Polymorphic assemblies of double strands of sickle cell hemoglobin. Manifold pathways of deoxyhemoglobin S crystallization

Phase diagram of two-patch colloids with competing anisotropic and isotropic interactions

Patchy particles are considered to be a good model for protein aggregation. We propose a novel method to generate different structures of glucose isomerase protein such as chains, crystals and bundles by utilising aggregation of two-patch colloidal particles in presence of competing isotropic and anisotropic potential. We calculate the equilibrium phase diagram of two-patch colloidal particles and demonstrates the coexistence of different phases like disordered clusters, chains, crystals and bundles depending on the relative strength of isotropic and anisotropic potential. We also show that the formation of network of bundles is metastable against the formation of thermodynamically favored finite sized bundles along with thermodynamically stable crystals. These bundles appear to be helical in structure similar to that observed in sickle cell hemoglobin. The simulation results show that the method can characterize phase behaviour of glucose isomerase protein, which provides a novel tool to unveil self-assembly mechanism of protein under different conditions.

Rapid and inefficient kinetics of sickle hemoglobin fiber growth

In sickle cell disease, the aberrant assembly of hemoglobin fibers induces changes in red blood cell morphology and stiffness, which leads to downstream symptoms of the disease. Therefore, understanding of this assembly process will be important for the treatment of sickle cell disease. By performing the highest spatiotemporal resolution measurements (55 nm at 1 Hz) of single sickle hemoglobin fiber assembly to date and combining them with a model that accounts for the multistranded structure of the fibers, we show that the rates of sickle hemoglobin addition and loss have been underestimated in the literature by at least an order of magnitude. These results reveal that the sickle hemoglobin self-assembly process is very rapid and inefficient (4% efficient versus 96% efficient based on previous analyses), where net growth is the small difference between over a million addition-loss events occurring every second.

Sickle Cell Hemoglobin with Mutation at αHis-50 Has Improved Solubility

The unliganded tetrameric Hb S has axial and lateral contacts with neighbors and can polymerize in solution. Novel recombinants of Hb S with single amino acid substitutions at the putative axial (recombinant Hb (rHb) (βE6V/αH20R) and rHb (βE6V/αH20Q)) or lateral (rHb (βE6V/αH50Q)) or double amino acid substitutions at both the putative axial and lateral (rHb (βE6V/αH20R/αH50Q) and rHb (βE6V/αH20Q/αH50Q)) contact sites were expressed in Escherichia coli and purified for structural and functional studies. The (1)H NMR spectra of the CO and deoxy forms of these mutants indicate that substitutions at either αHis-20 or αHis-50 do not change the subunit interfaces or the heme pockets of the proteins. The double mutants show only slight structural alteration in the β-heme pockets. All mutants have similar cooperativity (n50), alkaline Bohr effect, and autoxidation rate as Hb S. The oxygen binding affinity (P50) of the single mutants is comparable with that of Hb S. The double mutants bind oxygen with slightly higher affinity than Hb S under the acidic conditions. In high salt, rHb (βE6V/αH20R) is the only mutant that has a shorter delay time of polymerization and forms polymers more readily than Hb S with a dextran-Csat value of 1.86 ± 0.20 g/dl. Hb S, rHb (βE6V/αH20Q), rHb (βE6V/αH50Q), rHb (βE6V/αH20R/αH50Q), and rHb (βE6V/αH20Q/αH50Q) have dextran-Csat values of 2.95 ± 0.10, 3.04 ± 0.17, 11.78 ± 0.59, 7.11 ± 0.66, and 10.89 ± 0.83 g/dl, respectively. rHb (βE6V/αH20Q/αH50Q) is even more stable than Hb S under elevated temperature (60 °C).

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.

