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.     

Metastable polymerization of sickle hemoglobin in droplets

Sickle cell disease arises from a genetic mutation of one amino acid in each of the two hemoglobin beta chains, leading to the polymerization of hemoglobin in the red cell upon deoxygenation, and is characterized by vascular crises and tissue damage due to the obstruction of small vessels by sickled cells. It has been an untested assumption that, in red cells that sickle, the growing polymer mass would consume monomers until the thermodynamically well-described monomer solubility was reached. By photolysing droplets of sickle hemoglobin suspended in oil we find that polymerization does not exhaust the available store of monomers, but stops prematurely, leaving the solutions in a supersaturated, metastable state typically 20% above solubility at 37 degrees C, though the particular values depend on the details of the experiment. We propose that polymer growth stops because the growing ends reach the droplet edge, whereas new polymer formation is thwarted by long nucleation times, since the concentration of hemoglobin is lowered by depletion of monomers into the polymers that have formed. This finding suggests a new aspect to the pathophysiology of sickle cell disease; namely, that cells deoxygenated in the microcirculation are not merely undeformable, but will actively wedge themselves tightly against the walls of the microvasculature by a ratchet-like mechanism driven by the supersaturated solution.     

Electron microscopic studies of the intracellular polymerization of sickle hemoglobin

Transmission electron microscopy has been used to study intracellular sickle hemoglobin polymer in unfractionated cells from the arterial and venous blood of patients and after external deoxygenation. We detect polymerized hemoglobin in up to 10% of the cells in the venous circulation, especially in cells that are "cigar-shaped" and appear to be irreversibly sickled. We could not see well-defined polymer in mixed arterial samples; nevertheless, we found electron opaque spots, which could be ferritin granules, hemosiderin, or small aggregates of hemoglobin S. However, upon sequential chemical deoxygenation using 1.0% sodium metabisulphite, polymer formation was seen at oxygen saturation values of 75%-85%. Cells that were physically deoxygenated using gas mixtures containing nitrogen-carbon dioxide-oxygen mixtures were found to contain distinct polymers of deoxyhemoglobin S at oxyhemoglobin saturation values of 50%-75%. As deoxygenation increases, we detect short, randomly arranged polymer in a loose network, with occasional long polymers. Upon further deoxygenation, the length and number of polymer forms increased. Between 0% and 50% saturation, most erythrocytes were full of long, parallel, closely packed polymers that tend to align and run parallel to the cell membrane. In both chemical and physically deoxygenated blood samples, cells were seen at 50%-75% oxyhemoglobin saturation that retained their normal biconcave disc shape, although they contained significant amounts of polymer. The structural changes in sickle erythrocytes seen in vitro due to physical or chemical deoxygenation of cells, may reflect in vivo intracellular changes in the sickle cell patient.     

The rates of polymerization and depolymerization of sickle cell hemoglobin

The polymerization and depolymerization of concentrated solutions of sickle cell deoxyhemoglobin were initiated by raising and lowering the temperature, and the time courses of the reactions monitored by the change in apparent turbidity. The polymerization reaction exhibits a marked lag phase followed by a rapid increase in turbidity, and is dependent on a very high power of the hemoglobin concentration, roughly the fifteenth. The depolymerization reaction exhibits no such lag, and is much less dependent on concentration. The implications of these results for polymerization models are discussed.     

Influence of sickle hemoglobin polymerization and membrane properties on deformability of sickle erythrocytes in the microcirculation.

