Gelation of sickle cell hemoglobin IV. Phase transitions in hemoglobin S gels: Separate measures of aggregation and solution-gel equilibrium

Gelation of sickle cell hemoglobin IV. Phase transitions in hemoglobin S gels: Separate measures of aggregation and solution-gel equilibrium

J. Mol. Biol. (1978) 123, 521538 Gelation of Sickle Cell Hemoglobin IV.? Phase Transitions in Hemoglobin S Gels: Separate Measures of Aggregation and...

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J. Mol. Biol. (1978) 123, 521538

Gelation of Sickle Cell Hemoglobin IV.? Phase Transitions in Hemoglobin S Gels: Separate Measures of Aggregation and Solution-Gel Equilibrium ROBIN W. BRIEHL

Departments of Biochemistry and Physiology Albert Eilzstein Collegeof Medicine, Bronx, N. Y. 10461, U.X.A. (Received

18 August 1977, and in revisedform

6 April 1978)

Two assays of equilibrium properties in the gel&ion of deoxyhemoglobin S were carried out by analytical ultracentrifugetion on the same sample: Csat, the monomer concentration in equilibrium with the fully formed gel, was obtained as the supernatsnt concentration after sedimentation of a. preformed gel. The presence of a plateau region during sedimentation of the supernatant and the rate of sedimentation of the boundary from which C,,, was measured indicate that centrifugation did not alter the pre-existing equilibrium and that the supernatant consisted of monomers. The centrifugation was then continued to equilibrium to obtain a distribution showing a sharp increase in molecular weight at C,,,, the monomer concentration at which a small amount of polymerization to large aggregates begins. The primary result is that C,,, > C,,, under all conditions. The different values of the two parameters indicate that they reflect two separate transitions and that the overall monomer to gel process has a limited co-operativity. Within the limits of the method C,,, is independent of total hemoglobin concentration. The two transitions divide the overall range of total hemoglobin concentration into an essentially monomeric region at concentrations below C,,,, a region in which isotropically oriented polymers exist, occurring when monomer concentration lies between C,,, and Csat, and a two-phase region of conjugate isotropic and anisotropic phases when monomer concentration equals C,,,. These regions correspond to zones in the ultracentrifuge equilibrium distribution. In this scheme Cass depends only on the interaction energy of polymerization. C,,, depends on entropic factors which induce tactoid formation as well. Csat, while a monomer concentration, reflects a saturation not of monomers in relation to a polymeric phase, but of polymers in the isotropic phase in relation to the anisotropic or tactoidal polymerized phase. As such, C,,, represents a supersaturated state of isolated monomers . The ratio Csat/Cagg = 1.23 in stripped hemoglobin$ and equilibrium distributions in the zone of isotropically oriented polymers were both used to obtain an order of magnitude estimate of polymer size, found to be much smaller than that of hemoglobin S fibers. This further confirms that gel&ion does not consist of a single transition and phase change with near infinite co-operativity of polymerization. C,,, as well as C,,, are lowered by 2,3,diphosphoglycerate and inositol hexaphosphate. Decreasing pH near 7 also favors gelation; in stripped hemoglobin a pH optimum for gel&ion occurs near pH 6.8. The apparent van’t Hoff dH for stripped hemoglobin is about 3 kcal/mol for C,,, and 2 kcal/mol for C,,,. t Paper III in this $ Stripped indicates

series is Briehl BE Salhany (1975). hemoglobin in the absence of organic


521 0022-2836/78/1234-2138



1978 Academic

Press Inc.





1. Introduction Since the sickled rrytlrrocytt~ cat1 1~ c:onsidctwl a tnetnk)rattc~ c:ovc~tx~l tactoitl (Harris. 1950), sickle cell disease can bc approachctl as a (I~SHRSV tiw to ittt~ae~~t.l~~o~~t~( phase changes. However, kinetic studies (Hofrichter et ul.. 1974) have sho\\.n t,hat thtb solution to gel change cannot be treated as a single phase condensat’ion, but must include at least stages of nucleation, fiber growth and fiber alignment. Accordingly, hemoglobins may exist as monomerst in solution, as nuclei or as fibers consisting of helical arrays of monomers (Finch et al., 1973; ,Josephs et al., 1976). The fibers may be oriented isotropically, anisotropically with partial alignment (the tactoidal phase) or possibly in a highly aligned dense fibrous state (Flory. 1961,1972: Minton! 1974) to form distinct macroscopic phases, depending on entropic fact,ors resulting from particle asymmetry and on enthalpic interact,ions (Onsager, 1949: Flory, 1956; Minton, 1974). The purposes of the current study are t,o seek evidence of and characterize properties of multiple phases and states of aggregation in the gel at equilibrium, to determine what transitions and states various assays of gelat’ion reflect, and to provide approaches to the possible roles of different phases and states in producing t,he pathophysiological phenomena of sickle cell disease. Analysis of the phase structure of and polymerization in the gel has been limited by the assays of gelation employed. For example. the most common measure of gelation, minimal gelling concent,rat)ion, with end-point, judged by viscosity increase (Allison, 1957; Charache & Conley, 1964) or gross solidification (Singer & Singer, 1953 ; Bookchin et al., 1967), reflects only gross properties of an apparently homogeneous mass without regard to the variety of phases which may be present in it. In addition, minimal gelling concentration assays depend on kinetic factors resulting from the nucleation-dependence of gelation (Malfa & Steinhardt, 1974; Hofrichter et al., 1974; Moffat & Gibson, 1974) and thus are poorly adapted for characterization of equilibrium properties of the gel. Another common assay depends upon measurement of the solubility of hemoglobin 8 under saltsing out conditions (Itano, 1953; Benesch et aZ., 1974 ; Waterman et al., 1974) ; while result’s do correlat,e with gelation as observed at physiological ionic st,rengths. there may exist differences in intermolecular interactions under t’he different conditions. In the present workf two analytical ultracentrifllge methods which depend upon separate equilibria in gelation are employed. In the first method equilibrium is established (Williams, 1973; Briehl & Ewert, 1973) and the concentration in the distribution at which weight average molecular weight increases sharply is ascertained. Previously designated a minimal gelling concentration (Briehl & Exert. 1973), it is in fact a concentration needed to induce an arbitrarily defined small but measurable amount of aggregation : it is therefore called C,,, here. C,,, is less than the concentration required to induce mechanical gelation. In the second method, based on early experiments of Allison (1957) and Bertles et al. (1970) and employed in recent studies (Magdoff-Fairchild et al., 1976; Hofrichter et uZ., 1976; Briehl, 1976; Goldberg et al.. 1977), a preformed gel is sedimented and the concentration of hemoglobin in t,hr t The term “monomer” will be taken to designate the hemoglobin molecule of molecular weight, 64,500, consisting of four subunits. $ A preliminary report of this work has been given at the Symposium on the Moleculnr cmcl Cellular Aspects of Siclcle Cell Disease, Dallas, Dec. 10, 1975 (Briehl, 1976).







