Micromechanics of Isolated Sickle Cell Hemoglobin Fibers: Bending Moduli and Persistence Lengths Jiang Cheng Wang 1 , Matthew S. Turner 2 , Gunjan Agarwal 1 Suzanna Kwong 1 , Robert Josephs 3 , Frank A. Ferrone 4 and Robin W. Briehl 1 * 1 Department of Physiology & Biophysics, Albert Einstein College of Medicine, Bronx NY 10461 2 Center for Studies in Physics and Biology, Rockefeller University, New York NY 10021 3 Department of Molecular Genetics & Cell Biology, University of Chicago, Chicago IL 60637 4 Department of Physics, Drexel University, Philadelphia PA 19104 Pathogenesis in sickle cell disease depends on polymerization of deoxy- hemoglobin S into rod-like ®bers, 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 lack- ing. The basis of gel rheology, micromechanics of individual ®bers, has never been examined. Here, we isolate ®bers by selective depolymeriza- tion of gels produced under photolytic deliganding of CO hemoglobin S. Using differential interference contrast (DIC) microscopy, we measure spontaneous, thermal ¯uctuations in ®ber shape to obtain bending moduli (k) and persistence lengths (l p ). Some ®bers being too stiff to decompose shape accurately into Fourier modes, we measure deviations of ®ber midpoints from mean positions. Serial deviations, suf®ciently sep- arated to be independent, exhibit Gaussian distributions and provide mean-squared ¯uctuation amplitudes from which k and l p can be calcu- lated. l p ranges from 0.24 to 13 mm for the most ¯exible and stiffest ®bers, respectively. This large range re¯ects formation of ®ber bundles. If the most ¯exible are single ®bers, then l p 13 mm represents a bundle of seven single ®bers. Preliminary data on the bending variations of fro- zen, hydrated single ®bers of HbS obtained by electron microscopy indi- cate that the value 0.24 mm is consistent with the persistence length of single ®bers. Young's modulus is 0.10 GPa, less than for structural pro- teins but much larger than for extensible proteins. We consider how these results, used with models for cross-linking, may apply to macro- scopic rheology of hemoglobin S gels. This new technique, combining iso- lation of hemoglobin S ®bers and measurement of micromechanical properties based on thermal ¯uctuations and midpoint deviations, can be used to study ®bers of mutants, hemoglobin A/S, and mixtures and hybrids of hemoglobin S. # 2002 Academic Press Keywords: sickle hemoglobin; ®bers; persistence length; micromechanics; gel *Corresponding author Introduction Pathogenesis in sickle cell disease arises from the deoxygenation dependent polymerization of sickle cell hemoglobin (HbS) into long, stiff, rod-like ®bers. The 20 nm diameter ®bers form non- covalent cross-links, 1±3 creating a gel that deforms and rigidi®es red blood cells. These, in turn, obstruct the systemic microvasculature and induce sickle cell crises, leading to manifold and multior- gan pathologies. From this perspective, critical issues in sickle cell crises and sickle cell disease are (1) the equilibria and (2) kinetics of polymerization, and (3) the rheology of gels. Relations between the ®rst two of these and pathogenesis have been Present address: M. S. Turner, Department of Physics, Warwick University, Coventry, CV4 7AL, UK. Abbreviations used: HbS, sickle cell hemoglobin; DIC, differential interference contrast. E-mail address for the corresponding author: briehl@aecom.yu.edu doi:10.1006/jmbi.2001.5130 available online at http://www.idealibrary.com on J. Mol. Biol. (2002) 315, 601±612 0022-2836/02/040601±12 $35.00/0 # 2002 Academic Press