van Holde - Weischet Tutorial

The Basics

While in earlier years researchers had to rely on Model-E type instrumentation, which imposed certain limitations on the quality of the results, data analysis methods focused mainly on the characterization of simple ideal, single component systems. Standard methods employed generally were restricted to calculations of the second moment point, calculations of peak positions in Schlieren data, or transformations of data to derivative space to obtain peaks similar to Schlieren data.

A major disadvantage of these methods was that these methods would generally not provide any information on possible heterogeneity unless individual components were well resolved. This problem results from the boundary spreading of diffusion which is superimposed on the boundary spreading due to sedimentation transport. In the worst-case scenario, heterogeneity itself follows a gaussian distribution, making it virtually impossible to tell apart from the gaussian spreading of the boundary due to diffusion. Similarly, small differences in S due to conformational isomers can often be buried under the much larger diffusion signal. In such cases individual boundaries may be virtually identical in shape to boundaries from single component system which simply have a larger diffusion coefficient.

In such cases it is only possible to tell these systems apart, if the boundaries for the entire time course of the sedimentation velocity experiment are considered in a global analysis. K. van Holde and W. Weischet in 1979 realized that sedimentation and diffusion are separable processes of transport, since they proceed with different orders of magnitude. While sedimentation is a transport process proportional to the first power of time, diffusion proceeds with a velocity proportional to the square-root of time. Thus, if allowed to sediment for an infinite time in an infinitely long cell at sufficient acceleration, the diffusion spreading observed would only be local to the boundary of that component and all components would be well resolved.

Assuming that the sedimentation velocity of each component in the system stays constant throughout the sedimentation process (which is not always the case), plotting the apparent sedimentation coefficients (derived from the radial positions of corresponding positions in the boundary) against the square-root of the time of each scan, and extrapolating the corresponding apparent sedimentation coefficients to infinite time provides then the true S-value distribution of the system, corrected for diffusion.

Summary:

The only analysis method capable of unambigously distinguishing between heterogeneity and homogeneity in S is the van Holde - Weischet analysis, and thus it is an indispensable tool for the characterization of unknown samples or samples of known heterogeneity. In addition, the van Holde - Weischet analysis provides many important and useful diagnostics, which will be highlighted later in this tutorial.