Anisotropy in Sickle Hemoglobin Fibers from Variations in Bending and Twist

We have studied the variations of twist and bend in sickle hemoglobin fibers. We find that these variations are consistent with an origin in equilibrium thermal fluctuations, which allows us to estimate the bending and torsional rigidities and effective corresponding material moduli. We measure bending by electron microscopy of frozen hydrated fibers and find that the bending persistence length, a measure of the length of fiber required before it starts to be significantly bent due to thermal fluctuations, is 130microm, somewhat shorter than that previously reported using light microscopy. The torsional persistence length, obtained by re-analysis of previously published experiments, is found to be only 2.5microm. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6x10(-27)Jm, much less than their bending rigidity of 5x10(-25)Jm. For (normal) isotropic materials, one would instead expect these to be similar. Thus, we present the first quantitative evidence of a very significant material anisotropy in sickle hemoglobin fibers, as might arise from the difference between axial and lateral contacts within the fiber. We suggest that the relative softness of the fiber with respect to twist deformation contributes to the metastability of HbS fibers: HbS double strands are twisted in the fiber but not in the equilibrium crystalline state. Our measurements inform a theoretical model of the thermodynamic stability of fibers that takes account of both bending and extension/compression of hemoglobin (double) strands within the fiber.

Twisted protein aggregates and disease: the stability of sickle hemoglobin fibers

We describe how twist could play an essential role in stabilizing 20 nm diameter sickle hemoglobin fibers. Our theory successfully reproduces the observed variation of helical pitch length with fiber diameter. With no remaining adjustable parameters it also yields a prediction for the torsional rigidity of sickle hemoglobin fibers that is in good agreement with experiment and hence retains the striking feature that such fibers can be highly mechanically anisotropic, even with a ratio of bending to torsional rigidity of about 50. We discuss how our study might be relevant to the development of treatment strategies.

Flexibility and nucleation in sickle hemoglobin

We have studied the self-assembly of Hemoglobin C-Harlem (HbC-Harlem), a double mutant of hemoglobin that possesses the beta6 Glu-->Val mutation of sickle hemoglobin (HbS) plus beta73 Asp-->Asn. By electron microscopy we find it forms crystals, rather than the wrapped multistranded fibers seen in HbS. Fourier transforms of the crystals yield unit cell parameters indistinguishable from crystals of HbS. Differential interference contrast (DIC) microscopy and birefringence also show crystal formation rather than the polymers or domains seen for HbS, while the growth patterns showed radiating crystal structures rather than simple linear crystalline forms. The solubility of the assembly was measured using a photolytic micromethod over a temperature range of 17-31 degrees C in 0.15 M phosphate buffer and found to be essentially the same as that of fibers of HbS. The assembly kinetics were observed by photolysis of the carbon monoxide derivative, and the mass of assembled hemoglobin was found to grow exponentially, with onset times that were stochastically distributed for small volumes. The stochastic onset of assembly showed strong concentration dependence, similar to but slightly greater than that seen in sickle hemoglobin nucleation. These observations suggest that like HbS, HbC-Harlem assembly proceeds by a homogeneous nucleation process, followed by heterogeneous nucleation. However, relative to HbS, both homogeneous and heterogeneous nucleation are suppressed by almost 11 orders of magnitude. The slowness of nucleation can be reconciled with the similarity of the solubility to HbS by an increase in contact energy coupled with a decrease in vibrational entropy recovered on assembly. This also explains the linearity of the double-strands, and agrees with the chemical nature of the structural replacement.

