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

Sticking together: Polymerization of sickle hemoglobin drives the multiscale pathophysiology of sickle cell disease

Sickle cell disease is a hereditary disorder in which the pathophysiology is driven by the aggregation of a mutant (sickle) hemoglobin (HbS). The self-assembly of deoxygenated sickle hemoglobin molecules into ordered fiber structures has consequences extending to the cellular and rheological levels, stiffening red blood cells and inducing pathological flow behavior. This review explores the current understanding of the molecular processes involved in the polymerization of hemoglobin in sickle cell disease and how the molecular phase transition creates quantifiable changes at the cellular and rheological scale, as well as, identifying knowledge gaps in the field that would improve our understanding of the disease and further improve treatment and management of the disease.

The Sickle-Cell Fiber Revisited

Sickle cell disease is the consequence of a single point mutation on the surface of the β chains of the hemoglobin molecule leading to the formation of rigid polymers that disrupt circulation. It has long been established that the polymers are comprised of seven pairs of double strands that are twisted replicas of the double strands found in crystals. Here, we review several newer developments that elaborate on that simple model and provide deeper insights into the process.

The Genetic and Clinical Significance of Fetal Hemoglobin Expression in Sickle Cell Disease

Sickle cell disease (SCD) is phenotypically heterogeneous. One major genetic modifying factor is the patient's fetal hemoglobin (HbF) level. The latter is determined by the patient's β-globin gene cluster haplotype and cis- and trans-acting single nucleotide polymorphisms (SNPs) at other distant quantitative trait loci (QTL). The Arab/India haplotype is associated with persistently high HbF levels and also a relatively mild phenotype. This haplotype carries the Xmn1 (C/T) SNP, rs7482144, in the HBG2 locus. The major identified trans-acting QTL contain SNPs residing in the BCL11A on chromosome 2 and the HMIP locus on chromosome 6. These collectively account for 15-30% of HbF expression in different world populations and in patients with SCD or β-thalassemia. Patients with SCD in Kuwait and Eastern Saudi Arabia uniformly carry the Arab/India haplotype, but despite this, the HbF and clinical phenotypes show considerable heterogeneity. Pain episodes and avascular necrosis of the femoral head are particularly common, but severe bacterial infections, stroke, priapism, and leg ulcers are uncommon. Moreover, the HbF modifiers appear to be different; the reported BCL11A and HMIP SNPs appear to play insignificant roles. There are probably novel modifiers to be discovered in this population. This review examines the common clinical phenotypes in Kuwaiti patients with elevated HbF and the available information on HbF modifiers. The response of the patients to hydroxyurea is discussed. The presentation of patients with other sickle compound heterozygotes (Sβthal and HbSD), vis-à-vis their HbF levels, is also addressed critically.

Allosteric control of hemoglobin S fiber formation by oxygen and its relation to the pathophysiology of sickle cell disease

The pathology of sickle cell disease is caused by polymerization of the abnormal hemoglobin S upon deoxygenation in the tissues to form fibers in red cells, causing them to deform and occlude the circulation. Drugs that allosterically shift the quaternary equilibrium from the polymerizing T quaternary structure to the nonpolymerizing R quaternary structure are now being developed. Here we update our understanding on the allosteric control of fiber formation at equilibrium by showing how the simplest extension of the classic quaternary two-state allosteric model of Monod, Wyman, and Changeux to include tertiary conformational changes provides a better quantitative description. We also show that if fiber formation is at equilibrium in vivo, the vast majority of cells in most tissues would contain fibers, indicating that it is unlikely that the disease would be survivable once the nonpolymerizing fetal hemoglobin has been replaced by adult hemoglobin S at about 1 y after birth. Calculations of sickling times, based on a recently discovered universal relation between the delay time prior to fiber formation and supersaturation, show that in vivo fiber formation is very far from equilibrium. Our analysis indicates that patients survive because the delay period allows the majority of cells to escape the small vessels of the tissues before fibers form. The enormous sensitivity of the duration of the delay period to intracellular hemoglobin composition also explains why sickle trait, the heterozygous condition, and the compound heterozygous condition of hemoglobin S with pancellular hereditary persistence of fetal hemoglobin are both relatively benign conditions.

Hemoglobin S polymerization and sickle cell disease: A retrospective on the occasion of the 70th anniversary of Pauling's Science paper

70 years ago, Linus Pauling, the legendary genius of 20^th century chemistry, published his famous work on the molecular cause of sickle cell disease, a paper that gave birth to what is now called molecular medicine. In this paper, Pauling left important questions unanswered that have motivated an enormous amount of scientific and clinical research since then. This retrospective discusses the basic science studies that have answered those questions directly related to the kinetics and thermodynamics of hemoglobin S polymerization.

