Heterogeneous Nucleation and Crowding in Sickle Hemoglobin: An Analytic Approach

Sickle hemoglobin nucleation occurs in solution as a homogeneous process or on existing polymers in a heterogeneous process. We have developed an analytic formulation to describe the solution crowding and large nonideality that affects the heterogeneous nucleation of sickle hemoglobin by using convex particle theory. The formulation successfully fits the concentration and temperature dependence of the heterogeneous nucleation process over 14 orders of magnitude. Unlike previous approaches, however, the new formulation can also accurately describe the effects of adding nonpolymerizing agents to the solution. Without additional adjustable parameters, the model now describes the data of M. Ivanova, R. Jasuja, S. Kwong, R. W. Briehl, and F. A. Ferrone, (Biophys. J. 2000, 79:1016-1022), in which up to 50% of the sickle hemoglobin is substituted by cross-linked hemoglobin A, which does not polymerize, and which substitution causes the rates to decrease by 10⁵. The success of this approach provides insight into the polymerization process: from the size-dependence of the contact energy deduced here, it also appears that various contacts of unknown origin are energetically significant in the heterogeneous nucleation process.     

Molecular crowding limits the role of fetal hemoglobin in therapy for sickle cell disease

The dominant assumption central to most treatments for sickle cell anemia has been that replacement of sickle hemoglobin (HbS) by fetal hemoglobin (HbF) would have major clinical benefit. Using laser photolysis, we have measured polymerization kinetics including rates of homogeneous and heterogeneous nucleation on mixtures of 20% and 30% HbF with HbS. We find that the present model for polymerization, including molecular crowding, can accurately predict the rates of such mixtures, by using the single assumption that no significant amount of HbF enters the polymer. The effects of replacing HbS by HbF on the rates of polymer formation are found to be significantly lower than previous measurements appeared to indicate because the impact of the replacement is also highly dependent on the total hemoglobin concentration. This is because the molecular crowding of non-polymerizing HbF offsets substantially the effects of decreasing the concentration of HbS concentration, an effect that increases with concentration. Most strikingly, the demonstrated benefit of hydroxyurea therapy in slowing the kinetics of intracellular polymerization cannot be primarily due to enhanced HbF, but must have some other origin, which could itself represent a promising therapeutic approach.     

The effects of erythrocyte membranes on the nucleation of sickle hemoglobin

Pathology in sickle cell disease begins with nucleation-dependent polymerization of deoxyhemoglobin S into stiff, rodlike fibers that deform and rigidify red cells. We have measured the effect of erythrocyte membranes on the rate of homogeneous nucleation in sickle hemoglobin, using preparations of open ghosts (OGs) with intact cytoskeletons from sickle (SS) and normal adult (AA) red cells. Nucleation rates were measured by inducing polymerization by laser photolysis of carboxy sickle hemoglobin and observing stochastic variation of replicate experiments of the time for the scattering signals to reach 10% of their respective maxima. By optical imaging of membrane fragments added to a hemoglobin solution we contrast the rate of nucleation immediately adjacent to membrane fragments with nucleation in a region of the same solution but devoid of membranes. From analysis of 29,272 kinetic curves obtained, we conclude that the effect of AA OGs is negligible (10% enhancement of nucleation rates +/-20%), whereas SS OGs caused 80% enhancement (+/-20%). In red cells, where more membrane surface is available to Hb, this implies enhancement of nucleation by a factor of 6. These experiments represent a 10-fold improvement in precision over previous approaches and are the first direct, quantitative measure of the impact of erythrocyte membranes on the homogeneous nucleation process that is responsible for polymer initiation in sickle cell disease.     