supernatant, designated CSat, is measured. In the current work the two methods are employed sequentially in the same run on a single sample. The results show that C,,, is always greater than C,,, and the primary interpretation is that the monomer is a measure of the equilibrium between monomers and polymers, concentration C,,, whereas Csat, although also a monomer concentration, depends on the phase separation equilibrium between polymers in isotropic and bact’oidal states.

2. Materials

and Methods

Hemoglobin 8 was prepared as previously described (Brie111 & Ewert, 1973,1974). Buffers for experimental samples were 0.05 Ilr-bis Trist wit,h 0.1 M-N&I. Samples of about 90 ~1 were loaded into 1.5 mm analytical ultracentrifuge cells at 0°C without gelling as previously described (Briehl & Ewert,, 1973,1974) to give concentrations of 0.10 to O-26 g hemoglobin S/ml (previously deoxygenated under nitrogen), 10 mM-sodium dithionite (added to the cell) and, when used, 10 mM-inositol hexaphosphate or 2,3,diphosphoglycerate. The cells were then incubated, usually overnight, at the temperature of the run to induce gelation; as expected (Hofrichter et al., 1974) among cells identical but for hemoglobin concentration t,trr: most concentrated samples gelled first. To exclude possible effects of dithionite, two 3.cell runs wit,hout this reagent were done and showed results not different from those wit11 it. The centrifugation procedure consisted in the following steps, illustrated in Pig. 1 (Results, section (a)) : (1) centrifugation at top rotor speed (52,640 or 42,040 revs/min) to sediment the gel to a pellet and to form a free boundary between buffer and hemoglobin solution in the supernatant; (2) slowing of the centrifuge (2 to 6 11 later) to 12,000 to 15,000 revs/mill to permit difYusion of the boundary; (3) in most rims, continued centrifugation to equilibrium for 7 or more days at 19, I60 revs/mill, followed by cooling to 2”C, as previously described (Brie111 & Ewert, 1973,1974). Also as previously described, absorption spectra of the cell contents were obtainrId in s&u after centrifugation from 1200 to 600 nm to confirm the presence of deoxylremoglobin without reoxygenation or methemoglobin. pH values were obtained on cell contents as before (Briehl $ Ewert, 1973). In order to obtain Csat, equal to C,, t,he hemoglobin concentration in the supernatant corrected for radial dilution, t,lle free bolmdary schlieren (step (2), above) was measured with a Nikon model 6C comparator and int,egratrd llllrnprica811,v according to tile equation,

where T is the radial position in the cell, C is hemoglobin concentration and the subscripts m and p indicate meniscus and plateau region, respectively. The error in C, for a single run was about kO.003 g/ml, due to errors in baseline and/or slight deviations from a true plateau region as the boundary diffused. As a check on the values of C,,, thus obtained, a slumber of runs were done as described by Hofrichter et al. (1976) in quartz tubes in a Spinco preparative ultracentrifuge with an Sm-.50 rotor. Supernatant hemoglobin concentrations were measured in situ from the absorption spectrum with millimolar difference extinction coefficient (per heme) 6, =: eTs8 - l gaO = 0.21 and, except when prechtded by a repeat determination on the same sample (as in Table 2), also by removal of the supernatant and conversion to ferrihemoglobin cyanide: the two methods gave the same results. For these runs the buffer pH values are reported; they were within 0.1 pH unit of that of the supernatant when the lat,ter wa,s measured. as previously described (Brie111 & Ewert, 1973,1974) from measureC?agp was calculated rnent of the equilibrium run plates. Meniscus concentrations, C,, differed negligibly from zero. Serial plates were measured to observe the approach of the distribution to equilibrium.

i r\hbreviation


bis Tris.

bis (~-hydroxyethyl)imillot~i~(h,v(~r~xymethyl)-methan~.





