An improved function for fitting sedimentation velocity data for low-molecular-weight solutes

Many traditional approaches to the analysis of sedimentation velocity data work poorly with data for low-molecular-weight solutes, which have sedimentation boundaries that are severely broadened by diffusion. An approach that has previously had some success is to directly fit these broad boundaries to approximate solutions of the Lamm equation that directly account for the high diffusion. However, none of the available approximate solutions work well at times both early and late in the run, or give boundary shapes that are highly accurate, especially for species of molecular weight < 10,000. An improved fitting function has been developed to overcome some of these limitations. The new function adds two correction terms to the Fujita-MacCosham solution. The optimum coefficients for these new correction terms were determined by a least-squares approach. The accuracy and limitations of fitting with this new function were tested against synthetic data sets obtained by finite-element methods, for analysis of samples containing either single species or several noninteracting species. We also compare the strengths and weaknesses of this method of analysis, and its ability to work with noisy data, relative to recently developed time-derivative methodologies.