Dielectric constant of sickle cell hemoglobin

J. Mol. Biol. (1983) 168, 659-671

Dielectric Constant of Sickle Cell Hemoglobin Dielectric Properties o f Sickle Cell H e m o g l o b i n in Solution and Gel Z. DELALI(', S. TAKASHIMAt

Department of Bioengineering, D3 University of Pennsylvania Philadelphia, PA 19104, U.S.A. K. ADA('H! AND T. ASAKURA

Department of Pediatrics Department of Biochemistry and Biophysics The Children's Hospital of Philadelphia University of Pennsylvania Philadelphia, PA 19104, U.S.A. (Received 30 November 1982) The dielectric constants of sickle cell hemoglobin were determined before and after gelation. The dielectric properties of oxy and deoxy sickle cell hemoglobin in solution are nearly identical to those of oxy and deoxy hemoglobin A. Only in the gel state did deoxy sickle cell hemoglobin display dielectric behavior different from that in solution. Upon gelation of deoxy sickle cell hemoglobin, the dielectric constant showed a marked decrease, and the relaxation frequency shifted towards higher frequencies. This result suggests that dielectric constant measurement can be used for the investigation of the kinetics of polymerization of sickle cell hemoglobin molecules. Despite the marked decrease in the dielectric constant, deoxy sickle cell hemoglobin still showed a well-defined dielectric dispersion even in the gel state. This indicates that individual molecules have considerable freedom of rotation in gels. It was observed that the dielectric properties of gelled deoxy sickle cell hemoglobin were affected by electrical fields at the level of l0 to 20 V/cm. This observation suggests that electrical fields of moderate strengths are able to perturb the gel structure if the system is near the transition region. The non-linear electrical behavior of gelled sickle cell hemoglobin will be discussed further in subsequent papers.

1. Introduction Sickle cell anemia is an hereditary disease t h a t is due to an abnormal hemoglobin with a m u t a t i o n a t the fl-6 position. The sickling of e r y t h r o c y t e s occurs only under low oxygen pressure, when hemoglobin molecules are deoxygenated. The t Author to whom all correspondence should be addressed: Department of Bioengineering, D3, Univemity of Pennsylvania, 220 South 33rd Street, Philadelphia, PA 19104, U.S.A. 659 0022-2836/83/230659-13 $03.00/0 9 1983 Academic Press Inc. (London) Ltd. 23

660

Z. DELALIC ET AL.

process is reversed when normal oxygen pressure is restored and hemoglobin is reoxygenated. The deformation of erythrocytes is caused by the formation of liquid cl~r tactoids of deoxy Hb St in the cell. Studies on the kinetics of gelation have demonstrated the existence of a delay period before gelation occurs. The main event during the latency period is assumed to be the formation of nuclei (Hofrichter et al., 1974). This stage is followed by rapid gel formation as a result of the addition of Hb S molecules to nuclei. Gel formation is accelerated at high temperatures, whereas cooling melts the gels. This negative temperature dependence suggests that the process of gelation is predominantly hydrophobic in nature. The similarities and differences between gelation and crystallization of deoxy Hb S have been discussed by several investigators (Wishner et al., 1975; Pumphrey & Steinhardt, 1976,1977; Adachi & Asakura, 1981). Although the process of gelation is considered to be different from that of crystallization, X-ray crystallographic analyses reveal that the configuration of Hb S molecules in gels is almost the same as that in crystals (Josephs et al., 1976; Dykes et al., 1978; Wishner et al., 1976). In gels, Hb S molecules interlock at several contact points including valine at the sixth position of fl-chains. Hemoglobin tetramers are attached at the contact point side by side in a ring and are stacked along a vertical axis. Although the arrangement of Hb S molecules in gels is rather wellknown, the lateral and/or rotary diffusion of individual Hb S molecules in gels is only poorly understood. The purpose of this research is to investigate whether dielectric measurements can be used effectively to study the gelation of deoxy Hb S, especially the kinetics of the gelation process and the molecular dynamics of deoxy Hb S in gels. The feasibility of this method hinges upon the extent of the change in the dielectric behavior of Hb S upon gelation. Since the amplitude of the dielectric constant depends upon the freedom of the rotary diffusion of Hb S molecules in gels, it is reasonable to expect that the gelation of Hb S will cause a substantial decrease in the dielectric increment and shift in relaxation frequency. The dielectric properties of normal Hb A solution have been investigated by several workers (Oncley, 1938, Takashima & Lumry, 1958; Schlecht, 1969; Grant et al., 1971) and are well-known. However, virtually no information is available as to the dielectric behavior of the deoxy Hb S molecule either in solution or in the gel form. As will be discussed later, the present study encompasses a wide frequency range, which is sufficient to study the dipolar structure of Hb S molecules in solution as well as in the gel state. 2. Experimental Procedures (a) Preparation of hemoglobin S Blood containing Hb A and Hb S was obtained from a donor with sickle cell trait. Red blood cells were washed 3 times with 0-9% (w/v) saline solution and hemolyzed with 5 mMphosphate (pH 7"5), 5 mM-EDTA. After centrifugation, the supernatant was treated with CO. The CO-hemoglobin soh,tion was dialyzed overnight against 50 mM-Tris"HCI (pH 8"3), 1 mM-EDTA at 10~ After dialysis, the pH of the hemoglobin solution was readjusted to 8-3. Hb A and Hb S were separated using a column of DEAE-Sephadex (Sigma) with a t Abbreviations used: Hb S, sickle cell hemoglobin;Hb A, hemoglobinA.

