ARCHIVES
OF BIOCHEMISTRY
AND
BIOPHYSICS
181, 61-65 (1977)
Kinetics of Polymerization of Deoxyhemoglobin S and Mixtures of Hemoglobin A and Hemoglobin S at High Hemoglobin Concentrations’ G. LARRY
COTTAM,
MICHAEL
R. WATERMAN,
AND
B. CECIL
THOMPSON
Department ofBiochemistry, The Uniyersity of Texas Health Science Center at Dallas, Southwestern Medical School, 5323 Harry Hines Boulevard, Dallas, Texas 75235 and Department of Physics, University of Texas at Arlington, Arlington, Texas 76010 Received
September
2, 1976
Transverse water proton relaxation times (T,) have been measured as a function of time after deoxygenation of solutions containing hemoglobin S. The shortened T, values observed upon deoxygenation of hemoglobin S result from an increase in the correlation time (~~1of the water fraction irrotationally bound to deoxyhemoglobin S as it polymerizes. Therefore, the change in 7, as a function of time after deoxygenation can be used to measure the rate of polymer formation. The change in 7, observed is reasonably fit by the first-order equation r = r,, (1 - emkL) + r,,,. At a total hemoglobin concentration of approximately 300 mg/ml, the pseudo-first-order rate constant in a heterozygous AS sample is 25 times slower than in a homozygous S sample, k = 0.019 and 0.47 s-l, respectively. Since the transit time for an erythrocyte in vivo is approximately 15 s, these results suggest that the heterozygous A/S erythrocyte would traverse the circulation and become reoxygenated before extensive polymerization and, therefore, cell sickling could occur. For the homozygous S/S erythrocyte, there is ample time for polymerization and for cell sickling during circulation.
Polymerization of deoxyhemoglobin S molecules occurs upon deoxygenation of concentrated solutions of hemoglobin S at room temperature. Ultimately, the solution undergoes gelation, if the protein concentration exceeds the minimum gelation concentration. Several techniques, viscosity (l-4), linear birefringence and dichroism (1, 5-9), calorimetry (9, lo), light scattering (11, 12), and magnetic resonance (13, 14) have been used to monitor deoxyhemoglobin S polymerization. In several of these studies, time dependence has been studied and the kinetic profile has been similar, consisting of a delay time and the polymerization process. Both the delay period and the polymerization are dependent
upon .the hemoglobin concentration and the temperature. However, most of these studies have been carried out at hemoglobin concentrations well below the concentration of hemoglobin in erythrocytes. It is well known that there are significant differences in the clinical severity between sickle cell disease and sickle cell trait individuals. While equilibrium properties have been used to explain these clinical differences (15, 161, it is quite possible that differences in the kinetics of deoxyhemoglobin S polymerization would be reflected in erythrocytes. It has been recently suggested that increasing the length of the delay time before polymerization to longer than the erythrocyte circulation time is a potential clinical solution to sickle cell anemia (17). In this study, the rate of deoxyhemoglobin S polymerization has been measured in solutions of hemoglobin S and mixtures of hemoglobins A and S at concentrations approximately those found in erythrocytes. At total hemoglobin concentrations
1The research upon which this publication is based was performed pursuant to Contract No. NOlHB-2-2954 with the National Institutes of Health, Department of Health, Education, and Welfare. This work was supported, in part, by Grants I-381 (GLC) from The Robert A Welch Foundation and Research Grant l-ROl-AM16188 from the USPHS (MRW). 61 Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0003-9861
62
COTTAM,
WATERMAN,
around 300 mg/ml, there is a dramatic decrease in the rate of polymer formation in samples of 50% HbA2 -50% HhS as compared to samples containing only HbS. MATERIALS
AND
METHODS
Samples of blood collected in 3.8% sodium citrate were obtained from the Hematology Service of the Department of Internal Medicine, The University of Texas Health Science Center at Dallas. The hemoglobin was isolated from red cells via the procedure of Drabkin (18) and disc gel electrophoresis was carried out on the isolated hemoglobin samples to determine their homogeneity. Disc gel electrophoresis was carried out in 7.5% cross-linked polyacrylamide gels (19,20) using Tris-glycine buffer, pH 8.6, and 4 mA/gel of 4 mm diameter. Samples of electrophoretically homogeneous HbS and HbA were used without further purification. Hemoglobin S was isolated from heterogeneous hemolysates by ion-exchange chromatography on carboxymethyl cellulose (Whatman CM52) which had been equilibrated with 10 mM phosphate buffer, pH 7.0. The hemoglobin samples were then equilibrated with 0.25 M potassium phosphate buffer, pH 7.4, by dialysis and concentrated via ultrafiltration. Desired mixtures of hemoglobin A and hemoglobin S were prepared from stock solutions. The hemoglobin concentrations were determined by measuring the absorbance at 419 nm after reduction with sodium dithionite and bubbling with carbon monoxide using the millimolar absorption coefficient of 191 mr0 cm-’ (21). Deoxygenation of the hemoglobin sample which had been equilibrated at 37°C was accomplished by rapidly mixing (1 s or less) 100 ~1 of the hemoglobin solution with 10 ~1 of 0.5 M sodium dithionite. After mixing, the solution contained 0.25 M phosphate buffer and was pH 7.0. The mixing occurred in an nmr tube that had already been positioned properly in the nmr spectrometer and purged with nitrogen gas. The spectrometer had been previously tuned and data could be obtained immediately after mixing the sample. The spin-echo measurements were carried out using a Nuclear Magnetic Resonance Specialities PS-6OAW pulsed nuclear magnetic resonance spectrometer (22-24). The transverse relaxation time (T,),-d, was determined from the echo envelope of a series of 180” pulses as described by Carr and Purcell (25). The precision of the T, values is *lo%. The temperature of the sample in the nmr tube was maintained at 37 2 0.X by a stream of dry nitrogen and a Nuclear Magnetic Resonance Specialties P128 temperature controller. Analysis of the rehxation rate data. In the model ZAbbreviations used: HbA, hemoglobin A; HbS, hemoglobin S, nmr, nuclear magnetic resonance.