The rheological properties of normal erythrocytes appear to be largely determined by those of the red cell membrane. In sickle cell disease, the intracellular polymerization of sickle hemoglobin upon deoxygenation leads to a marked increase in intracellular viscosity and elastic stiffness as well as having indirect effects on the cell membrane. To estimate the components of abnormal cell rheology due to the polymerization process and that due to the membrane abnormalities, we have developed a simple mathematical model of whole cell deformability in narrow vessels. This model uses hydrodynamic lubrication theory to describe the pulsatile flow in the gap between a cell and the vessel wall. The interior of the cell is modeled as a Voigt viscoelastic solid with parameters for the viscous and elastic moduli, while the membrane is assigned an elastic shear modulus. In response to an oscillatory fluid shear stress, the cell--modeled as a cylinder of constant volume and surface area--undergoes a conical deformation which may be calculated. We use published values of normal and sickle cell membrane elastic modulus and of sickle hemoglobin viscous and elastic moduli as a function of oxygen saturation, to estimate normalized tip displacement, d/ho, and relative hydrodynamic resistance, Rr, as a function of polymer fraction of hemoglobin for sickle erythrocytes. These results show the transition from membrane to internal polymer dominance of deformability as oxygen saturation is lowered. More detailed experimental data, including those at other oscillatory frequencies and for cells with higher concentrations of hemoglobin S, are needed to apply fully this approach to understanding the deformability of sickle erythrocytes in the microcirculation. The model should be useful for reconciling the vast and disparate sets of data available on the abnormal properties of sickle cell hemoglobin and sickle erythrocyte membranes, the two main factors that lead to pathology in patients with this disease.     

Fluctuations in the polymerization of sickle hemoglobin. A simple analytic model

Using the stochastic theory of chemical reactions and the theory of first passage times, a simple analytic expression is derived for the distribution of delay times that has been observed in studies of the polymerization kinetics of sickle hemoglobin under conditions where the polymerization progress curves exhibit stochastic variation. The rate of homogeneous nucleation can be readily extracted from such experiments using this expression. This work constitutes a significant addition to the rather limited number of examples where contact can be successfully made between the stochastic theory of chemical kinetics and experiment.     

Kinetics of sickle hemoglobin polymerization. II. A double nucleation mechanism

A double nucleation mechanism for the polymerization of sickle hemoglobin is described. The mechanism accounts for all of the major kinetic observations: the appearance of a delay, the high concentration dependence of the delay time, and the stochastic behavior of slowly polymerizing samples in small volumes. The mechanism postulates that there are two pathways for polymer formation: polymerization is initiated by homogeneous nucleation in the solution phase, followed by nucleation of additional polymers on the surface of existing ones. This second pathway is called heterogeneous nucleation. Since the surface of polymers is continuously increasing with time, heterogeneous nucleation provides a mechanism for the extreme autocatalysis that is manifested as an apparent delay in the kinetic progress curves. In this mechanism, each spherulitic domain of polymers is considered to be initiated by a single homogeneous nucleation event. The mechanism explains the irreproducibility of the delay time for single domain formation as arising from stochastic fluctuations in the time at which the homogeneous nucleus for the first polymer is formed. Integration of the linearized rate equations that describe this model results in a simple kinetic form: A[cosh(Bt)-1] (Bishop & Ferrone, 1984). In the accompanying paper (Ferrone et al., 1985) it was shown that the initial 10 to 15% of progress curves, with delay times varying from a few milliseconds to over 10(5) seconds, is well fit by this equation. In this paper, we present an approximate statistical thermodynamic treatment of the equilibrium nucleation processes that shows how the nucleus sizes and nucleation equilibrium constants depend on monomer concentration. The equilibrium model results in expressions for B and B2A as a function of monomer concentration in terms of five adjustable parameters: the bimolecular addition rate of a monomer to the growing aggregate, the fraction of polymerized monomers that serve as heterogeneous nucleation sites, the free energy of intermolecular bonding within the polymer, and two parameters that describe the free energy change as a function of size for the bonding of the heterogeneous nucleus to a polymer surface. This model provides an excellent fit to the data for B and B2A as a function of concentration using physically reasonable parameters. The model also correctly predicts the time regime in which stochastic behavior is observed for polymerization in small volumes.     

