Chemical potential measurements of deoxyhemoglobin S polymerization

J. Xol. Biol. (1985) 184, 517-528

Chemical Potential Measurements of Deoxyhemoglobin S Polymerization Determination

of the Phase Diagram of an Assembling Protein Muriel S. Proutyf-, Alan N. Schechter Laboratory of Chemical Biology National Institutes of Arthritis, Diabetes, and Digestive and Kidney Diseases

and V. Adrian Parsegian Division

of Computer Research and Technology Physical Sciences Laboratory National Institutes of Health, Bethesda, MD 20205, U.S.A. (Received 12 October 1984, and in revised form 22 March 1985) We have used the “osmotic stress” method to determine the phase diagram of deoxyhemoglobin S polymerization. This method involves equilibration? through a semipermeable membrane, of the protein with solutions of inert polymers of known osmot,ic pressure. With deoxyhemoglobin A and S solutions, in which we have demonstrated achievement of equilibrium, plots of osmotic pressure versus concentration initially agree closely with the results of other methods of measurement of colligative properties. However, once the known solubility value is exceeded for the deoxyhemoglobin S solutions at various temperatures, there is a rapid rise in hemoglobin concentration over a narrow osmotic pressure range and then a more gradual increase in concentration. We believe that these two regions correspond, respectively, to the onset of the polymerization process, and of subsequent continuing growth and compression or alignment of polymer. We derive the thermodynamic values for these processes and show that the behavior of the deoxyhemoglobin S system is analogous to the phase transition for a simple chemical system. These results are relevant to understanding the intracellular polymerization of deoxyhemoglobin S in sickle cell disease, and these concepts are applicable to other protein assembly systems.

1. Introduction

double-stranded arrangement of hemoglobin tetramers that have been identified in X-ray photographs of a crystal form of hemoglobin S (Wishner et al., 1975). Minton (1973, 1974) originally argued that the polymerization of deoxyHbS$ could be treated as a two-step phase transition: a precipitation into polymer rods and an alignment of these rods to form a nematic phase. The first thermodynamic measurements of the poiymerization process were done using sedimentation equilibrium centrifugation (Briehl & Ewert, 1973; Williams, 1973).

The polymerization of deoxygenated sickle cell hemoglobin (hemoglobin S, or cQ,(6Glu -+ Val)) within the erythrocytes of patients with sickle cell anemia is the primary pathological event in this disease (Noguchi & Schechter, 1981, 1985). The polymer that forms inside the red cell, and in concentrated solutions of deoxyhemoglobin S, appears by electron microscopy to consist of seven double-stranded twisted helices (Dykes et al., 1979). These helices, in turn, appear to be composed of the

t Present address: Department of Chemistry, University of the District of Columbia. X.W.. Washington, DC 20008, U.S.A. 002%2836/85/150517-12

$03.00/O

1321 H Street.

$ Abbreviations used: HbS, hemoglobin S; HbA, hemoglobin A; HbAS, a mixture of HbA and HbS.

517

0 1985 Academic Press Inc. (London) Ltd.

518

M. S. Pro&y, A. N. Schechter and V. A. Parsegian

Subsequently, an extensive series of measurements of the thermodynamics of the polymerization process (Hofrichter et al., 1976; Ross et al., 1977; Jones & Steinhardt, 1979) have been reconciled with a supersaturation-precipitation model. Such analyses have been helpful in studying the effects of inhibitors of gelation (Noguchi & Schechter, 1978). In addition, this approach has led to a detailed analysis of polymerization kinetics in terms of a nucleation-controlled mechanism (Hofrichter et al., 1974; Ferrone et al., 1980). However, it has been necessary to correct for the large non-ideality of the unpolymerized hemoglobin (Minton, 1977 Ross et al., 1978) and of the aqueous solvent (Gill et aE., 1980) under physiological conditions. Indeed, the presence of polymer at very high levels of oxygen saturation, seen by direct 13C nuclear magnetic resonance monitoring of intracellular hemoglobin S polymerization (Noguchi et al., 1980), has been accounted for by recognizing this solution nonideality (and red cell heterogeneity: Noguchi et al., 1983). Herzfeld and Briehl (Herzfeld, 1982; Herzfeld & Briehl, 1981a,b; Briehl & Herzfeld, 1979) have taken an important step in developing a statistical mechanical model that treats polymerization and polymer packing as concurrent events, giving a distribution of polymer lengths at different stages of assembly. Such models require detailed, and hitherto unavailable, information about the phase diagram of hemoglobin S undergoing gelation, particularly of the energies on the reactions involved. To meet this need, we have adapted an “osmotic stress” method previously developed to measure forces between neutral phospholipid bilayers (LeNeveu et al., 1976; Parsegian et al., 1979; Rand, 1981; Lis et al., 1982), charged bilayers (Cowley et al., 1978; Loosley-Millman et al., 1982), muscle fibers and tobacco mosaic virus particles (Millman & Nickel, 1980; Millman et al., 1983, 1984) and DNA molecules (Rau et al., 1984). We monitor the concentration and state (gel versus solution) of hemoglobin S as a function of the imposed chemical potential of water. When water is removed from the hemoglobin S-water mixture, the molecular concentration reaches a temperature-dependent critical concentration at which the gel phase begins to form and there is a jump in total protein concentration. Further controlled removal of water compresses the gels to the very high concentrations often seen in sickled cells. By knowing the activity of water, and consequently of protein, at all stages of this compression and by following this process at several temperatures, we are able to extract the energetic parameters that describe both the processes of polymerization and polymer packing. We find that the energetics of gel formation differ from earlier results when we take into account the significant compressibility of the gel phase. We find also that the concentration versus compressive pressure plots can be recast in the form of traditional vapor-liquid isotherms to show that

