Ultracentrifugation: The derivation and use of the Svedberg Equation

What happens to a particle (macromolecule) in a centrifugal field?

Consider a particle m in a centrifuge tube filled with a liquid.

The particle (m) is acted on by three forces:

FC: the centrifugal force

FB: the buoyant force

Ff: the frictional force between the particle and the liquid

We can derive an equation that describes the motion of this particle as follows:

You remember that the force on the particle is given by the mass times the acceleration:

where m is the mass of the particle and a is the acceleration. If the particle is moving at a constant velocity (v), then the acceleration is zero and the net force is given by:

Each of these forces can be described as follows:

Substituting these in the equation for the net force, we get:

Now the mass of the displaced solvent can be written in terms of the density of the solvent and the partial specific volume of the particle:

Substituting this in our developing equation, we get:

This equation can be rearranged to give:

Now we collect motion and distance terms on the left and particle and solution terms on the right:

If we multiply the top and bottom of the equation by Avagadro's number we get:

This is the Svedberg equation and is used to describe the motion of the particle in terms of molecular weight (a size term) and frictional coefficient (a shape term). The equation also relates the motion to the solvent density.

Consequences of the Equation

Particles can be separated by size and shape criteria:

Particles can be separated by density:

The Svedberg coefficients are not additive. That is, 40S plus 60S does not equal 100S. This is the case for the ribosomal subunits, where the combination of a 40S small subunit and a 60S large subunit produces an 80S complete ribosome.

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