Gelation of sickle cell hemoglobin in mixtures with normal adult and fetal hemoglobins.

We report the results of thermodynamic and kinetic studies on the gelation of mixtures of sickle cell (S) deoxyhemoglobin with normal human adult (A) and fetal (F) deoxyhemoglobins. The delay time of thermally induced gelation was monitored by the increase in turbidity. At the completion of gelation the solubility was determined by sedimenting the polymers and measuring the supernatant concentration spectrophotometrically. Addition of hemoglobins A or F, at mole fractions from 0 to 0.6, resulted in large increases in both the solubility and the delay time. For a 50:50 mixture of deoxyhemoglobin F with deoxyhemoglobin S, the solubility increased by a factor of 1.8 and the delay time by a factor of 10⁷ relative to pure deoxyhemoglobin S at the same total concentration, while for a 50:50 mixture of deoxyhemoglobins A and S the solubility increased by a factor of 1.4 and the delay time by a factor of 10⁴. The relative delay times were independent of both temperature and total hemoglobin concentration. The data have been analyzed according to theoretical models which treat the effects of temperature, concentration, non-ideality and solution composition on the thermodynamics and kinetics of gelation. The increased solubility in mixtures with deoxyhemoglobin F is fully explained by a model in which only deoxyhemoglobin S molecules polymerize. The effect of fetal hemoglobin (α₂γ₂) and hybrid α₂γβ^S molecules is to increase the solution non-ideality through the contribution of their excluded volume. The smaller increase in the solubility observed in comparable mixtures with deoxyhemoglobin A requires that the hybrid α₂β^Aβ^S molecules copolymerize with the deoxyhemoglobin S. The kinetic results for the mixtures can be quantitatively accounted for using a nucleation model in which the equilibrium properties of the polymer are used to describe the critical nucleus. The very large increases in delay time observed for the $\text{S}\text{F}$ mixtures can be explained by assuming that only α₂β₂^S molecules participate in the formation of a nucleus containing about 25 monomers. As in the thermodynamic analysis, the smaller effect of adding deoxyhemoglobin A can be attributed to the contribution of the hybrid molecules in forming the critical nucleus. Thus the difference between the polymerization properties of mixtures of deoxyhemoglobin S with deoxyhemoglobins A and F can be attributed solely to the copolymerization of the α₂β^Aβ^S hybrid molecule and the absence of any significant copolymerization of the α₂γβ^S hybrid.     

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

Two assays of equilibrium properties in the gelation of deoxyhemoglobin S were carried out by analytical ultracentrifugation on the same sample: C_sat, the monomer concentration in equilibrium with the fully formed gel, was obtained as the supernatant 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_sat 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_agg, the monomer concentration at which a small amount of polymerization to large aggregates begins.The primary result is that C_sat > C_agg 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_sat 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_agg, a region in which isotropically oriented polymers exist, occurring when monomer concentration lies between C_agg and C_sat, and a two-phase region of conjugate isotropic and anisotropic phases when monomer concentration equals C_sat. These regions correspond to zones in the ultracentrifuge equilibrium distribution. In this scheme C_agg depends only on the interaction energy of polymerization. C_sat depends on entropic factors which induce tactoid formation as well. C_sat, 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_sat represents a supersaturated state of isolated monomers.The ratio $\text{C}{}_{\mathrm{<mtext>sat</mtext>}}\text{C}{}_{\mathrm{<mtext>agg</mtext>}}\text{= 1.23}$ in stripped hemoglobin³ 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 gelation does not consist of a single transition and phase change with near infinite co-operativity of polymerization.C_sat as well as C_agg are lowered by 2,3,diphosphoglycerate and inositol hexa-phosphate. Decreasing pH near 7 also favors gelation; in stripped hemoglobin a pH optimum for gelation occurs near pH 6.8. The apparent van't Hoff ΔH for stripped hemoglobin is about 3 kcal/mol for C_sat and 2 kcal/mol for C_agg.     

