Measuring forces between protein fibers by microscopy

We propose a general scheme for measuring the attraction between mechanically frustrated semiflexible fibers by measuring their thermal fluctuations and shape. We apply this analysis to a system of sickle hemoglobin (HbS) fibers that laterally attract one another. These fibers appear to “zip” together before reaching mechanical equilibrium due to the existence of cross-links into a dilute fiber network. We are also able to estimate the rigidities of the fibers. These rigidities are found to be consistent with sickle hemoglobin “single” fibers 20 nm in diameter, despite recent experiments indicating that fiber bundling sometimes occurs. Our estimate of the magnitude of the interfiber attraction for HbS fibers is in the range 8 ± 7 kBT/μm, or 4 ± 3 kBT/μm if the fibers are assumed, a priori to be single fibers (such an assumption is fully consistent with the data). This value is sufficient to bind the fibers, overcoming entropic effects, although extremely chemically weak. Our results are compared to models for the interfiber attraction that include depletion and van der Waals forces. This technique should also facilitate a similar analysis of other filamentous protein assembles in the future, including β-amyloid, actin, and tubulin

Nonideality and the nucleation of sickle hemoglobin.

The homogeneous and heterogeneous nucleation kinetics of sickle hemoglobin (HbS) have been studied for various degrees of solution crowding by substitution of cross-linked hemoglobin A, amounting to 50% of the total hemoglobin. By cross-linking hemoglobin A, hybrid formation between hemoglobin A and hemoglobin S was prevented, thus simplifying the analysis of the results. Polymerization was induced by laser photolysis, and homogeneous nucleation kinetics were determined by observation of the stochastic behavior of the onset of light scattering. Heterogeneous nucleation was determined by observing the exponential growth of the progress curves, monitored by light scattering. At concentrations between 4 and 5 mM tetramer (i.e., approximately 30 g/dl), the substitution of 50% HbA for HbS slows the reaction by a factor of 10(3) to 10(4). Using scaled particle theory to account for the crowding of HbA, the observed decrease in the homogeneous nucleation rate was accurately predicted, with no variation of parameters required. Heterogeneous nucleation, on the other hand, is not well described in the present formulation, and the theory for this process appears to require modification of the way in which nonideality is introduced. Nonetheless, the accuracy of the homogeneous nucleation description suggests that such an approach may be useful for other assembly processes that occur in a crowded intracellular milieu

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 130 mu m, 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 2.5 mu m. Strikingly this means that the corresponding torsional rigidity of the fibers is only 6 x 10(-27) J m, much less than their bending rigidity of 5 x 10(-25) J m. 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. (c) 2006 Elsevier Ltd. All rights reserved