Sedimentation Equilibrium

Circular Dichroism Laser Light Scattering Sedimentation Equilibrium Sedimentation Velocity

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Sedimentation equilibrium is an analytical ultracentrifugation (AUC) method  for measuring protein molecular masses in solution and for studying protein-protein interactions. It is particularly valuable for:

bulletestablishing whether the native state of a protein is a monomer, dimer, trimer, etc.
bulletmeasuring the equilibrium constant (Kd) for association of proteins which reversibly self-associate to form oligomers
bulletmeasuring the stoichiometry of complexes between two or more different proteins (e.g. a soluble receptor and its ligand or an antigen-antibody pair), or between a protein and a non-protein ligand
bulletmeasuring the equilibrium constants for reversible protein-protein and protein-ligand interactions (approximate Kd range 1 nanomolar to 1 millimolar)

In sedimentation equilibrium the sample is spun in an analytical ultracentrifuge at a speed high enough to force the protein toward the outside of the rotor, but not high enough to cause the sample to form a pellet. As the centrifugal force produces a gradient in protein concentration across the centrifuge cell, diffusion acts to oppose this concentration gradient. Eventually an exact balance is reached between sedimentation and diffusion, and the concentration distribution reaches an equilibrium. This equilibrium concentration distribution across the cell is then measured while the sample is spinning, using either absorbance or refractive index detection in our Beckman XL-I (picture).

The key point about sedimentation equilibrium is that the concentration distribution at equilibrium depends only on molecular mass, and is entirely independent of the shape of the molecule. The precision of the molecular masses determined by this technique is usually 1-2%. 

Furthermore, for proteins which self-associate to oligomers, or for mixtures of molecules that bind to one another, the overall distribution will also be in chemical equilibrium for the association process, and therefore will reflect the higher molecular weight of the associated states and their proportion in the sample. 

Example 1: Is a Sequence Homolog a True Structure Homolog?

Tumor necrosis factor alpha (TNF) was the first known member of a family of signaling molecules involved in inflammation, apoptosis, and many other important functions. A hallmark of this family is that these proteins normally occur as trimers in solution.

A potential new member of this family was identified on the basis of sequence homology. However, when it was expressed in E. coli and refolded from inclusion bodies, it appeared to be a monomer based on its elution relative to standards on size-exclusion chromatography (SEC). Did this mean it was not truly a member of this family, or simply that it was not correctly refolded, or was the mass estimate from SEC wrong?raw data for TNF homolog

The graph to the right shows some sedimentation equilibrium data for this molecule, showing the concentration as a function of position within the cell as monitored by absorbance at 230 nm. Note that the total amount of protein for this experiment was <10 micrograms.

 

This next graph shows that data re-plotted as the natural log of absorbance vs. radius2/2. In this type of plot a single species gives a straight line whose slope is proportional to mass. linearized plot of TNF homolog data The light blue line indicates the theoretical slope calculated for the monomer mass (~17 kDa). The dark blue line (mostly hidden behind the data points) has the theoretical slope for the trimer mass. This plot therefore makes it obvious that this protein is indeed a trimer, and therefore it is indeed a homolog of TNF (and presumably is correctly folded).

Although the results for only a single sample and rotor speed are shown here, in general to quantitatively characterize a protein and whether it self-associates we run 3-9 samples over a broad range of loading concentrations and at two or more rotor speeds, and these data are then simultaneously ("globally") analyzed.

Example 2: Functional Characterization of a Monoclonal Antibody

The function of many proteins is to bind to other proteins, and sedimentation equilibrium is a very powerful tool for studying such binding interactions. overlay of antibody-antigen mixtures and fitted curves

The graph at the right summarizes the data (points) and fitted curves for 8 experiments on mixtures of a monoclonal antibody and its ~25 kDa protein antigen. The data sets cover experiments at different mixing ratios of antibody to antigen, and by using scans at either 280 or 230 nm they also cover a wide range of concentrations. (Note that this entire set of experiments used only ~80 micrograms of antibody.)

To analyze these data  an appropriate binding model is needed. The model shown to the right is the simplest one possible for an antibody with two binding sites, antibody-antigen binding modeland simply assumes that both sites have the same binding affinity and bind independently of one another (no cooperativity and no steric blocking of one site by antigen bound to the other).

In fitting these data one is essentially asking: Is there a single value of the dissociation constant, K1, that can explain all 8 experiments? The solid lines in the graph above represent the best fit of this model, with K1 = 48 nanomolar, and the fact that the lines follow the data points quite well shows that this is a good fit. Importantly, this good fit also implies that both binding sites on the antibody are active, and active simultaneously. This data analysis was done using custom software available only at Alliance Protein Laboratories.

The value of K1 is actually quite well determined, with statistical analysis indicating we can be 95% confident the true value is between 43 and 52 nM (a 5% standard error, or only 60 cal/mol in terms of binding energy!) While this statistical analysis probably overestimates the true precision at least several-fold, nonetheless it is clear this approach can give very precise binding affinities.

Importantly, this approach could be used to quantitatively compare different antibodies, different lots of the same antibody, loss of activity of aged samples, etc.

See also our AUC services page

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