Determination of the absolute fringe number in Rayleigh interference patterns in systems at sedimentation equilibrium via a newly defined function (kΔ)

Abstract

Analysis of data from the analytical ultracentrifuge used in sedimentation equilibrium modes calls for knowledge of the absolute (as distinct from relative) final solute mass distribution as a function of radial distance. This poses particular problems when Rayleigh interference optics are used, as the resultant fringe patterns provide estimates only for the relative concentration values. Methods for circumventing this problem are discussed, and their limitations described. Computer simulation is used to demonstrate the limitations of the most popular approach (“floating” the offset value in nonlinear fitting). A new approach to tackling this problem is defined, which is not limited by the number of components present, nor by their interactions if any. A function kΔ (E) is shown to have the value zero only when an assumed offset (E) in the values acquired is equal to the “genuine” offset. A “proof of concept numerical algorithm” has been constructed, which shows that the new approach is capable in principle of yielding offset values of a precision similar to that of the data set.