Free energy of sickle hemoglobin polymerization: a scaled-particle treatment for use with dextran as a crowding agent

Fundamental to the analysis of protein polymerization is the free energy of association, typically determined from solubility. It has been previously shown that concentrated 70 kDa dextran lowers the solubility of sickle hemoglobin, due to molecular crowding, and provides a useful ranking tool for the effects of inhibitors and molecular modifications. Because hemoglobin occupies a substantial volume as well, crowding effects of both hemoglobin and dextran contribute to the nonideality of the solution. We show how scaled-particle theory can be used to account for both types of crowding, thus allowing the determination of solubility in the absence of dextran, given data measured in its presence. The approach adopted approximates dextran as a sphere with a volume that decreases as the concentration of dextran increases. We use an asymptotic relation to describe the volume, which decreases nearly linearly by a factor of two over the range studied, from 60 to 230 mg/ml. This compression is similar to previously observed compression of sephadex beads and ficoll solutions. In the limit of low hemoglobin concentrations, the theory reduces to the previously-used approach of Ogston. Our method therefore provides a means of measuring the free energy of association of molecules that occupy significant volume fractions, even when assisted by the crowding of dextran and we present a tabulation of all known free energies of polymerization of sickle hemoglobin measured in the presence of dextran.