the same kind of information is now available for assembling proteins that one normally associates with the condensation of simpler materials. The osmotic stress method can now be applied to hemoglobin S in the presence of controlled activities of perturbing ligands. It also offers a new way to characterize the assembly of other proteins.

2. Materials and Methods (a)

Osmometers

We measure the osmotic pressure of protein systems using a simple “secondary” osmometer, shown in Fig. l(a). This osmometer was assembled from materials generally found in all laboratories. For most experiments, a 13 mm x 100 mm test-tube served as the osmometer, with 8 mm flat-width dialysis tubing for the sac, and Intramedic polyethylene tubing no. 320 and a serum cap. The sample volume in the sac was 02 to 0.3 ml, giving a large surface to volume ratio for fast equilibration, and at least 0.1 ml final volume for tests. The sac was immersed in 6 ml of polymer solution. We also used a “carousel” osmometer, in which 6 sacs of protein solution were equilibrated against a single polymer solution (Fig. l(b)). The carousel was sealed with contents under nitrogen for deoxygenation, and was designed so that single samples could be removed under a stream of nitrogen gas, preserving the deoxygenated condition of the remainder of the contents. A small magnetic stirrer precessed around the support post of the carousel, assuring adequate mixing. The same tubing was used for the carousel osmometer; the sample size was 0.1 to 0.2 ml for each sac in a total polymer solution volume of 40 ml. Equilibration at 2O”C, 30°C and 37°C was carried out, in a shaker water-bath, thermostatically controlled to within +O.l deg.C. Equilibration at 3°C was in a cold room maintained to kO.5 deg.C. (b) Membranes The semipermeable sac was made from standard regenerated cellulose dialysis tubing (Union Carbide, M, cutoff 12,000 to 14,000). For the lysozyme solution measurements, Spectrapor no. 3 regenerated cellulose tubing (M, cutoff 3500 from Spectrum Medical Industries, Los Angeles, CA) was used. (c) Inert polymer The macromolecule used in these experiments was dextran T500 (Pharmacia), a fractionated sample of number average molecular weight between 180,000 and 190,000 for the lots used. The osmotic pressure of dextran solutions was measured in 2 ways: for concentrations up to 10% (w/w), in water and in 0.15 M-phosphate buffer, a Knauer Membrane Osmometer (Utopia Instrument Co., Joliet, IL in the laboratory of Dr Andrew Shrake, Bureau of Biologics) was used. At concentrations greater than S%, osmotic pressures were found to be the same as those measured by LeNeveu et al. (1976) for Dextran fraction T250, number average molecular weight 100,000. At high concentrations, apparently, non-ideality terms are large enough to overwhelm the initial molecular-weightdependent term in the virial expansion for osmotic pressure. Thus we are able to use the values given by LeNeveu et al. (1976), measured directly with a pressure beyond the gauge or manometer, for concentrations

DeoxyhemogEobin

S Polymerization

519

Teflon

cap

With O-ring Stainless

Serum

Lucite rubber

cap

N2 above Solutions

steel screw cover with samplmg opening, stopper, and positioning notches

r7

Polyethylene tubing

seal

2

N, inlet

with

stopcock

Lucite carousel sample holder

Semi-permeable membrane Concentrated dextran solution Hemoglobltn solution a

WA

/,

Magnetic

iuc1te

stirrer

carousel

Sample holder (top view) Opening for sample tube Opening for gas equilibration

(0)

(b)

Figure 1. (a) Test-tube osmometer. A single sample of protein solution contained in dialysis tubing ran be equilibrated to a much larger volume of polymer solution of known osmotic pressure. (b) Carousel osmomet,er. Up to 6 separate sample solutions can be equilibrated to the same polymer osmotic pressure.

