Non-linear curve-fitting methods for data from the XL-A analytical utltracentrifuge

Abstract

In equilibrium or velocity sedimentation experiments with the XL-A analytical ultracentrifuge it is customary to acquire absorbance data. The least-squares method is most widely used for fitting non-linear models to such collected data. It is here shown that due to the non-Gaussian characteristics of the noise in the absorbance data, the least-squares method is not optimal and introduces a systematic bias to the estimated parameters. This bias can be eliminated by either using the maximum-likelihood method on the absorbance data or otherwise by fitting the intensity data directly. The probability distribution of the noise in the latter is Gaussian and the least-squares estimation is equivalent to maximum likelihood. The methodology for using the intensity data is developed and simulations for a variety of systems are performed.