Analysis of the Intermolecular Contacts within Sickle Hemoglobin Fibers: Effect of Site-Specific Substitutions, Fiber Pitch, and Double-Strand Disorder

An atomic model of the sickle hemoglobin (HbS) fiber was synthesized by combining the molecular coordinates of the fiber (obtained from electron microscopy) with atomic coordinates of the sickle hemoglobin double strand (obtained from X-ray crystallography). The model is stereochemically acceptable. The majority of polymerization-sensitive HbS mutants are located at fiber contact sites and the majority of the mutants that do not affect polymerization are not located at contact sites. The residues at intermolecular contacts in the fiber model are reported. We have searched the coordinate space in the vicinity of the EM reconstructions to find models with alternative sets of coordinates that satisfy the mutant data, contain 5-Å contacts between double strands, and are stereochemically acceptable. This involved a systematic examination over 297 different models. The alternative fiber models were generated with a range of fiber pitch, double-strand positions, and double-strand polarity. Models which had unacceptably close contacts between atoms, failed to satisfy the mutant data, or did not have 5-Å contacts between double strands were considered unacceptable. None of the acceptable alternative fiber models improved the agreement between the polymerization behavior of HbS mutants and their contact site location. However, several models could account for the polymerization data equally well. Residue locations for single-site HbS mutations that could discriminate between alternative fiber models are proposed. The twist of HbS fibers varies in an apparent random manner with an average rotation of 7.8 ± 2.5° per molecule and a maximum rotation of 16° per molecule. The number of interdouble-strand contacts as a function of fiber twist shows a broad maximum around 9° and may account for the observed range of fiber pitch. This study shows that the upper limit on the fiber twist could result from a loss of axial contacts and repulsive van der Waals interactions between residues involved in interstrand contacts. The loss of axial contacts limits the radial growth of the fiber. In the appendix we analyze the methodology used by I. Cretegny and S. J. Edelstein [(1993) J. Mol. Biol. 230, 733-738] to build a model of the fiber. Our examination reveals shortcomings in the methodology of Cretegny and Edelstein. One result of these shortcomings is that the model synthesized by Cretegny and Edelstein is not stereochemically acceptable because it gives rise to a large number of excessively close (less than 1.4 Å) atom-atom contacts, suggesting interpenetration of the molecular envelopes.     

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.     

Role of the beta4Thr-beta73Asp hydrogen bond in HbS polymer and domain formation from multinucleate-containing clusters

Fiber formation and domain formation from deoxy-HbS as well as from beta4 and beta73 HbS variants were investigated after temperature jump using DIC microscopy to gain a basic understanding of the determinants involved. Oversaturated deoxy-HbS generated numerous 14-stranded fibers and formed ovoid-shaped, multispherulitic domains. Domain number increased linearly as a function of time. Oversaturated deoxy-alpha2beta2(E6V,T4S) also generated time-dependent, ovoid-shaped spherulitic domains like HbS and alpha 2beta2(E6V,D73H) in the deoxy form. In contrast, alpha 2beta2(E6V,T4Y) and HbC-Harlem (alpha2beta2(E6V,D73N)) in the deoxy form generated time-dependent, ball-shaped domains containing many straight, crystalline-like fibers without evidence of branching. Some of these domains formed large needlelike crystals after overnight incubation. The inhibitory effect on polymer formation by beta4Tyr in HbS was stronger than that by beta4Ser but weaker than that by beta73Asn or beta73Leu. In contrast, both deoxy- and oxy-alpha2beta2(E6V,T4V) promoted formation of tiny, disordered amorphous aggregates without a delay time like oxy-HbS, which is in contrast to formation after a delay time of needlelike fibers for alpha 2beta2(E6V,D73L). Solubilities for both deoxy- and oxy-alpha 2beta2(E6V,T4V) were similar to that of deoxy-alpha 2beta2(E6V,D73H) but approximately 10-fold lower than that of deoxy-HbS. These results suggest that the strength of the hydrogen bond between beta4Thr and beta73Asp and the balance between the hydrogen bond and beta6Val hydrophobic interactions in deoxy-HbS polymers control formation of different types of fibers in a single domain or lead to formation of disordered, non-nucleated amorphous aggregates. These results also lead to a model in which multinucleation rather than a single-nucleation event occurs in a single cluster to generate numerous fibers growing from a single domain.     

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.     