Free energy of sickle hemoglobin polymerization: a scaled-particle treatment for use with dextran as a crowding agent

Fundamental to the analysis of protein polymerization is the free energy of association, typically determined from solubility. It has been previously shown that concentrated 70 kDa dextran lowers the solubility of sickle hemoglobin, due to molecular crowding, and provides a useful ranking tool for the effects of inhibitors and molecular modifications. Because hemoglobin occupies a substantial volume as well, crowding effects of both hemoglobin and dextran contribute to the nonideality of the solution. We show how scaled-particle theory can be used to account for both types of crowding, thus allowing the determination of solubility in the absence of dextran, given data measured in its presence. The approach adopted approximates dextran as a sphere with a volume that decreases as the concentration of dextran increases. We use an asymptotic relation to describe the volume, which decreases nearly linearly by a factor of two over the range studied, from 60 to 230 mg/ml. This compression is similar to previously observed compression of sephadex beads and ficoll solutions. In the limit of low hemoglobin concentrations, the theory reduces to the previously-used approach of Ogston. Our method therefore provides a means of measuring the free energy of association of molecules that occupy significant volume fractions, even when assisted by the crowding of dextran and we present a tabulation of all known free energies of polymerization of sickle hemoglobin measured in the presence of dextran.     

Understanding the shape of sickled red cells

To understand the physical basis of the wide variety of shapes of deoxygenated red cells from patients with sickle cell anemia, we have measured the formation rate and volume distribution of the birefringent domains of hemoglobin S fibers. We find that the domain formation rate depends on the approximately 80th power of the protein concentration, compared to approximately 40th power for the concentration dependence of the reciprocal of the delay time that precedes fiber formation. These remarkably high concentration dependences, as well as the exponential distribution of domain volumes, can be explained by the previously proposed double nucleation model in which homogeneous nucleation of a single fiber triggers the formation of an entire domain via heterogeneous nucleation and growth. The enormous sensitivity of the domain formation rate to intracellular hemoglobin S concentration explains the variable cell morphology and why rapid polymerization results in cells that do not appear sickled at all.     

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. 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.     

Water proton magnetic resonance studies of normal and sickle erythrocytes. Temperature and volume dependence.

The temperature and cell volume dependence of the NMR water proton line-width, spin-lattice, and spin-spin relaxation times have been studied for normal and sickle erythrocytes as well as hemoglobin A and hemoglobin S solutions. Upon deoxygenation, the spin-spin relaxation time (T2) decreases by a factor of 2 for sickle cells and hemoglobin S solutions but remains relatively constant for normal cells and hemoglobin A solutions. The spin-lattice relaxation time (T1) shows no significant change upon deoxygenation for normal or sickle packed red cells. Studies of the change in the NMR linewidth, T1 and T2 as the cell hydration is changed indicate that these parameters are affected only slightly by a 10-20% cell dehydration. This result suggests that the reported 10% cell dehydration observed with sickling is not important in the altered NMR properties. Low temperature studies of the linewidth and T1 for oxy and deoxy hemoglobin A and hemoglobin S solutions suggest that the "bound" water possesses similar properties for all four species. The low temperature linewidth ranges from about 250 Hz at -15 degrees C to 500 Hz at -36 degrees C and analysis of the NMR curves yield hydration values near 0.4 g water/g hemoglobin for all four species. The low temperature T1 data go through a minimum at -35 degrees C for measurements at 44.4 MHz and -50 degrees C for measurements at 17.1 MHz and are similar for oxy and deoxy hemoglobin A and hemoglobin S. These similarities in the low temperature NMR data for oxy and deoxy hemoglobin A and hemoglobin S suggest a hydrophobically driven sickling mechanism. The room temperature and low temperature relaxation time data for normal and sickle cells are interpreted in terms of a three-state model for intracellular water. In the context of this model the relaxation time data imply that type III, or irrotationally bound water, is altered during the sickling process.     