Polymerization of deoxy-sickle cell hemoglobin in high-phosphate buffer

Deoxy-sicklecell hemoglobin (HbS) polymerizes in 0.05 M phosphate buffer to form long helical fibers. The reaction typically occurs when the concentration of HbS is about 165 mg/ml. Polymerization produces a variety of polymorphic forms. The structure of the fibers can be probed by using site-directed mutants to examine the effect of altering the residues involved in intermolecular interactions. Polymerization can also be induced in the presence of 1.5 M phosphate buffer. Under these conditions polymerization occurs at much lower concentrations (ca. 5 mg/ml), which is advantageous when site-directed mutants are being used because only small quantities of the mutants are available. We have characterized the structure of HbS polymers formed in 1.5 M phosphate to determine how their structures are related to the polymers formed under more physiological conditions. Under both sets of conditions fibers are the first species to form. At pHs between 6.7 and 7.3 fibers initially form bundles and then crystals. At lower pHs fibers form macrofibers and then crystals. Fourier transforms of micrographs of the polymers formed in 1.5 M phosphate display the 32- and 64-A(-1) periodicity characteristic of fibers formed in 0.05 M phosphate buffer. The 64-A(-1) layer line is less prominent in Fourier transforms of negatively stained fibers formed in 1.5 M phosphate possibly because salt interferes with staining of the fibers. However, micrographs and Fourier transforms of frozen hydrated fibers formed in high and low phosphate display the same periodicities. Under both sets of reaction conditions HbS polymers form crystals with the same unit cell parameters as Wishner-Love crystals (a = 64 A, b = 185 A, c = 53 A). Some of the polymerization intermediates were examined in the frozen-hydrated state in order to determine whether their structures were significantly perturbed by negative staining. We have also carried out reconstructions of the frozen-hydrated fibers in high and low phosphate to compare their molecular coordinates. The helical projection of the reconstructions in low phosphate shows the expected 14-strand structure. In high phosphate the 14-strand fibers are also formed and their molecular coordinates are the same (within experimental error) as those of fibers formed in 0.05 M phosphate. In addition, the reconstructions of high-phosphate fibers reveal a new minor variant of fiber containing 10 strands. The polymerization products in 1.5 M phosphate buffer were generally indistinguishable from those formed in 0.05 M phosphate buffer. Micrographs of frozen hydrated specimens have facilitated the interpretation of previously published micrographs using negative staining.

Polymer structure and solubility of deoxyhemoglobin S in the presence of high concentrations of volume-excluding 70-kDa dextran. Effects of non-s hemoglobins and inhibitors

Earlier observations indicated that volume exclusion by admixed non-hemoglobin macromolecules lowered the polymer solubility ("Csat") of deoxyhemoglobin (Hb) S, presumably by increasing its activity. In view of the potential usefulness of these observations for in vitro studies of sickling-related polymerization, we examined the ultrastructure, solubility behavior, and phase distributions of deoxygenated mixtures of Hb S with 70-kDa dextran, a relatively inert, low ionic strength space-filling macromolecule. Increasing admixture of dextran progressively lowered the Csat of deoxyHb S. With 12 g/dl dextran, a 5-fold decrease in apparent Csat ("dextran-Csat") was obtained together with acceptable sensitivity and proportionality with the standard Csat when assessing the effects of non-S Hb admixtures (A, C, and F) or polymerization inhibitors (alkylureas or phenylalanine). The volume fraction of dextran excluding Hb was 70-75% of total deoxyHb-dextran (12 g/dl) volumes. Electron microscopy showed polymer fibers and fiber-to-crystal transitions indistinguishable from those formed without dextran. Thus when Hb quantities are limited, as with genetically engineered recombinant Hbs or transgenic sickle mice, the dextran-Csat provides convenient and reliable screening of effects of Hb S modifications on polymerization under near-physiological conditions, avoiding problems of high ionic strength.

The polymerization of sickle hemoglobin in solutions and cells

The polymerization of sickle hemoglobin occurs by the same mechanisms in solutions and in cells, and involves the formation of 14 stranded fibers from hemoglobin molecules which have assumed a deoxy quaternary structure. The fibers form via two types of highly concentration-dependent nucleation processes: homogeneous nucleation in solutions with hemoglobin activity above a critical activity, and heterogeneous nucleation in similarly supersaturated solutions which also contain hemoglobin polymers. The latter pathway is dominant, and creates polymer arrays called domains. The individual polymers bend, but also cross-link, and the resulting mass behaves as a solid. The concentration of polymerized hemoglobin increases exponentially unless clamped by rate limiting effects such as oxygen delivery.