D I E L E C T R I C P R O P E R T I E S OF Hb S

661

starting buffer at pH 8"3 (50 mM-Tris, 1 mM-EDTA) and a finishing buffer a t p H 7-2. After chromatographic separation, the fraction containing H b S was collected. The CO form of H b S was then converted to oxy Hb S in a rotating evaporator under strong light. The hemoglobin solution thus purified was stored a t -70~ A small amount of solution (0"5 to l'0 ml) was dialyzed overnight against distilled water to reduce the conductance of the sample. The concentration was determined spectrophotometrically by measuring the absorbance at 541 nm, using an extinction coefficient of 1"42 • l04 l/mol. (b) Dielectric measurement Conventional 2-terminal bridge techniques were used throughout this research. The 2 bridges used were a W a y n e - K e r r B601 (15 kHz to 5 MHz) and a Hewlett-Paekard Boonton R X meter (500 kHz and 200 MHz). These bridges were designed to measure capacitance and resistance, and the measured quantities were converted to dielectric constant and conductivity using the following equation: C s - Cair

= - (~,,,-- 1 ) + 1, C s o l - Cair

(1)

where Cs and C~oI are the capacitances of the hemoglobin solution and the solvent. ~w is the dielectric constant of water. The conductivity of the solution was calculated by the empirical equation : K = GJKo,

(2)

where K 0 is the cell constant, which was determined using a standard KC1 solution with a known conductivity value. (c) Systematic errors of measurements There are 2 sources of systematic errors in dielectric measurements with conductive aqueous solutions: electrode pola~rization a t low frequencies and inductance effects at high frequencies. The error due to electrode polarization manifests itself as a sharp rise in the dielectric constant a t low frequencies. Eqn (3) shows the capacitance of a solution in the presence of electrode polarization (Schwan, 1963): l

C = Cs ~ 2p2Cp. where oJ is angular frequency, p is the resistance of the solution and Cp is electrode polarization capacitance. As indicated, errors due to electrode polarization can be reduced by increasing the value of Cp by coating the electrodes with platinum black and decreasing the conductance of the solution by dialysis. Since dialysis inevitably causes dilution of the H b S solution, care was taken to minimize the dilution of Hb S during dialysis. Inductance effects are usually due to connecting leads, and even binding pins contribute inductive reactance. The error becomes serious at high frequencies. However, the correction for inductive reactance can be performed efficiently using the following 2 equations for capacitance and resistance (Schwan, 1963):

C,

C(1 +co2LC)+ L/o 2

(5)

where L is inductance, C and p are measured capacitance and resistance, respectively. The correction can be done easily using an appropriate computing facility. The inductance of our system including the dielectric cell used for these measurements was estimated to be 1"8 x 10 - s H. 23*

662

g. DELALIC ET AL.