Metastable mesoscopic clusters in solutions of sickle-cell hemoglobin

Sickle cell hemoglobin (HbS) is a mutant, whose polymerization while in deoxy state in the venous circulation underlies the debilitating sickle cell anemia. It has been suggested that the nucleation of the HbS polymers occurs within clusters of dense liquid, existing in HbS solutions. We use dynamic light scattering with solutions of deoxy-HbS, and, for comparison, of oxy-HbS and oxy-normal adult hemoglobin, HbA. We show that solutions of all three Hb variants contain clusters of dense liquid, several hundred nanometers in size, which are metastable with respect to the Hb solutions. The clusters form within a few seconds after solution preparation and their sizes and numbers remain relatively steady for up to 3 h. The lower bound of the cluster lifetime is 15 ms. The clusters exist in broad temperature and Hb concentration ranges, and occupy 10(-5)-10(-2) of the solution volume. The results on the cluster properties can serve as test data for a potential future microscopic theory of cluster stability and kinetics. More importantly, if the clusters are a part of the nucleation mechanism of HbS polymers, the rate of HbS polymerization can be controlled by varying the cluster properties.     

Two-step mechanism of homogeneous nucleation of sickle cell hemoglobin polymers

Sickle cell anemia is a debilitating genetic disease that affects hundreds of thousands of babies born each year worldwide. Its primary pathogenic event is the polymerization of a mutant, sickle cell, hemoglobin (HbS); and this is one of a line of diseases (Alzheimer's, Huntington's, prion, etc.) in which nucleation initiates pathophysiology. We show that the homogeneous nucleation of HbS polymers follows a two-step mechanism with metastable dense liquid clusters serving as precursor to the ordered nuclei of the HbS polymer. The evidence comes from data on the rates of fiber nucleation and growth and nucleation delay times, the interaction of fibers with polarized light, and mesoscopic metastable HbS clusters in solution. The presence of a precursor in the HbS nucleation mechanism potentially allows low-concentration solution components to strongly affect the nucleation kinetics. The variations of these concentrations in patients might account for the high variability of the disease in genetically identical patients. In addition, these components can potentially be utilized for control of HbS polymerization and treatment of the disease.     

Cell-size space effects on phase separation of binary polymer blends

Within living cells, a diverse array of biomolecules is present at high concentrations. To better understand how molecular behavior differs under such conditions (collectively described as macromolecular crowding), the crowding environment has been reproduced inside artificial cells. We have previously shown that the combination of macromolecular crowding and microscale geometries imposed by the artificial cells can alter the molecular behaviors induced by macromolecular crowding in bulk solutions. We have named the effect that makes such a difference the cell-size space effect (CSE). Here, we review the underlying biophysics of CSE for phase separation of binary polymer blends. We discuss how the cell-size space can initiate phase separation, unlike nano-sized spaces, which are known to hinder nucleation and phase separation. Additionally, we discuss how the dimensions of the artificial cell and its membrane characteristics can significantly impact phase separation dynamics and equilibrium composition. Although these findings are, of themselves, very interesting, their real significance may lie in helping to clarify the functions of the cell membrane and space size in the regulation of intracellular phase separation.     

Free Heme and the Polymerization of Sickle Cell Hemoglobin

In search of novel control parameters for the polymerization of sickle cell hemoglobin (HbS), the primary pathogenic event of sickle cell anemia, we explore the role of free heme, which may be excessively released in sickle erythrocytes. We show that the concentration of free heme in HbS solutions typically used in the laboratory is 0.02-0.04 mole heme/mole HbS. We show that dialysis of small molecules out of HbS solutions arrests HbS polymerization. The addition of 100-260 μM of free heme to dialyzed HbS solutions leads to rates of nucleation and polymer fiber growth faster by two orders of magnitude than before dialysis. Toward an understanding of the mechanism of nucleation enhancement by heme, we show that free heme at a concentration of 66 μM increases by two orders of magnitude the volume of the metastable clusters of dense HbS liquid, the locations where HbS polymer nuclei form. These results suggest that spikes of the free heme concentration in the erythrocytes of sickle cell anemia patients may be a significant factor in the complexity of the clinical manifestations of sickle cell anemia. The prevention of free heme accumulation in the erythrocyte cytosol may be a novel avenue to sickle cell therapy.     