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.

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.

X-ray diffraction studies of 14-filament models of deoxygenated sickle cell hemoglobin fibers. II. Models based on the deoxygenated sickle hemoglobin crystal structure

The calculated transforms of a number of crystal-based models of the deoxygenated sickle cell hemoglobin fiber have been compared with X-ray diffraction data of 15 A (1 A = 0.1 nm) resolution. The fiber models consist of 14 single strands of sickle cell hemoglobin (HbS) molecules, which associate into seven protofilaments arranged similarly to those present in the crystal structure. Six of the protofilaments are arranged in three crystallographic until cells extending in the c-axis direction with the seventh protofilament positioned so as to provide an elliptical cross-section when the assemblage is viewed down the fiber axis. Models were generated by systematically and independently translating each of the model's three subcells in steps of 3.5 A along the fiber axis. The seventh protofilament was kept fixed as a point of reference. Each translation of a subcell corresponded to a different fiber model whose transform was then compared with observed data. In all, over 46,000 transforms were computed; of these, three models with minimal residuals were identified. The free energy of packing for all crystal-based models was evaluated to find configurations of protofilaments possessing minimal free energies. The results of the calculations support the subcell configurations of two of the three models with minimal residuals.

Structural analysis of polymers of sickle cell hemoglobin. I. Sickle hemoglobin fibers

The structure of fibers of deoxyhemoglobin S has been under investigation for several years and a number of different models have been proposed for the arrangement of molecules within the particles. We have used reconstruction and modeling techniques in our analysis of these structures. Several new approaches have been employed in this analysis in order to provide improved estimates of the co-ordinates, pairing, and polarity of the hemoglobin S molecules. Fibers have a variable pitch and, in order to minimize distortions in the reconstructed density maps associated with these variations in pitch, we have developed an iterative procedure to measure the instantaneous pitch and have modified the reconstruction algorithm to incorporate the measured values. This procedure improves the accuracy with which the hemoglobin S molecules can be located in the density maps. Furthermore, the determination of the instantaneous pitch allows us to measure directly the rotation of the individual hemoglobin molecules. These measurements are in excellent agreement with the values predicted using a random angular walk model (as originally proposed for F-actin) to describe the variable pitch. The reconstructions confirm that the fiber consists of 14 strands of hemoglobin S arranged in a hexagonally shaped cross-section. We have determined the pairing of the molecules to form double strands directly from the density maps by identifying the molecules that have intermolecular distances that conform to those of double strands in the Wishner-Love crystal. The seven double strands identified in this manner are consistent with the strand pairings proposed by Dykes et al. (1979) rather than the alternate pairings proposed by Rosen & Magdoff-Fairchild (1985). In addition, we have for the first time determined the polarity of the double strands directly from the reconstruction data. This was achieved using a procedure that amounts to essentially "dissecting" individual double strands from the reconstructed density maps so that their density distribution could be examined independently of the neighboring double strands. Knowledge of the relative polarities of the double strands is essential for determining the intermolecular interactions that stabilize the fiber.

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.