On the Nonaggregation of Normal Adult Hemoglobin and the Aggregation of Sickle Cell Hemoglobin

Sickle cell disease is a genetic disorder associated with a single mutation (Glu-β6 → Val-β6) in the β chains of hemoglobin, causing the polymerization of deoxygenated sickle cell hemoglobin (deoxy-HbS). The deoxy-HbS binding free energy was recently studied through molecular simulations, and a value of -14 ± 1 kcal mol^-1 was found. Here, we studied the binding free energy of normal adult hemoglobin (deoxy-HbA), which does not polymerize at normal physiological conditions, with the aim of elucidating the importance of the presence of Val-β6 and of the absence of Glu-β6 on the aggregation of deoxy-HbS. A binding free energy of -4.4 ± 0.5 kcal mol^-1 was found from a one-dimensional potential of mean force. Hydrophobic interactions are shown to represent less than 20% of the interactions in the contact interface, and despite similarly strong hydrogen-bonded ion pairs (i.e., salt bridges) and water bridged electrostatic interactions are found for deoxy-HbA and deoxy-HbS, a large repulsive potential energy is associated with Glu-β6, whereas a mild attractive potential energy is connected with Val-β6. Interestingly, Asp-β73 switches from forming a major electrostatic repulsive pair with Glu-β6 in deoxy-HbA, to forming a major attractive residue pair with Val-β6 in deoxy-HbS, consistent with the view that damping of electrostatic repulsions involving Glu-β6, namely, those associated with Asp-β73, could be responsible for the polymerization of deoxy-HbA at high potassium phosphate concentrations. Solvation analysis shows that functional groups forming salt bridges and water bridged interactions preserve a nearly intact first hydration sphere, avoiding a complete dewetting free energy penalty. These results support the view that the absence of Glu-β6 is more important than the presence of Val-β6, and that although hydrophobic effects, associated with the Val-β6 dehydration and interaction with the hydrophobic pocket in the neighbor tetramer, are important, electrostatic interactions are dominant, opposite to a picture where HbS association is driven by hydrophobic interactions.

Molecular insights into the irreversible mechanical behavior of sickle hemoglobin

Sickle cell disease is caused by the amino acid substitution of glutamic acid to valine, which leads to the polymerization of deoxygenated sickle hemoglobin (HbS) into long strands. These strands are responsible for the sickling of red blood cells (RBCs), making blood hyper-coagulable leading to an increased chance of vaso-occlusive crisis. The conformational changes in sickled RBCs traveling through narrow blood vessels in a highly viscous fluid are critical in understanding; however, there are few studies that investigate the origins of the molecular mechanical behavior of sickled RBCs. In this work, we investigate the molecular mechanical properties of HbS molecules. A mechanical model was used to estimate the directional stiffness of an HbS molecule and the results were compared to adult human hemoglobin (HbA). The comparison shows a significant difference in strength between HbS and HbA, as well as anisotropic behavior of the hemoglobin molecules. The results also indicated that the HbS molecule experienced more irreversible mechanical behavior than HbA under compression. Further, we have characterized the elastic and compressive properties of a double stranded sickle fiber using six HbS molecules, and it shows that the HbS molecules are bound to each other through strong inter-molecular forces.

Mesoscopic Adaptive Resolution Scheme toward Understanding of Interactions between Sickle Cell Fibers

Understanding of intracellular polymerization of sickle hemoglobin (HbS) and subsequent interaction with the membrane of a red blood cell (RBC) is important to predict the altered morphologies and mechanical properties of sickle RBCs in sickle cell anemia. However, modeling the integrated processes of HbS nucleation, polymerization, HbS fiber interaction, and subsequent distortion of RBCs is challenging as they occur at multispatial scales, ranging from nanometers to micrometers. To make progress toward simulating the integrated processes, we propose a hybrid HbS fiber model, which couples fine-grained and coarse-grained HbS fiber models through a mesoscopic adaptive resolution scheme (MARS). To this end, we apply a microscopic model to capture the dynamic process of polymerization of HbS fibers, while maintaining the mechanical properties of polymerized HbS fibers by the mesoscopic model, thus providing a means of bridging the subcellular and cellular phenomena in sickle cell disease. At the subcellular level, this model can simulate HbS polymerization with preexisting HbS nuclei. At the cellular level, if combined with RBC models, the generated HbS fibers could be applied to study the morphologies and membrane stiffening of sickle RBCs. One important feature of the MARS is that it can be easily employed in other particle-based multiscale simulations where a dynamic coarse-graining and force-blending method is required. As demonstrations, we first apply the hybrid HbS fiber model to simulate the interactions of two growing fibers and find that their final configurations depend on the orientation and interaction distance between two fibers, in good agreement with experimental observations. We also model the formation of fiber bundles and domains so that we explore the mechanism that causes fiber branching.