AND
THOMPSON
for analysis of the relaxation data presented here, it was assumed that the protons which contribute to the observed relaxation rates are in three environments, each having a characteristic correlation time. These environments are free bulk water, water hydrated to the .macromolecules, and a third region where the water is assumed to be tightly bound to the protein (23). With this model, the observed transverse relaxation rate (T,& may be expressed in the form UP
+
fb (T&l
PI + (T&i
paramagnetic.
The first three terms are the contributions from the three respective environments, with the fourth term being the paramagnetic contribution of the dissolved oxygen. In a sample containing both hemoglobin A and hemoglobin S, each of the first three terms in Eq. 111 become two terms, with the corresponding mole fraction reduced by one-half. It has been shown that the contribution to the relaxation rate from all three environments remains unchanged upon deoxygenation of hemoglobin A and the first two terms remain unchanged upon deoxygenation of hemoglobin S (23). Hence, when the relaxation rate of the oxygenated hemoglobin S is subtracted from the relaxation rate after deoxygenation, Eq. 121 is obtained:
- fb z (T&O-:y - (T&l
paramagnetic.
The paramagnetic contribution that is due to dissolved oxygen, (T&l paramagnetic, will vary from sample to sample. Since an excess of dithionite is used to deoxygenate, the paramagnetic term in the deoxygenated sample will be zero. However, Eq. [21 still contains the paramagnetic term contributed by the oxygenated sample. For analysis of the results in this study, the values of the latter two terms in Eq. [2] were estimated by extrapolating each individual set of deoxygenation data to zero time after deoxygenation. In this manner, slight differences in oxygen concentrations in the individual samples were minimized. Thevalues of fb and (T&~,. for deoxyhemoglobin S have been reported to be 0.00465 and 537 s-l (16). By assuming that the value of fb does not change upon gelation, one can determine the value of as a function of time. The analytical form (T&&Y for this relaxation rate may be derived only for a limited distribution of protons. However, the generally accepted form for (T&l is given in Eq. 131 (26): LJJ
KINETICS
OF HEMOGLOBIN
where o, is the resonance frequency, 7, is the correlation time, and B is a constant related to the rigid lattice second moment with a value of 7 x 10m9smz. With the observed values of (!I’,,)-’ and Eq. [21, the correlation time 7, may be determined as a function of time after deoxygenation. This average correlation time will be determined by the size of the macromolecule and, hence, is a method to observe polymerization. The value of 7, determined from a (T&l observation will be an average value from all sizes of polymers in the sample. If we assume that the polymers, regardless of size, are formed by a pseudo-first-order process, the concentration (C) of free hemoglobin S at a time t is C = C,e-** ,
[41
where C, is the initial concentration of hemoglobin S and k is the rate constant of polymerization. The concentration of hemoglobin S that is polymerized
CC,)is C, = C, - C = C,(l - emkt).
[51
The amount of hemoglobin S that is polymerized will determine the observed correlation time, 7,. Hence, 7, should increase from the oxygenated value in the following manner.
