concentrations, if polymers are present, their concentration is small. Support for equating saturation with critical concentration arises from the fact that absorbance of the supernatant, after centrifugation, was that expected for a solution of deoxy-Hb A at the same concentration. The increment of absorbance, the difference between that observed and that calculated for deoxy-Hb A, reflects turbidity (Fig. 2), and increases with the excess of initial concentration above critical concentration. Such linear dependence of turbidity indicates an increase in polymer mass with increasing ci, analoous to the increase in mp depicted in Figs. 1 and 3. The data of Fig. 1 present evidence that the 2 hr equilibration time routinely used was sufficient for attainment of equilibrium. Had this not been the case, csat would not be independent of Ci, and the data points for two different sets of
Proc. Nat. Acad. Sci. USA 73 (1976)
Chemistry: Magdoff-Fairchild et al. 35 30
20
25
10
15
5
E
I I
Ca
I
0
-2.01
I
U..
0
-5.6
I1
0
-5.4
4-
I
I
I
T (0C)
993
F
U)
_
o v¢
III -4.0
_~.
280
-5.8
w
290
300
310
T (OK) 3.2
3.3
3.4
3.5
3.6
T x103 (OK)-I FIG. 5. Relationship between in crat and 1T (OK)-' for two pH values: 6.45 (0), and 7.20 (v). The values of solubility, cst, are taken as numerically equal to moles/liter.
conditions (Fig. 1) would not be superposable. Additional evidence that equilibrium conditions were satisfied is provided by consideration of mechanisms of macromolecular polymerization. The rate-limiting step is usually that of nucleation (13). In the case of deoxy-Hb S, delay times have been demonstrated by a variety of experimental techniques (14-16). An empirical equation (16) relating delay time, td, to supersaturation ratio S, which in our notation is c/C~at, is expressed as 1/td
TS"
where n is about 30, the number of hemoglobin monomers forming a nucleus for polymerization, and the constant y = 10-6/sec. With this equation, calculations from our data over the range of Ci/Csat between 1.2 and 1.9 at pH 6.45 and 380 give delay times that span a large interval, between 1.2 hr and several milliseconds, well within the equilibration time of 2 hr routinely used. Where the minimum value of cil csat was 1.06 at pH 7.20, 250, the delay time would be about 48 hr. The apparent discrepancy between the calculated delay time of 48 hr and the attainment of equilibrium suggests that the empirical equation is not obeyed at low ratios of Ci/Cat. Although delay time is sharply temperature dependent (16), the data presented in Fig. 3, where the values of mp are temperature independent, show that equilibrium had indeed been attained at all temperatures studied. Solubility-pH profiles (Fig. 4) cannot be interpreted as for other proteins because of the polymerization of deoxy-Hb S above a critical concentration. Similar work on deoxy-Hb S evaluating the minimum gelling concentration, at a fixed temperature (8), gave results in general agreement with our data. It might, however, be expected that some minimum in solubility of deoxy-Hb S would occur at or near its isoelectric pH, as it does for other proteins. For example, insulin (17) has a minimum solubility at its isoelectric pH, and the solubility increases rapidly with increasing net charge on the molecule above and below its isoelectric pH. The pH-solubility profile of horse carboxyhemoglobin (18) is more complex in that it displays two minima, one at pH 5.5 and the other at pH 6.6. A different crystalline phase is associated with each pH. Although a minimum solubility of deoxy-Hb S at its isoelectric pH has been predicted theoretically (19), it is not observed. On the contrary, a marked decrease in satu-
FIG. 6. The enthalpy of solution, AH, (0) and pH 7.20 (v).