The reconstruction of helical particles with variable pitch

In the reconstruction of helical particles, it is normally assumed that translation along the length of a particle is coupled to rotation about its axis. This assumption is not valid for particles whose pitch varies along the particle length (e.g. actin, HbS fibers), and application of the usual algorithms results in significant errors in both the shape and coordinates of subunits in the reconstructed density map. We have developed an iterative procedure for reconstructing particles with variable pitch. The goal of this procedure is to obtain an accurate estimate of the local pitch of the particle which can then be incorporated into the reconstruction algorithm. This involves synthesis of trial model structures which have constant pitch. The local pitch is derived from a cross-correlation analysis between these trial models and the variable pitch particles. The constant pitch models are constructed using coordinates measured from the reconstructed density maps. Each iteration of the procedure provides an improved estimate of the pitch which is incorporated into the succeeding iteration. The fidelity of the reconstruction is determined from cross-correlation between the original micrograph and a variable pitch model. The iterations are continued until the cross-correlation coefficient between the variable pitch model and the micrograph of the particle is maximized. The implementation of the iterative procedure is described and its behavior is evaluated using model structures which incorporate variations in pitch similar to those actually occurring in sickle hemoglobin fibers. The results indicate that the iterative reconstruction procedure considerably reduces the errors associated with constant pitch reconstructions. These tests provide a basis for applying this procedure in the structural analysis of micrographs of helical particles which display variable pitch. Application to sickle hemoglobin fibers resulted in an improvement in the accuracy with which the hemoglobin S molecules can be located in the density maps.

Rheologic behavior of deoxyhemoglobin S gels

The physical properties of deoxyhemoglobin S gels formed from solutions at concentrations and temperatures approaching those in vivo have been characterized by stress relaxation using a rotational rheometer. Gels were annealed in the rheometer and then subjected to a constant shear strain; thereafter the stress sustained was followed with time. Gels with solid-like behavior held stress indefinitely, and were characterized by yield temperature (the temperature at which stress decreased). Gels with less solid behavior were unable to hold target stress, and were characterized by yield stress (maximum stress attained) and equilibrium stress (final stress held). The samples were ultracentrifuged to calculate pellet and polymer masses. The solidity of the gels, as measured by yield temperature or yield stress, was related to the initial hemoglobin concentration, pellet and polymer masses, shear history, temperature, and the temperature and time of annealing. Solidity increased significantly with time when gels were annealed at 37 degrees C, whereas, when annealed at 25 degrees C, no or minimal increases in solidity were noted. Studies suggest that polymerization occurs rapidly and is completed early in or before the gel annealing period and that the increase in solidity with time of annealing is mainly due to factors other than polymer mass, i.e. alignment, increasing bond strength, water loss. The chemical activity of deoxyhemoglobin S did not affect the solidity of the formed gels. When the resultant polymer masses were comparable, gels formed from samples with albumin present (higher initial total protein concentration, but lower initial deoxyhemoglobin S concentration), had the same behavior as gels formed from solutions with higher initial hemoglobin S concentration. These findings demonstrate that gel annealing conditions must be standardized when comparing the rheologic behaviors of deoxyhemoglobin S gels and indicate that the gel's physical properties (influenced by polymer mass, shear history, annealing time) must be considered in understanding pathophysiology of sickling disorders.

Design, synthesis, and testing of potential antisickling agents. 9. Cyclic tetrapeptide homologs as mimics of the mutation site of hemoglobin S

As part of our continuing search for new agents which might be useful for the treatment of sickle-cell anemia, we have synthesized two cyclic tetrapeptide homologs, cyclo(-Val-Glu[-Thr-Pro-]-OH) (1a) and cyclo(-Phe-Glu[-Thr-Pro-]-OH (1b), and a tetrapeptide lactone homolog cyclo(H-Thr-Pro-Val-Glu-OH) (2). The intent was that these peptides would mimic a tetrapeptide region around the mutation site of HbS and thus be able to bind at the acceptor site of HbS and thereby inhibit polymerization. The synthesis of the linear peptides was accomplished in solution using both the polymeric reagent (PHBT) and DCC/HOBT methods; cyclization was accomplished by an improved method. 13C-n.m.r. studies were performed which allowed us to assign the conformation about the Thr-Pro bond in 1a and 2 as trans. The cyclic peptides were tested for their ability to increase the solubility of HbS under deoxygenating conditions, but only 1a had any antigelling activity, albeit low.