63
S POLYMERIZATION 7, = (TJOXY+ ~~(1- e+*) ,
WI
is the value observed in the oxygenated where (~&,XY sample, r0 is a constant, and k is the rate constant for polymerization. The value of (T&~ used was h)oxu = 2.23 x lo-* s, as previously determined (16). Using this value for (T&. and the observed values of rc as a function of time, one may use a Taylor’s nonlinear differential correction technique with Eq. [61 to determine the constant r0 and the rate constant k . RESULTS AND DISCUSSION
The observed values of T2 have been measured as a function of time after deoxygenation of a sample of hemoglobin at 294 mg/ml. The sample contained 151 mg/ml of hemoglobin S and 143 mg/ml of hemoglobin A in 0.25 M potassium phosphate buffer at pH 7.4. Table I tabulates the T2 values obtained from four separate mixtures of hemoglobin S and hemoglobin A up to 240 s after deoxygenation. The decrease in T2 values observed upon deoxygenation of hemoglobin S samples presum-
TABLE I TRANSVERSE WATER PROTON RELAXATION TIMES AS A FUNCTION OF TIME AVER DEOXYGENATION OF A SOLUTION CONTAINING BOTH HEMOGLOBIN S AND HEMOGLOBIN Aa
Sample A
Sample B
Sample C
Sample D
Time after deoxygenation (s)
(Td,,, (ms)
Time after deoxygenation (8)
(T&x (ms)
Time after deoxygenation (8)
(Tdo, Cm.31
Time after deoxygenation (8)
VA,,, (ms)
2 8 18 25 33 40 45 51 70 77 80 100 113 133 152 173 195 214 238
221 196 172 150 136 128 125 120 126 122 117 117 106 106 108 104 107 111 99
2 7 13 21 27 42 48 56 63 72 81 95 104 118 127 139 161 179 201 218 239
207 184 149 142 141 132 127 119 120 135 111 114 108 103 116 109 104 100 102 94 96
2 10 20 30 40 50 60 70 90 100 110 120 130 140 150 160
288 265 265 257 236 212 192 172 164 154 164 148 148 144 143 144
6 9 12 15 18 30 40 50 60 70 80 90 100 120 150 180 210
250 257 250 230 220 200 185 195 153 165 150 144 125 135 125 120
a Upon deoxygenation, the samples contained 294 mg/ml of hemoglobin (151 mg/ml of hemoglobin S and 143 mg/ml of hemoglobin A), 0.25 M phosphate buffer, pH 7.0, and 45 mM sodium dithionite; temperature, 37°C.
64
COTTAM,
WATERMAN,
ably results from an increased mean correlation time for water protons in the sample. The primary contribution to the increased correlation time is the small fraction of water “irrotationally” bound to the hemoglobin molecules as deoxyhemoglobin S polymerizes (23). No dramatic decrease in the T, value is observed upon deoxygenation of hemoglobin A solutions (22). As seen in Table I, the value of T, continually decreases over the first 240 s after deoxygenation of mixtures containing both hemoglobin A and hemoglobin S. In sharp contrast, the T, value observed with a solution of 100% hemoglobin S at 300 mg/ml has dropped within the first 2 s after deoxygenation to essentially its final value (Table II). The oxygenated hemoglobin S sample has an observed T, of -210 ms. By comparing the data tabulated in Table I and Table II, one can see a dramatic difference in the rate of change of T, as a function of time after deoxygenation. In an attempt to compare the respective rates of polymerization, the value of 7c has been calculated from the data in Tables I and II as described under Analysis of the Relaxation Rate Data. A calculated value of Tc as a function of time after deoxygenation for each of the data sets was obtained. This value of TVis the average correlation time for the ir’rotationally bound water fraction. Therefore, the rate of change of this value of T, should be a measure of the rate of TABLE
II
TRANSVERSE WATER PROTON RELAXATION TIME AS A FUNCTION OF TIME AFTER DEOXYGENATION OF A SOLUTION OF HEMOGLOBIN So Time after deoxygenation (s) 2 4 6 8 10 12 14 16
T, values observed
Expt B
63 53 56 52
50 48 44 44 39 38 37
50
THOMPSON
formation of the deoxyhemoglobin S polymer. The assumption is that polymerization can adequately be described by a pseudo-first-order process, i.e., the addition of one deoxyhemoglobin S molecule at a time to the growing polymer. Figure 1 illustrates the time dependence of Tc for all of the data sets in Tables I and II. A simultaneous fit of all of the data in Table I to the first-order expression (Eq. 161)has been obtained, as seen by the solid lines in Fig. 1. This analysis yields the values of To = 113 ns and a rate constant k = 0.019 s-l for the mixtures of hemoglobin S and hemoglobin A. Independent fitting of each data set in Table I yielded the following values of 70 and k: 107 ns and 0.022 s-l for A, 112 ns and 0.017 s-l for B, 117 ns and 0.017 s-l for C, 127 ns and 0.016 ss’ for D. A similar analysis of the 100% hemoglobin S sample (Table II) yields a much poorer fit because of the extremely rapid changes in the value of T2 shortly after deoxygenation. The solid line in Fig. 1 that yields the best fit of Eq. 161to the hemoglobin S data has the following constants: 7. = 192 ns and a rate constant of 0.47 s-l. This latter rate constant should be considered to be a lower limit for hemoglobin S samples. These rate constants suggest that hemoglobin S at 300 mg/ml polymerizes approximately 25 times faster than an equivalent concentration of hemoglobin containing 50% hemoglobin S and 50% hemoglobin A. Another way to compare these samples would be half-lives, i.e., the time for onehalf of the hemoglobin monomer to become
(ms)
Expt A
45 42 44
AND
(1Upon deoxygenation, the samples contained 300 mg/ml of hemoglobin S, 0.25 M phosphate buffer, pH 7.0, and 45 mM sodium dithionite; temperature, 37°C.
