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This mini-tutorial discusses ways in which you can optimize the information obtained from equilibrium experiments. Factors such as instrument settings, sample preparation, data collection, and data selection all play an important role in the design of equilibrium experiments.
Since most methods used for analyzing sedimentation equilibrium data utilize some sort of nonlinear least squares fitting algorithm, the quality and amount of experimental data available for fitting is important. The following guidelines should help you to design a good experiment:
Each wavelength will allow you to measure a different concentration range of the sample, which presumably has different extinction properties at each selected wavelength. In order to be able to compare all collected wavelengths in a global fit (especially for self-association models) it is important that the extinction coefficients are known. If you do not know the extinction properties of your sample at each wavelength, you should also perform wavelength scans for all your samples at the beginning of the run. Those wavelength scans can later be globally fitted with the Extinction Profile Calculator to an extinction profile function that describes the exinction properties of your sample at each wavelength.
You should collect wavelength scans also at the beginning of the experiment (for example, right after the initial scan has been collected at 3000 rpm, with the instrument still spinning at this low speed) at a point near the middle of the sample column, where the change in absorbance is minimal at low speed. Collect data with 1 nm increments, scanning 2 or 3 times with 50 averages.
Fitting experimental data using a nonlinear least squares model always faces the question of correct model selection. If a model independent analysis is possible, it can be used as a guide for the selection of a more specific model, as can the residual run patterns and the variance. In addition, the investigator should be aware of the degrees of freedom that the model provides, because additional degrees of freedom may provide an improvement of variance, but only through fitting of instrumental noise, not because the model is more appropriate for the data.
A general approach may be to start with a model independent fit of the data using a Fixed Molecular Weight distribution model to get an idea about the molecular weight distribution in the system. This model is quite degenerate, because it contains a lot of parameters, and a slight variation of the input parameters can generate a large change in result, with almost no change in the variance. But in general it can be used to provide a good overview of the composition of the sample. Next, a single ideal species model may be tried, which is the most restrictive model. If this model provides a good fit, which can only be marginally improved by going to a more relaxed model, chances are that the data is well described by a single component. If however the single ideal species model results in run patterns indicating systematic noise in the data, it is necessary to attempt a fit with a model allowing for more parameters to be fitted.
Due to the lack of resolution when describing data by sums of exponentials, the most relaxed model that can provide reasonable results in an equilibrium experiment performed on the Beckman XL-A is a two or three component noninteracting model. It should only be chosen as a representation of the data if the variance improves significantly when changing the model from an interacting or single ideal species model to the multi-component model. Most systems will generate a good fit when this model is chosen (even when more components are present), so use this model with caution. The molecular weights generated by fits with this model do not necessarily represent the species present in the system, but, when taking together can describe well the molecular weight average at each point in the cell. If the molecular weight for the two component model corresponds to the expected monomer and dimer molecular weight of a system, then a monomer-dimer model should be tried instead.
The difference between the 2-component ideal noninteracting model and the reversibly self-associating models is an additional constraint in the model when samples are fit with the interacting (reversibly associating) monomer-oligomer model. In fact, there are two additional constraints. In the noninteracting model there are no assumptions made about one species being a certain multiple in MW of another species. In the reversibly associating model, the MW is constraint to be an integer multiple. For each oligomer, the multiple is an integer multiple of the monomer. In addition, there is a constraint that enforces that the amplitude of each exponential term satisfies the equilibrium constant for the reversible association, for example: K1,2 = [dimer]/[monomer]^2 or K1,3 = [trimer]/[monomer]^3.
So the noninteracting model is a much more relaxed fit which should always fit better than the constrained model. Sometimes a situation can arise where the MW constraint is satisfied, but not the Keq constraint. In such a case often incompetent monomers or dimers (monomers that cannot associate, or dimers that cannot dissociate, perhaps due to disulfide bridges) are present.
What decides which model is most appropriate is a balance between degrees of freedom in the fit, and the variance observed when applying a particular model. The difference in variance between one model and another is a deciding factor for selecting one model over another. If the improvement in variance from going to a noninteracting model to a reversible model is only marginal, then the reversible model should be accepted, otherwise the noninteracting model applies.
This document is part of the UltraScan Software Documentation
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Last modified on January 2, 2001.