Kinetics of sickle hemoglobin polymerization. I. Studies using temperature-jump and laser photolysis techniques

Using a combination of laser photolysis and temperature-jump techniques, the kinetics of hemoglobin S polymerization have been studied over a wide range of delay times (10(-3) to 10(5)s), concentrations (0.2 to 0.4 g/cm3) and temperatures (5 to 50 degrees C). A slow temperature-jump technique was used to induce polymerization in samples with delay times between 10(2) seconds and 10(5) seconds by heating a solution of completely deoxygenated hemoglobin S. For samples with shorter delay times, polymerization was induced by photodissociating the carbon monoxide complex in small volumes (10(-9) cm3) using a microspectrophotometer equipped with a cw argon ion laser. The photolysis technique is described in some detail because of its importance in studying hemoglobin S polymerization at physiological concentrations and temperatures. In order, to establish conditions for complete photodissociation with minimal laser heating, a series of control experiments on normal human hemoglobin was performed and theoretically modeled. The concentration dependence of the tenth time is found to decrease with increasing hemoglobin S concentration. In the range 0.2 to 0.3 g/cm3, the tenth time varies as the 36th power of the hemoglobin S concentration, while in the range 0.3 to 0.4 g/cm3 it decreases to 16th power. As the tenth times become shorter, the progress curves broaden, with the onset of polymerization becoming less abrupt. For tenth times greater than about 30 seconds, measurements with the laser photolysis technique on small volumes yield highly irreproducible tenth times, but superimposable progress curves, indicating stochastic behavior. The initial part of the progress curves from both temperature-jump and laser photolysis experiments is well fit with an equation for the concentration of polymerized monomer, delta (t) = A[cosh (Bt) -1], which results from integration of the linearized rate equations for the double nucleation mechanism described in the accompanying paper (Ferrone et al., 1985). The dependence of the parameters A and B on temperature and concentration is obtained from fitting over 300 progress curves. The rate B has a large concentration dependence, varying at 25 degrees C from about 10(-4) S-1 at 0.2 g/cm3 to about 100 s-1 at 0.4 g/cm3.     

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%.     

On the assembly of sickle hemoglobin fascicles

Deoxyhemoglobin S fibers associate into bundles, or fascicles, that subsequently crystallize by a process of alignment and fusion. We have used electron microscopy to study the formation of fascicles and the changes in fiber packing that occur during the conversion of fascicles to crystals. The first event in crystallization involves fibers forming fascicles that are initially small and poorly ordered but, with time, become progressively larger and more highly ordered. After six to eight hours, the fibers in a fascicle form a crystalline lattice. The three-dimensional unit cell parameters of this lattice are a = 1300 A, b = 365 A, and c = 210 A (the a axis is parallel to the fiber axis). Fibers have an elliptical cross-section whose major and minor axes are 250 A and 185 A, respectively. When projected on to the unit cell vectors, these dimensions are 210 A and 155 A, so the unit cell dimension of 365 A implies that there are two fibers per unit cell. Theoretically, fibers could pair so that each member of the unit cell is oriented in the same direction (parallel) or opposite directions (antiparallel). Fourier transforms of electron micrographs (or models) cannot distinguish between these alternatives, since the two arrangements produce very similar intensity distributions. The orientation of the fibers was determined from cross-sections of the fascicles in which the fibers are seen end-on. In this view the images of the fibers are rotationally blurred because the fibers twist 30 degrees to 40 degrees about their helical axis through the 300 A to 400 A thick section. We have been able to remove the rotational blur from each of the fibers in the unit cell using the procedures described by Carragher et al. The deblurred images of the two fibers in the unit cell are related by mirror symmetry. This relationship means that the fibers are antiparallel. These observations suggest that crystallization of fibers in fascicles is mediated by assembly of the fibers into antiparallel pairs that contain equal numbers of double strands running in each direction.     