Probing the Twisted Structure of Sickle Hemoglobin Fibers via Particle Simulations

Polymerization of sickle hemoglobin (HbS) is the primary pathogenic event of sickle cell disease. For insight into the nature of the HbS polymer fiber formation, we develop a particle model-resembling a coarse-grained molecular model-constructed to match the intermolecular contacts between HbS molecules. We demonstrate that the particle model predicts the formation of HbS polymer fibers by attachment of monomers to rough fiber ends and the growth rate increases linearly with HbS concentration. We show that the characteristic 14-molecule fiber cross section is preserved during growth. We also correlate the asymmetry of the contact sites on the HbS molecular surface with the structure of the polymer fiber composed of seven helically twisted double strands. Finally, we show that the same asymmetry mediates the mechanical and structural properties of the HbS polymer fiber.

Visualizing red blood cell sickling and the effects of inhibition of sphingosine kinase 1 using soft X-ray tomography

Sickle cell disease is a destructive genetic disorder characterized by the formation of fibrils of deoxygenated hemoglobin, leading to the red blood cell (RBC) morphology changes that underlie the clinical manifestations of this disease. Using cryogenic soft X-ray tomography (SXT), we characterized the morphology of sickled RBCs in terms of volume and the number of protrusions per cell. We were able to identify statistically a relationship between the number of protrusions and the volume of the cell, which is known to correlate to the severity of sickling. This structural polymorphism allows for the classification of the stages of the sickling process. Recent studies have shown that elevated sphingosine kinase 1 (Sphk1)-mediated sphingosine 1-phosphate production contributes to sickling. Here, we further demonstrate that compound 5C, an inhibitor of Sphk1, has anti-sickling properties. Additionally, the variation in cellular morphology upon treatment suggests that this drug acts to delay the sickling process. SXT is an effective tool that can be used to identify the morphology of the sickling process and assess the effectiveness of potential therapeutics.

Crystal structure of carbonmonoxy sickle hemoglobin in R-state conformation

The fundamental pathophysiology of sickle cell disease is predicated by the polymerization of deoxygenated (T-state) sickle hemoglobin (Hb S) into fibers that distort red blood cells into the characteristic sickle shape. The crystal structure of deoxygenated Hb S (DeoxyHb S) and other studies suggest that the polymer is initiated by a primary interaction between the mutation βVal6 from one Hb S molecule, and a hydrophobic acceptor pocket formed by the residues βAla70, βPhe85 and βLeu88 of an adjacent located Hb S molecule. On the contrary, oxygenated or liganded Hb S does not polymerize or incorporate in the polymer. In this paper we present the crystal structure of carbonmonoxy-ligated sickle Hb (COHb S) in the quaternary classical R-state at 1.76Å. The overall structure and the pathological donor and acceptor environments of COHb S are similar to those of the isomorphous CO-ligated R-state normal Hb (COHb A), but differ significantly from DeoxyHb S as expected. More importantly, the packing of COHb S molecules does not show the typical pathological interaction between βVal6 and the βAla70, βPhe85 and βLeu88 hydrophobic acceptor pocket observed in DeoxyHb S crystal. The structural analysis of COHb S, COHb A and DeoxyHb S provides atomic level insight into why liganded hemoglobin does not form a polymer.

Structural basis for the antipolymer activity of Hb ζ2βs2 trapped in a tense conformation

The phenotypical severity of sickle-cell disease (SCD) can be mitigated by modifying mutant hemoglobin S (Hb S, Hb α₂β^s₂) to contain embryonic ζ-globin in place of adult α-globin subunits (Hb ζ₂β^s₂). Crystallographical analyses of liganded Hb ζζ₂β^s₂, though, demonstrate a tense (T-state) quaternary structure that paradoxically predicts its participation in--rather than its exclusion from--pathological deoxyHb S polymers. We resolved this structure-function conundrum by examining the effects of α→ζ exchange on the characteristics of specific amino acids that mediate sickle polymer assembly. Superposition analyses of the β^s subunits of T-state deoxyHb α₂β^s₂ and T-state CO-liganded Hb ζ₂β^s₂ reveal significant displacements of both mutant β^sVal6 and conserved β-chain contact residues, predicting weakening of corresponding polymer-stabilizing interactions. Similar comparisons of the α- and ζ-globin subunits implicate four amino acids that are either repositioned or undergo non-conservative substitution, abrogating critical polymer contacts. CO-Hb ζ₂β^s₂ additionally exhibits a unique trimer-of-heterotetramers crystal packing that is sustained by novel intermolecular interactions involving the pathological β^sVal6, contrasting sharply with the classical double-stranded packing of deoxyHb S. Finally, the unusually large buried solvent-accessible surface area for CO-Hb ζ₂β^s₂ suggests that it does not co-assemble with deoxyHb S in vivo. In sum, the antipolymer activities of Hb ζ₂β^s₂ appear to arise from both repositioning and replacement of specific α- and β^s-chain residues, favoring an alternate T-state solution structure that is excluded from pathological deoxyHb S polymers. These data account for the antipolymer activity of Hb ζ₂β^s₂, and recommend the utility of SCD therapeutics that capitalize on α-globin exchange strategies.

