Although the use of high rotor speeds is not always necessary, most ultracentrifuges are designed to operate safely at rotor speeds of up to 60,000 or even 100,000 rpm. Despite the use of high speed, the sedimenting forces involved are only small and the technique is extremely gentle, providing a valuable method for the separation of large, labile molecules or particles.
Preparative ultracentrifugation uses rotors with relatively large capacities to separate various components of a mixture while analytical ultracentrifugation involves the measurement of sedimentation velocities in small volumes under carefully controlled conditions.
Because particles sediment in a tube during centrifugation, it may appear that a force is acting radially outwards whereas, in fact, there is no such force. Any particle which is rotating in a circle will always tend to move away at a tangent to the circle and to prevent this a force has to be applied towards the centre of rotation. This is known as the centripetal force and is provided in a centrifuge by the rotor arms and spindle.
Particles suspended in solution, when rotated in a centrifuge tube, are not connected to the axis of rotation and, therefore, tend to move at a tangent to the circle. Their movement, however, relative to the centrifuge tube is radially down the tube and appears to be determined by a force equal and opposite to the centripetal force (Fig. 3.1).
It is convenient, therefore, in ultracentrifugation to assume that this movement in an apparently stationary tube is due to centrifugal force and to compare this force to that due to gravity by quoting the intensity of the centrifugal force with respect to that of gravity. This is known as the Relative Centrifugal Force (RCF) and enables quick and simple comparisons of the forces applied by different centrifuges and different rotors.
The effective centrifugal force may be calculated as:
F = Mω2r
where M is the mass of the particle, co (omega) is the angular velocity in radians per second, and r is the radius of rotation in centimeters.
The effect of centrifugation is, therefore, dependent upon the mass of the particle. The convenience of using the relative centrifugal force is that the value for the mass of the particle is eliminated from the equation, permitting more general comparisons of centrifuge performance:
RCF = fc/fg = Mω2r/Mg = ω2r × g-1
It is more usual to monitor the speed of a centrifuge in terms of revolutions per minute (rpm) rather than in radians per second. Hence,
RCF = (2π r. p. m/60)2 r × g-1
In comparing the relative centrifugal forces developed by different centrifuges it is important to appreciate that the values vary considerably from the top to the bottom of a centrifuge tube. For a particle to sediment it must displace an equal volume of the solvent from beneath it.
This can only be achieved by centrifugation if the mass of the particle is greater than the mass of the solvent displaced. Hence, density as well as mass is an important consideration and explains the phenomenon of low density particles floating rather than sedimenting during centrifugation (Fig. 3.2).