operating range of the Knauer instrument. At these concentrations, the osmotic pressure of dextran is also virtually independent of buffer used, and of temperature. For speed of equilibration, the use of lower molecular weight dextran or of polyethylene giyeol would give the advantage of lower concentrations and viscosity for the same osmotic pressure; but “tighter” semipermeable membranes might be necessary, thus slowing down equilibration. Dextran solutions were made up and diluted by weight using degassed buffer of the same composition (including dithionite) as the hemoglobin solution against which they were to be dialyzed. Equal concentrations of permeant species was preset. Concentrations of dextran solutions were determined after final equilibration by measuring refractive index, using an Abbe Refractometer. The refractive index increment. for dextran in each buffer system used was determined by measurements on carefully prepared and diluted samples. When dithionite had been added to the solution, a correction was made in the measured refractive index. (d) Hemoglobin

samples

Hemoglobin S was prepared from blood of individuals homozygous or heterozygous for HbS by ion-exchange chromatography on DEAE-Sephacel. HbAS used (a mixture of Hba and HbS) was a lysate from blood obtained by exchange transfusion. Hemoglobin samples were dialyzed into 0.15 M-phosphate buffer (pH 7.4), and concentrated by vacuum filtration and ultrafiltration. For osmotic stress experiments, samples were diluted

with buffer to a concentration about loo,6 greater than the expected equilibrium value. Gelled samples were first cooled or oxygenated upon removal from dialysis sacs in order to permit good volume measurement before dilution. Solutions of sodium dithionite (1 M) were made up with degassed buffer and used within 10 min of preparation. Hemoglobin concentrations were measured by dilution of a portion in KCN buffer (Van Assendelft, 1970) and measurement of cyanomethemoglobin absorbance at 540 nm. The solubility of the stock solution for each run was determined at the appropriate temperature by ultracentrifugation as described by Hofrichter et al. (1976). (e) Lysozymr Egg-white lysozyme (2 x crystallized) was obtained from Worthington Biochemical Co., Freehold, 1\;J. Measurements were carried out in 0.10 M-sodium acetate buffer (pH 4.70), 0.5 M-sodium chloride, conditions chosen to maintain lysozyme in monomeric form and achieve moderate solubility. The concentration of lysozyme solutions after equilibration was determined by measuring the absorbance of a portion at 280 nm. ( f ) Procedure

Osmometer assembly for deoxygenated hemoglobins was carried out in a “glove box” in a nitrogen atmosphere. Oxygen pressure was monitored by an

520

M. 8. Prouty,

A. N. Schechter and V. A. Parsegian

oxygen electrode. Only final mixing and addition of dithionite solution are carried out in the glove box under nitrogen. No more than 4 osmometer tubes are assembled at one time so that fresh sodium dithionite solutions are used always. Sample sacs were performed and stored under buffer in a filter flask; the buffer was degassed immediately before use. Tubes are filled with 5.7 ml of prediluted dextran solution, and kept on ice. as is prediluted hemoglobin. Dithionite solution (1 M) was measured and mixed into 4 dextran tubes (0.3 ml each). A fresh dithionite solution sufficient for 4 hemoglobin samples was mixed into 1.2 ml of hemoglobin, which was kept on ice. A portion (0.3 ml) was measured with a Hamilton syringe and delivered to a sample sac; the sac was fitted with a serum cap, inserted into a tube of deoxygenerated dextmn and the cap used to seal the osmometer. The procedure was repeated, 4 tubes at a time for all tube osmometers in the run. Finally, serum caps on sealed tubes were painted with Glyptal paint (General Electric) and the tubes were transferred to a shaker water-bath thermostatically controlled for . eqmhbration. The procedures for the carousel osmometer were similar. Although other protein samples do not require a nitrogen atmosphere, all samples were kept sealed as a precaution: because equilibration takes several days in many cases. Cautions in equilibration. Although the osmotic stress technique outlined here is simple and straightforward in principle. pressure artifacts can occur easily. Because the polymer stressing solutions are usually concentrated and viscous, solvent drawn out of the sample sac through the semipermeable membrane and into the dextran may, without adequate mixing. form a solvent layer on the surface of the membrane, which can slow, halt or reverse attainment of equilibrium. To solve this problem, we equilibrated all samples in a shaker water-bath and occasionally inverted the entire tube to mix the contents of each chamber (inner and outer compartments are wellsealed from each other). When solvent flow is from the inner to the outer compartment (concentrating the sample), the membrane tends to collapse, bringing about equilibration of gas pressure above the liquids. However, when sample dilution occurs, a back pressure of gas above the sample may halt solvent flow. We seek to prevent this in 2 ways: either by anticipation of final equilibrium values so that equilibration always occurs by concentration, or by making a small puncture in the neck of the sample sac, well above both fluid levels. This second procedure, of course, precludes inversion of the tube, and shaker mixing must suEice. We repeated the measurements that required dilution in the inner sac under conditions where solvent flow was in the reverse dire&ion. with no change in results.

3. Results (a) Proof of equilibrium Although measurement of protein solution osmotic pressures by equilibration against polymer solutions of known osmotic pressure is, in principle, perfectly feasible, it has been used only to a limited extent (Alexandrowicz, 1959). It is a relatively slow procedure. To validate the method, especially for hemoglobin, we carried out a series of experiments designed to show that the equilibrium concentration of the protein sample solution in our

osmometer

is a function

only

of the

osmotic

pressure (concentration) of the stressing polymer solution and of the final temperature. (i) Vuriation

with time

All solutions reached a constant concentration after one to four days, which concentration was then maintained over a period of several weeks while care was taken to prevent denaturation or contamination. For hemoglobin, we were careful to achieve and maintain a completely deoxygenated condition, using a small excess of dithionite. In samples from newly opened osmometers, which had been equilibrated for more than two weeks, the content of methemoglobin was found by spectroscopic measurement to below 5%. After conditions for equilibration were established, preset sample concentrations, where we could anticipate them, were used to speed equilibration. (ii) Variation with initial