Dissecting the energies that stabilize sickle hemoglobin polymers

Sickle hemoglobin forms long, multistranded polymers that account for the pathophysiology of the disease. The molecules in these polymers make significant contacts along the polymer axis (i.e., axial contacts) as well as making diagonally directed contacts (i.e., lateral contacts). The axial contacts do not engage the mutant β6 Val and its nonmutant receptor region on an adjacent molecule, in contrast to the lateral contacts which do involve the mutation site. We have studied the association process by elastic light scattering measurements as a function of temperature, concentration, and primary and quaternary structure, employing an instrument of our own construction. Even well below the solubility for polymer formation, we find a difference between the association behavior of deoxy sickle hemoglobin molecules (HbS), which can polymerize at higher concentration, in comparison to COHbS, COHbA, or deoxygenated Hemoglobin A (HbA), none of which have the capacity to form polymers. The nonpolymerizable species are all quite similar to one another, and show much less association than deoxy HbS. We conclude that axial contacts are significantly weaker than the lateral ones. All the associations are entropically favored, and enthalpically disfavored, typical of hydrophobic interactions. For nonpolymerizable Hemoglobin, ΔH(o) was 35 ± 4 kcal/mol, and ΔS was 102.7 ± 0.5 cal/(mol-K). For deoxyHbS, ΔH(o) was 19 ± 2 kcal/mol, and ΔS was 56.9 ± 0.5 cal/(mol-K). The results are quantitatively consistent with the thermodynamics of polymer assembly, suggesting that the dimer contacts and polymer contacts are very similar, and they explain a previously documented significant anisotropy between bending and torsional moduli. Unexpectedly, the results also imply that a substantial fraction of the hemoglobin has associated into dimeric species at physiological conditions.

Determination of the transition-state entropy for aggregation suggests how the growth of sickle cell hemoglobin polymers can be slowed

Sickle cell anemia is associated with the mutant hemoglobin HbS, which forms polymers in red blood cells of patients. The growth rate of the polymers is several micrometers per second, ensuring that a polymer fiber reaches the walls of an erythrocyte (which has a 7-microm diameter) within a few seconds after its nucleation. To understand the factors that determine this unusually fast rate, we analyze data on the growth rate of the polymer fibers. We show that the fiber growth follows a first-order Kramers-type kinetics model. The entropy of the transition state for incorporation into a fiber is 95 J mol(-1) K(-1), very close to the known entropy of polymerization. This agrees with a recent theoretical estimate for the hydrophobic interaction and suggests that the gain of entropy in the transition state is due to the release of the last layer of water molecules structured around contact sites on the surface of the HbS molecules. As a result of this entropy gain, the free-energy barrier for incorporation of HbS molecules into a fiber is negligible and fiber growth is unprecedentedly fast. This finding suggests that fiber growth can be slowed by components of the red cell cytosol, native or intentionally introduced, which restructure the hydration layer around the HbS molecules and thus lower the transition state entropy for incorporation of an incoming molecule into the growing fiber.

Sickle-cell haemoglobin polymerization: is it the primary pathogenic event of sickle-cell anaemia?

Sickle cell anaemia is associated with a mutant haemoglobin, HbS, which forms polymers in the red blood cells of patients. The primary role of the HbS polymerization for the pathophysiology has been questioned: observations in patients and model organisms contradict deterministic scenarios of sickling crises triggered by polymerization. However, results with knock-out sickle-cell mice, which were cured by delaying HbS polymerization, reconfirm polymerization's primary role. To reconcile the contradictory observations, this article reviews recent findings on two steps in polymerization: homogeneous nucleation of fibres, and their growth. The fibre growth is faster by far than for any other protein ordered structure. This is due to a negligible free-energy barrier for incorporation into a fibre, determined by an entropy gain, stemming from the release of water molecules structured around HbS. The kinetics of fibre nucleation have shown that the formation of the polymer nucleus is preceded by a metastable droplet of a dense liquid. The properties of the dense liquid are sensitive functions of solution composition, including components in micro- and nanomolar amounts. This mechanism allows low-concentration solution components to strongly affect the nucleation kinetics, accounting for the high variability of the disease. These insights can potentially be utilized for control of HbS polymerization and treatment of the disease.

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.

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.

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.