Direct determinations of hemoglobin concentration were made by conversion to ferrihemoglobin cyanide based on a millimolar extinction coefficient (per heme), ~a~,, ~= Il.0 (van Assendelft, 1970). The schlieren optical systems of the analytical ultracentrifuges were calibrated (1) by synthetic boundary and sedimentation velocity runs on non-gelling samples of known concentration, (2) with a calibration cell (Beckman Spinco part no. 306386), and (3) by measuring Rayleigh interference fringe spacing with monochromatic light obtained from an interference filter. Method (1) combined with (2) or (3) gave a value for the refractive index gradient dn/dC = 0.195, in good agreement, with the data summarized by Huglin (1972) and the vahie used by Rossi-Fanelli et al. (1961) in the same near infra-red spectral region. Approximate sedimentation coefficients, szO, were calculated from meniscus and boundary positions, the latter at the second moment, corrected for acceleration time and speed changes. This rough method gives a value between 0 and 10% too high when compared with true values from a few runs in which the boundary was serially measurable over a long period of time; the error was due mostly to decompression of the solution and/or changes in cell shape when the centrifuge was slowed to permit the boundary to diffuse.

3. Results (a) The sequence of schlieren Figure

1 shows

a typical


in the




of C,,,



Figure l(a) to (d) shows the rapid sedimentation of the gel as it forms a pellet at the cell base. A free boundary has formed in the supernatant in Figure l(e) and has diffused so as to be measurable to obtain C,,, in (f). Figure l(g) shows the equilibrium distribution which gives C,,, and is followed by demonstration of the endothermic nature of the gel in (h). As shown in Figure 2, an increase in initial hemoglobin concentration in otherwise identical samples usually slowed gel sedimentation as the runs began. (b) Attainment

of equilibrium

The true value of C,,, is that obtained when both sedimentation and solution-gel equilibrium are obtained. Figure 3 shows the course, under a variety of conditions, Preparations, such as those of stripped hemoglobin, with of G,, before equilibrium. values usually came to equilibrium relatively rapidly whereas conditions high G,, inducing low Csgg, such as organic phosphate, delayed equilibrium, sometimes to the This deextent that a slow decrease in C,,, remained at the end of the experiment. crease depends on solution-gel equilibrium since sedimentation equilibrium alone, while dependent upon concentration, required of the order of 150 hours. Although attainment of equilibrium is slow, the measured C,,, value always falls below the corresponding C,,, value early in the run, usually at about 30 hours, as shown in Figure 3. Figure 3 also shows the increase in C,,, value with cooling, confirming the endothermic nature of gelation. In addition, the movement of condensed material back into solution phase (Fig. l(h) and implicit in Fig. 3) shows that the condensed phase is not irreversibly aggregated or precipitated.

(i) Attainment

of gelation

(c) Validity

of the procedure



for Csat


Table 1 shows that Csat is independent of time of incubation and transient increase in temperature when only these parameters differ among the cells in a multi-cell run.

FIG. 1. Measurement of C,,, and C,,, in a single run. Deoxyhemoglobin S in 0.05 M-bis Tris with 0.1 M-N&I and 10 mnr-2,3,diphosphoglycerate, pH 6.80, 20°C. All bar angles are 75”. A single cell in this 3.cell run is shown, with the remaining two schlieren removed by movement of the light source trimmers. (a) 2500 revs/min, 1 min after the beginning of centrifugation. No schlieren is seen since the gel has not yet begun to sediment. (b) 15,000 revs/min and 6 min. The gel has sedimented about l/3 of the way down the cell. (c) 33,000 revs/min, 9 min. The gel is forming a pellet, at the cell base. (d) 52,640 revs/min, 19 min. The gel is fully sedimented. (e) 52,640 revs/min, 2 h 22 min. There is a free boundary, but it is not measurable due to high refractive index gradients. (f) 12,590 revs/min, 3 h 23 min. The free boundary is measurable. The concentration in the plateau region is 0.136 g/ml giving, after correction for radial dilution, C, : 0.160 g/ml. (g) 19,160 revs/min (changed from 12,690 at 4 h), 283 h. An equilibrium dist,ribution occurs with the schlieren terminating in an opaque region at the limit of solubility, C,,, == 0.099 g/ml. (h) 19,160 revs/min, 26 h after the temperature was lowered to 2°C. The area under the schlieren has increased, indicating that some of the condensed material has returned to the solution phase, consistent with the endothermic nature of gel&ion.


FIG. 2. Rates of sedimentation of the gel as a fun&on of initial concentration. Three-cell run on deoxyhemoglobin S in 10 mM-inositol hexaphosphate, pH 6.1, 20°C; aft,er 6 min of centrifugation accc$erating to about 16,000 revs/min. Initial hemoglobin concentrations: upper schlieren, 0.133 g/ml; middle, 0.151 g/ml; lower, 0.166 g/ml. The gel in t,hc lower cell has barely begun to sediment. That in the middle cell has sedimentrcl through about 3/5 of the cell. The most dilute gel, in thb upper cell, has sedimented furthest.

Therefore, the overnight incubation at constant temperat,ure employed in all runs except those in Ta.ble 1 was sufficient to attain gelation equilibrium prior to centrifugation. Sonication also did not, affect C,,,. (ii) Absence of effect of the w~easurkg


Gel compression and/or hydrostatic early in a run before the gel sediments.

T 3

i”I I 0.15



g k 0



; I


A 1.. . . .


pressure might aher solution-gel equilibrium Such effects would be greatest toward t,he cell


1, .

_I ., ,I /I t L, ; . . . .