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 helix clock: a potential biomechanical cell cycle timer

A model based upon helical geometry that provides cylindrically shaped cells with a means to measure their length during growth and to time cell cycle events is presented. The helix clock arises from the change in pitch angle that accompanies the parallel packing of strands on a cylinder surface. A single strand inserted into the cylinder surface nearly perpendicular to the long axis of the cylinder starts the clock running. As additional strands are inserted parallel to those in place, the pitch angle of all strands must reorient. A limit is reached when all strands lie parallel to the long axis of the cylinder. By sensing either the pitch angle or a physical ramification thereof, cells can measure their length during growth and time events of the cell cycle. The helix clock model is discussed in relationship to the bacterial cell cycle. The idea that bacterial cells use one helix hand for cylinder elongation, the other for septation is presented. The negative twist so generated apparently drives folding in the helical bacterial macrofiber system of Bacillus subtilis.     

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 Å. The effect of rotation on the appearance of macrofiber cross-sections 300 to 400 Å thick can be simulated by a 15 ° 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.     

The kinetics of nucleation and growth of sickle cell hemoglobin fibers

Polymerization of sickle cell hemoglobin (HbS) in deoxy state is one of the basic events in the pathophysiology of sickle cell anemia. For insight into the polymerization process, we monitor the kinetics of nucleation and growth of the HbS polymer fibers. We define a technique for the determination of the rates J and delay times theta of nucleation and the fiber growth rates R of deoxy-HbS fibers, based on photolysis of CO-HbS by laser illumination. We solve numerically time-dependent equations of heat conductance and CO transport, coupled with respective photo-chemical processes, during kinetics experiments under continuous illumination. After calibration with experimentally determined values, we define a regime of illumination ensuring uniform temperature and deoxy-HbS concentration, and fast (within <1 s) egress to steady conditions. With these procedures, data on the nucleation and growth kinetics have relative errors of <5% and are reproducible within 10% in independent experiments. The nucleation rates and delay times have steep, exponential dependencies on temperature. In contrast, the average fiber growth rates only weakly depend on temperature. The individual growth rates vary by up to 40% under identical conditions. These variations are attributed to instability of the coupled kinetics and diffusion towards the growing end of a fiber. The activation energy for incorporation of HbS molecules into a polymer is E(A)=50 kJ mol(-1), a low value indicating the significance of the hydrophobic contacts in the HbS polymer. More importantly, the contrast between the strong theta(T) and weak R(T) dependencies suggests that the homogenous nucleation of HbS polymers occurs within clusters of a precursor phase. This conclusion may have significant consequences for the understanding of the pathophysiology of sickle cell anemia and should be tested in further work.     

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.     

A twisted four-sheeted model for an amyloid fibril

The formation of amyloid fibers and their deposition in the body is a characteristic of a number of devastating human diseases. Here, we propose a structural model, based on X-ray diffraction data, for the basic structure of an amyloid fibril formed by using the variants of the B1 domain of IgG binding protein G of Streptococcus. The model for the fibril incorporates four beta sheets in a bundle with a diameter of 45 A. Its cross-section, or layer, consists of four strands, one strand from each sheet. Layers stack on top of each other to form the fibril, which has an overall helical twist with a periodicity of about 154 A. Each strand interacts in a parallel fashion with the strands in the layers above and below it, in an infinite beta sheet. Some geometric features of this model and the logic behind it may be applicable for constructing other related cross-beta amyloid fibrils.     

A model for the sickle hemoglobin fiber using both mutation sites

The standard molecular model of the fiber of the sickle hemoglobin (HbS: beta6 Glu-->Val) has been revised to allow both beta6 mutation sites to participate in intermolecular contacts, rather than only one beta6 site as previously thought, for four molecules per 14-molecule fiber cross section. This structure accurately predicts the copolymerization of hybridized mixtures of HbS with HbA or HbC (beta6 Glu-->Lys), which could not be reconciled with prior models in which only half the beta6 sites were required for assembly. This model suggests new contacts within the fiber and raises the question of whether these cross-linked double strands could possess added stability important in such processes as nucleation.     