Micromechanics of isolated sickle cell hemoglobin fibers: bending moduli and persistence lengths

Pathogenesis in sickle cell disease depends on polymerization of deoxyhemoglobin S into rod-like fibers, forming gels that rigidify red cells and obstruct the systemic microvasculature. Fiber structure, polymerization kinetics and equilibria are well characterized and intimately related to pathogenesis. However, data on gel rheology, the immediate cause of obstruction, are limited, and models for structure and rheology are lacking. The basis of gel rheology, micromechanics of individual fibers, has never been examined. Here, we isolate fibers by selective depolymerization of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal fluctuations in fiber shape to obtain bending moduli (kappa) and persistence lengths (lambda(p)). Some fibers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of fiber midpoints from mean positions. Serial deviations, sufficiently separated to be independent, exhibit Gaussian distributions and provide mean-squared fluctuation amplitudes from which kappa and lambda(p) can be calculated. Lambda(p) ranges from 0.24 to 13 mm for the most flexible and stiffest fibers, respectively. This large range reflects formation of fiber bundles. If the most flexible are single fibers, then lambda(p) =13 mm represents a bundle of seven single fibers. Preliminary data on the bending variations of frozen, hydrated single fibers of HbS obtained by electron microscopy indicate that the value 0.24 mm is consistent with the persistence length of single fibers. Young's modulus is 0.10 GPa, less than for structural proteins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macroscopic rheology of hemoglobin S gels. This new technique, combining isolation of hemoglobin S fibers and measurement of micromechanical properties based on thermal fluctuations and midpoint deviations, can be used to study fibers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S.

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.

Automated identification of filaments in cryoelectron microscopy images

Since the foundation for the three-dimensional image reconstruction of helical objects from electron micrographs was laid more than 30 years ago, there have been sustained developments in specimen preparation, data acquisition, image analysis, and interpretation of results. However, the boxing of filaments in large numbers of images--one of the critical steps toward the reconstruction at high resolution--is still constrained by manual processing even though interactive interfaces have been built to aid the tedious and sometimes inaccurate boxing process. This article describes an accurate approach for automated detection of filamentous structures in low-contrast images acquired in defocus pairs using cryoelectron microscopy. The performance of the approach has been evaluated across various magnifications and at a series of defocus values using tobacco mosaic virus (TMV) preserved in vitreous ice as a test specimen. By integrating the proposed approach into our automated data acquisition and reconstruction system, we are now able to generate a three-dimensional map of TMV to approximately 10-A resolution within 24 h of inserting the specimen grid into the microscope.

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.

Analysis of the stability of hemoglobin S double strands

The deoxyhemoglobin S (deoxy-HbS) double strand is the fundamental building block of both the crystals of deoxy-HbS and the physiologically relevant fibers present within sickle cells. To use the atomic-resolution detail of the hemoglobin-hemoglobin interaction known from the crystallography of HbS as a basis for understanding the interactions in the fibers, it is necessary to define precisely the relationship between the straight double strands in the crystal and the twisted, helical double strands in the fibers. The intermolecular contact conferring the stability of the double strand in both crystal and fiber is between the beta6 valine on one HbS molecule and residues near the EF corner of an adjacent molecule. Models for the helical double strands were constructed by a geometric transformation from crystal to fiber that preserves this critical interaction, minimizes distortion, and makes the transformation as smooth as possible. From these models, the energy of association was calculated over the range of all possible helical twists of the double strands and all possible distances of the double strands from the fiber axis. The calculated association energies reflect the fact that the axial interactions decrease as the distance between the double strand and the fiber axis increases, because of the increased length of the helical path taken by the double strand. The lateral interactions between HbS molecules in a double strand change relatively little between the crystal and possible helical double strands. If the twist of the fiber or the distance between the double strand and the fiber axis is too great, the lateral interaction is broken by intermolecular contacts in the region around the beta6 valine. Consequently, the geometry of the beta6 valine interaction and the residues surrounding it severely restricts the possible helical twist, radius, and handedness of helical aggregates constructed from the double strands. The limitations defined by this analysis establish the structural basis for the right-handed twist observed in HbS fibers and demonstrates that for a subunit twist of 8 degrees, the fiber diameter cannot be more than approximately 300 A, consistent with electron microscope observations. The energy of interaction among HbS molecules in a double strand is very slowly varying with helical pitch, explaining the variable pitch observed in HbS fibers. The analysis results in a model for the HbS double strand, for use in the analysis of interactions between double strands and for refinement of models of the HbS fibers against x-ray diffraction data.

Influence of the A helix structure on the polymerization of hemoglobin S

Hb S variants containing Lys-beta132 --> Ala or Asn substitutions were engineered to evaluate the consequences of the A helix destabilization in the polymerization process. Previous studies suggested that the loss of the Glu-beta7-Lys-beta132 salt bridge in the recombinant Hb betaE6V/E7A could be responsible for the destabilization of the A helix. The recombinant Hb (rHb) S/beta132 variants polymerized with an increased delay time as well as decreased maximum absorbance and Hb solubility values similar to that of Hb S. These data indicate that the strength of the donor-acceptor site interaction may be reduced due to an altered conformation of the A helix. The question arises whether this alteration leads to a true inhibition of the polymerization process or to qualitatively different polymers. The oxygen affinity of the beta132 mutated rHbs was similar to that of Hb A and S, whereas the cooperativity and effects of organic phosphates were reduced. This could be attributed to modifications in the central cavity due to loss of the positively charged lysine. Since Lys-beta132 is involved in the stabilization of the alpha1-beta1 interface, the loss of the beta132(H10)-beta128(H6) salt bridge may be responsible for the marked thermal instability of the beta132 mutated rHbs.