..* i I


I I 00



on the gel&ion


. . . . . l



. l




. “..f




FIG. 3. The approach to equilibrium in measurements of C,,, on deoxyhemoglobin S at 2O’C. (0) Stripped, pH 6.87; (0) stripped, pH 6.89; (A.) in 10 mix-2,3,diphosphoglycerate, pH 6.11; hexaphosphate, pH 6.51. (0) in 10 mix-inositol hexaphosphate, pH 6.92; ( n ) in 10 mM-inositol The values of C,,, for each sample are indicated by lines on the ordinate with the corresponding in the run. Equilibrium for symbol. The transient value of C,,, decreases below that of C,,, early c ~=B is achieved most rapidly for preparations with high C,,, values, such as those at high pH and stripped. For each run a vertical line indicates the time at which the temperature was lowered) to 2°C. At this time C,,, increases as the gel melts. The pH values are given at 20°C.







base where compression and pressures are greatest and where gel and solution coexist for t,ha longest time; in addition, centripetal regions are rapidly clea’red of gel before full speed is attained, furt,her minimizing exposure to high pressure. Such a dependence of the equilibrium on position would prrcludr a constant hemoglobin concentration and thus a plateau region above the pelleted gel. Since plateau regions were observed, as shown in Figure l(b) to (f), there is no significant’ alteration of the solution-gel equilibria existing prior tjo cent’rifugation. 1


The effects qf conditions

of incubutio,L

on Cant

Initial hemoglobin COllCtl (g/ml)


Temp. (“(I)






22 h 3.5 h 1.5 11

0.191 0.192 0.193





21 h 3h

0.127 0.132




0.1 74

after Sonicated No sonication Sonicated during





At 20°C Gelled at 26°C. Then before centrifugation Gelled at 26°C. Then


1 C,,*t


0.113 0.112 0.114


0,133 at 2O’C


15 min

at 20°C




each of the multi-cell same except as noted. as noted. For each multi-cell inositol hexaphosphate.

runs the contents of the celln wore identical All incubations were overnight at 20°C and run the values of C,,, are thr same within

(iii) Lack of dependence

of C, on tiwse of centrifugation


and the incubations without sonication experimental error.

0.130 0.129 were except IHP,

Polymerization and/or gelation occurring in the plateau region would induce a fall in the concentration in this region, C,, beyond that dictated by radial dilution, thus decreasing the calculated C,. Such changes in C, values were not seen in the limited periods of time in which it could be measured. The absence of more than one sedimenting peak and the presence of a plateau region are also consistent with the absence of additional aggregation. Finally, centrifugation itself. through radial dilution, would markedly inhibit any potential aggregation because of the fall in C, value and the high power dependence of nucleation (Hofrichter et al., 1974). To confirm further the absence of effect of centrifugation time on C,, a separate set of experiments was done with paired cells loaded identically in successive runs. One run was terminated as soon as the gel pellet was formed. C,,, was measured directly by removal of the supernatant and conversion to ferrihemoglobin cyanide. The other run was continued with measurement of C, from the schlieren boundary. For 26 pairs of cells in the analytical ultracentrifuge the average difference (direct - schlieren) was [email protected] g/ml (standard deviation of the difference, (T = 0.006 g/ml); for 15 pairs in which the direct measurement was done in the preparative ultracentrifuge, the difference was $0.003 g/ml (U = 0.007 g/ml). Therefore, the measured value of G,,, does not depend significantly on time of centrifugation.





(d) The nature of the supernatant Predominance of monomers in the supernatant, necessary to establish because Csat is defined as a monomer concentration, is confirmed in Figure 4. The approximate (see Materials and Methods) and, where obtainable, true s2,, values of the supernatant hemoglobin are the same as for monomeric oxyhemoglobin controls. The presence of slowly interacting aggregates was further excluded by the presenceof a single sedimenting boundary. l-5





O-10 Concentration


0.15 (g/ml)



0. 5

Pm. 4. Approximate sedimentation coefficients, ss0, as calculated from boundary and meniscus positions (see Materials and Methods), with true values shown for comparison where obtainable. + , Oxyhemoglobin A or S control, approximate saO value (see text); single cell. $, Oxyhemoglobin control, true aa,, value based on serial peak positions; single cell. ( 0, 0, a) Deoxyhemoglobin S, approximate aas. l , n , A, Deoxyhemoglobin S, true azO value. Circles: point represents average from a 3-cell run in which the cells were identical but for initial concentration or incubation conditions. Squares: average of 2 cells. Triangles: single cell. Parentheses indicate deoxyhemoglobin S sample that did not gel. The abscissa represents C,,, for samples which gelled and the total hemoglobin concentration for controls. The line is drawn through approximate ~a,, values of the controls.

(e) Reversibility In order to consider the reversibility of the condensationsobserved in these assays, a number of determinations were repeated after melting of the gel pellets in the centrifuge cells on ice. For stripped hemoglobin total melting could always be achieved when desired; Table 2 shows that repeat determinations of C,,, gave unchanged results, whether upon immediate repetition or after long C,,, runs. In inositol hexaphosphate it was possibleto return all of the condensateto solution after short runs, but not always after long C,,, studies. This failure depended upon a gelling of the supernatant even at O”C, so that no solution phaseremained, suggestingthe presence of a new, more stable, phase requiring long periods of centrifugation for its development. Repeat C,,, determinations in inositol hexaphosphate showed no change if done after the previous Csst,but showeda decreaseif following a C,,. determination. Under these latter conditions, consistent with the lowered Csat, gelling during the repeat incubation was attained sooner and/or at lower temperature than the first time. (f) Relations betweenCsatand initial concentration In Figure 5 the areas under the boundaries, and thus also C,,, values, are nearly the same for three cells differing only in initial hemoglobin concentration, C,. In







multi-cell analytical ultracentrifuge runs there was a total of 47 pairs of cells (lowest concentration paired with middle, middle paired with highest) ; the increase in C, value was usually 0.016 g/ml (with some differences up to 0.032). The average increase in in Gat value was O-003 g/ml (U = [email protected] g/ml). In preparative ultracentrifugation 25 pairs the average C,,, value increase was 0.002 g/ml (u = 0904 g/ml). These results, corresponding to changes of only 1 or 2% in Csat, fail to show a significant TABLE


