Some statistical properties of differencing schemes for baseline correction of sedimentation velocity data

For the detailed analysis of sedimentation velocity data, the consideration of radial-dependent baseline offsets is indispensable. Two main approaches are data differencing ("delta-c" approach) and explicit inclusion of baseline parameters in the model ("direct boundary model" of the raw data). The current work aims to clarify the relationships between the two approaches. To this end, a simple model problem is examined. We show that the explicit consideration of the baseline in the model is equivalent to a differencing scheme where the average value is subtracted from all data points. Pairwise differencing in the delta-c approach always results in higher parameter uncertainty. For equidistant time points, the increase is smallest when the reference points are taken at intervals of 1/3 or 2/3 of the total number of time points. If the difference data are misinterpreted to be statistically independent samples, errors in the calculation of the parameter uncertainties can occur. Contrary to claims in the literature, we observe that there is no distinction in the approaches regarding their "model dependence"; both approaches arise from the integral or differential form of the same model, and both approaches can and should provide explicit estimates of the baseline values in the original data space for optimal discrimination between macromolecular sedimentation models.