(d) Dielectric cell under air-tight condition The electrodes are a pair of stainless steel pins 2 mm long and 1 mm apart. The teflon cup around the electrodes contains 0"5 ml hemoglobin solution. This assembly is fitted into a cylindrical compartment, which in turn is wrapped with a water jacket for temperature control. Finally, a gas chamber is connected to both an air pump and a nitrogen tank using a 3-way stop-cock. The cell was evacuated gently using the pump and then the system was filled with nitrogen. The same procedure was repeated several times during the waiting period. Great care was taken to prevent the sample solution from boiling during evacuation. Measurements were undertaken between 29 and 42~ it being necessary to maintain a temperature above 35~ for measurements with gelled samples. The voltage across the sample was monitored using a high frequency oscilloscope. As discussed later, input voltages were kept as low as possible in order not to perturb the gelation process or gel structure. The perturbation of gel by applied fields was found to be serious, particularly when the concentration of hemoglobin and the temperature were near the critical point. Therefore, it was essential to maintain the field strength as low as possible and so we used 15 mV (0"015 V/cm) for most measurements.

3. Results (a) Measurements with Hb A Before we investigated the dielectric constants of H b S, we studied the dielectric behavior of normal H b A in its o x y and d e o x y forms. H b A has been reported to form gels in concentrated p h o s p h a t e buffer (Adachi & Asakura, 1979), although H b A does not form a gel under physiological conditions even in the absence of oxygen. The effects of ligands such as oxygen a n d carbon monoxide on the dielectric properties of H b A were discussed b y T a k a s h i m a & L u m r y (1958), Schlecht et al. (1968) and H a n s s & Baneljee (1967). Despite some controversies surrounding this issue, it is believed t h a t d e o x y g e n a t i o n of hemoglobin does not produce m a r k e d changes in the dielectric properties of H b A. However, these previous m e a s u r e m e n t s were performed a t low concentrations. The present studies were conducted a t very high concentrations, a t least a b o v e 25 g/dl. Therefore, it was necessary to reinvestigate the dielectric properties of H b A a t these concentrations. Figure 1 shows the dielectric c o n s t a n t of H b A in the o x y and d e o x y forms. The concentration of the sample was 28-2 g/dl and the t e m p e r a t u r e was 38~ As shown in Figure 1, dielectric constants of both samples display a m a r k e d frequency dependence and reach a high frequency limiting value of a b o u t 56 to 57 dielectric units at a b o u t 100 MHz. The low frequency plateau was e s t i m a t e d using the Cole-Cole plot (Cole & Cole, 1941). Despite the slight differences in value of dielectric increments, the slope of the curves and center frequencies ( 1 8 0 k H z versus 200 k H z ) for oxy and d e o x y H b A were essentially the same. These curves were obtained after a sufficiently long waiting period in nitrogen or in the presence of oxygen. I n view of these results, we concluded t h a t the dielectric properties of concentrated solutions of o x y and deoxy H b A are essentially the same except for a small decrease in dielectric increment upon deoxygenation.

DIELECTRIC

PROPERTIES

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(b) Measurements with Hb S Having confirmed that the dielectric properties of Hb A do not display marked changes upon deoxygenation, we performed a series of measurements with Hb S solutions in the oxy and deoxy forms under various conditions. Figure 2 shows the frequency profile of the dielectric constant of oxy Hb S. Comparing the center frequency of this curve (140 kHz) and dielectric increment (/le/g = 0"305) with those for oxy Hb A, we can readily conclude that the dielectric behavior of Hb S in the oxy form is quite similar to that of oxy Hb A. 120 I10 -

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This observation is not surprising in view of the minute structural differences between oxy Hb S and oxy Hb A. In general, the slope of the dispersion curves of concentrated hemoglobin solutions is broader than t hat of dilute solutions. Figure 3 shows the dielectric dispersion curve of deoxy Hb S. This curve was obtained several hours after incubation of the solution at 37~ under nitrogen. Clearly, this curve differs from that shown in Figure 2 in three respects. (1) The dielectric increment of deoxy Hb S is considerably smaller than t hat of oxy Hb S; (2) the relaxation frequency is markedly shifted toward higher frequencies (1"35 MHz v e r s u s 140 kHz); and (3) the slope of the dispersion curve is much steeper than that of oxy Hb S in solution. The small dielectric increment of deoxy Hb S in the gel state can be readily understood, because steric hindrance due to interlocking of deoxy Hb S molecules in the gel would restrict the orientation of individual molecules and reduce the dielectric increment. The shift of relaxation frequency to a higher region indicates t hat the rate of orientation of deoxy Hb S molecules in gel is faster than that in solution. Also, the steep dispersion curve suggests that the relaxation process in the gel is due to relatively simple molecular motions. These two observations are quite contrary to our expectation that the relaxation of molecules in the liquid crystalline gel state would be a complex dynamic process because of the close proximity of individual molecules. Figure 4 illustrates the time-course of the change in the dielectric behavior of H b S after deoxygenation. Thus, Figure4, curve B, is the curve obtained immediately after gas exchange and perhaps represents the behavior of only partially deoxygenated Hb S solution. Figure 4, curve C, was obtained four hours after deoxygenation. Figure 4, curves D and E, were obtained seven and nine hours after the onset of polymerization. These Figures show clearly how the