Repeat determination-sof Csat Cofactor



0.213 0.230 0.148 0.100 0.119 0.131


0.201 0.208 0.225 0,104 0.124 0.143 0.132 0.132

c aa


0.186 0.188 0.111 no gel 0.107 0.117**

0.150** 0.155** 0.057 4 * 0.077* 0.076 $ ** -

0.189** 0.187** 0.063* 0.074 0.089 0.117**

0.1s5* 0.184** 0.183* no gel 0.111** o-120* 0*120* 0.122**


0.181 0.184 0.183 no gel 0*113t 0.118 0.120 0.124

Csat 1


cssat 3 0.187** 0.183** 0.067

cm&, 4 0.186 0.184


The upper portion of the Table reports results from analytical ultracentrifugation and the lower portion runs in the preparative uhracentrifuge. All runs were at 2O”C, pH 6.6. Concentrations are in g/ml. STR indicates stripped hemoglobin and IHP indicates the presence of 10 mM-inositol are indicated in sequence, &s is the hexaphosphate. The values of successive C.,, determinations value of C,,, when such a determination was carried out after the fist C,,,. * Indicates the pelleted gel was partially melted after the run by cooling to 0°C. ** Indicates the pellet w&s fully melted. t Indicates a full gel was not obtained, although there was a definite increase in viscosity. 4 Indicates the value of C,,, was still decreasing with time at the termination of the run. The first, 3 O,,, determinations were continued for 12 days. The ot,her 2 were terminated after 5 days.

Fro. 6. C,,, determinations on 3 samples identical but for initial concentration. Deoxyhemoglobin S in 10 mM-inositol haxaphosphate, pH 6.35, 20°C. 14,290 revs/min, 2 h 11 min after start of centrifugation with speed slowed from 62,640 to 14,290 revs/min at 2 h. Bar angle 76”. Initial hemoglobin concentrations were: upper schlieren, 0.128 g/ml; middle, 0.144 g/ml; lower, 0.169 g/ml. C,,, values were: upper, 0.108 g/ml; middle, 0.111 g/ml; lower, 0.113 g/ml. The nearly identical values derive from the nearly identical areas under the three peaks.





dependence of C,,, on C,, although a small dependence cannot be excluded. The-y are t,herefore consist,ent with a sharp phase condensation, t:he nature of which is discussed below. (g)



Csal und


In Figure l(f) t,he area under the boundary is much greater than that under the schlieren in Figure l(g), indicating that C,,, > C,,,. Figure 6 summarizes results from analytical ultracentrifugation at 20°C and shows that C,,, is always greater than C,,,. For stripped hemoglobin (Fig. 6(a)) the ratio Csst/Cagg varied from 1.09 to 1.29 ; when three low values deriving from runs in which C,,, was still decreasing at the t,ermination of the run were eliminated. t’he range was 1.17 to 1.29 with an average of 1.23. Tn organic phosphate the highest ratio was 5 and t’he range was much larger.










PH (bl


FIG. 6. Values of C,,, and C,,, for deoxyhemoglobin 6 at 20°C as measured from optical patterns in analytical ultracentrifugation. Filled symbols and solid lines: Csst; open symbols and broken lines : C,,, ; circles: stripped; triangles: in 10 mM-2,3,diphosphoglycerate; squares: in 10 mMinositol hexaphosphate. pH values were measured directly on the supernatant after centrifugation. (a) Results on hemoglobin stripped and in 2,3,diphosphoglycerate. (b) Results in inositol hexaphosphate (heavy lines) along with t,he curves (light lines) of (a) summarizing the results for hemoglobin stripped (STR) and in 2,3,diphosphoglycerate (DPG). 4 Indicates that C,,, was still decreasing at the time the equilibrium run was terminated, so that the true value is lower than shown. Parentheses indicate the sample did not gel at this concentration. (h)




and C,,,

The results in Figure 6 show that gelation as measured by C,,, is favored by organic phosphates and by lowering pH toward 6.8. They also confirm and extend previous results with similar conclusions concerning gelation as reflected in C,,, (Briehl & Ewert, 1973,1974). Inositol hexaphosphate favors gelation more than 2,3,diphosphoyglcerate. For stripped hemoglobin there is an optimum for gelation as measured by C,,, near pH 6% In inositol hexaphosphate and in the more limited data in 2,3,diphosphoglycerate, C,,, remains nearly constant at lower pH values suggesting that any optimum for gelation lies at a lower value than in stripped hemoglobin.





by preparative 7 shows Csat values obtained firms the dependences on pH and organic phosphates Figure

(i) Tem,perature




ultracentrifugation shown in Figure

and con6.

of Csat cud C,,,

at four temperatures Figure 8 shows values of C,,, and C,,, for stripped hemoglobin for runs near pH 7.0. The Figure also shows these results corrected to pH 7.00 on the 0.25


z E \ .E c 2 5 z K 0







PH Fro. 7. Velues of c,,, at 20°C BY obtained globin cyanide after preparative ultracentrifugation. 2,3,diphosphoglycerate; ( n ) in 10 mnr-inositol only from runs in which C,., was obtained followed by a repeat determination.


conversion of the supernatant to ferrihemo( l ) Stripped hemoglobin; (A) in 10 mnrhexaphosphate. The bracketed points represent the near-infra-red spect,rum because the run w&s Temperature



x IO’

