Theory of nematic order with aggregate dehydration for reversibly assembling proteins in concentrated solutions: Application to sickle-cell hemoglobin polymers

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Abstract
The reversible association of globular protein molecules in concentrated solution leads to highly polydisperse fibers, e.g., actin filaments, microtubules, and sickle-cell hemoglobin fibers. At high concentrations, excluded-volume interactions between the fibers lead to spontaneous alignment analogous to that in simple lyotropic liquid crystals. However, the phase behavior of reversibly associating proteins is complicated by the threefold coupling between the growth, alignment, and hydration of the fibers. In protein systems aggregates contain substantial solvent, which may cause them to swell or shrink, depending on osmotic stress. Extending previous work, we present a model for the equilibrium phase behavior of the above-noted protein systems in terms of simple intra- and interaggregate interactions, combined with equilibration of fiber-incorporated solvent with the bulk solvent. Specifically, we compare our model results to recent osmotic pressure data for sickle-cell hemoglobin and find excellent agreement. This comparison shows that particle interactions sufficient to cause alignment are also sufficient to squeeze significant amounts of solvent out of protein fibers. In addition, the model is in accord with findings from independent sedimentation and birefringence studies on sickle-cell hemoglobin.

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