Nitric oxide reduces sickle hemoglobin polymerization: potential role of nitric oxide-induced charge alteration in depolymerization

We previously demonstrated that inhaling nitric oxide (NO) increases the oxygen affinity of sickle red blood cells (RBCs) in patients with sickle cell disease (SCD). Our recent studies found that NO lowered the P₅₀ values of sickle hemoglobin (HbS) hemolysates but did not increase methemoglobin (metHb) levels, supporting the role of NO, but not metHb, in the oxygen affinity of HbS. Here we examine the mechanism by which NO increases HbS oxygen affinity. Because anti-sickling agents increase sickle RBC oxygen affinity, we first determined whether NO exhibits anti-sickling properties. The viscosity of HbS hemolysates, measured by falling ball assays, increased upon deoxygenation; NO treatment reduced the increment. Multiphoton microscopic analyses showed smaller HbS polymers in deoxygenated sickle RBCs and HbS hemolysates exposed to NO. These results suggest that NO inhibits HbS polymer formation and has anti-sickling properties. Furthermore, we found that HbS treated with NO exhibits an isoelectric point similar to that of HbA, suggesting that NO alters the electric charge of HbS. NO–HbS adducts had the same elution time as HbA upon high performance liquid chromatography analysis. This study demonstrates that NO may disrupt HbS polymers by abolishing the excess positive charge of HbS, resulting in increased oxygen affinity.     

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.     

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.     

Enhanced inhibition of polymerization of sickle cell hemoglobin in the presence of recombinant mutants of human fetal hemoglobin with substitutions at position 43 in the gamma-chain

Four recombinant mutants of human fetal hemoglobin [Hb F (alpha2gamma2)] with amino acid substitutions at the position 43 of the gamma-chain, rHb (gammaD43L), rHb (gammaD43E), rHb (gammaD43W), and rHb (gammaD43R), have been expressed in our Escherichia coli expression system and used to investigate their inhibitory effect on the polymerization of deoxygenated sickle cell hemoglobin (Hb S). Oxygen-binding studies show that rHb (gammaD43E), rHb (gammaD43W), and rHb (gammaD43R) exhibit higher oxygen affinity than human normal adult hemoglobin (Hb A), Hb F, or rHb (gammaD43L), and all four rHbs are cooperative in binding O2. Proton nuclear magnetic resonance (NMR) studies of these four rHbs indicate that the quaternary and tertiary structures around the heme pockets are similar to those of Hb F in both deoxy (T) and liganded (R) states. Solution light-scattering experiments indicate that these mutants remain mostly tetrameric in the liganded (R) state. In equimolar mixtures of Hb S and each of the four rHb mutants (gammaD43L, gammaD43E, gammaD43R, and gammaD43W), the solubility (Csat) of each of the pairs of Hbs is higher than that of a similar mixture of Hb S and Hb A, as measured by dextran-Csat experiments. Furthermore, the Csat values for Hb S/rHb (gammaD43L), Hb S/rHb (gammaD43E), and Hb S/rHb (gammaD43R) mixtures are substantially higher than that for Hb S/Hb F. The results suggest that these three mutants of Hb F are more effective than Hb F in inhibiting the polymerization of deoxy-Hb S in equimolar mixtures.     

Intermolecular contacts within sickle hemoglobin fibers

By combining X-ray crystallographic co-ordinates of sickle hemoglobin (HbS) molecules with three-dimensional reconstructions of electron micrographs of HbS fibers we have synthesized a model for the structure of the clinically relevant HbS fiber. This model largely accounts for the action of 55 point mutations of HbS whose effect on fiber formation has been studied. In addition, it predicts locations at which additional point mutations are likely to affect fiber formation. The number of intermolecular axial contacts decreases with radius until, at the periphery of the fiber, there are essentially no axial contacts. We suggest that this observation accounts for the limited radial growth of the HbS fiber and that a similar mechanism may be a factor in limiting the size of other helical particles. The methodology for the synthesis of the fiber model is applicable to other systems in which X-ray crystallographic and electron microscopic data are available.     

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.