Saturation-transfer electron paramagnetic resonance detection of anisotropic motion by sickle hemoglobin molecules in the polymer state

The motional behavior of spin-labeled deoxygenated sickle hemoglobin has been studied by using both 9- and 35-GHz saturation-transfer electron paramagnetic resonance (EPR). Using spectral subtraction techniques and saturation-transfer EPR parameter correlation plots, we find that the saturation-transfer EPR spectra for the sickle hemoglobin gel state at high temperature and high hemoglobin concentration cannot be described as a simple superposition of spectra from immobilized hemoglobin plus solution-state hemoglobin but instead suggest that the individual sickle hemoglobin molecules exhibit limited, anisotropic, rotational oscillation within the polymer fiber. The spectra also imply that the symmetry axis for sickle hemoglobin rotational oscillation is approximately coincident with the nitroxide z axis of the covalently attached spin-label. We suggest that this anisotropic rotational motion may be produced by one or two of the known intermolecular contact sites within the sickle hemoglobin fiber acting as strong intermolecular binding sites, and producing "motional alignment" within the fiber; determining the location of the strong binding site should be important in focusing the future development of antisickling agents.     

Specific antibodies to hemoglobin A1 (anti-Glu) and hemoglobin S (anti-Val) in the guinea pig: immunologic and structural correlations.

Like goats and sheep, guinea pigs can produce, in response to human sickle cell hemoglobin (beta6 Glu leads to Val), an antibody population (anti-Val) that will bind sickle cell hemoglobin but not normal hemoglobin HbA. Unlike goats and sheep, guinea pigs can produce in response to human hemoglobin A1 an antibody fraction, anti-Glu, that will not react with human sickle cell hemoglobin. These anti-Glu antibodies have been isolated by affinity chromatography and their specificity confirmed by fluorescence-quenching titrations. The sequence of the first 10 amino acids of the beta-chain of guinea pig hemoglobin has been determined. This sequence differs from those of both hemoglobin HbA and sickle cell hemoglobin by two residues, those at positions 5 and 6. This explains the similarity of the immunogenicity of this site on the two human hemoglobins when administered to guinea pigs. Both goats and sheep are identical to hemoglobin A1 at the beta-6 position.     

The binding of hemoglobin to membranes of normal and sickle erythrocytes.

The binding of hemoglobins A, S, and A2 to red cell membranes prepared by hypotonic lysis from normal blood and blood from persons with sickle cell anemia was quantified under a variety of conditions using hemoglobin labelled by alkylation with 14C-labelled Nitrogen Mustard. Membrane morphology was examined by electron microscopy. Normal membranes were found capable of binding native hemoglobin A and hemoglobin S in similar amounts when incubated at low hemoglobin: membrane ratios, but at high ratios hemoglobin saturation levels of the membranes increased progressively for hemoglobin A, hemoglobin S and hemoglobin A2, respectively, in order of increasing electropositivity. Binding was unaffected by variations in temperature (4-22 degrees C) and altered little by the presence of sulfhydryl reagents, but was inhibited at pH levels above 7.35; disrupted at high ionic strength; and dependent on the ionic composition of the media. These findings suggest that electrostatic, but not hydrophobic or sulfhydryl bonds are important in membrane binding of the hemoglobin under the conditions studied. An increased retention of hemoglobin in preparations of membranes from red cells of patients with sickle cell anemia (homozygote S) was attributable to the dense fraction of homozygote S red cells rich in irreversibly sickled cells, and the latter membranes had a smaller residual binding capacity for new hemoglobin. This suggests that in homozygote S cells which have become irreversibly sickled cells in vivo, there are membrane changes which involve alteration and/or blockade of hemoglobin binding sites. These findings support the notion that hemoglobin participates in the dynamic structure of the red cell membrane in a manner which differs in normal and pathological states.     