Fm. 8. The dependence of c’,,, and C,,, on temperature for stripped hemoglobin. Closed symbols : C sat; open symbols: CaKB; circles: C,., and C,,, values at the pH of the experiment (15% data were at pH 6.90; 2O’C data were at pH 6.86 for the lower values and pH 7.10 for the higher values; 26°C data were at pH 7.16 and the 28°C data were at pH 7.12). Squares: datacorrected to pH 7.00 on the basis of the pH dependence measured at 20°C (see text). Each point represents the average of 3 cells in a multi-cell run in which the samples were identical but for initial concentration. The lines ( represent least-squares fits to the data corrected ) for C,,, and (-----) for C,,, to pH 7.00 and give AH values of 3.0 and 2.1 kcal/mol for CJat and C,,,, respectively.





basis of the pH dependence obtained from a least-squares fit, of In C,,, or In C,,, as a linear function of pH at 20°C. ‘lk correcM poink give apparent van’t, Hoff enthalpies, calculated by a least-squares fit, equal to 3.0 and 2.1 kaal/n~ol for f,‘s,t ant1 c Wkz~respectively (the difference in the t’wo values is probably not, significant). The value of C sgg is the same asthat implicit in our previous results,obtained byrepeatedl) changing the temperature of a single sample and waiting for IWW sedimentation equilibria to be established (Briehl & Ewert,, 1973). ( j) Co-operativity

of polymer formations

As shown in Figure 9, there was a narrow region (zone II, Briehl & Ewert, 1973) in each equilibrium distribution between the monomeric solution (zone I) and the gel (zone III) in which the schlieren rose steeply indicating the presence of large polymers. In five runs with C,,, near 0.15 g/ml, where the monomer schlieren slope is near zero, this pattern could be subtracted from the total to give polymer concentrations and rough (within a factor of 2) weight average apparent molecular weights (corrected for the effect of solute on solution density). These were in the range 1 x lo* to 2 x 106. If the effect of non-ideality on the molecular weights of monomers and polymers is the same, this corresponds to 40 to 75mers.

FIG. 9. Enlargement of ultracentrifugal zone II showing the sharp rise transition zone between monomeric solution on the left and opaque gel schlieren, which largely overlaps the upper, is that for the run on stripped for which the attainment of equilibrium is shown in Figure 3. The pattern time of attainment of equilibrium to the Figure shown, taken at 436 h, the angle is 76” and the speed 19,160 revs/min.

in the schlieren in this on the right. The lower hemoglobin at pH 6.89 did not change from the end of the run. The bar

4. Discussion The central issue in interpretation of the results that C,,% is always greater than C,,,. The primary that C,,, is a measure of polymerization equilibria

is the basis for the observation conclusion, developed below, is whereas C,,, reflects the equili-



brium of phase separation, merization per se.





on a number


of factors

in addition


to poly-

(4 C,,,

is the hemoglobin concentration required for the presence of a very small quantity of polymerized hemoglobin, just observable in the form of an upward turn choice in the equilibrium schlieren pattern. While C,,, does depend on an arbitrary of a point in the schlieren pattern, this arbitrariness is minimal since the schlieren t,urns upward very sharply, associated with the high co-operativity of polymerization. Since very few polymers are present, C,,, is essentially a monomer concentration and as such it is inversely proportional to the equilibrium constant for aggregation; it measures the free energy change in polymerization. There is no viscous gel present at C,,, and its value is independent of the phase separation equilibrium which commences only at higher concentrations. or due to C,,, might differ from C,,, because it represents a different equilibrium kinetic factors.

(b) Csat > Cagg : possible



In inositol hexaphosphate the observations that (i) C,,, > C,,, and (ii) C,,, can decrease after a long C,,, run could arise from denaturation or from the existence of’ polymorphism with metastable polymeric or condensed states. Denaturation is not a likely explanation since (1) the near infrared spectra were normal after runs and no peak of methemoglobin at 630 nm was seen ; (2) the decrease in C,,, on repetition occurred only in inositol hexaphosphate and not in stripped hemoglobin; (3) C,,, runs can be continued for many weeks with repeatable results when temperatures are cycled between high and low values (Briehl & Ewert, 1973); (4) equilibrium was established in C,,, in many runs after sufficient time (Pigs 3 and 6). Interconvertible, polymorphic and metastable condensed states of deoxyhemoglobin S can exist in 1.7 M-phosphate (Briehl, 1976) and at physiological ionic strengths (Pumphrey & Xteinhardt, 1976,1977). In the present studies. (1) the decrease in C sat in inositol hexaphosphate after a C,,, run, (2) the difficulty in melting condensates in inositol hexaphosphate after a C,,, run and (3) the shorter incubation times required for a repeat C,,, determination could depend on the presence of forms more stable than the gel or their nuclei, created as a result of long equilibrium runs and/or pressure and packing of the gel pellet. Under this interpretation AC for the transition from initial gel to stable form in inositol hexaphosphate is between -0.1 and -0.3 kcal/mol calculated from C,,, values in Table 2. In stripped hemoglobin, on the other hand, metastable states cannot explain was unchanged in repeat determinations whether the pellet C,,, > C,,, since Csat was fully or partially melted. The strongest argument against a purely kinetic basis for C,,, > C,,, depends on the presence under all conditions of the ultracentrifugal zone II (Briehl $ Ewert, 1973) at equilibrium. This zone begins at C,,,, contains monomers and polymers, and ends at the gel pellet, thus separating two distinct transitions. Its existence is not consistent with a single infinitely co-operative transition present for either of two condensed states.