concentration

of

sample or polymer

Solutions of hemoglobin initially at 6, 12, or 18 g/d1 all reached the same concentration when equilibrated in the same dextran solution; samples of a hemoglobin solution of 12 g/d1 were diluted to 5 g/d1 or concentrated to 20 g/d1 in appropriate dextran solutions. In using the carousel osmometer, in which duplicate samples were to be equilibrated to the same polymer osmotic pressure, the initial concentrations of hemoglobin in the six tubes were set so that three were at the same concentration higher than the expected equilibrium concentration, and three were at the same concentration lower. Samples equilibrated both in the test-tube and in the carpusel osmometers gave the same result. (iii)

Variation

with temperature

Hemoglobin solutions initially equilibrated at 3°C and 37°C reached the same final concentration when placed in a 30°C bath, as did the sample initially equilibrated at 30°C. (iv) Variation with initial state In equilibration of deoxyhemoglobin S solutions at concentrations where gelation could be expected to occur, experiments in which the following transitions occurred all confirm that final concentration and state of the deoxy sickle hemoglobin depended only on the osmotic pressure of the stressing solution (the sacs containing HbS, after equilibration against concentrations of dextran that produced the initial conditions, were transferred (under N2) to the dextran solutions that could be expected to equilibrate to the final state): solution *gel dilute gel s concentrated gel. (v) Equilibration

of p,rotein solutions

To demonstrate the equilibration of buffer across dialysis tubing separating protein solutions, we made up samples where sacs of hemoglobin were immersed in myoglobin solution (or sacs of

Deoxyhemoglobin S Polymerization myoglobin in hemoglobin solutions). The initial weight concentration ratios of the inside versus the outside solutions were 4 : 1, 1 : 1 and 1 : 4. In all six samples, the final weight concentration ratio of hemoglobin to myoglobin was 3.8 : 1.

521

associated with the crystal structure) over the range of these experiments, but we have not carried out any tests on the lysozyme powder found in these tubes. (c) Osmotic stress of hemoglobin in solution

(b) Osmotic stress of lysozyme solutions The result of the equilibration of solutions of eggwhite lysozyme against dextran T500 solutions in 0.1 M-sodium acetate buffer (pH 4*70), 0.5 M-sodium chloride is shown in Figure 2. In all protein solution experiments, we measure the final concentration of protein in the inner sac and the final concentration of dextran solution (from which we calculate dextran osmotic pressure). Data are plotted as concentration of protein against imposed stress, x. In the solution regime, our data for lysozyme osmotic pressure gives an acceptable molecular weight value; namely 14,000. As the osmotic pressure of a saturated solution is reached and exceeded, every tube shows complete conversion of lysozyme solution to a powdery deposit, presumably crystalline protein. For a protein that crystallizes from solution as the imposed stress is made greater than that for a saturated solution (%3t), solvent will be drawn from the protein solution leading to a phase separation (saturated solution e crystalline solid). However, when protein is transferred to the solid state, any remaining saturated solution cannot be in equilibrium with the stressing solution and, finally, in every tube for which stress > sat, all solution will be converted to solid. Because the excess stress we imposed on the crystallizing protein was not great, we do not believe that there was any change in crystal structure (removal of water molecules

Figure 3 gives the results of osmotic stress equilibration of deoxyhemoglobin A solutions at 3O”C, and of deoxyhemoglobin S in the soluble range at 3, 20, 30 and 37°C against dextran T500, all in 0.15 M-phosphate buffer (pH 7.0). The points shown are experimental, the curve is from Adair’s results for sheep hemoglobin in water at 0°C (Adair, 1928). We find that measured hemoglobin solution osmotic pressure is negligibly dependent on temperature, buffer, and the kind of hemoglobin measured. Osmotic stress runs for deoxyhemoglobin S over the concentration range up to 50 g/d1 are shown in Figure 4. In each case, samples that gelled are distinguished from those that remained fluid. We considered those solutions to have gelled in which we could observe no flowing when the tubes were tipped or inverted. The first observed gel occurred at a concentration about 10% greater than the solubility measured for the stock solution and indicated on Figure 4. This represents an amount of hemoglobin above saturation sufficient to give enough polymer to form the gel, and confirms that deoxyhemoglobin S solutions will always gel at or above a critical concentration, no matter how that

30

p...

1

.

.

.-v

s I 5

I20

c

IO

2

4

8

6 77strers(cm 4)

IO

-

Figure 2. Osmotic stress plot for lysozyme equilibrated against dextran TM0 in 0.1 u-sodium acetate buffer, 0.5 M-sodium chloride at 30°C. Open circles show the concentration of lysozyme samples that remained in solution at equilibrium. Filled circles indicate the lysozyme samples in which only a white crystalline powder remained in the sample sac after equilibration to the designated dextran osmotic pressure. The concentration of lysozyme in the apparently crystallized samples was not measured. 18

IO

I 20

C,,(g/dl) Figure 3. Osmotic pressure of hemoglobin A (filled circles) and S solutions in 0.15 M-phosphate buffer function of hemoglobin concentration, equilibration against dextran TWO continuous line is the theoretical fit by (1977) to Adair’s (1928) data.