The structural link between polymerization and sickle cell disease

Sickle hemoglobin molecules assemble into polymers composed of seven helically twisted double strands. Intermolecular contacts involving the mutation sites within the double strands are well established. We show that the same contact sites are present at the polymer surface on four of the ten exterior molecules in each layer, and demonstrate that the identical contact geometry can be achieved between polymers as found within the double strands. This provides a structural rationale for the exponential rate of polymer growth that characterizes the kinetics of gelation. This also gives a structural basis for the cross-linking which solidifies the polymer gel. In the absence of these surface contact regions sickle cell disease would be a much milder syndrome.

Functional studies and polymerization of recombinant hemoglobin Glu-alpha2beta26(A3) --> Val/Glu-7(A4) --> Ala

In hemoglobin (Hb) S the hydrophobic mutated residue Val-beta6(A3) (donor site) closely interacts with the hydrophobic side groups of Phe-beta85(F1) and Leu-beta88(F4) (EF pocket, acceptor site) of a neighboring tetramer, resulting in decreased solubility and polymerization of the deoxy-Hb. The beta6(A3) residue is followed by two charged residues Glu-beta7(A4) and Lys-beta8(A5). This cluster has no attraction for the hydrophobic EF pocket. We have modified the beta7(A4) residue next to the donor site Val-beta6(A3), replacing the charged Glu by a hydrophobic Ala-(rHb betaE6V/E7A). The single mutant Glu-beta7 --> Ala-(rHb betaE7A) was also engineered. Both rHbs exhibit a heat instability and an increased oxygen affinity compared to Hb A and Hb S. There was a concentration dependence of the ligand binding properties (1-300 microM in heme) indicating an increased amount of dimers relative to Hb A. The deoxy form of rHb betaE6V/E7A polymerizes in vitro, with a decreased rate of polymer formation relative to Hb S, while the single mutant betaE7A does not polymerize in the same experimental conditions. The Glu-beta7(A4) --> Ala substitution does not increase the hydrophobic interaction between donor and acceptor site. We speculate that the loss of the normal saline bridge between Glu-beta7(A4) and Lys-beta132(H10) leads to an increased flexibility of the A helix and may account for the difference of the polymerization for this Hb S mutant.

Solubility of sickle hemoglobin measured by a kinetic micromethod

We have developed a photolytic method to determine the concentration of reactive hemes in a solution in the presence of a trace amount of CO. By measurement of the bimolecular rate of CO binding, and by calibration of the rate constant under equivalent conditions, the concentration of the reactive hemes can be determined. In a solution of sickle hemoglobin, the molecules in the gel contribute negligibly to the recombination rate, allowing the concentration of the molecules in the solution phase to be determined. To optimize signal to noise, modulated excitation methods were employed, although the method could also be used with pulse techniques and suitable signal averaging. Because the optical method employs a microspectrophotometer, only a few microliters of concentrated Hb solution is required to reproduce the entire temperature dependence of the solubility previously determined by centrifugation using milliliter quantities of solutions of the same concentration. This should be especially useful for studies of site-directed mutants, and we present results obtained on one such HbS in which Leu 88 beta has been replaced by Ala. The free energy difference in the polymerization of the Leu 88 beta double mutant is consistent with known differences in the amino acid hydrophobicities. The calibration required for these experiments also provides an excellent determination of the activation energy for binding the first CO to deoxy Hb.

Variable pitch in frozen-hydrated sickle hemoglobin fibers: an image analysis model study

The intracellular polymerization of deoxyhemoglobin S (HbS) into helical fibers is the primary pathological event which gives rise to sickle cell disease. The structure of these fibers has previously been studied by electron microscopy of negatively stained specimens. We are extending these studies with unstained frozen-hydrated HbS fibers (cryo-EM), which afford better visualization of the internal details of the fiber structure than can be achieved by negative staining, but have lower signal-to-noise ratio images. The pitch of the HbS fiber structure varies locally along any given particle. Because rotation about the particle axis thus is partially decoupled from translation along the axis, the pitch and angular rotation of a fiber unit cell cannot be inferred by symmetry (as is the case with constant pitch helices). Image analysis procedures are presented which are capable of explicitly identifying the pitch and angular rotation of individual HbS fiber unit cells having low signal-to-noise ratios. Fiber images are divided into segments one unit cell long (63 A) which are analyzed in two steps. First each unit cell is aligned with constant pitch electron density reference models by cross-correlation. Correlation coefficients are then used to determine angular rotation and pitch. This procedure was tested, and found to be robust, using model images corrupted to simulate experimental problems normally encountered in the analysis of cryo-electron micrographs. The effects of limited resolution, low signal-to-noise ratio, scaling errors, and rotational and axial misalignment are described.