Structural analysis of polymers of sickle cell hemoglobin. III. Fibers within fascicles

We have examined the structure of hemoglobin S fibers, which are associated into large bundles, or fascicles. Electron micrographs of embedded and cross-sectioned fascicles provide an end-on view of the component fibers. The cross-sectional images are rotationally blurred as a result of the twist of the fiber within the finite thickness of the section. We have applied restoration techniques to recover a deblurred image of the fiber. The first step in this procedure involved correlation averaging images of cross-sections of individual fibers in order to improve the signal-to-noise ratio. The rotationally blurred image was then geometrically transformed to polar co-ordinates. In this space, the rotational blur is transformed into a linear blur. The linearly blurred image is the convolution of the unblurred image and a point spread function that can be closely approximated by a square pulse. Deconvolution in Fourier space, followed by remapping to Cartesian co-ordinates, produced a deblurred image of the original micrograph. The deblurred images indicate that the fiber is comprised of 14 strands of hemoglobin S. This result provides confirmation of the fiber structure determined using helical reconstruction techniques and indicates that the association of fibers into ordered arrays does not alter their molecular structure.     

Gelation of sickle cell haemoglobin. II. Methaemoglobin

Sickle cell methaemoglobin was assayed for gel formation by an equilibrium ultracentrifugation method previously described. A phase change from sol to gel, indicative of gelation, occurred, depending on conditions, at concentrations between 0.35 and 0.5 g/ml, considerably higher than concentrations observed previously for gelation of deoxyhaemoglobin S. Inositol hexaphosphate favours gelation, but gelation is seen also in its absence. Lowering pH toward 6 favours gelation. If gelation is assumed to require molecules in the T quaternary conformation, these results provide further evidence that methaemoglobin exists in R-T equilibrium in solution and that this equilibrium lies between the extremes exhibited by deoxyhaemoglobin (T-state) and carbon monoxide or oxyhaemoglobin (R-state).     

Nitrosyl hemoglobin: EPR components at low temperatures

The EPR spectrum of nitrosyl hemoglobin has been studied from 7.5 K to 104 K. It is composed of at least three components (A, B and C) which have a different dependence on temperature and power level. The A component decreases with increasing temperature. The B component disappears at around 30 K and is replaced by C. Relaxation of A follows the Orbach mechanism with an energy of 28 cm-1. This behavior can be attributed to phonon induced changes in the orientation of NO with respect to the heme plane.     

Dielectric constant of sickle cell hemoglobin. Dielectric properties of sickle cell hemoglobin in solution and gel

The dielectric constants of sickle cell hemoglobin were determined before and after gelation. The dielectric properties of oxy and deoxy sickle cell hemoglobin in solution are nearly identical to those of oxy and deoxy hemoglobin A. Only in the gel state did deoxy sickle cell hemoglobin display dielectric behavior different from that in solution. Upon gelation of deoxy sickle cell hemoglobin, the dielectric constant showed a marked decrease, and the relaxation frequency shifted towards higher frequencies. This result suggests that dielectric constant measurement can be used for the investigation of the kinetics of polymerization of sickle cell hemoglobin molecules. Despite the marked decrease in the dielectric constant, deoxy sickle cell hemoglobin still showed a well-defined dielectric dispersion even in the gel state. This indicates that individual molecules have considerable freedom of rotation in gels. It was observed that the dielectric properties of gelled deoxy sickle cell hemoglobin were affected by electrical fields at the level of 10 to 20 V/cm. This observation suggests that electrical fields of moderate strengths are able to perturb the gel structure if the system is near the transition region. The non-linear electrical behavior of gelled sickle cell hemoglobin will be discussed further in subsequent papers.     

Oxygen binding to sickle cell hemoglobin.

The extent of oxygen binding and light scattering of concentrated solutions of hemoglobin S have been determined as a function of oxygen partial pressure using a thin film optical cell. Nearly reversible oxygen binding is observed as witnessed by the small hysteresis found between slow deoxygenation and reoxygenation runs. High co-operativity is noted from unusually large concentration-dependent Hill coefficients when aggregated hemoglobin S is present. The application of linkage theory with the inclusion of non-ideal solution properties permits a test of various simple models for oxygen binding to both the monomer (α₂β₂^s) and polymer (aggregated) phase. It is concluded that oxygen binding to the polymer is either negligible or small under present experimental conditions. Phase diagrams of the solution concentration in equilibrium with polymer phase as a function of oxygen partial pressure are derived using best fit values of polymer parameters.     