DIELECTRIC PROPERTIES

OF Hb S

665

dielectric constant of Hb S changes with time after deoxygenation. This experiment was carried out at a concentration of 28"6 g/dl at 37~ a condition very close to the critical region for solution-gel transition, which may explain why gelation was very slow. In erythrocytes, the concentration of Hb S is about 40 g/dl and the sickling process occurs within several minutes at 37~ It is well known that the rate of gelation is proportional to the nth power of the Hb S concentration, as shown by equation (6): 1/t~ = k(c/Cs)',

(6)

where Q is delay time, c is the Hb S concentration and Cs is the solubility; k is an empirical constant. The value of n is known to be about 30. Therefore, a slight decrease in deoxy Hb S concentration drastically slows the rate of gelation. I f higher concentrations had been used, the change in dielectric constant would have been much faster. Dielectric measurements, as shown above, can be used for studies of the kinetics of gelation of Hb S, since the dielectric behavior of Hb S in solution and in gel are different. The results shown in Figure 4 were obtained by initiating the gelation by gas exchange. However, because the gas exchange method requires considerable time, the onset of the gelation process is obscured by the time required for the deoxygenation of hemoglobin molecules.. Therefore, faster methods are required to initiate the gelation process for rigorous kinetic studies. Figure 5 shows the dielectric constant of a deoxy Hb S solution below and above critical temperatures (29"9 and 41~ at a deoxy Hb S concentration of 23"5 g/dl. The measurements were repeated by changing temperature between these extremes in order to confirm the reversibility of the process. These Figures demonstrate that the dispersion characteristics of Hb S can be changed drastically by raising and lowering the temperature of the sample. Figure 6 summarizes the change in dielectric increment between 25 and 42~ These data clearly indicate that a sudden temperature jump can be used to initiate gelation or de-gelation to study reaction kinetics. This experiment will be undertaken in the near future.

(c)

Effects of input voltage

As stated before, low input voltages must be used in order to observe the change in the dielectric constant and relaxation time of Hb S upon gelation. I t is particularly important to maintain the field intensity across the sample as low as possible if the concentration and temperature are near the critical region. Figure 7 shows the dielectric dispersion curves of deoxy Hb S at field intensities of 15 mV (150 mV/cm) and 1 V (10 V/cm). As illustrated, the dielectric behavior of deoxy Hb S with 10 V/cm resembles remarkably that of deoxy Hb S in solution (see Fig. 2). Whether high intensity fields would really decompose the gel structure and transform it to a solution is uncertain. However, these Figures clearly show that a field intensity of 10 V/cm is sufficient to change the dielectric behavior of deoxy Hb S in the gel state. Systematic studies on this problem are necessary.

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4. D i s c u s s i o n

As has been discussed, the dielectric properties of over-saturated Hb S change drastically upon gelation. However, contrary to our expectation, deoxy Hb S molecules still display a well-defined dielectric polarization in the gel state, indicating that a certain freedom of molecular motion still exists even under this condition. It was observed by Takashima (1958) that a well-defined dielectric relaxation persisted even when hemoglobin solutions were frozen. The dielectric relaxation observed by him under these conditions is different from that of hemoglobin in solution, in that the relaxation frequency was shifted to a high frequencY region. It was concluded that the relaxation process in the frozen state

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was due either to limited molecular rotation of hemoglobin or to ion movements along the surface of hemoglobin molecules. The low dielectric constant of gelled hemoglobin molecules can be produced by fluctuations of counterions along the surface of tactoids in the transverse or longitudinal directions. Equations (7) and (8) show the dielectric increment and relaxation time (t) due to counterion fluctuation across a cylindrical particle (Ishiwatari & Schwan, unpublished work). This equation is nearly identical to the counterion theory derived originally by Schwarz (1962) for spherical particles, except for a numerical factor:

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FI(L 5. Dielectric constants of deoxyhemoglobin S below and above tile critical temperature. at 35"5~ curve B, at 41~ curve C, at 29-4~ Concentration, 28"9g/dl.