Cc)Cal ->


Caqo : ~qdihriwnt


Relation of hemoglobin 8 is known to involvcb a highly co-operative process of aggregation (Malfa & Steinhardt’, 1974: Hofrichter et t&l., 1974: Moffat & Gibson, 1974) producing long fiber-like polymers which align t’o form tactoids (Harris, 1950). Onsager (1949), Flory (1956), DiMarzio (1961) and, as applied to hemoglobin 8, Minton (1974) have developed models to show that non-ideality of rod-like particles in the form of excluded volumes can result in an entropically driven separation into conjugate isotropic and anisotropic (tactoidal) phases. with solute concentrations C* and C*‘, respectively, which differ only slightly. Under such models a number of regions can be defined as total hemoglobin concentration, C, and monomer concentrat’ion. P, 1, increase; these are shown and applied to the present results in Figure 10. (71 = c < c,,,. This region corresponds to t#he ult8racentrifugal zone 1 and contains only monomeric hemoglobin. c,,,< c< c*; c,,,< c, < CT. This one phase region corresponds to ultracentrifuge zone II and contains monomers and isotropically oriented polymers, each increasing in concentration with C. At’ C -: C* the isotropic phase becomes saturated with polymers relative to the tactoidal state. In the equilibrium distributions, however, G* cannot’ be measured because refractrive index gradients at the base of zone II



Zone II concentration) Moncrners isotropic polymers






2MlJcmscopic chases, %+IlF

Monomers anisotropic polymers ., //




FIG. 10. Phases and concentration ranges in polymerization and gelation. The weight concentrations of monomeric and polymeric hemoglobin are plotted as functions of total concentration: (--) monomers in the purely monomeric and isotropic regions; (---) polymers in the monomers for an idealized condensation exhibiting unlimiting coisotropic phase; (...,.....) operativity; (-- x --x --) polymers for such an idealizedcondensation; (--. --. --) polymers in the anisotropic phase; (-.-.-.-) monomers in the anisotropic phase. The diagram is independent of centrifugation, but the centrifugal zones into which each concentration falls are indicated. That marking the onset of and reflecting only indicates the existence of 2 transitions, C,,, c,,t > G,, the monomer concentration in equilibrium with the polymerization, and C,,, = CT representing :! conjugate phases; it also indicates a limited co-operativity of polymerization in contrast to the (See text for further description). idealized condensation with C,,, = C,,,.







are too large to be accommodated by the schlieren optical system. At C = C*, C, is designated C:. P C,,, depends, in stripped hemoglobin totally and in inositol hexaphosphate in part, on the presence of separate equilibria. In inositol hexaphosphat,e t,here is, in addition, evidence for metastable states, consistent with higher values of and greater variation in the ratio Csat/Capp observed in inositol hexaphosphate. (d) The ratio Csat/Cass; co-oper&kit!/ Increasing co-operativity of polymerization appears as an increase in schlieren steepness and a decrease in the width of zone II and as a decrease in the ratio CSst/Csgg. In the limit of infinite co-operativity and a single transition. zone IL does not exist and cslat- Gw Under the model of Oosawa & Kasai (1962) and Oosawa & Higashi (1967), a helical nucleus which elongates into a helical polymer by monomer addition exhibits near infinite co-operativity and, therefore, C,,, G C,,, (the idealized condensation shown in Fig. lo), inconsistent with the present results. On the other hand, C,,, > C,,, and the existence of zone II are consistent with isodesmic assembly of units into a linear polymer. Since nucleation and co-operativity do occur in the hemoglobin S system (Malfa t Steinhardt, 1974; Hofrichter et al., 1974; Moffat & Gibson, 1974) the units would correspond to co-operatively formed nuclei undergoing linear condensation. The observed value of Csat/C,gg, 1.23 in stripped hemoglobin, can be used to obtain an order of magnitude estimate for the co-operativity. 77, of monomer-polymer equilibria under the simplifying assumption C, == KC; ,where C, and C, are weight concentrations of polymer and monomer, respecbively, and K is the equilibrium constant. are polymer concentrations in equilibrium with C,,, and C,,,, If G,,, and G,,, howrespectjively, (CSat/CBgg)n = C, ,,JC, n8g.The C, values can only be estimated;





