A model for sedimentation in inhomogeneous media. II. Compressibility of aqueous and organic solvents.

The effects of solvent compressibility on the sedimentation behavior of macromolecules as observed in analytical ultracentrifugation are examined. Expressions for the density and pressure distributions in the solution column are derived and combined with the finite element solution of the Lamm equation in inhomogeneous media to predict the macromolecular concentration distributions under different conditions. Independently, analytical expressions are derived for the sedimentation of non-diffusing particles in the limit of low compressibility. Both models are quantitatively consistent and predict solvent compressibility to result in a reduction of the sedimentation rate along the solution column and a continuous accumulation of solutes in the plateau region. For both organic and aqueous solvents, the calculated deviations from the sedimentation in incompressible media can be very large and substantially above the measurement error. Assuming conventional configurations used for sedimentation velocity experiments in analytical ultracentrifugation, neglect of the compressibility of water leads to systematic errors underestimating sedimentation coefficients by approximately 1% at a rotor speeds of 45000 rpm, but increasing to 2-5% with increasing rotor speeds and decreasing macromolecular size. The proposed finite element solution of the Lamm equation can be used to take solvent compressibility quantitatively into account in direct boundary models for discrete species, sedimentation coefficient distributions or molar mass distributions. Using the analytical expressions for the sedimentation of non-diffusing particles, the ls-g*(s) distribution of apparent sedimentation coefficients is extended to the analysis of sedimentation in compressible solvents. The consideration of solvent compressibility is highly relevant not only when using organic solvents, but also in aqueous solvents when precise sedimentation coefficients are needed, for example, for hydrodynamic modeling.