I 30

deoxygenated (open symbols) (pH 7.0) as a measured by solutions. The Ross Q Minton

522

M. S. Prouty, A. N. Schechter and V. A. Parsegian

Figure 4. Concentrations of gelled deoxyhemoglobin solutions as a function of osmotic pressure. ( x ) Single samples measured in test-tube osmometers at the temperature indicated. All other symbols represent multiple samples measured in a carousel osmometer. Each symbol represents a separate carousel experiment. Open symbols indicate that the initial concentration of HbS was set below the expected gelation concentration. Filled symbols indicate that the initial concentration of HbS was greater than the expected gelation concentration. The continuous line is fitted to data for non-gelled samples as in Fig. 3; for clarity, experimental values are not shown again for the solution state.

concentration is brought about. From these plots, it becomes obvious that the concentration versus stress curves at each temperature (except possibly at 3°C) can be divided into three regions: the soluble portion, discussed above; a sharply rising curve beginning where gelation occurs; and, finally, a region of moderate, almost linear slope, which can be described as a gel compression region. The onset of gelation marks the departure of the measured osmotic pressure (chemical potential) of the gel from that of liquid hemoglobin solutions. The change of slope at this point is further evidence that gel formation represents a phase change rather than simply an increase in the viscosity of the system, and leads into a region of gel activity not previously accessible experimentally.

In the sharply rising portion of the plot, over a range of concentration, we may visualize that a gel formed at a hemoglobin concentration low in the range can be stressed very easily to give up buffer until it reaches a concentration at which considerably more work must be done to remove the next and subsequent water increments. The extent of the concentration range of easy compressibility depends on the temperature, and covers a broadening range of concentrations as temperature increases. This feature becomes clearer when the complete curves for all temperatures are drawn on one graph with the Adair solution osmotic pressure curve, Figure 5. We can then see more easily that the osmotic pressures of all hemoglobin solutions the same c versu.s 7~curve at pH 7.

fall on

523

Deoxyhemoglobin 8 Polymerization

I 20 30 77 (cm Hg)

Y 0

IO

I 40

Figure 5. Concentrations of deoxyhemoglobin solutions and gels as a function of osmotic pressure at 2O”C, 30°C

and 37°C. The continuous line was drawn through solution values (Fig. 3); the broken lines represent best fit to data for gelled samples.

the

1 0

IO

20 30 77 (cm Hg)

40

--

1

Figure 6. Osmotic pressure of deoxy HbAS lysate (70% S) in 0.15 M-phosphate buffer (pH 7.0) at 3O”C, aa a

function of total hemoglobin concentration equilibrated At the appropriate stress (or hemoglobin solubility), the plot for each temperature “peels off” the solution curve as the system gels, and from then on exhibits its own gel behavior. The temperature dependence

of the extent

of the easily

of

an

increment

of

water

is

here

independent of temperature and concentration. The osmotic stress behavior at 30°C of a mixture of HbA and HbS (a lysate containing 70% S obtained

from an exchange

transfusion)

is shown in

Figure 6. The data points for the HbAS mixture are shown superimposed on the curve drawn through the experimental data for pure HbS at 30°C. The solubility of the mixture (26.3 g/dl) is greater, as expected. At higher stresses and greater concentration, the behavior of the HbS and HbAS gel systems are identical. This behavior depends on three factors: (1) the medium in which the polymer exists contains buffer and hemoglobin tetramers according to which, Ross & Minton (1977) function as hard spheres, giving rise only t,o excluded

volume

effects.

No

points (( 0) mixture; the and is taken HbS gels and

compressible

range is more evident. We note also in the gel compression region that as stress is increased, the concentration response of the gel is almost linear at each temperature, and that the slopes of these lines are remarkably close to each other. The work of removal

against dextran T500 solutions. Data solution; (0) gel) are for the HbA/HbS continuous line is for hemoglobin solution from Fig. 3; the broken line represents pure is taken from Fig. 5.

difference

is to

be expected between HbA and HbS molecules in this regard. (2) Compression and alignment of polymerized hemoglobin fibers in the two systems, which appear to reflect the behavior of identically compressible fibers: and (3) formation and growth to occur. In the of polymers, which continue conventional gelat*ion assay at constant total concentration, it has been shown hemoglobin (Sunshine et al., 1979) that HbA tetramers do not enter into the polymer fiber structure, but that hybrid (HbAS) hemoglobin can go in. However, as total protein concentration increases, the pool of

monomer available is HbS only in the pure case, and an increasingly HbA-rich mixture in the HbAS system. Thus, the observed identical c versus 71 curves in Figure 6 may reflect some incorporation of HbA or HbAS hybrid into fibers at high concentrations. AlternatiSely, polymerization behavior may be overshadowed here by the processes involving the fibers.

