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.