Mechanism of inhibition of sickling by dimethyl adipimidate. Effects of intertetramer cross-linking

Dimethyl adipimidate (DMA), an effective antisickling agent in vitro, reacts with free amino groups producing chemically modified and cross-linked molecules. In this report, we have investigated the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization. Since the extent of cross-linking is pH-dependent, we first compared the solubilities of deoxygenated hemolysates prepared from sickle cells previously treated with dimethyl adipimidate at either pH 7.4 or 8.4. The solubility of the hemolysate increased from 18.6 +/- 0.8 g/dl in the untreated sample to 20.9 +/- 1.5 g/dl (pH 7.4) and to 25.4 +/- 3.0 g/dl (pH 8.4) after dimethyl adipimidate treatment. Removal of cross-linked hemoglobin tetramers from hemolysate obtained from dimethyl adipimidate-treated cells abolished part of this effect; at pH 7.4, the solubility decreased from 20.9 +/- 1.5 to 19.4 +/- 0.2 and at pH 8.4 from 25.4 +/- 3.0 to 21.0 +/- 1.5. However, the ratio of [14C]DMA-labelled hemoglobin in the sol phase to that in the gel phase in the unfractionated hemolysate was 1.17 at pH 7.4 and 1.25 at pH 8.4, suggesting that part of the cross-linked hemoglobin tetramers was incorporated into the gel. In order to further investigate the effect of cross-linked hemoglobin tetramers on sickle hemoglobin polymerization, we separated cross-linked hemoglobin tetramers on a gel-filtration column, prepared mixtures of untreated sickle hemoglobin and cross-linked hemoglobin tetramers and studied the polymerization of these mixtures. The Csat of the untreated hemolysate increased progressively from 18.6 +/- 0.8 to 22.5 +/- 0.8 g/dl with 33% cross-linked hemoglobin tetramers. The hemoglobin concentration in the gel decreased from 43 +/- 1.0 to 33.8 +/- 1.0 g/dl with 33% cross-linked hemoglobin tetramers, while the pellet volume fraction, phi p, increased with and almost approached 1 at 50% cross-linked hemoglobin tetramers. In addition, the sol phase contained a higher molecular weight distribution of cross-linked hemoglobin tetramers than the gel phase. These observations suggest that a loose polymer was formed in the gel phase with a hemoglobin concentration much lower than that of the control. Thus, polymerization of sickle hemoglobin is inhibited by: (1) exclusion of higher molecular weight cross-linked hemoglobin tetramers from the gel, and (2) loose incorporation of cross-linked hemoglobin tetramers into the gel, perhaps preventing lateral packing and formation of tightly ordered fibers.     

Water proton magnetic resonance studies of normal and sickle erythrocytes Temperature and volume dependence

The temperature and cell volume dependence of the NMR water proton linewidth, spin-lattice, and spin-spin relaxation times have been studied for normal and sickle erythrocytes as well as hemoglobin A and hemoglobin S solutions. Upon deoxygenation, the spin-spin relaxation time (T₂) decreases by a factor of 2 for sickle cells and hemoglobin S solutions but remains relatively constant for normal cells and hemoglobin A solutions. The spin-lattice relaxation time (T₁) shows no significant change upon dexygenation for normal or sickle packed red cells. Studies of the change in the NMR linewidth, T₁ and T₂ as the cell hydration is changed indicate that these parameters only slightly by a 10–20% cell dehydration. This result suggests that the reported 10% cell dehydration observed with sickling is not important in the altered NMR properties. Low temperature studies of the linewidth and T₁ for oxy and deoxy hemoglobin A and hemoglobin S solutions suggest that the “bound” water possesses similar properties for all four species. The low temperature linewidth ranges from about 250 Hz at ?15°C to 500 Hz at ?36°C and analysis of the NMR curves yield hydration values near 0.4 g water/g hemoglobin for all four species. The low temperature T₁ data go through a minimum at ?35°C for measurements at 44.4 MHz and ?50°C for measurements at 17.1 MHz and are similar for oxy and deoxy hemoglobin A and hemoglobin S. These similarities in the low temperature NMR data for oxy and deoxy hemoglobin A and hemoglobin S suggest a hydrophobically driven sickling mechanism. The room temperature and low temperature relaxation time data for normal and sickle cells are interpreted in terms of a three-state model for intracellular water. In the context of this model the relaxation time data imply that type III, or irratationally bound water, is altered during the sickling process.     

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.