C u r v e A,

of free space. I n equation (8), u is the mobility of counterions, in this case m o s t likely to be Na + and C1-. Although similar equations were derived for cylinders along the longitudinal direction (Takashima, 1967), usually this polarization appears at very low fl'equencies for a rod of 5 to l0 ~m and should be excluded from our consideration. I n order to calculate the dielectric increment using equation (7), we used the following values of various p a r a m e t e r s : volume fraction p of a p p r o x i m a t e l y 0"3, e = 4-8 x 10-1~ a n d R - - 6 0 Ausing Finch's model (Finch et al., 1973). The charge density a is calculated from the n u m b e r of t i t r a t a b l e groups on the surface of hemoglobin molecules. Using a c i d - b a s e t i t r a t i o n d a t a , ionizable groups at neutral p H are a b o u t 150 per molecule. Converting this value for unit area, we find the value o f o to be 20 x 1013/cm 2 and s u b s t i t u t i n g these values in equation (7), we find the dielectric increment to be 110 for a 30% hemoglobin solution. This value is almost three times as large as t h a t observed e x p e r i m e n t a l l y (40 units).

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670

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Likewise, the relaxation time is calculated using a value for the mobility u of 4"78 x 10s cm 2 -1equiv.-1 (Robinson & Stokes, 1959) assuming the counterion to be predominantly Na +. At 35~ the relaxation time is found to be-0"9 • 1 0 - s seconds using equation (8). This value is equivalent to a frequency of 18 MHz, which is considerably higher than the observed value, i.e. 1 MHz. However, the mobility of Na ions near the surface of charged macromolecules may be lower than that in free solution. In any case, the calculations are based on crude estimates of various parameters, and refinement of these estimates may bring calculated values closer to those observed. Thus, the results of the above calculations are inconclusive either for or against the counterion hypotheses. The second possibility is to attribute the small increment to the fluctuation of protons along the surface of protein molecules (Kirkwood & Shumaker, 1952). Because of their small size, the mobility of protons is greater than that o f any other counterions. The possible contribution of proton fluctuation to the dipole moment of protein molecules has been discussed by several investigators (Schlecht, 1969; South & Grant, 1972). Of particular interest is the recent statement by Gascoyne et al. (1981), t hat the chemical modification of lysozyme in an attemp t to alter protonic surface transport resulted in a change in dielectric behavior. In view of these analyses, proton fluctuation is one of the mechanisms that may explain the behavior of Hb S in the gel state, where the orientational polarization may be restricted because of interlocking. Another possible influence on the dielectric dispersion for gelled deoxy Hb S is the limited orientation of individual Hb S molecules in the lattice of semicrystalline structure. The polarization of H b S molecules in the gel is characterized by a well-defined dispersion curve, indicating t hat the orientation of Hb S is limited to one or, at most, two molecular axes. The interlocking of Hb S molecules in the gel is stabilized by several hydrophobic interactions between various amino acid residues between adjacent molecules, including a fl-6 valine. Of these interactions, that involving the fl-6 valine may be the dominant bond. If the application of external fields disrupts these hydrophobic bonds except that involving the fl-6 valine, Hb S molecules may rotate around this axis. As is well known, the relaxation time of spherical molecules is proportional to the viscosity of the medium (Debye, 1929), i.e. : t--

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where R is the gas constant, ~ is viscosity and a is the radius of a sphere. The macroscopic viscosity of the Hb S gel is considerably higher than t hat of Hb S solution. Therefore, the shift of the relaxation frequency of Hb S upon gelation to a higher region cannot be explained unless we assume limited but rapid orientation of individual molecules in the lattice. Whether this type of molecular motion is common in liquid crystals or unique to Hb S gel is unknown.

This work was performed as partial fulfilment of Z. Delalic's Ph.D. requirements. This work is supported by ONR N00014-82-K-0321. One of us (T.A.) is supported by

DIELECTRI(' P R O P E R T I E S OF Hb S

671

National Institutes of Health grants HL-20750 and GM 20138, another (K.A.) is a recipient of Career Development Award l K04-HL-00774 from the United States National Institutes of Health.

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