4. Discussion The methods and results presented above can be considered from three different aspects. First, we have introduced and demonstrated a new method for measuring the thermodynamic parameters that characterize protein polymerization and gelation. Second, we report the chemical activit,y of deoxygenated HbS both in solutions of unaggregated molecules and under conditions of transition into polymers and then for the compression of those polymers in the “gel” state. Third, we have found that at the temperatures and protein concentrations characteristic of sickleshaped red cells, the packing of the gel fibers is as important a factor in protein free energy as is the initial polymerization that creates fibers. (a) Osmotic stress for studying protein assembly It is popular practice in creating crystals of proteins for X-ray diffraction analysis to mix

524

M. S. Prouty, A. N. Schechter and V. A. Parsegian

polyethyleneglycol or dextran polymer with protein solutions to “exclude” the protein molecules into The common and aggregates. assumption experience is that the polyethyleneglycol or dextran does not co-aggregate with the protein. Our observation that lysozyme appears to crystallize within a dialysis sac immersed in dextran solutions of known osmotic pressure suggests that one may measure the crystallization free energies of many proteins. Indeed, phase transitions have already been so characterized in lipid bilayers under osmotic stress (Lis et al., 1982). Traditionally, osmotic pressures have been used to determine the amount of work needed to remove “non-ideal” water from a solution. However, behavior, due to protein interaction, is generally avoided by using very dilute solutions in measuring properties of individual molecules. Molecular interactions, central to studying aggregation, are treated as deviations from ideal behavior. Also, experimental difficulties limit the utility of traditional osmotic pressure measurements. For example, direct measurements of the osmotic pressure of a gelled preparation would require transfer of the highly concentrated sample into an osmometer chamber. Osmotic stress measurements, in contrast, are deliberately designed to measure behavior in concentrated non-ideal preparations. The chemical potential of the dialysis-permeant species is set by adjusting the concentration of impermeant polymer (dextran in these measurements: LeNeveu et al., 1976; Parsegian et al., 1979; Rand, 1981). The external polymer solution exerts a constant stress to which the internal protein solution responds; ultimately the outward pressure of the protein suspension is equal to the pre-set inward osmotic pressure of the imposing solution. At low stress, the procedure is effectively a traditional osmotic measurement in pressure solution reverse; concentration is measured as a function of osmotic pressure. At higher stress, when protein polymerization or crystallization occurs because water is drawn out from the protein preparation, one can measure the amount of thermodynamic work needed to create and to pack those aggregates. Since the protein-containing medium can be immersed in a polymer medium of much greater volume, the stressing medium can act as a reservoir for any species that can diffuse across the dialysis membrane. Hence, one can set the chemical potential of all permeant species that affect aggregation. One can create phase diagrams of aggregating proteins at all appropriate values of temperature, salt concentration, pH and activities of liganding species. These capabilities are amply illustrated by our findings with deoxygenated HbS. Under conditions where the material exists as single hemoglobin molecules, we measure concentrations as a function of osmotic stress identical to what would have been expected from earlier osmotic pressure measurements (Fig. 3, continuous line). In clear support of

the reasoning of Ross & Minton (1977), that the non-ideality of hemoglobin is due primarily to the finite volume and mutual impenetrability of the individual molecules, we see that all hemoglobins stressed showed the same concentration as a function of activity. Novel behavior important to this study begins when the measured values of protein concentration deviated from those found for hemoglobin solutions at the same osmotic pressure. These deviations are the rapidly rising segments of the HbS curves at 37”C, 3O”C, 20°C and (slightly) at 3°C (Fig. 5). The designated as osmotic pressures of activities, solvent at which the deviations occur, give the protein free energies at which the protein begins to polymerize. We will show below how these free energies are to be used to derive the thermodynamic changes that attend polymerization. It is possible that the sudden rise in concentration of HbS may not be the vertical jump characteristic of sudden chain condensation into crystals. There may be a finite slope to the concentration versus stress, indicating that further work is needed to pack the (rodlike?) products of aggregation. Rather than collapsing to a crystalline state, HbS begins to form aggregates that resist the removal of water that is required for tighter aggregate packing. Herzfeld (1985) suggests that growth of a thick polymer might create a finite slope different from that expected for a purely firstorder transition. In all cases, the regions of rapid polymerization are bounded at higher concentrations by regions of moderate slope. It is probably significant that the slopes of all HbS curves in this gel region are essentially the same at all temperatures. We suggest that these highconcentration gels show the dominant effect of polymer/fiber packing rather than the work of polymerization itself, and we treat them as a distinct phase. (b) Extraction

of thermodynamic parameters

We use the chemical potential ~(n, T) per molecule (or mol) protein as a function of and osmotic pressure. Following temperature traditional definitions of potential as a work function derived from the internal energy li, we write: dU = TdS-XdV,

(1) where S and V are the entropy and volume per molecule (or mol) protein, and we define: p = U-TS+nV,

(2)

to obtain: dp = -SdT+

Vdn.