Modification of Axial Fiber Contact Residues Impact Sickle Hemoglobin Polymerization by Perturbing a Network of Coupled Interactions

The identity of intermolecular contact residues in sickle hemoglobin (HbS) fiber is largely known. However, our knowledge about combinatorial effects of two or more contact sites or the mechanistic basis of such effects is rather limited. Lys16, His20, and Glu23 of the α-chain occur in intra-double strand axial contacts in the sickle hemoglobin (HbS) fiber. Here we have constructed two novel double mutants, HbS (K16Q/E23Q) and (H20Q/E23Q), with a view to delineate cumulative impact of interactions emanating from the above contact sites. Far-UV and visible region CD spectra of the double mutants were similar to the native HbS indicating the presence of native-like secondary and tertiary structure in the mutants. The quaternary structures in both the mutants were also preserved as judged by the derivative UV spectra of liganded (oxy) and unliganded (deoxy) forms of the double mutants. However, the double mutants displayed interesting polymerization behavior. The polymerization behaviour of the double mutants was found to be non-additive of the individual single mutants. While HbS (H20Q/E23Q) showed inhibitory effect similar to that of HbS (E23Q), the intrinsic inhibitory propensity of the associated single mutants was totally quelled in HbS (K16Q/E23Q) double mutant. Molecular dynamics (MD) simulations studies of the isolated α-chains as well as a module of the fiber containing the double and associated single mutants suggested that these contact sites at the axial interface of the fiber impact HbS polymerization through a coupled interaction network. The overall results demonstrate a subtle role of dynamics and electrostatics in the polymer formation and provide insights about interaction-linkage in HbS fiber assembly.     

Contact inhibition within hemoglobin S polymer by thiol reagents

N-Ethylmaleimide, a thiol reagent, increases the solubility of deoxyhemoglobin S. We investigated which of the two reacted beta 93 cysteine residues of the Hb tetramer was responsible for the inhibition of Hb S polymerization. Accordingly we compared the solubility of equal mixtures of HbA + HbS, HbA NEM + HbS and HbA + HbS NEM. Upon deoxygenation these mixtures contain about 50% a stable and asymmetrical hybrid alpha 2A beta A beta S, alpha 2A beta A,NEM beta S or alpha 2A beta A beta S,NEM respectively and 25% parental molecules as confirmed by ion-exchange HPLC performed in anaerobic conditions. Within the hybrid molecule, beta A or beta A,NEM chain has to be present in the alpha beta dimer located in trans to the dimer which contains the only beta 6 valine residue participating in intermolecular contacts (dimer in cis), while beta S or beta S,NEM must be in cis position in the hybrid molecule. The solubility of mixtures increases 4% for HbA NEM + HbS and 20% for HbA + HbS NEM mixtures compared to HbA + HbS mixture, indicating that the inhibitory effect of N-ethylmaleimide is more effective in cis than in trans position. The absence of a major role played by N-ethylmaleimide located in trans was supported by the solubility study of a mixture of HbS + Hb Créteil beta 89 Ser----Asn. The beta 89 residue in trans next to the cysteine beta 93 modified the T structure similarly to N-ethylmaleimide, and did not affect intermolecular contacts. Crystallographic studies of molecular contacts within deoxyHbS crystals suggest that the cis inhibitory effect of N-ethylmaleimide can be explained by direct inhibition of 'external' contacts between double strands involving the CD corner of the alpha chains.     

A role for the alpha 113 (GH1) amino acid residue in the polymerization of sickle hemoglobin. Evaluation of its inhibitory strength and interaction linkage with two fiber contact sites (alpha 16/23) located in the AB region of the alpha-chain

A cluster of amino acid residues located in the AB-GH region of the alpha-chain are shown in intra-double strand axial interactions of the hemoglobin S (HbS) polymer. However, alphaLeu-113 (GH1) located in the periphery is not implicated in any interactions by either crystal structure or models of the fiber, and its role in HbS polymerization has not been explored by solution experiments. We have constructed HbS Twin Peaks (betaGlu-6-->Val, alphaLeu-113-->His) to ascertain the hitherto unknown role of the alpha113 site in the polymerization process. The structural and functional behavior of HbS Twin Peaks was comparable with HbS. HbS Twin Peaks polymerized with a slower rate compared with HbS, and its polymer solubility (C(sat)) was found to be about 1.8-fold higher than HbS. To further authenticate the participation of the alpha113 site in the polymerization process as well as to evaluate its relative inhibitory strength, we constructed HbS tetramers in which the alpha113 mutation was coupled individually with two established fiber contact sites (alpha16 and alpha23) located in the AB region of the alpha-chain: HbS(alphaLys-16-->Gln, alphaLeu-113-->His), HbS(alphaGlu-23-->Gln, alphaLeu-113-->His). The single mutants at alpha16/alpha23 sites were also engineered as controls. The C(sat) values of the HbS point mutants involving sites alpha16 or alpha23 were higher than HbS but markedly lower as compared with HbS Twin Peaks. In contrast, C(sat) values of both double mutants were comparable with or higher than that of HbS Twin Peaks. The demonstration of the inhibitory effect of alpha113 mutation alone or in combination with other sites, in quantitative terms, unequivocally establishes a role for this site in HbS gelation. These results have implications for development of a more accurate model of the fiber that could serve as a blueprint for therapeutic intervention.     