as a
function of temper-
ature for pH 6.45
ration concentration occurs below pH 7.0, whereas, above pH 7.0 the solubility-pH profiles resemble those for other proteins, as indicated by an increase in solubility with pH. Thus, from examination of the profiles in Fig. 4, particularly
higher temperatures, it becomes apparent that polymerization is enhanced by a net positive charge on the deoxy-Hb at
S molecule. Aligned polymers are present throughout this whole range of pH, as evidenced by birefringence when "gels" are examined between crossed linear polarizers. This does not necessarily imply, however, that the pellet is composed exclusively of aligned polymers. Isotropically dispersed polymers and amorphous aggregates may occur as
well. The temperature coefficient of solubility of deoxy-Hb S is negative between 6° and 220 for all values of pH investigated (Fig. 5), and agrees with that obtained by analytical centrifugation (8). Such a relationship has been associated with hydrophobic interactions, since increasing temperature promotes the stability of these interactions (20). It has also been shown that sickled erythrocytes assume their normal biconcave form when the temperature is lowered to 00 (21). Interpretation of viscosity studies (22) shows that polymers form when the temperature is raised and disaggregate into monomers when it is lowered. One of the salient features of the data presented in Fig. 5 is that at pH 7.20, over a range of temperature between 220 and 380, the saturation concentration is temperature independent. The resultant zero enthalpy of polymerization (Fig. 6) does not necessarily mean that the mechanism of polymer formation is different near physiological pH and temperature than under other conditions, but rather may indicate that exothermic interactions accompany and balance the endothermic polymerization process. Similar temperature independence was observed for the critical concentration of porcine brain tubulin (23), and it was suggested that, within this range, differences in the heat capacities of polymeric and monomeric forms of tubulin may occur. A similar rationale may account for the temperature-independent solubility of deoxy-Hb S at pH 7.20 between 220 and 380. The alternative possibility invoked for the tubulin polymer is that of a conformational change. Such a change, however, does not appear to occur with deoxy-Hb S polymers, since x-ray diffraction patterns, albeit at low resolution (B. Magdoff-Fairchild, unpublished results), are similar for pH values where the temperature coefficient of solubility is zero and where it is negative. Fig. 5 is essentially a phase diagram of the monomerpolymer system of deoxy-Hb S. The parameter cst is used in the phase diagram inasmuch as the fractional pellet vol-
994
Chemistry: Magdoff-Fairchild et al.
umes, as measured directly or calculated from other parameters (mp, cj, and c,,t), are independent of temperature in the same manner as that depicted for mP in Fig. 3. Above and to the left of each of the curves shown in Fig. 5, polymers are in equilibrium with monomers; below these curves only monomers are present. Moreover, the trend of the curves at lower temperatures shows no indication that CSat increases independently of temperature at any critical value, as predicted theoretically (Fig. 6, ref. 24). Rather the monomer-polymer equilibrium appears to maintain temperature dependence as the temperature approaches the freezing point of solutions of monomeric hemoglobin. The enthalpy of polymerization is about 3 kcal/ruol at about 220 or below, a value similar to that found by calorimetry (25) and predicted theoretically (24). Examination of Figs. 5 and'6, however, shows that a transition in the enthalpy of about 1-3 kcal/mol occurs near 220. No such transition occurs when enthalpies are measured calorimetrically (25). This discrepancy may arise because each technique could be examining different aspects of polymerization. The transition (Fig. 6) involving energies of a few kcal/Mol may be associated with a change in crystalline phase. At temperatures above 220 it has been shown that microtubules of deoxy-Hb S pack into a square lattice (4). It may be that at lower temperatures the lattice is hexagonal, as is the case for tobacco mosaic virus (26). From our data, it is apparent that the polymerization of deoxy-Hb S is entropically controlled; e.g., at 200 the ipcrease in entropy is about 25 cal/degree-mol. The polymerizations of tubulin and tobacco mosaic virus protein are also entropically controlled. By comparison, the entropy increase for the former system is about 100 cal/degree.mol (23), and for the latter over 700 cal/degree-mol (27). The negative free energy change upon polymerization of deoxy-Hb S is thus four times smaller than that of tubulin and 30 times smaller than that of tobacco mosaic virus protein. Because of the large free energy change associated with the polymerization of tobacco mosaic virus protein, it is not surprising that stable intermediates have been identified and characterized (28). In the case of tubulin, although the free energy change is smaller, intermediates have also been observed (29). The much smaller free energy change of about 7 kcal/ mol associated with the polymerization of deoxy-Hb S does not preclude the existence of stable intermediates. Suggestive evidence for the existence of intermediates is provided by the presence of a transition zone between solute and polymer (8). Should it be possible to"stabilize such intermediates, their thermodynamic parameters could be evaluated
Proc. Nat. Acad. Sci. USA 73 (1976)
and an understanding of the overall mechanism of the polymerization of deoxy-Hb S would emerge. This research was supported by NIH Grant HL 15293 and by NHLI Contract 72-2925-B.
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