Sedimentation analysis of noninteracting and self-associating solutes using numerical solutions to the Lamm equation

The potential of using the Lamm equation in the analysis of hydrodynamic shape and gross conformation of proteins and reversibly formed protein complexes from analytical ultracentrifugation data was investigated. An efficient numerical solution of the Lamm equation for noninteracting and rapidly self-associating proteins by using combined finite-element and moving grid techniques is described. It has been implemented for noninteracting solutes and monomer-dimer and monomer-trimer equilibria. To predict its utility, the error surface of a nonlinear regression of simulated sedimentation profiles was explored. Error contour maps were calculated for conventional independent and global analyses of experiments with noninteracting solutes and with monomer-dimer systems at different solution column heights, loading concentrations, and centrifugal fields. It was found that the rotor speed is the major determinant for the shape of the error surface, and that global analysis of different experiments can allow substantially improved characterization of the solutes. We suggest that the global analysis of the approach to equilibrium in a short-column sedimentation equilibrium experiment followed by a high-speed short-column sedimentation velocity experiment can result in sedimentation and diffusion coefficients of very high statistical accuracy. In addition, in the case of a protein in rapid monomer-dimer equilibrium, this configuration was found to reveal the most precise estimate of the association constant.