Polymorphism of sickle cell hemoglobin aggregates: structural basis for limited radial growth

Fibers composed of molecules of deoxygenated sickle cell hemoglobin are the basic cause of pathology in sickle cell disease. The hemoglobin molecules in these fibers are arranged in double strands that twist around one another with a long axial repeat. These fibrous aggregates exhibit a pattern of polymorphism in which the ratio of their helical pitch to their radius is approximately constant. The observed ratio agrees with an estimate of its value calculated from the geometric properties of helical assemblies and the degree of distortion that a protein-protein interface can undergo. This agreement indicates that the radius of an aggregate is limited by the maximum possible stretching of double strands. The geometric properties limiting the radial extent of sickle hemoglobin fibers are fundamental to all cables of protein filaments and could contribute to the control of diameter in other biological fibers such as collagen or fibrin.

The effect of 2,3-diphosphoglycerate on the solubility of deoxyhemoglobin S

Although highly charged polyanions, such as inositol hexaphosphate, have been clearly shown to decrease the solubility of deoxyhemoglobin S, the effect of 2,3-diphosphoglycerate (DPG), the endogenous allosteric effector within the red cell, has been more controversial. In this work we have compared the effect of DPG on the solubility of native deoxyhemoglobin S and a derivative in which the DPG binding site is blocked by cross-linking the two beta 82 lysine residues. At pH 6.6 and 30 degrees C the solubility of deoxyhemoglobin S was found to be decreased by 15% (i.e., from 18.8 to 16.0 g/dl) in the presence of saturating concentrations of DPG. Under the same conditions DPG had no effect on the solubility of the cross-linked derivative. This result establishes unequivocally that the binding of DPG within the beta cleft directly facilitates the polymerization of deoxyhemoglobin S. Under physiological conditions, the solubility of deoxyhemoglobin S was found to be decreased by 6% in the presence of an equimolar concentration of DPG. A solubility decrease of this magnitude is sufficient to enhance the tendency of SS cells to sickle and may exacerbate the clinical symptoms of sickle cell disease.

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.

Fibers, crystals, and other forms of HbS polymers in deoxygenated sickle erythrocytes

We have examined by electron microscopy the formation of fibers and crystals from sickle hemoglobin within sickle erythrocytes following deoxygenation during capillary storage from 1 to 132 days. Intracellular fibers were found on the first day and throughout the period of study. The fibers exhibited a diameter (mean +/- SD) of 17.4 +/- 0.62 nm and were aligned in the cell with a fiber-to-fiber spacing of 18.6 nm (x-axis) by 22.7 nm (y-axis). Between 65 and 132 days, extracellular hemoglobin crystals developed, with a lattice periodicity of 9.63 +/- 0.6 nm. Fibers and crystals coexist as separate structures. These results suggest that crystal formation upon storage of packed deoxygenated sickle erythrocytes may proceed via a phase of fiber dissolution followed by hemoglobin reassembly into extracellular crystals, rather than by a progressive alignment and direct fusion of existing fibers.

X-ray diffraction studies of 14-filament models of deoxygenated sickle cell hemoglobin fibers. Models based on electron micrograph reconstructions

The transforms of a large number of models of deoxygenated sickle hemoglobin fibers, related to that derived from image reconstruction of electron micrographs, have been calculated and compared with X-ray diffraction data of 15 A resolution. The model of the fiber, determined from the reconstructed image, is a helix consisting of 14 filaments that associate in a specific mode to form seven pairs, or protofilaments. Pairs were identified through the pattern of filament loss in partially disassembled fibers and by the separation between molecules, in adjacent filaments, of half a molecular diameter, along the fiber axis. An alternative mode of filament association can be derived also from the surface lattice of the reconstruction, which meets these criteria for the pairing of molecular filaments. Both pairing modes have been used in the search for structures whose transforms show the best agreement with the diffraction data. Models were generated by the systematic translation of six protofilaments, taken in symmetry related pairs, in steps of 3.5 A along the fiber axis relative to a fixed central protofilament. Each translation of a protofilament corresponds to a different fiber model, whose transform was compared with observed data. In all, over 11,000 transforms were calculated. Of all the models considered, three have been found whose residuals are minimal. At 30 A resolution, similar to that of electron micrographs, the model derived from image reconstruction and the three found through our search procedure are indistinguishable. At 15 A, however, the transforms of these models show better agreement with the observed data than the transform of the reconstructed image. Comparison of residuals shows that the model derived from the reconstructed image can be rejected with 99.5% probability relative to the model, with the same pairing scheme, found by our search procedures. The two other models, derived from the alternative pairing scheme, are also more credible than the reconstructed image, but at a lower confidence level. Each of our three models is equally acceptable. Their existence may reflect structural polymorphism of the fiber.