Cryo-electron microscopy of deoxy-sickle hemoglobin fibers

Deoxy-sickle hemoglobin (HbS) polymerizes in vivo into long helical fibers which fill the red cell and make it rigid. This impedes red cell passage through the capillaries and is responsible for the clinical manifestations of sickle cell disease. Images of individual and laterally associated HbS fibers were obtained by electron microscopy of frozen hydrated specimens. Each fiber possesses variable pitch, having from 6 degrees to 12 degrees rotation per unit cell. Laterally associated HbS fibers display systematic inter-fiber contacts in spite of their pitch variations, and exhibit better order than isolated fibers. This suggest that inter-fiber contacts can act to couple fibers mechanically and might therefore be a factor in rigidifying red cells in vivo. Fiber variability was attributed to local torsional variations with a standard deviation of 2.5 degrees, but which are weakly coupled over a length of 2.25 unit cells. Variable pitch produces structural changes of as large as 5 A azimuthally and 6 A axially in HbS fiber unit cells.

Truncated desmin in PtK2 cells induces desmin-vimentin-cytokeratin coprecipitation, involution of intermediate filament networks, and nuclear fragmentation: a model for many degenerative diseases

The earliest expression of truncated desmin in transfected PtK2 cells results in the formation of dispersed microprecipitates containing not only the truncated desmin, but also endogenous vimentin and cytokeratin proteins. Desmin microprecipitates without vimentin or vimentin microprecipitates without desmin are not observed. The microprecipitates involving cytokeratin invariably are also positive for desmin and vimentin. Over time, the precipitates enlarge into 1- to 2-microns spheroids and then fuse into amorphous chimeric juxtanuclear masses that can occupy > 30% of the cell volume. Concurrently, first the vimentin and then the cytokeratin networks are resorbed. The chimeric precipitates are not recognized or marked for degradation by the lysosomal system. Ultimately the cell nucleus fragments and the cell dies. Similar protein complexes appear in many human and animal pathologies, suggesting that a similar protein-precipitation sequence initiated by the introduction of a mutationally or environmentally altered protein molecule is at work.

Steric and hydrophobic determinants of the solubilities of recombinant sickle cell hemoglobins

Models for the structure of the fibers of deoxy sickle cell hemoglobin (Hb Hb S, beta 6 Glu-->Val) have been obtained from X-ray and electron microscopic studies. Recent molecular dynamics calculations of polymer formation give new insights on the various specific interactions between monomers. Site-directed mutagenesis with expression of the Hb S beta subunits in Escherichia coli provides the experimental tools to test these models. For Hb S, the beta 6 Val residue is intimately involved in a specific lateral contact, at the donor site, that interacts with the acceptor site of an adjacent molecule composed predominantly of the hydrophobic residues Phe 85 and Leu 88. Comparing natural and artificial mutants indicates that the solubility of deoxyHb decreases in relation to the surface hydrophobicity of the residue at the beta 6 position with Ile > Val > Ala. We also tested the role of the stereospecific adjustment between the donor and acceptor sites by substituting Trp for Glu at the beta 6 location. Among these hydrophobic substitutions and under our experimental conditions, only Val and Ile were observed to induce polymer formation. The interactions for the Ala mutant are too weak whereas a Trp residue inhibits aggregation through steric hindrance at the acceptor site of the lateral contact. Increasing the hydrophobicity at the axial contact between tetramers of the same strand also contributes to the stability of the double strand. This is demonstrated by associating the beta 23 Val-->Ile mutation at the axial contact with either the beta 6 Glu-->Val or beta 6 Glu-->Ile substitution in the same beta subunit.(ABSTRACT TRUNCATED AT 250 WORDS)

Binding of the dye congo red to the amyloid protein pig insulin reveals a novel homology amongst amyloid-forming peptide sequences

The three-dimensional structure has been determined of a complex of the dye Congo Red, a specific stain for amyloid deposits, bound to the amyloid protein insulin. One dye molecule intercalates between two globular insulin molecules at an interface formed by a pair of anti-parallel beta-strands. This result, together with analysis of the primary sequences of other amyloidogenic proteins and peptides suggests that this mode of dye-binding to amyloid could be general. Moreover, the structure of this dye-binding interface between protein molecules provides an insight into the polymerization of amyloidogenic proteins into amyloid fibres. Thus the detailed characterization, at a resolution of 2.5 A, of the dye binding site in insulin could form a basis for the design of agents targeted against a variety of amyloid deposits.