Structural analysis of polymers of sickle cell hemoglobin. II. Sickle hemoglobin macrofibers

Sickle cell hemoglobin macrofibers are an important intermediate in the low pH crystallization pathway of deoxygenated hemoglobin S that link the fiber to the crystal. Macrofibers are a class of helical particles differing primarily in their diameters but are related by a common packing of their constituent subunits. We have performed three-dimensional reconstructions of three types of macrofibers. These reconstructions show that macrofibers are composed of rows of Wishner-Love double strands in an arrangement similar to that in the crystal. We have measured the orientation and co-ordinates of double strands in macrofibers using cross-correlation techniques. In this approach, the electron density projections of double strands calculated from the known high-resolution crystal structure are compared with regions along the length of the particles in which the distinct pattern of double strands in c-axis projection may be observed. Contrary to assertions by Makinen & Sigountos (1984), our results unambigously demonstrate that adjacent rows of double strands in macrofibers are oriented in an antiparallel manner, as in the Wishner-Love crystal. Adjacent rows of antiparallel double strands are displaced along the helical axis relative to their co-ordinates in the crystal. Electron density models of macrofibers based on the crystallographic structure of the sickle hemoglobin double strand are in good agreement with the projections of macrofibers observed in electron micrographs. We have studied the structure of a closely related crystallization intermediate, the sickle hemoglobin paracrystal. The arrangement of double strands in paracrystals is similar to that in Wishner-Love crystals, except that they are displaced along the a-axis of the crystal. Measurements of the double strand co-ordinates reveal that the distribution of strand positions is bimodal. These results further establish the close structural relationship between macrofibers and paracrystals as intermediates in the crystallization of deoxygenated sickle hemoglobin.     

Kinetics of sickle hemoglobin polymerization. III. Nucleation rates determined from stochastic fluctuations in polymerization progress curves

The polymerization kinetics of sickle cell hemoglobin are found to exhibit stochastic variations when observed in very small volumes (approximately 10(-10) cm3). The distribution of progress curves has been measured at several temperatures for a 4.50 mM-hemoglobin S sample using a laser-photolysis, light-scattering technique. The progress curves at a given temperature are superimposable when translated along the time axis, showing that the variability of the kinetic progress curves results primarily from fluctuations in the time at which polymerization is initiated. The shapes of the initial part of the progress curves are well-fitted using the functional form I(t) = Io + As exp (Bt), derived from a dual nucleation model. When the distribution of the measured tenth times is broad, the rate of homogeneous nucleation can be obtained by fitting the exponential tail of the distribution. As the distribution sharpen, the rate of homogeneous nucleation can be estimated by modelling the width of the distribution function using a simple Monte-Carlo simulation of the polymerization kinetics. Using the rates of homogeneous nucleation obtained from the distributions, the rates of heterogeneous nucleation and polymer growth can be obtained from the experimental parameters As and B. The resulting nucleation rates are roughly 1000 times greater than those obtained from an analysis of bulk kinetic data. The results provide strong support for the dual-nucleation mechanism and show that the distribution of progress curves provides a powerful independent method for measuring the rate of homogeneous nucleation and thereby obtaining values for the other principal rates of the mechanism.     

Differential polarization imaging. III. Theory confirmation. Patterns of polymerization of hemoglobin S in red blood sickle cells.

In this paper we test the predictions of the differential polarization imaging theory developed in the previous two papers. A characterization of the patterns of polymerization of hemoglobin in red blood cells from patients with sickle cell anemia is presented. This system was chosen because it is relatively easy to handle and because previous studies have been done on it. A differential polarization microscope designed and built in our laboratory was used to carry out this study. This microscope uses an image dissector camera, a photoelastic modulator, and a phase-lock amplifier. This design represents a substantial modification with respect to the instrumentation used in the previous results communicated on this system. Therefore, the results presented here also permit us to confirm the validity of our conclusions. On the basis of the differential polarization images obtained, models of the patterns of polymerization of the hemoglobin S inside the sickle cells are proposed and their M12 and regular images are calculated by the theory. Good agreement between those models and the experimental systems is found, as well as with the results previously reported.     

