Theory of boundary spreading in velocity ultracentrifugation of polydisperse solutes

Abstract

AbstractUnder the assumptions that the rectangular approximation to the sector‐shaped cell is valid and that both the sedimentation coefficient s and the diffusion coefficient D are independent of concentration, asymptotic solutions to the boundary spreading equation for velocity ultracentrifugation of polydisperse solutes have been derived for three cases: case A, D = constant for all s; case B, sD = constant; case C, \documentclass{article}\pagestyle{empty}\begin{document}$ \sqrt {sD} = {\rm constant} $\end{document}. Case A is the situation treated by all of the previous authors but supposed to be unrealistic for ordinary macromolecular solutes. Cases B and C may be associated with synthetic polymers under theta conditions and globular proteins in aqueous media, respectively. The solutions obtained have been used to explore the theoretical background of the empirical Gralén method for evaluating the distribution of s from sedimentation boundary curves, with special interest in the behavior of a plot for Sversus 1/t. Here S is the value of s for a fixed value of the apparent integral distribution of s and t is the time of centrifugation. It was found that when the distribution of s is Gaussian‐like and fairly narrow, this plot becomes linear over a more extended range of t in the order case B > case C > case A.