Computer models of a new deoxy-sickle cell hemoglobin fiber based on x-ray diffraction data

A new x-ray fiber diffraction pattern from deoxygenated sickle cell erythrocytes has been observed. It displays 14 layer lines with a 109 A periodicity compared with the 64 A periodicity of the "classic" sickle cell hemoglobin (HbS) fiber. These data and association energy calculations serve as a basis for computer model building. Systematic searches over four-dimensional parameter space yielded twelve protofilament models that satisfy the following constraints: (a) two HbS molecules be related by twofold screw symmetry with a translational repeat of 109 A; (b) at least one of the substituted residues in HbS, val beta 6, should participate in intermolecular contacts; and (c) the energy of intermolecular interaction be less than -24 kcal/mol. Each of the protofilament models is a zigzag mono-strand that stands in contrast to the double-stranded protofilament of the "classic" fiber. Fiber models were constructed with each of the 12 protofilament models, pseudo-hexagonally packed. Searches of variable packing parameters showed four fiber models with minimal protofilament association energies and minimal differences between calculated transforms and observed data. The R-factor was less than 0.24 for each of these four models. In three of the fiber models the protofilament association energy is between -(93 and 130) kcal, and in a fourth, the energy is -64 kcal. One protofilament model constituted three distinct fiber models of the lower energy class, and a second protofilament model packed with a higher association energy into a fourth fiber model. The selection of a unique fiber model from among these four cannot be made because of the limited available data. Fibers models constructed with any of the ten other protofilament models do not satisfy the conditions of minimal association energy and R-factor.

Mapping the entry of reactive oxygen metabolites into target erythrocytes during neutrophil-mediated antibody-dependent cellular cytotoxicity

Transmitted Soret band optical microscopy has been used to image the entry and passage of reactive oxygen metabolites across target erythrocytes. Due to the rapid cytosolic diffusion of hemoglobin in comparison to video rates, it was necessary to use erythrocytes with relatively immobilized hemoglobin. To achieve this, erythrocytes from patients with sickle cell anemia were used. The movement of reactive oxygen metabolites across rabbit IgG-opsonized sickle cells was observed in real time. These observations indicate that reactive oxygen metabolites can enter and cross targets in an asymmetric fashion.

The hand of the helix of deoxyhemoglobin S fibers

Electron micrographs of deoxyhemoglobin S fiber cross sections provide an end-on view of the fiber whose appearance is sensitive to small changes in orientation. We have developed a procedure to exploit this sensitivity in order to determine the hand of these particles. In a sickle hemoglobin fiber the hemoglobin molecules form long pitch helical strands which twist about the particle axis with a pitch of about 3000 A. Tilting a 400-A-thick cross section by a few degrees aligns one of the long pitch helices so that it is nearly parallel to the direction of view. When a strand of hemoglobin molecules in a fiber is aligned in this manner it appears as a strongly contrasted bright spot. It is this spot, rather than the fiber axis, which appears to be the apparent center of rotation of the cross section. The direction of the displacement of the spot from the particle axis depends upon the particle hand and tilt direction. We have used this property to determine that sickle hemoglobin fibers are right-handed particles. This method may be applicable to other particles with long pitch helices as well.

On the structure of erythrocyte spectrin in partially expanded membrane skeletons

Spectrin is generally believed to play an important role in the erythrocyte membrane's ability to deform elastically. We have studied the structure of negatively stained spectrin in partially expanded membrane skeletons to determine how its molecular structure confers elastic properties on the cell membrane. Fourier analysis of electron micrographs of spectrin reveals that the alpha and beta subunits are twisted about a common axis, forming a two-start helix with twofold rotational symmetry. We propose that elastic deformation of the cell is mediated by transient extension of the helix by mechanical forces.

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.

Computer image processing of electron micrographs of biological structures with helical symmetry

Methods are described for the analysis of electron micrographs of biological objects with helical symmetry and for the production of three-dimensional models of these structures using computer image reconstruction methods. Fourier-based processing of one- and two-dimensionally ordered planar arrays is described by way of introduction, before analysing the special properties of helices and their transforms. Conceiving helical objects as a sum of helical waves (analogous to the sum of planar waves used to describe a planar crystal) is shown to facilitate analysis and enable three-dimensional models to be produced, often from a single view of the object. The corresponding Fourier transform of such a sum of helical waves consists of a sum of Bessel function terms along layer lines. Special problems deriving from the overlapping along layer lines of terms of different Bessel order are discussed, and methods to separate these terms, based on analysing a number of different azimuthal views of the object by least squares, are described. Corrections to alleviate many technical and specimen-related problems are discussed in conjunction with a consideration of the computer methods used to actually process an image. A range of examples of helical objects, including viruses, microtubules, flagella, actin, and myosin filaments, are discussed to illustrate the range of problems that can be addressed by computer reconstruction methods.

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

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

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.