(3) This last relation shows how the chemical potential of protein enclosed in the dialysis sac rise 3 with applied pressure. Protein chemical potential relative to its value at any other concentration is obtained by integrating dy at constant temperature, i.e. integrating Vdn.

Deoxykemo&bin S Polymerization

525

Table 1 T W) 293 298 303 310

XI (g/W

@fi WV

21.5

26.5

18.5 16.5

33.9 36.7

10-572 (dyne/cm’)

10-5AVt (cm”/mol) - 0.569 - 1.0751 - 1.548 -2.164

t Hb JI, = 64,800. $ Calculated from the relations given below: n(T) = 43.334 x lo’-@2340x 105T+31.993TZ

AH

As (cal/mol K)

(kcal/mol)

6.4 11.3 15.1 18.8

2.2 3.8 5.2 6.5

2.10 1.871 1.66 1.39

dyne cm-‘.

AV(T) = 79416x 105-044498x lo5 T+58~235TZcm”mol-‘. AS(T) = (dn(T)/dT)(AV(T))/4.184

x 10’ cal (mol K)-‘.

Note that this relation holds, normalized per hemoglobin (tetramer) molecule, at all concentrations and conditions of aggregation. Note also that we are treating the entire population of permeant species as the effective solvent. Although hemoglobin is a polyelectrolyte, the Donnan effect can be ignored because we are working at sufficiently high concentrations of salt. In squeezing that solvent out of the hemoglobin-containing sac, we are doing physical work on the impermeant species only. It is normalized for the amount of that work, impermeant species, that is of interest. In particular, we can use the chemical potentials with the Clausius-Clapeyron equation to extract the AS change in entropy and AH enthalpy of gelation from the osmotic pressures 8, at the onset of polymerization as a function of the temperature T, at which the transition occurs. Specifically, the Clausius-Clapeyron relation for transition pressure X, and transition the temperatures T, reflects the fact that along the line of coexistence between two (here “gel” and “solution”) phases the chemical potentials of each phase necessarily change identically, i.e. (Landau & Lifshitz, 1958):

@gel @L,o,u -=dT,

dT,

or

-Ass,,,+V*=,g+ = -&,“+ This immediately

VW,”2.

t t assumes the more familiar

Since these are the actual AH and AS terms of a first-order phase transition, they are not automatically comparable to estimates based on solution theory or calorimetry, where the intent is to derive AH and AS for the addition of individual molecules to the polymeric fiber at fixed protein to buffer ratios (e.g. see Ross et al., 1977). The rapid increase in the magnitude of AS with increasing temperature must reflect, in part, the dramatic decrease in gel hydration with increasing temperature. This decrease in gel volume, hitherto unavailable for thermodynamic analyses of sickle cell hemoglobin gelation, is much greater than temperature-dependent changes in the volume of critically saturated solutions. AS, which is of course positive, as expected from the decrease in it, with temperature and loss of aqueous buffer upon gelation under osmotic stress, reflects an increase in entropy much as has been proposed in hydrophobic bonding (Kauzmann, 1959). However, protein association at hydrophobic sites does not yield the great changes in the amount of water in the gel at constant osmotic stress that occur upon heating after gelation. It seems more likely to us that the water-soluble surfaces of the individual hemoglobin molecules or of the polymeric fibers show long-range hydration similar to that observed around bilayer membranes (e.g. see Rand, 1981; Lis et aZ.,1982) and around DNA

(5) 1

form:

-&o,u AS AH = dnt Sge, -= = E = T,dv + T&’ dTt Vge,--VSO,”

(6) -6

where we use AC = 0 = AH-TAS+nAV. In Table 1 we list three sets of data: temperature, osmotic pressure, gel and solution Hb concentrations where transitions are observed. From these concentrations we calculate the respective volumes and tabulate the difference: A V = VW1 sat_ V-In sat . We write quadratic equations for nt(Tt) and A V(T,), see Table 1, and use the Clausius-Clapeyron relation to derive AS. These relations are plotted in Figure 7.

I

I 290

I

I

I

I

I

I

310 T(K)

Figure 7. The entropy AS () and enthalpy AH ( - - - ) of gel formation under osmotic stress oepw transition

temperature

as calculated

by eqn (6).

526

M. S. Pro&y, A. N. Schechter and V. A. Parwgian

I

0

100

I

200

I

I

300

400

Molar

volume (1 )

I

500

Figure 8. Osmotic pressure-molar volume isotherm& for deoxygenated volume isotherms for carbon dioxide, taken from a standard ;;hysical to classical gas condensation.

double helices (Reu et al., 1984). Only in these systems are there the large numbers of ordered water molecules that are seen here “melting off)’ the fiber and dominating the thermal changes in gelation . An appealing and instructive analogy between gel formation and classical gas-to-liquid condensation is apparent when we replot nosmoticand concentration in the units of a pressure-volume diagram (Fig. 8). The use of such diagrams makes more intuitive the comparison of measurements with models of condensation. (c) Cellular consequences This polymer-packing regime occurs at the and concentrations occurring in temperature sickled cells. Hemoglobin is present at approximately 34% (w/w) in normal red cells at 37°C (Harris & Kellermeyer, 1970), a density achieved in vitro by the application of an osmotic pressure of approximately 35 cm Hgt. This same pressure applied to deoxygenated HbS creates gels of greater than 50% (w/w), similar to concentrations observed in the most dense sickle erythrocytes (Noguchi et al., 1983). Noguchi et al. (1980) have measured the fraction

t Non-S1 unite used in this paper: 1 mm Hg = 13.5951 x 980.665 x lo-’ 1 dyne = 10s5 N; 1 cal = 4.184 J.