ever, n is relatively insensitive to changes in the C, values. In reading the plates. C,,, was chosenas the schlieren began to rise sharply and, based on extrapolation of the schlieren pattern due to monomers alone, the additional area represented a polymer concentration, C, agg,of roughly 1 x 10e5 to 4~ 10F5 g/ml. For G,,,, values an upper limit is set by the total gel plus polymer concentration, equal to the difference CL- csat, which averaged 0.03 g/ml for stripped hemoglobin. In some runs it was lessthan 0.01 g/ml, indicat,ing that this polymer concentration is sufficient to form a viscous gel. An extreme lower limit of 2 x 10m4g/ml was obtained from the maximum concentration above monomers in zone II before the schlieren were lost to the optical system. With C,,,, = 2 x low5 and C,sat = 0.01 g/ml, n = 30; a factor of 5 error in cn satlCnaggchangesn only by 8. Non-ideality int’roduces further errors, but this is in part cancelled by the small difference between C,,, and C,,,. The approximate size of t’he polymers obtained from n and t’he rough molecular weights in zone II calculated above are similar and indicate that the polymers arc much smaller than hemoglobin S fibers of the order of 1 pm length (Bertles et al., 1970), which would contain about IO3 monomers. That these short polymers exist at equilibrium further establishes that co-operativity of assembly is limited and that there is not a single sharp transition from monomers on the one hand to full length polymers and gel on the other. (e) The relations betweenC,,, and Ci If C,,, were to increaseslightly with C, under someconditions, a possibility not fully excluded by the data, it might be interpreted: (1) C, lies in the single phase region C,,, < C, < C*, implying that tactoids are not needed for gelation; or (2) C, lies in the other one phase region C*’ < C,. Finally, (3) monomer concent’rations in the isotropic and anisotropic regions might be different in consequenceof differing nonidealities, and/or the two phasesmight contribute differently to the monomers in Csat9so that gels with different fractions of the two phasescould give different C,,, values. (f) Relations to the kinetics of gel assembly The current definition of two equilibria in gelation is consistent with the demonstration of separate kinetic processesof polymerization and alignment by Hofrichter et al. (1974). The order of magnitude of co-operativity measuredhere is also consistent with that obtained in kinetic studies (Hofrichter et al., 1974,1976; Moffat & Gibson, 1974). Although monomers at C,, are in equilibrium with the conjugate phases,they are, since G,,, > C,,,, supersaturated in isolated solution relative to a mixture of monomers and polymers. The maintenance of the monomeric state in the supernatant during C,,, studies is attributable to the met&stability of supersaturated solutions, well established at supersaturation ratios greater than that in the current studies (Hofrichter et al., 1974; Malfa t Steinhardt, 1974; Moffat & Gibson, 1974). (g) Possibleapplications and clinical implications The gelling propensity of hemoglobin S can be altered by various covalent modifications, weak interactions and changesin solvent conditions (for example, Nigen et al., 1974; Benesch et al., 1974; Freedman et al., 1973; Briehl & Ewert, 1973; Waterman






9. -3” I

pt al., 1974; Elbaum et al., 1974; Magdoff-Fairchild et al., 1976; Kubota et al., 1976; Votano et al., 1977). The mechanism of alteration might’ depend on changes in the free energy of polymerization or on other factors which control tactoid formation? including lengths and enthalpic interactions of fibers. Tn the former case O,,, and (‘lsat would be expected to change while in the lat,ter only C!,,, should be altered. Thus t,he two assays may serve in elucidation of the mechanism of action of modifiers of gelation. Similarly, if polymorphic st’ates (Josephs et ul.. 1976: Briehl, 1976 ; Pumphrey & Steinhardt, 1976,1977) or possible states of different fiber length resulting from overshoot. (Cantor, 1968; Oosawa. 1970; Scheele & Schuster, 1974) or fiber breakage differ in causing red cell rigidity or other pathogenic phenomena, distinction between changes in polymerizat)ion free energy and in phase separation might be useful in understanding the natural hisborp of sickle cell disease. Such interpretations, however. would require demonstration that the phases in gel are similar at 37°C t.o t,hosc seen here at 20°C. While it is generally considered t’hat sickle cell disease depends on tactoid formation. it remains to be demonstrated that the anisotropic phase is more pathogenic or induces red cell rigidity and diminished filterability more t’han the isotropic state. To thr contrary, the work of Hermans (1962,1967) indicates t,hat in model systems of rodlike poly-y-benzyl-L-glutamate, t)he t’ransition from isotropy to tactoid is associated wit’h a large decrease in viscosity. The current method of using cYsstand C,,, to defint, the phase or phases present in va.rious concentration ranges might then serve in conjunction with viscosity studies to determine which phase is most pathogenic. A furt.her suggest.ion that viscosity may be highly sensitivcs to t,hp phase structure of the gel is contained in the work of Harris & Bensusall (1975) showing a time-dependent, decrease in viscosity following a maximum, perhaps associated with the slow alignment. into a t,actoidal st,ate. I ttlank


E. Suzuka

for impeccable

and devoted work

and technical


in performing the analytical ultracentrifuge runs ; also Nina Louie for her excellent assistance and Scott Cohen for precisely reading innumerable ult.racentrifuge plates. J also thank Dr Samuel Charache of the Department, of Medicine, .Johns Hopkins School of Medicine and Dr Hugh Chaplin Jr, Departments of Medicine and Preventive Medicine, \r’ashington University School of Medicine, for their kind gifts of sickle cell blood. This work \vas supported in part by United States Public Health Service grant number HL07451 from tllo National Heart, Lung and Blood Institute and in part by a (:rant-in-Aid from the New >‘ork Heart Association. REFERENCES Allison, A. 0. (1!)57). B&hem. J. 65, 212-219. Benesch, R., Benesch, R. E. & Yung, S. (1974). Proc. iVat. Acad.Sci., U.S.A. 71, 1504-1505. Bertles, J. F., Rabinowitz, R. & DBbler, J. (1970). Science, 169, 375-377. Bookchin, R. M., Nagel, R. L. & Ranney, H. M. (1967). J. Biol. Chem. 242, 248-255. Briehl, I%. W. (1976). In Proceedings of the Symposium on Molecular and Cellular Aspects of Sickle Cell Disease, Dallas, Texas, Dec. 9 to 10, 1975 (Hercules, ,J. I., Cottam, G. L., Waterman. M. R. & Schechter, A. N., eds), pp. 145~~181. U.S. Dept of Health, Education and Welfare, publ. no. (NIH) 76-1007. Briehl, R. W. & Ewert, S. (1973). J. Mol. Biol. 80, 445-458. Briehl, R. W. & Ewert, S. M. (1974). J. Mol. Biol. 89, 759-766. Briehl, R. W. & Salhany, J. M. (1975). ,7. Mol. Biol. 96, 733 743. Cantor. (1. R. (1968). Biopolymers, 6, 369-383. 10





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