Manual

Global Equilibrium Analysis Tutorial:

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.

1. Instrument Settings:

   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:

   • Stepsize settings:
     Select the smallest radial increment available for equilibrium scans (0.001 cm/point). This will provide the largest number of datapoints for each scan, and hence better define the fitting surface.

   • Repetition/Replicates Setting
     Choose the maximum number of replicates (50) when collecting equilibrium data. Time is not of the essence (remember, your scan is at equilibrium!) and you can safely record 50 averages to improve the signal, even if it takes longer. Keep in mind that this means a lot of Xenon Lamp-flashes, which over time will collect lamp dirt. So only measure scans that really are at equilibrium and will be used for the data analysis this way, so your lamp emission strength doesn't degrade before you have all your data collected. Clean the lamp before the equilibrium run.

   • Wavelength settings:
     Select wavelengths that provide emission maxima for the Xenon flash lamped used in the XLA. Run an intensity scan on your lamp to see where the emission peaks are. Use those wavelengths to make sure that you get good signal-to-noise ratio for your measurements. Clean the lamp before each run.

   • Scan Settings:
     Scan twice in stepmode with 2-3 hours difference and subtract the scans to assure that equilibrium has been reached. Simulate the experiment using the UltraScan simulation programs before the experiment so you can get a good idea of when equilibrium may be reached. Add 10% - 20% time to make sure you have reached equilibrium. If the change is less than 0.01 OD, which is the noise level for a good experiment, any further equilibration will be lost in noise and not matter for the purpose of the fit. Equilibrium has been reached at that point for all practical purposes.

   • Scan settings and column height:
     If you do not use 6-channel centerpieces, you can create a little higher column by loading about 120-130 microliters. This will provide more datapoints, and provide more information on your scan. However, a longer column also means that it will take longer to achieve equilibrium. Load the reference column just a little higher, to make sure your reference meniscus doesn't obliterate the sample scan. Do not load much more than the sample side of the cell so the pressure differential doesn't become too large, which may bend and destroy the septum of the centerpiece.

   • Speed selection:
     Always select multiple speeds for a global analysis. When equilibrium is reached at different speeds, the equilibrium gradients will have different shapes, but still represent the same system. Global analysis takes advantage of this by forcing all scans to be fitted to the same model.

   • Initial Scan:
     Always collect an initial scan at low speed (3000 rpm) immediately after after the run is started. This scan will allow you to determine the total absorption in the cell and serve as a control to determine if material has precipitated or leaked. Collect initial scans in continuous mode, with 0.001 cm radial stepsize setting.

   • Multiple Wavelengths:
     While the monochromator of the XLA is known not to reset to exactly the same wavelength between different wavelength settings, it will at least report the incorrect wavelength it has reset itself to. Thus, it is still possible (and prudent) to collect data at different wavelengths in equilibrium experiments, because UltraScan has program features built into the equilibrium data analysis software which will automatically correct for these problems.

     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.

2. Experimental Design:
   • Data Selection:
     To obtain a confident analysis answer for your project, it is advisable to analyze the same sample under varying conditions, and to compare all of the conditions simultanously in a global fit. Keep in mind that some parameters may not be global anylonger when certain run attributes are changed, for example, association constant could be quite sensitive to buffer conditions and temperature, however, the monomer molecular should not be.

   • Samples
     One of the easiest ways to assay the same sample under different conditions is to measure the sample at different loading concentrations. For self-associating systems this has the effect that increasing concentration of the sample will provide increasing signal on the associated species. A further expansion of the concentration range can be obtained by using different wavelength, taking advantage of the various extinction properties of the protein at wavelengths such as 208-210 nm, 230 nm, and 278-280 nm. For each wavelength, the protein should be loaded at 3-8 different loading concentrations ranging between 0.2 - 0.7 OD. By changing only the concentration, and keeping buffer and temperature the same, the association constant can be fitted as a global parameter, since it should be constant regardless of concentration.

   • Speeds
     Another way to examine a sample at different conditions without changing temperature or buffer is to use different speeds. At equilibrium, each speed will produce a different gradient which still describes the same system, and hence both molecular weight and association constants can be fitted globally. It appears that for most cases a range of speeds using sigmas between 1.5 and 5 provides best results. Sigma in this case is the reduced monomer molecular weight as defined by Johnson et al.. The UltraScan equilibrium speed calculation module can assist you in determining the correct speeds for a given sigma. I suggest using scans from 4-5 speeeds, at equilibrium.

3. Models and fitting strategies:

   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.