Pa;

I

600

sickle hemoglobin. Inset: PV pressurechemistry text, show the resemblance

of polymerized HbS versus HbS concentration in preparations in vitro at 30°C. We use their results to infer the concentration C, of protein actually polymerized at each of our measured total CT protein concentrations also at 30°C: C, = f&J,. The pressure needed to pack this polymerized fraction is taken to be the difference between the measured pressure 71s,, in the gel state and the saturating of pressure Z,,, seen at the commencement polymerization. Figure 9 shows the polymer pressure nPolY as computed from the assumed form: J&l = =,o”o + ~poly = %at + J-&olyr against the concentration of polymer. It is clear that for the concentrations of >30% (w/w) known to occur in sickle cells at 37”C, the system will be in the region where the work of concentrating protein is as much work of polymer packing as of polymer formation. What can we say about the polymerization of sickle hemoglobin in cells as opposed to solution? In the context of the osmotic stress picture we have one must note that normal been developing, hemoglobin in normal cells is under a stress that corresponds to 35 cm Hg or more. This stress is far in excess of the osmotic pressures of the surrounding plasma and is presumably maintained by the controlled exchange and leakage of small ionic species across the cell membrane (e.g. see Freedman & Hoffman, 1979). (From the success of the Minton-Ross excluded volume model, we

Deoxyhemoglobin S Polymerization

40

t

IL1 0

IO

20

30

40

CP

Figure 9. Gel osmotic pressure (n,,,) and polymer osmotic pressure (APly = lclcl-s,J aa a function of polymer concentration (C, = C, xfr) for deoxy HbS gels at 30°C.

know that this estimate cannot be far off, even though it neglects the dependence of hemoglobin activities on the activities of all other components.) The clear difference between the normal hemoglobin pressures (Fig. 4, continuous lines) and the data at 37°C for HbS (Fig. 4, broken lines) suggest that, under a constant stress imposed by membrane transport, one should expect large differences in intracellular sickle hemoglobin concentration as it successively takes on and loses oxygen. Under membrane-controlled osmotic stress, at 12 cm Hg or less, sickle cell deoxyhemoglobin S would look little different from normal HbA. Mixtures of oxygenated and deoxygenated hemoglobin would be expected to show critical gelation pressures higher than the critical 12 cm Hg pressure necessary to create gels at 37°C. The extra pressure should reflect the extra entropic work of demixing species evident in the data on mixed sickle and normal hemoglobins shown in Figure 6. To make the connection between our present studies in vitro and the properties of hemoglobin in sickle cells, it is necessary to couple equilibrium osmotic stress results with the kinetic properties of membrane transport, oxygen exchange rates and polymerization rates. The osmotic change accompanying polymerization should cause a decrease in cell volume unless accompanied by a change in membrane properties or ion balance requirements. This possible shrinkage might account for the existence of the dense cells that are important determinants of the severity of sickle cell disease. Fabry & Nagel (1982) observed that homozygous sickle cells shrink or maintain constant

volume

when

sickled

cells

deoxygenated, become

always

while more

irreversibly dense. The

527

tendency toward shrinkage is affected by pH value and K+ concentration. Our results suggest that the polymerization process will be accompanied by a loss of water (increase in density or Hb concentration), except when constraints such as membrane impermeability or ion balance prevent or limit the extent of solvent flow. An additional condition was studied by Horiuchi et al. (1983, 1985), who have incubated sickle cells in vitro with all cell nutrients except calcium ions. On repeated deoxygenation and oxygenation, they find that, although polymer is formed in the deoxy cells, there is no change in cell volume or density. When Ca2+ is added to the extracellular medium, several cycles of oxygen removal and addition cause the cells to decrease in volume and become more dense, as they do in vivo, where calcium ions are known to enter the sickle cells and render them somewhat ion-permeable. In osmotic stress experiments, in which buffers can move easily across the dialysis membrane, we observe a marked decrease in volume (increase in Hb concentration) upon gel formation. In sickle cells in viva, and in sickle cells in vitro when calcium ions are present, gel volume decreases and Hb concentration increases. On the other hand, in deoxyhemoglobin solutions where the total amount of material is fixed, in a viscometer (Kowalczykowsi & Steinhardt, 1977) or a dilatometer (Kahn & Briehl, 1982), no change in density is observed on gelation; the gel occupies the same volume as did the liquid solution.

This

situation

parallels

that

of

intact

sickle cells in the absence of calcium. We thank Drs W. Eaton. J. Herzfeld, J. Hofrichter, A. Minton, C. Noguchi and P. Ross for helpful discussions.

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by M. Gellert