FIG. 1. The correlation time vs the time after deoxygenation of solutions containing hemoglobin S (upper) and 1:l mixtures of hemoglobin S and hemoglobin A. The points are the values calculated from the data seen in Tables I and II. The lines are the best-tit lines through the accumulated sets of data using the analysis discussed in the text.
KINETICS
OF HEMOGLOBIN
part of the polymer. The half-life in the hemoglobin S sample is 1.5 s and in the 50% hemoglobin S + 50% hemoglobin A sample is 37 s. This latter value is considerably longer than the 15 s required for an erythrocyte transit from the lung through the capillary bed and back to the lung where it is reoxygenated. Because of the short half-life of the hemoglobin S sample, one can speculate that deoxyhemoglobin S would be extensively polymerized in an erythrocyte containing only hemoglobin S during deoxygenation in Go. In contrast, erythrocytes from a sickle cell trait individual would have a much slower rate of hemoglobin S polymerization and would be able to transverse the capillary beds and be reoxygenated in the lungs before extensive deoxyhemoblobin S polymerization could occur. Thus, kinetic observations such as these may explain, in large part, why the #sicklecell trait is a clinically benign state as compared to sickle cell disease. ACKNOWLEDGMENTS The authors thank Dr. Eugene P. Frenkel for supplying samples of blood containing hemoglobin S. The technical assistance of R. Earl Nelson and Ana Garcia is appreciated. We would like to thank William Lawley from the University of Texas at Arlington, Department of Mathematics, for his assistance with the numerical techniques used in this manuscript. REFERENCES 1. HARRIS, J. W. (195O)Proc. Sot. Exp. Biol. Med. 75, 197-201. 2. ALLISON, A. C!. (1957)Biochem. J. 65,212-219. 3. MALFA, R., AND STEINHARDT, J. (1974)Biochem. Biophys. Res. Commun. 59, 887-893. 4. HARRIS, J. W., AND BENSUSAN, H. B. (1975) J. Lab. Clin. Med. 86, 564-575. 5. SHERMAN, I. J. (1940) Bull. Johns Hopkins Hosp. 67, 309-324. 6. PERUTZ, M. F., AND MITCHISON, J. M. (1950) Nature (London) 166, 677-679.
S POLYMERIZATION
65
7. MURAYAMA, M., OLSON, R. A., AND JENNINGS, W. H. (1965) Biochim. Biophys. Actu 94, 194199. 8. HOJFRICHTER, J., HENDRICKER, D. G., AND EATON, W. A. (1973) PFOC. Nat. Acad. Sci. USA 70, 3604-3608. 9. HOFRICHTER, J., Ross, P. D., AND EATON, W. A. (1974) PFOC. Nat. Acad. Sci. USA 71, 48644868. 10. Ross, P. D., HOFRICHTER, J., AND EATON, W. A. (1975) J. Mol. Biol. 96, 239-256. 11. WILSON, W. W., LUZZANA, M. R., PENNISTON, J. T., AND JOHNSON, C. S., JR. (1974) PFOC. Nat. Acad. Sci. USA 71, 1260-1263. 12. MOFFAT, K., AND GIBSON, Q. H. (1974) Biochem. Biophys. Res. Commun. 61, 237-242. 13. EATON, W. A., HOFRICHTER, J., Ross, P. D., TSCHUDIN, R. G., AND BECKER, E. D. (1976) Biochem. Biophys. Res. Commun. 69,538-547. 14. WATERMAN, M. R., AND COTTAM, G. L. (1976) Biochem. Biophys. Res. Commun. 73,639-645. 15. BOOKCHIN, R. M., AND NAGEL, R. L. (1971) J. Mol. Biol. 60, 263-270. 16. COTTAM, G. L., AND WATERMAN, M. R. (1976) Arch. Biochem. Biophys. 177, 293-298. 17. EATON, W. A., HOFRICHTER, J., AND Ross, P. D. (1976) Blood 47, 621-627. 18. DRABKIN, D. L. (1946) J. Biol. Chem. 164, 703723. 19. ORNSTEIN, L. (1964)Ann. N. Y. Acad. Sci. 121, 321-349. 20. DAVIS, B. J. (1964) Ann. N. Y. Acad. Sci. 121, 404-427. 21. ANTONINI, E., AND BRUNORI, M. (1971) in Hemoglobin and Myoglobin and Their Reactions with Ligands, p. 19, North-Holland, Amsterdam. 22. COTTAM, G. L., VALENTINE, K. M., YAMAOKA, K., AND WATERMAN, M. R. (1974) AFC~. Biothem. Biophys. 162, 487-492. 23. THOMPSON, B. C., WATERMAN, M. R., AND COTTAM, G. L. (1975) Arch. Biochem. Biophys. 166, 193-200. 24. CHUANG, A. H., WATERMAN, M. R., YAMAOKA, K., AND C~TTAM, G. L. (1975)Arch. Biochem. Biophys. 167, 145-150. 25. CARR, H. Y., AND PURCELL, E. M. (1954) Phys. Reu. 94, 630-638. 26. SOLOMON, 1. (1955) Phys. Reu. 99, 559-565.
