Susan Cates Department of Biochemistry and Cell Biology, MS-140 Rice University, 6100 S. Main Street Houston, Texas 77005 713-348-5777 (phone) 713-348-5154 (fax)
from spin6.mcb.uconn.edu/
Contents: Introduction Theory Analytical Ultracentrifugation Examination of Sedimentation Velocity Examination of Sedimentation Equilibrium Examination of Sample Purity Determination of Molecular Weight Analysis of Associating Systems Ligand Binding Ultracentrifugation Instruments at Rice University References
The analytical ultracentrifuge was first developed by Svedberg and associates in the 1920s. This tool proved invaluable in the study of macromolecules and provided some of the first evidence that proteins were indeed macromolecule composed of a huge number of atoms linked by covalent bonds. Since its creation, ultracentrifugation has fostered a further understanding of the behavior of macromolecules
back to topA particle suspended in a solvent that is subjected to a gravitational field experiences several forces. We can draw the following diagram describing three forces acting on a solute particle:
The sedimenting, or gravitational force, Fs, is proportional to the mass of the particle and the acceleration. For a particle subjected to a rotation, the acceleration is determined by the distance from the axis of rotation, r, and the square of the angular velocity, w (in radians per second) such that:
where m is the mass of the single particle in grams, M is the molar weight of the solute in g/mole, and N is Avogadro’s number.
The buoyant force, Fb, from Archimedes’ principle, is equal to the weight of the fluid displaced:
where m0 is the mass of fluid displace by the particle:
Here, n is the volume in mL that each gram of solute occupies in the solution and r is the density of the solvent in grams per mL. If the density of the particle is greater than that of the solvent, the particle will sediment or sink. As the particle begins to move along a radial path towards the bottom of the cell, its velocity, u, will increase because of increasing radial resistance. Since the particle is moving through a viscous fluid, it will experience a frictional drag, Ff, which is proportional to the velocity:
where f is the coefficient of friction, which depends on the size and shape of the particle.
Within a very short time (on the order of 10-6s) the forces come into balance. Then we can write the following force balance:
Rearranging:
Collecting the terms that relate to the particle size on one side, and those terms that relate to the experimental conditions on the other, we can write:
We have defined the term u/w2r, the velocity of the particle per unit gravitational acceleration, as the sedimentation coefficient. This coefficient depends on properties of the particle, and in particle, it is proportional to the buoyant effective molecular weight of the particle. Also, it is independent of the operating conditions. Therefore, molecules with different molecular weights, or different shapes and sizes, will, in general, move with different velocities in a given centrifugal field, i.e., they will have different sedimentation coefficients.
An analytical ultracentrifuge spins a rotor at an accurately controlled speed and temperature. The concentration distribution of the sample is determined at known times using absorbance measurements. The concentration, c, is determined for solutes obeying the Beer-Lambert law:
where the absorbance, A, of the sample is measured at a given wavelength, e, knowing the fixed position in the cell, l.
This figure displays a schematic diagram of the Beckman Optima XL-A absorbance system. A high intensity xenon flask lamp allows the use of wavelengths between 190 and 800nm. The lamp is fired briefly as a selected sector passes the detector.
An example of an analytical ultracentrifuge (Beckman Optima XL-A):
Sedimentation velocity cells are cylindrical, and have a double-sector centerpiece (figure is a top-down view of the cylindrical centerpiece). One sector is for loading samples, the other is the reference sector and contains the solvent. The reference sector is filled slightly more than the sample sector so that the reference meniscus does not obscure the sample profile.
For a sedimentation velocity experiment, an initially uniform solution is placed in a cell and a sufficiently high angular velocity is applied to cause rapid sedimentation of solute towards the cell bottom. As a result, there is a depletion of solute near the meniscus, causing a characteristic spectrum as shown in the following figure. A sharp boundary occurs between the depleted region and the sedimenting solute (the plateau).
The velocity of the individual particles in SV experiments cannot be resolved, but the rate of movement of the boundary region can be measured. From this, the sedimentation coefficient (s) can be determined. Remember, s depends directly on the mass of the solute particles and inversely on the frictional coefficient, which is a measure of size of the solute particles.
Sedimentation equilibrium experiments have a lower rotor speed than sedimentation velocity experiments. Solute particles do not pellet at the bottom of the cell, but instead the process of diffusion opposes the process of sedimentation until after a period of time, the two opposing forces reach equilibrium and the apparent concentration profile does not change. At equilibrium, the concentration of the solute increases exponentially towards the cell bottom. Each column displays a different absorbance profile, because the concentrations of sample are varied in each.
There are 6 columns in the sedimentation equilibrium experiment. One row is the sample row, the other is the reference row, containing only solvent (specifically, the sample buffer). As in the sedimentation equilibrium experiment, the reference columns are filled more than the sample columns. In the solvent columns, the concentrations are varied, usually 0.25, 0.5 and 0.8 OD (280), or the same fraction of absorbance at any selected wavelength, where that wavelength will be monitored by the AU.
S
everal scans are taken at a given rotor speed to try to ascertain definitely that equilibrium has been reached (if it has been reached in scan 1, then if you take scan 2 an hour later, they should look the same).
Sample heterogeneity can be examined by both sedimentation equilibrium (SE) and sedimentation velocity (SV) methods.
In SE experiments, each species of a heterogeneous solution will be distributed at sedimentation equilibrium such that higher MW species will be distributed toward the cell bottom and lower MW species will dominate the distribution at the top of the cell.
SV techniques assess sample heterogeneity through detection of sedimentation boundaries. The general rule (although stated in an over-simplified manner) is that a single sedimentation boundary exists in a homogeneous solution, while multiple boundaries indicate heterogeneity.
AU techniques for MW measurement are superior because they work with small sample sizes. The method is applicable to MW ranges from 100 to 1,000,000 (proteins, nucleic acids, carbohydrates, all work with AU methods). AU techniques do not rely on assumptions or calibration; they work on any substance whose absorbance differs from that of the solvent. A final advantage is the fact that experimental design is simple in comparison with some other techniques for MW determination.
from http://www.cores.utah.edu/interaction/
Sedimentation analysis can yield valuable information relating to changes in molecular weight when molecule associate to form more complex structures.
SE experiments can yield:
Absorbance measurement is well suited for the study of ligand binding since the technique can distinguish ligands from acceptors. Ligands and acceptors can be labeled with a chromophore, provided that the modification does not alter binding. When the ligand and acceptor differ greatly in sedimentation coefficient, AU analysis of ligand/acceptor binding interactions is a simple matter.
The Beckman Optima XL-A located in Keck
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Center for Analytical Ultracentrifugation of Macromolecular Assemblies (CAUMA)
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Last modified on December 8, 2003