Analytical Zone Centrifugation

Model | Analytical Zone Centrifugation | Analytical Zone Centrifugation Indep. Species

Model | Analytical Zone Centrifugation | Analytical Zone Centrifugation c(s)

Model | Analytical Zone Centrifugation | Analytical Zone Centrifugation ls-g*(s)

Analytical zone centrifugation is a technique in which a small volume of sample (typically 20 ml) is layered on top of solvent (e.g. 330 ml of solvent with slightly higher density), and the sedimentation process of the macromolecules is observed. For technical details on the experiment, see ref 1.

Typical data may look like Gaussians that move and broaden with time (these data are from an experiment with BSA).

The sedimentation process is described by the Lamm equation, just like ordinary sedimentation velocity experiments. The only difference is the starting condition: Usually, the sedimentation starts with macromolecular concentration uniform across the cell, while in the analytical zone centrifugation the starting condition is a small lamina of uniform concentration near the meniscus up to the interface, and then zero concentration from the interface to the cell bottom.

There are two different approaches for the quantitative analysis of these
data by direct boundary modeling: First, one could chose the first scan as
initial condition, and use the conventional Lamm equation model. In more
detail, this can be done by using the **Data | Set
Initial Data** command. As described on the help
website of the experimental initial function, first select the model
for non-interacting discrete species, then invoke the parameter
box and switch on the experimental
initial condition. Then load
the initial data. The advantage of this method is that any
imperfections in the overlaying process is irrelevant, as only the evolution
after the time of the first scan will be modeled. Disadvantage is that
this model can strictly be only used with a single species model, or with
self-association models. (The reason is that for multiple macromolecular
components, we would need separate initial conditions for all of them.)

**As an alternative, we can assume that the overlaying process is ideal and
instantaneous. **This means that we can build into the Lamm equation
solutions the initial condition of a homogeneously loaded layer of a certain
thickness. This is the strategy the specialized analytical zone
centrifugation models are for.

The lamina thickness will be an additional parameter, but we will be able to use any of the direct boundary sedimentation models. The lamina thickness (e.g. ~ 0.09 - 0.10 cm for 20 ml over 330 ml buffer) will introduce some correlation with the sedimentation or diffusion parameters. I would recommend to keep the lamina thickness a floating parameter in the analysis, together with the meniscus position.

It should be kept in mind that the solvent
density and partial-specific volume of the macromolecules should be entered
in SEDFIT, in particular if D_{2}O
was used in the solvent, the buoyancy of the molecules can be much
different. (Also there is a large viscosity effect of D_{2}O).
For tabulated data, see ref 1 and ref 2.

Because of the difference in composition of the sample and the solvent required for formation of the diffusional density gradient, only absorbance optics can be used in this experiment.

Model | Analytical Zone Centrifugation | Analytical Zone Centrifugation Indep. Species

This model works like the model for independent and ideally sedimenting species for conventional loading. The parameter box is slightly different:

It allows only for 3 components instead of four, but it has an additional parameter for the lamella width. As mentioned above, I recommend keeping the lamella width a floating parameter (check the box left to "lamella width"), as well as the meniscus. For the BSA data shown above, we can fit the data well with the three main species:

With consideration of TI noise (because of the clear dust spikes on the data), we get ~ 15% dimer, and 1-2% trimer, with a rmsd of the fit 0.0043 OD.

**
Model | Analytical
Zone Centrifugation | Analytical Zone Centrifugation c(s)
**

This model is very analogous to the c(s) distribution for conventional loading, but there are some differences.

Because of the higher correlation, I recommend the use of the Tikhonov-Phillips
regularization, and the use of a higher confidence
level, such as 0.95. Otherwise, I suggest using the same optimization
procedure as described in the step-by-step
tutorial, with **floating meniscus, lamella thickness, and frictional ratio**.

The best-fit distribution might look like this:

**
Model | Analytical
Zone Centrifugation | Analytical Zone Centrifugation
ls-g*(s)
**

Like the other models, also the ls-g*(s) model can be modified to take the
initial layer into account. As described in the introduction
to ls-g*(s), this model is based on step-functions that describe the
sedimentation in the absence of diffusion. The modification required for
analytical zone centrifugation is that the basic step-function is actually two
steps (with concentrations zero - c_{plat} - zero). Details of the
model will be described elsewhere (ref 2).

The complete analysis can be done analogous to the ls-g*(s) model for conventional loading, similar to the procedure shown in the tutorial. The parameter box will have the additional parameter for the lamella width:

and fitting for the meniscus position is not implemented. I do not recommend fitting for the lamella width here, as there can be some slight correlation with the distribution shape.

As described in the introduction to the ls-g*(s) method, we can use a very large data set, and the result may look like this:

**References**

(1) J. Lebowitz, M. Teale, P. Schuck (1998) Analytical band centrifugation of proteins and protein complexes. Biochem. Soc. Trans. 26:745-749

(2) manuscript in preparation