OF BIOCHEMISTRY
AND
BIOPHYSICS
181, 61-65 (1977)
Kinetics of Polymerization of Deoxyhemoglobin S and Mixtures of Hemoglobin A and Hemoglobin S at High Hemoglobin Concentrations’ G. LARRY
COTTAM,
MICHAEL
R. WATERMAN,
AND
B. CECIL
THOMPSON
Department ofBiochemistry, The Uniyersity of Texas Health Science Center at Dallas, Southwestern Medical School, 5323 Harry Hines Boulevard, Dallas, Texas 75235 and Department of Physics, University of Texas at Arlington, Arlington, Texas 76010 Received
September
2, 1976
Transverse water proton relaxation times (T,) have been measured as a function of time after deoxygenation of solutions containing hemoglobin S. The shortened T, values observed upon deoxygenation of hemoglobin S result from an increase in the correlation time (~~1of the water fraction irrotationally bound to deoxyhemoglobin S as it polymerizes. Therefore, the change in 7, as a function of time after deoxygenation can be used to measure the rate of polymer formation. The change in 7, observed is reasonably fit by the first-order equation r = r,, (1 - emkL) + r,,,. At a total hemoglobin concentration of approximately 300 mg/ml, the pseudo-first-order rate constant in a heterozygous AS sample is 25 times slower than in a homozygous S sample, k = 0.019 and 0.47 s-l, respectively. Since the transit time for an erythrocyte in vivo is approximately 15 s, these results suggest that the heterozygous A/S erythrocyte would traverse the circulation and become reoxygenated before extensive polymerization and, therefore, cell sickling could occur. For the homozygous S/S erythrocyte, there is ample time for polymerization and for cell sickling during circulation.
Polymerization of deoxyhemoglobin S molecules occurs upon deoxygenation of concentrated solutions of hemoglobin S at room temperature. Ultimately, the solution undergoes gelation, if the protein concentration exceeds the minimum gelation concentration. Several techniques, viscosity (l-4), linear birefringence and dichroism (1, 5-9), calorimetry (9, lo), light scattering (11, 12), and magnetic resonance (13, 14) have been used to monitor deoxyhemoglobin S polymerization. In several of these studies, time dependence has been studied and the kinetic profile has been similar, consisting of a delay time and the polymerization process. Both the delay period and the polymerization are dependent
upon .the hemoglobin concentration and the temperature. However, most of these studies have been carried out at hemoglobin concentrations well below the concentration of hemoglobin in erythrocytes. It is well known that there are significant differences in the clinical severity between sickle cell disease and sickle cell trait individuals. While equilibrium properties have been used to explain these clinical differences (15, 161, it is quite possible that differences in the kinetics of deoxyhemoglobin S polymerization would be reflected in erythrocytes. It has been recently suggested that increasing the length of the delay time before polymerization to longer than the erythrocyte circulation time is a potential clinical solution to sickle cell anemia (17). In this study, the rate of deoxyhemoglobin S polymerization has been measured in solutions of hemoglobin S and mixtures of hemoglobins A and S at concentrations approximately those found in erythrocytes. At total hemoglobin concentrations
1The research upon which this publication is based was performed pursuant to Contract No. NOlHB-2-2954 with the National Institutes of Health, Department of Health, Education, and Welfare. This work was supported, in part, by Grants I-381 (GLC) from The Robert A Welch Foundation and Research Grant l-ROl-AM16188 from the USPHS (MRW). 61 Copyright 0 1977 by Academic Press, Inc. All rights of reproduction in any form reserved.
ISSN 0003-9861
62
COTTAM,
WATERMAN,
around 300 mg/ml, there is a dramatic decrease in the rate of polymer formation in samples of 50% HbA2 -50% HhS as compared to samples containing only HbS. MATERIALS
AND
METHODS
Samples of blood collected in 3.8% sodium citrate were obtained from the Hematology Service of the Department of Internal Medicine, The University of Texas Health Science Center at Dallas. The hemoglobin was isolated from red cells via the procedure of Drabkin (18) and disc gel electrophoresis was carried out on the isolated hemoglobin samples to determine their homogeneity. Disc gel electrophoresis was carried out in 7.5% cross-linked polyacrylamide gels (19,20) using Tris-glycine buffer, pH 8.6, and 4 mA/gel of 4 mm diameter. Samples of electrophoretically homogeneous HbS and HbA were used without further purification. Hemoglobin S was isolated from heterogeneous hemolysates by ion-exchange chromatography on carboxymethyl cellulose (Whatman CM52) which had been equilibrated with 10 mM phosphate buffer, pH 7.0. The hemoglobin samples were then equilibrated with 0.25 M potassium phosphate buffer, pH 7.4, by dialysis and concentrated via ultrafiltration. Desired mixtures of hemoglobin A and hemoglobin S were prepared from stock solutions. The hemoglobin concentrations were determined by measuring the absorbance at 419 nm after reduction with sodium dithionite and bubbling with carbon monoxide using the millimolar absorption coefficient of 191 mr0 cm-’ (21). Deoxygenation of the hemoglobin sample which had been equilibrated at 37°C was accomplished by rapidly mixing (1 s or less) 100 ~1 of the hemoglobin solution with 10 ~1 of 0.5 M sodium dithionite. After mixing, the solution contained 0.25 M phosphate buffer and was pH 7.0. The mixing occurred in an nmr tube that had already been positioned properly in the nmr spectrometer and purged with nitrogen gas. The spectrometer had been previously tuned and data could be obtained immediately after mixing the sample. The spin-echo measurements were carried out using a Nuclear Magnetic Resonance Specialities PS-6OAW pulsed nuclear magnetic resonance spectrometer (22-24). The transverse relaxation time (T,),-d, was determined from the echo envelope of a series of 180” pulses as described by Carr and Purcell (25). The precision of the T, values is *lo%. The temperature of the sample in the nmr tube was maintained at 37 2 0.X by a stream of dry nitrogen and a Nuclear Magnetic Resonance Specialties P128 temperature controller. Analysis of the rehxation rate data. In the model ZAbbreviations used: HbA, hemoglobin A; HbS, hemoglobin S, nmr, nuclear magnetic resonance.
