of a macromolecule. A uniform solution of the sample is placed into the centrifuge cell, which is spun at
high speed. This causes sedimentation of the macromolecule towards the bottom of the cell. This means that
the macromolecule is depleted at the top of the cell (i.e.near the meniscus) and there is a sharp boundary, in
terms of solute concentration, between the depleted region and the uniform concentration of the sedimenting
molecule. A series of scans, where the sample concentration is measured as a function of radial distance, is
taken at discrete time intervals and these measurements allow the rate of movement and broadening of the
boundary to be monitored over time. From these data, the sedimentation coefficient (s) can be determined
and this is directly proportional to the mass (m) of the solute and inversely proportional to the frictional
coefficient (f), which is in effect a measure of size. These relationships are summarised in the Svedberg
Equation (11.5).
(11.5)where vis the velocity of the molecule, ^2 r the strength of the centrifugal field ( 2 .rpm/60 and r is the
radial distance from the centre of rotation), solvthe density of the solvent, NAvogadro’s number, Dthe
diffusional coefficient, R the gas constant and Tthe temperature.
Sedimentation equilibrium is a thermodynamic technique that is sensitive to the mass but not to the
shape of the molecular species. The principal difference between sedimentation velocity and sedimentation
equilibrium is that in the latter the initially uniform sample is spun at lower angular velocities than those
employed in sedimentation velocity experiments. At the slower speeds used here, the macromolecule
again starts to sediment towards the bottom of the cell and thus the concentration towards the bottom
begins to increase. However, diffusion processes begin to oppose sedimentation, and after a suitable period of
time the two opposing forces reach equilibrium. If several different species with different molecular weights
exist, for example DNA that is free and bound to a ligand, or different association states of multi-subunit
proteins, then each of the species will be distributed over the solution until it is at equilibrium. Higher
molecular weight species will be nearer the bottom of the cell, whilst lower molecular weight species will
be present at the top of the cell.
Sedimentation equilibrium is particularly useful for evaluation of the equilibrium association constant
for reversible interactions such as ligand binding or protein self-association. The technique is sensitive to
Kobsvalues in the range 10–100M^1 but can also be used to measure affinities up to 10^7 M^1. The detailed
mathematical theory that underlies both sedimentation velocity and equilibrium can be very complex, but
there are several useful data analysis software packages that allow a non-expert to analyse and extract useful
information.
Another type of ultracentrifugation is useful for examination of viscosity changes through use of sucrose
density gradients. This method is sometimes used for studying various RNA species where separation
depends largely on the size of the RNA molecule or for separating different classes of ribozymes. All these
nucleic acid species have a higher buoyant density than the sucrose gradient and hence equilibrium is
never reached. Thus separation depends on the different rates of migration of molecules through the
sucrose gradient.
11.4.2 Light Scattering
Light scattering is another useful technique for determination of the molecular weight and size of biological
macromolecules. Light scattering occurs when polarisable particles are exposed to an oscillating electric
field present in a light beam. The varying field induces oscillating dipoles in the particles, which radiate
light in all directions. The amount of light scattered is directly proportional to the product of the average
sv
rmv
ffRT
ND
2() (^1) solv
Physical and Structural Techniques Applied to Nucleic Acids 441