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

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.

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.

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

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

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.

Pairings and polarities of the 14 strands in sickle cell hemoglobin fibers

Sickle cell anemia results from the formation of hemoglobin S fibers in erythrocytes, and a greater understanding of the structure of these fibers should provide insights into the basis of the disease and aid in the development of effective antisickling agents. Improved reconstructions from electron micrographs of negatively stained single hemoglobin S fibers or embedded fiber bundles reveal that the 14 strands of the fiber are organized into pairs. The strands in each of the seven pairs are half-staggered, and from longitudinal views the polarity of each pair can be determined. The positions of the pairs and their polarities (three in one orientation; four in the opposite orientation) suggest a close relationship with the crystals of deoxyhemoglobin S composed of antiparallel pairs of half-staggered strands.

Rheologic behavior of deoxyhemoglobin S gels

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