Alpha helical crossovers favor right‐handed supersecondary structures by kinetic trapping: The phone cord effect in protein folding

The remarkable predominance of right‐handedness in beta‐alpha‐beta helical crossovers has been previously explained in terms of thermodynamic stability and kinetic accessibility, but a different kinetic trapping mechanism may also play a role. If the beta‐sheet contacts are made before the crossover helix is fully formed, and if the backbone angles of the folding helix follows the energetic pathway of least resistance, then the helix would impart a torque on the ends of the two strands. Such a torque would tear apart a left‐handed conformation but hold together a right‐handed one. Right‐handed helical crossovers predominate even in all‐alpha proteins, where previous explanations based on the preferred twist of the beta sheet do not apply. Using simple molecular simulations, we can reproduce the right‐handed preference in beta‐alpha‐beta units, without imposing specific beta‐strand geometry. The new kinetic trapping mechanism is dubbed the “phone cord effect” because it is reminiscent of the way a helical phone cord forms superhelices to relieve torsional stress. Kinetic trapping explains the presence of a right‐handed superhelical preference in alpha helical crossovers and provides a possible folding mechanism for knotted proteins.     

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.     

Modeling sickle hemoglobin fibers as one chain of coarse-grained particles

Sickle cell disease (SCD) is caused by a single point mutation in the beta-chain hemoglobin gene, resulting in the presence of abnormal hemoglobin S (HbS) in the patients' red blood cells (RBCs). In the deoxygenated state, the defective hemoglobin tetramers polymerize forming stiff fibers which distort the cell and contribute to changes in its biomechanical properties. Because the HbS fibers are essential in the formation of the sickle RBC, their material properties draw significant research interests. Here, a solvent-free coarse-grain molecular dynamics (CGMD) model is introduced to simulate single HbS fibers as a chain of particles. First, we show that the proposed model is able to efficiently simulate the mechanical behavior of single HbS fibers. Then, the zippering process between two HbS fibers is studied and the effect of depletion forces is investigated. Simulation results illustrate that depletion forces play a role comparable to direct fiber-fiber interaction via Van der Waals forces. This proposed model can greatly facilitate studies on HbS polymerization, fiber bundle and gel formation as well as interaction between HbS fiber bundles and the RBC membrane.     

Chromatin fibers are left-handed double helices with diameter and mass per unit length that depend on linker length

Four classes of models have been proposed for the internal structure of eukaryotic chromosome fibers--the solenoid, twisted-ribbon, crossed-linker, and superbead models. We have collected electron image and x-ray scattering data from nuclei, and isolated chromatin fibers of seven different tissues to distinguish between these models. The fiber diameters are related to the linker lengths by the equation: D(N) = 19.3 + 0.23 N, where D(N) is the external diameter (nm) and N is the linker length (base pairs). The number of nucleosomes per unit length of the fibers is also related to linker length. Detailed studies were done on the highly regular chromatin from erythrocytes of Necturus (mud puppy) and sperm of Thyone (sea cucumber). Necturus chromatin fibers (N = 48 bp) have diameters of 31 nm and have 7.5 +/- 1 nucleosomes per 10 nm along the axis. Thyone chromatin fibers (N = 87 bp) have diameters of 39 nm and have 12 +/- 2 nucleosomes per 10 nm along the axis. Fourier transforms of electron micrographs of Necturus fibers showed left-handed helical symmetry with a pitch of 25.8 +/- 0.8 nm and pitch angle of 32 +/- 3 degrees, consistent with a double helix. Comparable conclusions were drawn from the Thyone data. The data do not support the solenoid, twisted-ribbon, or supranucleosomal particle models. The data do support two crossed-linker models having left-handed double-helical symmetry and conserved nucleosome interactions.     

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.