Differential polarization imaging. III. Theory confirmation. Patterns of polymerization of hemoglobin S in red blood sickle cells.

In this paper we test the predictions of the differential polarization imaging theory developed in the previous two papers. A characterization of the patterns of polymerization of hemoglobin in red blood cells from patients with sickle cell anemia is presented. This system was chosen because it is relatively easy to handle and because previous studies have been done on it. A differential polarization microscope designed and built in our laboratory was used to carry out this study. This microscope uses an image dissector camera, a photoelastic modulator, and a phase-lock amplifier. This design represents a substantial modification with respect to the instrumentation used in the previous results communicated on this system. Therefore, the results presented here also permit us to confirm the validity of our conclusions. On the basis of the differential polarization images obtained, models of the patterns of polymerization of the hemoglobin S inside the sickle cells are proposed and their M12 and regular images are calculated by the theory. Good agreement between those models and the experimental systems is found, as well as with the results previously reported.     

Simulated formation of polymer domains in sickle hemoglobin.

Using experimentally observed processes of linear growth, heterogeneous nucleation, and polymer bending, with no additional assumptions, we have been able to model the two-dimensional formation of polymer domains by sickle hemoglobin. The domains begin with twofold symmetry and proceed toward closure into spherulites at a constant rate. Relationships derived from the simulations presented and the requirements of scaling result in simple expressions for the sensitivity of the closure times to the model input parameters and allow the results to be extended to regions not actually simulated. For concentrations above approximately 25 g/dl, closure times are longer than the time required for the conclusion of the polymerization reaction, and thus incomplete spherulites will be the dominant geometry at high concentrations. Moreover, spherulites are not predicted to form in times less than a few seconds, implying that spherulites will not form during the transit of erythrocytes through the capillaries. Polymer-polymer exclusion, surface nucleation, and monomer exhaustion were also explored and found to have only weak effects on the results.     

Alternative diaspirins for modification of hemoglobin and sickle hemoglobin

Studies of modification of hemoglobin and of sickle hemoglobin by alternative aspirins have been extended to a series of new bis esters with a variety of substituted bridging diacids and to a group of mono esters with polar acyl groups. Rates of hydrolysis of these alternative aspirins have also been examined, and they reveal that a careful balance between stability and reactivity is essential for optimal activity. Four-carbon bridging groups have been found to be particularly effective, two of these raising the minimum gelling concentration of sickle hemoglobin by as much as 100%.     

Monomer diffusion into polymer domains in sickle hemoglobin.

The gelation of sickle hemoglobin includes the formation of spherulitic arrays of polymers, known as polymer domains, which are an intrinsic result of the polymer formation mechanism. We have observed the diffusion of monomers into domains as they form, which substantially increases the total concentration of hemoglobin within the domain. The maximum total concentration attained is comparable with the pellet concentration of 0.5-0.55 g/cm3 obtained in sedimentation experiments. The half time for this process is approximately 50 s for domains of 25 microns radius, and is approximately independent of temperature. The shape of the diffusion progress curves as well as the deduced diffusion constants, and their weak temperature dependence are consistent with a simple model of hemoglobin monomer diffusion into the domain.     

The growth of sickle hemoglobin polymers

The measurement of polymer growth is an essential element in characterization of assembly. We have developed a precise method of measuring the growth of sickle hemoglobin polymers by observing the time required for polymers to traverse a photolytically produced channel between a region in which polymers are created and a detection region. The presence of the polymer is functionally detected by observing its ability to create new polymers through the well-established process of heterogeneous nucleation. Using this method, we have determined the rate constants for monomer addition to and release from polymer ends, as well as their temperature dependences. At 25°C we find k₊ = 84 ± 2 mM⁻¹ s⁻¹ and k₋ = 790 ± 80 molecules/s from each end. These numbers are in accord with differential interference contrast measurements, and their ratio gives a solubility measured on individual fibers. The single-fiber solubility agrees with that measured in sedimentation experiments. The concentration dependence of the monomer addition rate is consistent with monomer addition, but not oligomer addition, to growing polymers. The concentration dependence suggests the presence of an activation enthalpy barrier, and the rate of monomer addition is not diffusion-limited. Analysis of the temperature dependence of the monomer addition rate reveals an apparent activation energy of 9.1 ± 0.6 kcal/mol.     