AND
THOMPSON
for analysis of the relaxation data presented here, it was assumed that the protons which contribute to the observed relaxation rates are in three environments, each having a characteristic correlation time. These environments are free bulk water, water hydrated to the .macromolecules, and a third region where the water is assumed to be tightly bound to the protein (23). With this model, the observed transverse relaxation rate (T,& may be expressed in the form UP
+
fb (T&l
PI + (T&i
paramagnetic.
The first three terms are the contributions from the three respective environments, with the fourth term being the paramagnetic contribution of the dissolved oxygen. In a sample containing both hemoglobin A and hemoglobin S, each of the first three terms in Eq. 111 become two terms, with the corresponding mole fraction reduced by one-half. It has been shown that the contribution to the relaxation rate from all three environments remains unchanged upon deoxygenation of hemoglobin A and the first two terms remain unchanged upon deoxygenation of hemoglobin S (23). Hence, when the relaxation rate of the oxygenated hemoglobin S is subtracted from the relaxation rate after deoxygenation, Eq. 121 is obtained:
- fb z (T&O-:y - (T&l
paramagnetic.
The paramagnetic contribution that is due to dissolved oxygen, (T&l paramagnetic, will vary from sample to sample. Since an excess of dithionite is used to deoxygenate, the paramagnetic term in the deoxygenated sample will be zero. However, Eq. [21 still contains the paramagnetic term contributed by the oxygenated sample. For analysis of the results in this study, the values of the latter two terms in Eq. [2] were estimated by extrapolating each individual set of deoxygenation data to zero time after deoxygenation. In this manner, slight differences in oxygen concentrations in the individual samples were minimized. Thevalues of fb and (T&~,. for deoxyhemoglobin S have been reported to be 0.00465 and 537 s-l (16). By assuming that the value of fb does not change upon gelation, one can determine the value of as a function of time. The analytical form (T&&Y for this relaxation rate may be derived only for a limited distribution of protons. However, the generally accepted form for (T&l is given in Eq. 131 (26): LJJ
KINETICS
OF HEMOGLOBIN
where o, is the resonance frequency, 7, is the correlation time, and B is a constant related to the rigid lattice second moment with a value of 7 x 10m9smz. With the observed values of (!I’,,)-’ and Eq. [21, the correlation time 7, may be determined as a function of time after deoxygenation. This average correlation time will be determined by the size of the macromolecule and, hence, is a method to observe polymerization. The value of 7, determined from a (T&l observation will be an average value from all sizes of polymers in the sample. If we assume that the polymers, regardless of size, are formed by a pseudo-first-order process, the concentration (C) of free hemoglobin S at a time t is C = C,e-** ,
[41
where C, is the initial concentration of hemoglobin S and k is the rate constant of polymerization. The concentration of hemoglobin S that is polymerized
CC,)is C, = C, - C = C,(l - emkt).
[51
The amount of hemoglobin S that is polymerized will determine the observed correlation time, 7,. Hence, 7, should increase from the oxygenated value in the following manner.