Kinetics of nucleation-controlled polymerization. A perturbation treatment for use with a secondary pathway

We present a perturbation method for analyzing nucleation-controlled polymerization augmented by a secondary pathway for polymer growth. With this method, the solution to the kinetic equations assumes a simple analytic closed form that can easily be used in fitting data. So long as the formation of polymers by the secondary pathway depends linearly on the concentration of monomers polymerized, the form of the solutions is the same. This permits the analysis of augmented growth models with a minimum number of modeling assumptions, and thus makes it readily possible to distinguish between a variety of secondary processes (heterogeneous nucleation, lateral growth, and fragmentation). In addition, the parameters of the homogeneous process, such as the homogeneous nucleus size, can be determined independent of the nature of the secondary mechanism. We describe applications of this method to the polymerization of actin, collagen, and sickle hemoglobin. We present an extensive analysis of data on actin polymerization (Wegner, A., and P. Savko, 1982, Biochemistry, 21:1909-1913) to illustrate the use of the method. Although our conclusions generally agree with theirs, we find that lateral growth describes the secondary pathway better than the fragmentation model originally proposed. We also show how this method can be used to study the degree of polymerization, the parentage of polymers, and the behavior of polymers in cycling experiments.

Comparison of the state of deoxyhemoglobin S molecules in solution and in fibers by hydrogen exchange kinetics

Hydrogen exchange kinetics of deoxyhemoglobin S gel and deoxyhemoglobin A solution were compared at 4.8 mM tetramer concentration, 25 degrees C, and in sodium phosphate buffer at pH 7.0 with gamma/2 = 0.2 by means of microdialysis using tritium as a trace label. Cyanomethemoglobin A in solution and as crosslinked crystals were compared under the same conditions. The exchange values from 15 to 10(4) min were fitted to a power law, and the distribution function of exchange rates was calculated. There was no significant difference in the distribution for deoxyhemoglobin S gel and deoxyhemoglobin A. Exchange from crosslinked cyanomethemoglobin crystals was less in the early time region than for the solution state, but after 600 min the exchange curves were the same. This resulted in a larger area for the distribution function, although the predominate rates were nearly the same. The effect of polymerization on conformational fluctuations was very small, smaller than the effect of crosslinking hemoglobin crystals.

Structural basis and dynamics of the fiber-to-crystal transition of sickle cell hemoglobin