Universal metastability of sickle hemoglobin polymerization

Sickle hemoglobin (HbS) polymerization occurs when the concentration of deoxyHbS exceeds a well-defined solubility. In experiments using sickle hemoglobin droplets suspended in oil, it has been shown that when polymerization ceases the monomer concentration is above equilibrium solubility. We find that the final concentration in uniform bulk solutions (i.e., with negligible boundaries) agrees with the droplet measurements, and both exceed the expected solubility. To measure hemoglobin in uniform solutions, we used modulated excitation of trace amounts of CO in gels of HbS. In this method, a small amount of CO is introduced to a spatially uniform deoxyHb sample, so that less than 2% of the sample is liganded. The liganded fraction is photolyzed repeatedly and the rate of recombination allows the concentration of deoxyHbS in the solution phase to be determined, even if polymers have formed. Both uniform and droplet samples exhibit the same quantitative behavior, exceeding solubility by an amount that depends on the initial concentration of the sample, as well as conditions under which the gel was formed. We hypothesize that the early termination of polymerization is due to the obstruction in polymer growth, which is consistent with the observation that pressing on slides lowers the final monomer concentration, making it closer to solubility. The thermodynamic solubility in free solution is thus achieved only in conditions with low polymer density or under external forces (such as found in sedimentation) that disrupt polymers. Since we find that only about 67% of the expected polymer mass forms, this result will impact any analysis predicated on predicting the polymer fraction in a given experiment.     

Helical crystals of sickle cell hemoglobin

Thin ribbon-like crystals are intermediates in the formation of large crystals of deoxyhemoglobin S from many individual fibers. The thin crystals show foldedover regions when observed by electron microscopy. Some crystals are sufficiently long to have several folds each separated by a distance of about 4.4 μm, suggesting that the crystals are helical in solution. The thickness of the crystals varies from 500 to 900 Å as shown by heavy-metal shadowing and by measurements of the thickness at the crossover point where an edge-on view of the crystal is obtained.     

Ligand binding and the gelation of sickle cell hemoglobin.

The solubility equilibrium between monomer and polymer which has been shown to exist in deoxyhemoglobin S solutions is examined in solutions partially saturated with carbon monoxide. The total solubility is found to increase monotonically with increasing fractional saturation. At low fractional saturations the increase is nearly linear, amounting roughly to an increase of 0.01 g cm^?3 in solubility for each 10% increase in fractional saturation. Linear dichroism measurements on the spontaneously aligned polymer phase are used to examine the composition of the polymer as a function of the fractional saturation of the corresponding solution phase. The dichroism experiments show that the polymer phase contains less than 5% of CO-liganded hemes even at supernatant fractional saturations in excess of 70%. The polymer selects against totally liganded hemoglobin molecules by a minimum factor of 65 and against singly liganded molecules by a factor of at least 2.5. Consequently, polymerized hemoglobin S has a ligand affinity which is significantly lower than that of monomeric hemoglobin S in the deoxy quaternary structure.The kinetics of the polymerization reaction in the presence of CO are similar to those observed in pure deoxyhemoglobin S solutions. The polymerization is preceded by a pronounced delay, the duration of which, t_d, is proportional roughly to the 30th power of the solubility. At low fractional saturations, this amounts to a tenfold increase in t_d for each 10% increase in the fractional saturation.These results show that the polymerization reaction is nearly specific for deoxyhemoglobin. Models for the dependence of the solubility and the polymer saturation on ligand partial pressure demonstrate the importance of solution phase non-ideality in determining the solubility of mixtures. The results require selection against partially liganded species which is significantly greater than is predicted by the two-state allosteric model. The data are compatible with either sequential or allosteric models in which the major polymerized component is the unliganded hemoglobin molecule.