63
S POLYMERIZATION 7, = (TJOXY+ ~~(1- e+*) ,
WI
is the value observed in the oxygenated where (~&,XY sample, r0 is a constant, and k is the rate constant for polymerization. The value of (T&~ used was h)oxu = 2.23 x lo-* s, as previously determined (16). Using this value for (T&. and the observed values of rc as a function of time, one may use a Taylor’s nonlinear differential correction technique with Eq. [61 to determine the constant r0 and the rate constant k . RESULTS AND DISCUSSION
The observed values of T2 have been measured as a function of time after deoxygenation of a sample of hemoglobin at 294 mg/ml. The sample contained 151 mg/ml of hemoglobin S and 143 mg/ml of hemoglobin A in 0.25 M potassium phosphate buffer at pH 7.4. Table I tabulates the T2 values obtained from four separate mixtures of hemoglobin S and hemoglobin A up to 240 s after deoxygenation. The decrease in T2 values observed upon deoxygenation of hemoglobin S samples presum-
TABLE I TRANSVERSE WATER PROTON RELAXATION TIMES AS A FUNCTION OF TIME AVER DEOXYGENATION OF A SOLUTION CONTAINING BOTH HEMOGLOBIN S AND HEMOGLOBIN Aa
Sample A
Sample B
Sample C
Sample D
Time after deoxygenation (s)
(Td,,, (ms)
Time after deoxygenation (8)
(T&x (ms)
Time after deoxygenation (8)
(Tdo, Cm.31
Time after deoxygenation (8)
VA,,, (ms)
2 8 18 25 33 40 45 51 70 77 80 100 113 133 152 173 195 214 238
221 196 172 150 136 128 125 120 126 122 117 117 106 106 108 104 107 111 99
2 7 13 21 27 42 48 56 63 72 81 95 104 118 127 139 161 179 201 218 239
207 184 149 142 141 132 127 119 120 135 111 114 108 103 116 109 104 100 102 94 96
2 10 20 30 40 50 60 70 90 100 110 120 130 140 150 160
288 265 265 257 236 212 192 172 164 154 164 148 148 144 143 144
6 9 12 15 18 30 40 50 60 70 80 90 100 120 150 180 210
250 257 250 230 220 200 185 195 153 165 150 144 125 135 125 120
a Upon deoxygenation, the samples contained 294 mg/ml of hemoglobin (151 mg/ml of hemoglobin S and 143 mg/ml of hemoglobin A), 0.25 M phosphate buffer, pH 7.0, and 45 mM sodium dithionite; temperature, 37°C.
64
COTTAM,
WATERMAN,
ably results from an increased mean correlation time for water protons in the sample. The primary contribution to the increased correlation time is the small fraction of water “irrotationally” bound to the hemoglobin molecules as deoxyhemoglobin S polymerizes (23). No dramatic decrease in the T, value is observed upon deoxygenation of hemoglobin A solutions (22). As seen in Table I, the value of T, continually decreases over the first 240 s after deoxygenation of mixtures containing both hemoglobin A and hemoglobin S. In sharp contrast, the T, value observed with a solution of 100% hemoglobin S at 300 mg/ml has dropped within the first 2 s after deoxygenation to essentially its final value (Table II). The oxygenated hemoglobin S sample has an observed T, of -210 ms. By comparing the data tabulated in Table I and Table II, one can see a dramatic difference in the rate of change of T, as a function of time after deoxygenation. In an attempt to compare the respective rates of polymerization, the value of 7c has been calculated from the data in Tables I and II as described under Analysis of the Relaxation Rate Data. A calculated value of Tc as a function of time after deoxygenation for each of the data sets was obtained. This value of TVis the average correlation time for the ir’rotationally bound water fraction. Therefore, the rate of change of this value of T, should be a measure of the rate of TABLE
II
TRANSVERSE WATER PROTON RELAXATION TIME AS A FUNCTION OF TIME AFTER DEOXYGENATION OF A SOLUTION OF HEMOGLOBIN So Time after deoxygenation (s) 2 4 6 8 10 12 14 16
T, values observed
Expt B
63 53 56 52
50 48 44 44 39 38 37
50
THOMPSON
formation of the deoxyhemoglobin S polymer. The assumption is that polymerization can adequately be described by a pseudo-first-order process, i.e., the addition of one deoxyhemoglobin S molecule at a time to the growing polymer. Figure 1 illustrates the time dependence of Tc for all of the data sets in Tables I and II. A simultaneous fit of all of the data in Table I to the first-order expression (Eq. 161)has been obtained, as seen by the solid lines in Fig. 1. This analysis yields the values of To = 113 ns and a rate constant k = 0.019 s-l for the mixtures of hemoglobin S and hemoglobin A. Independent fitting of each data set in Table I yielded the following values of 70 and k: 107 ns and 0.022 s-l for A, 112 ns and 0.017 s-l for B, 117 ns and 0.017 s-l for C, 127 ns and 0.016 ss’ for D. A similar analysis of the 100% hemoglobin S sample (Table II) yields a much poorer fit because of the extremely rapid changes in the value of T2 shortly after deoxygenation. The solid line in Fig. 1 that yields the best fit of Eq. 161to the hemoglobin S data has the following constants: 7. = 192 ns and a rate constant of 0.47 s-l. This latter rate constant should be considered to be a lower limit for hemoglobin S samples. These rate constants suggest that hemoglobin S at 300 mg/ml polymerizes approximately 25 times faster than an equivalent concentration of hemoglobin containing 50% hemoglobin S and 50% hemoglobin A. Another way to compare these samples would be half-lives, i.e., the time for onehalf of the hemoglobin monomer to become
(ms)
Expt A
45 42 44
AND
(1Upon deoxygenation, the samples contained 300 mg/ml of hemoglobin S, 0.25 M phosphate buffer, pH 7.0, and 45 mM sodium dithionite; temperature, 37°C.
