van Holde - Weischet Tutorial

Data Editing

The van Holde - Weischet analysis is based on a solution of the Lamm equation which assumes an infinitely long cell. This solution does not consider the exisiting boundary conditions, the meniscus and the bottom of the cell. In an infinitely long cell, material never pellets. In addition, in an infinitely long cell there will never be any back-diffusion from the bottom of the cell. Both pelleting and back-diffusion occurs because material accumulates at the bottom of the cell. Since these boundary conditions are not considered in the solution of the Lamm equation employed by the van Holde- Weischet analysis, all data scans that contain absorption profiles resulting from boundary effects will distort the solution.

Thus, all data included in the van Holde - Weischet analysis needs to be free of boundary effects. Therefore, you need to exclude any data containing boundary effects during editing or at runtime. Another requirement is that all scans included in the data analysis represent the same chemical composition of the sample(s) contained in the system. This is very important because the analysis attempts a global fit including all data in the extrapolation to infinite time. If the scans included in the analysis represent different compositions (for example, time dependent aggregation or degradation), the extrapolations will be misleading, although some diagnostic indicator can usually be obtained for such cases from the van Holde - Weischet extrapolation plot (please see the section on diagnostics for more information on indicators and analysis complications).

The following section explores which scans can be included in the analysis and which scans should be excluded.

Figure 10:This figure shows a heterogeneous system of scans, outlined in 3 different colors. Only scans outlined in blue should be included in the analysis.

• The yellow scans did not clear the meniscus and do not exhibit the necessary baseline. A minimal section of baseline is required for analysis to assure that the full concentration range C_baseline to C_plateau is available for the divisions. Therefore, the yellow lines need to be excluded from the analysis.

• Scans outlined in pink can also not be included in the analysis, because they do not contain the necessary stable (horizontal) plateau to provide the full concentration range. The sample sedimenting at the very top of the boundary is already precipitated in those scans and the plateau therefore is lower than what would be expected by radial dilution alone. If the pink scans would be included, the composition of the sample would be different in the earlier scans from the composition in the later scans, and respective boundary fractions would not correspond to eachother and the extrapolations would be misleading.

Figure 11:The scans shown below are appropriate for inclusion in the van Holde - Weischet analysis since they meet all necessary criteria, such as baseline and stable plateau.

Please consider the following points when selecting the baseline and plateau region:

• The baseline is easiest determined by averaging a small stretch of datapoints near the meniscus from the last scan in the dataset (it has the moving boundary closest to the bottom of the cell and thus a good baseline).
• The plateau is best determined by averaging a few datapoints near the bottom of the cell where the moving boundary has levelled out to form a plateau. This plateau region shown in the above plot is an appropriate range to be used for plateau determination. All scans have levelled out in this region. If a large amount of heterogeneity exists, or large of diffusion, this region may be very short. To average several points from the plateau region only use points from a truly horizontal region.

The UltraScan software will guide you during editing to define these points and automatically averages the points.

Speed Selection:

Attempt to select a speed as fast as possible with the shortest intervals between scans, such that the boundary transverses approximately 2/3 of the cell with at least 15-20 scans. The faster the sample is spun, the less time it has to diffuse, and the more pronounced will be the difference between multiple components and the resolution of the analysis. Please review the section on experimental design for more information on optimal experimental setup.

Summary:

• Do not include scans without a proper baseline (scans that haven't cleared the meniscus)
• Do not include scans that have a plateau lower than what would be expected from radial dilution alone.
• Select the plateau absorbance by averaging a few points near the bottom of the cell where absorbance has levelled out
• If your sample is not at chemical equilibrium (in the process of aggregation or degradation during the course of the experiment), the van Holde - Weischet extrapolations will be misleading