The kinetics of the assembly of structurally distinct, polymeric aggregates constituting the fiber-to-crystal transition of sickle cell hemoglobin in slowly stirred, deoxygenated solutions has been studied with the use of electron microscopy as a function of pH, as a function of the crystal structures of mutant forms of human deoxyhemoglobins employed as nucleating seeds, and as a function of hemoglobin S chemically modified at the Cys F9 (beta 93) position. The temporal order of appearance of fibers of approximately 210 A diameter, bundles of aligned fibers, macrofibers of greater than or equal to 650 A diameter, and microcrystals is observed. Microscopic fragments of end-stage crystals formed under slowly stirred conditions and introduced as nucleating seeds enhance the rate of crystallization only when added prior to the formation of large bundles of aligned fibers, while microscopic seed crystals added after the formation of bundles of aligned fibers do not alter the rate of crystallization. Over the pH range 6.3 to 7.1, the presence of macrofibers does not influence modulation of the kinetics of the transition with seed crystal fragments. Microscopic seed crystals of deoxyhemoglobin S and deoxyhemoglobin C formed under acidic conditions (pH less than 6.5) have a comparable influence on the kinetics of the fiber-to-crystal transition to that of end-stage crystals. Microscopic seed crystals of deoxyhemoglobin C formed under alkaline conditions (pH greater than 6.5) enhance the formation of macrofibers but do not alter the rate of crystallization. Under conditions associated with enhanced formation of macrofibers, metastable microscopic crystals having axial periodicities of approximately 64 A and approximately 210 A are observed in the intermediate phase of the transition, while end-stage crystals have axial unit cell dimensions identical to those of deoxyhemoglobin S crystallized from polyethylene glycol solutions of pH less than 6.5. Although the metastable crystals may arise from fragments of macrofibers, it is shown that they cannot be transformed directly into end-stage crystals under slowly stirred conditions without undergoing dissolution. These results stipulate that the pathway of the fiber-to-crystal transition proceeds according to the reaction: (Formula: see text) wherein the rate-limiting step is the alignment of fibers into large bundles, and macrofibers are not an intermediate of the fiber-to-crystal transition.(ABSTRACT TRUNCATED AT 400 WORDS)

Macrofiber structure and the dynamics of sickle cell hemoglobin crystallization

Fibers of deoxyhemoglobin S undergo spontaneous crystallization by a mechanism involving a variety of intermediate structures. These intermediate structures, in common with the fiber and crystal, consist of Wishner-Love double strands of hemoglobin S molecules arranged in different configurations. The structure of one of the key intermediates linking the fiber and crystal, called a macrofiber, has been studied by a variety of analytical procedures. The results of the analysis indicate that the intermediates involved in the fiber to crystal transition have many common structural features. Fourier analysis of electron micrographs of macrofibers confirms that they are composed of Wishner-Love double strands of hemoglobin molecules. Electron micrographs of macrofiber cross-sections reveal that the arrangement of the double strands in macrofibers resembles that seen in micrographs of the a axis projection of the crystal. This orientation provides an end-on view of the double strands which appear as paired dumb-bell-like masses. The structural detail becomes progressively less distinct towards the edge of the particle due to twisting of the double strands about the particle axis. Serial sections of macrofibers confirm that these particles do indeed rotate about their axes. The twist of the particle is right handed and its average pitch is 10,000 A. The effect of rotation on the appearance of macrofiber cross-sections 300 to 400 A thick can be simulated by a 15 degrees rotation of an a axis crystal projection. The relative polarity of the double strands in macrofibers and crystals can be determined easily by direct inspection of the micrographs. In both macrofibers and crystals they are in an anti-parallel array. On the basis of these observations we conclude that crystallization of macrofibers involves untwisting and alignment of the double strands.

Polarity of the 14-strand fibers of sickle cell hemoglobin determined by cross-correlation methods

Images of negatively stained fibers of sickle cell hemoglobin have been analyzed by cross-correlation methods. These methods are used to compensate for the curvature and variable repeat distance characteristic of negatively stained fibers. Averaged images obtained by the correlation procedure display considerably more detail than the filtered images obtained earlier by Fourier methods. The averaged images are sufficiently detailed that the back-projection method for obtaining cross-sections can now be applied directly to the correlation-averaged images. This method was used previously to deduce the 14-strand structure on Fourier-filtered images that incorporated only the near-equatorial maxima. In this way the 14-strand structure has been reconfirmed without utilizing the partial Fourier reconstructions employed earlier that might conceivably have introduced spurious features. In addition, application of the correlation procedure with and without inversion of the reference reveals a consistent polarity in all of the fibers examined. The confirmation of the 14-strand structure by a new procedure and the determination of fiber polarity would appear to eliminate the alternative model of the fibers with a 16-strand structure with equal numbers of strands (eight) of each polarity.