FIG. 1. The correlation time vs the time after deoxygenation of solutions containing hemoglobin S (upper) and 1:l mixtures of hemoglobin S and hemoglobin A. The points are the values calculated from the data seen in Tables I and II. The lines are the best-tit lines through the accumulated sets of data using the analysis discussed in the text.
KINETICS
OF HEMOGLOBIN
part of the polymer. The half-life in the hemoglobin S sample is 1.5 s and in the 50% hemoglobin S + 50% hemoglobin A sample is 37 s. This latter value is considerably longer than the 15 s required for an erythrocyte transit from the lung through the capillary bed and back to the lung where it is reoxygenated. Because of the short half-life of the hemoglobin S sample, one can speculate that deoxyhemoglobin S would be extensively polymerized in an erythrocyte containing only hemoglobin S during deoxygenation in Go. In contrast, erythrocytes from a sickle cell trait individual would have a much slower rate of hemoglobin S polymerization and would be able to transverse the capillary beds and be reoxygenated in the lungs before extensive deoxyhemoblobin S polymerization could occur. Thus, kinetic observations such as these may explain, in large part, why the #sicklecell trait is a clinically benign state as compared to sickle cell disease. ACKNOWLEDGMENTS The authors thank Dr. Eugene P. Frenkel for supplying samples of blood containing hemoglobin S. The technical assistance of R. Earl Nelson and Ana Garcia is appreciated. We would like to thank William Lawley from the University of Texas at Arlington, Department of Mathematics, for his assistance with the numerical techniques used in this manuscript. REFERENCES 1. HARRIS, J. W. (195O)Proc. Sot. Exp. Biol. Med. 75, 197-201. 2. ALLISON, A. C!. (1957)Biochem. J. 65,212-219. 3. MALFA, R., AND STEINHARDT, J. (1974)Biochem. Biophys. Res. Commun. 59, 887-893. 4. HARRIS, J. W., AND BENSUSAN, H. B. (1975) J. Lab. Clin. Med. 86, 564-575. 5. SHERMAN, I. J. (1940) Bull. Johns Hopkins Hosp. 67, 309-324. 6. PERUTZ, M. F., AND MITCHISON, J. M. (1950) Nature (London) 166, 677-679.
S POLYMERIZATION
65
7. MURAYAMA, M., OLSON, R. A., AND JENNINGS, W. H. (1965) Biochim. Biophys. Actu 94, 194199. 8. HOJFRICHTER, J., HENDRICKER, D. G., AND EATON, W. A. (1973) PFOC. Nat. Acad. Sci. USA 70, 3604-3608. 9. HOFRICHTER, J., Ross, P. D., AND EATON, W. A. (1974) PFOC. Nat. Acad. Sci. USA 71, 48644868. 10. Ross, P. D., HOFRICHTER, J., AND EATON, W. A. (1975) J. Mol. Biol. 96, 239-256. 11. WILSON, W. W., LUZZANA, M. R., PENNISTON, J. T., AND JOHNSON, C. S., JR. (1974) PFOC. Nat. Acad. Sci. USA 71, 1260-1263. 12. MOFFAT, K., AND GIBSON, Q. H. (1974) Biochem. Biophys. Res. Commun. 61, 237-242. 13. EATON, W. A., HOFRICHTER, J., Ross, P. D., TSCHUDIN, R. G., AND BECKER, E. D. (1976) Biochem. Biophys. Res. Commun. 69,538-547. 14. WATERMAN, M. R., AND COTTAM, G. L. (1976) Biochem. Biophys. Res. Commun. 73,639-645. 15. BOOKCHIN, R. M., AND NAGEL, R. L. (1971) J. Mol. Biol. 60, 263-270. 16. COTTAM, G. L., AND WATERMAN, M. R. (1976) Arch. Biochem. Biophys. 177, 293-298. 17. EATON, W. A., HOFRICHTER, J., AND Ross, P. D. (1976) Blood 47, 621-627. 18. DRABKIN, D. L. (1946) J. Biol. Chem. 164, 703723. 19. ORNSTEIN, L. (1964)Ann. N. Y. Acad. Sci. 121, 321-349. 20. DAVIS, B. J. (1964) Ann. N. Y. Acad. Sci. 121, 404-427. 21. ANTONINI, E., AND BRUNORI, M. (1971) in Hemoglobin and Myoglobin and Their Reactions with Ligands, p. 19, North-Holland, Amsterdam. 22. COTTAM, G. L., VALENTINE, K. M., YAMAOKA, K., AND WATERMAN, M. R. (1974) AFC~. Biothem. Biophys. 162, 487-492. 23. THOMPSON, B. C., WATERMAN, M. R., AND COTTAM, G. L. (1975) Arch. Biochem. Biophys. 166, 193-200. 24. CHUANG, A. H., WATERMAN, M. R., YAMAOKA, K., AND C~TTAM, G. L. (1975)Arch. Biochem. Biophys. 167, 145-150. 25. CARR, H. Y., AND PURCELL, E. M. (1954) Phys. Reu. 94, 630-638. 26. SOLOMON, 1. (1955) Phys. Reu. 99, 559-565.
