One of the most common pieces of equipment used to separate materials into subfractions in a biochemistry lab is the centrifuge. A centrifuge is a device that spins liquid samples at high speeds and thus creates a strong centripetal force causing the denser materials to travel towards the bottom of the centrifuge tube more rapidly than they would under the force of normal gravity.

Types of centrifuges. The major distinguishing features between centrifuge types are speed and capacity. In a typical biochemistry laboratory you will find three different centrifuges (this is true in your biochemistry teaching lab as well). The smallest are the so-called microfuge centrifuges. These are made for spinning 1 to 2 ml plastic centrifuge tubes at speeds up to 12 or 13 thousand rounds per minute. They have very small, light rotors in them (the rotor is the part of the centrifuge that contains the holes for the sample tubes) which speed up and slow down rapidly. These centrifuges are very convenient for low to medium speed centrifugation of small quantities of material.

The next common size centrifuge is the large superspeed centrifuge. These have speeds up to about 20,000 rpm and can take tubes of various sizes, depending on the rotors (the larger the rotor, the slower the maximum speed). Typical tubes hold 25 or 30 mls but bottles as large as several hundred mls can be run with the correct rotor.

Finally, most biochemistry laboratories have access to an ultracentrifuge. Speeds up to 70,000 rpm are available on typical modern versions. Again the size of tube and the maximum speed vary from rotor to rotor, but tube sizes up to about 60 mls are available.

The theory behind centrifugation. The idea here is pretty straight forward and mechanical. If you want the more dense materials to be separated from the less dense materials, you need a force that differentiates between particles of different density. Think about a swimming pool with a rock and a piece of styrofoam. The rock is denser than water and thus it sinks. The styrofoam is less dense than water, and thus it floats. Density is of course mass per unit volume. So, if you have a bag full of rocks and styrofoam and you want to separate one from the other, just dump the mixture into some water under the influence of the earth's gravity. The rocks will displace the water because they have greater mass for a given volume and gravity will pull them through the water. On the other hand, the water will displace the styrofoam because a certain volume of water weighs more than the same volume of styrofoam.

However, there are many things that are much closer in density than rocks and styrofoam and it is much harder to separate them just under the Earth's gravity. In addition, diffusion is always at work as random motion smears out small differences due to density. To overcome this, or sometimes just to make the separation process faster, it would be nice to come up with a way of generating larger mass (density) dependent forces than are available from the Earth's gravity alone. Another way to generate a mass dependent force is to spin something. As you know from physics, a body in motion tends to continue in motion along a straight path unless some force is exerted on it to change its path. Thus in order to force something to go in a circle, we must exert force on it pulling it in towards the center. An equal and opposite force will always result, pushing out from the center. This is cetripital force, and it is just the mass of the object times the acceleration required to keep it from flying outward along a straight line. Thus, things with larger mass (for a given volume) will have a greater force exerted on them and they will move towards the outer edge of the container more quickly than the things with a lower mass per volume.

The acceleration required to keep the object from flying outward along a straight path is given by w2r where the greek letter omega stands for the speed of revolution (see below for units) and r is the distance from the axis of the revolution to the position of the sample. To get a the force felt by the sample, we multiply this by the mass of the sample: F = mw2r, where F is the force and m is the mass. Please notice two things about this equation. It is linearly proportional to the mass of the object, but the force increases with the square of the rotation speed. Thus, going from 1000 rpm to 10,000 rpm increases the forces involved by a factor of 100.

Some practical considerations. So let's say I want to spin two 30 mls tubes of water at 50,000 rpm. What kinds of forces are involved? Well, for comparison, consider the force that the acceleration of gravity exerts on the 30 mls of water when it is sitting on a bench top. The acceleration of gravity is about 10 m/s2 (10 meters per second squared). The mass of 30 mls of water is about 30 g or about 0.03 kg. Thus the force involved at 1 g (1 times the acceleration of gravity) is 0.3 kg m/s2 or 0.3 Newtons. How about at 50,000 rpm? First we need to do some units conversion. 50,000 rpm is 50,000/60 = 830 rounds per second. Further, in order to make the units work out, we must convert rounds per second to radians per second (there are 2p radians in a complete round or circle so multiply by this factor). This gives 5200 radians per second (this is omega in the equation). The force is mw2r so the total force is 66,000 N (assuming that the sample is about 8 cm from the center of rotation). To get the number of times greater this is than gravity along, we divide by 0.3 (see above) and get about 220,000 g's. That means that the water sample spinning at 50,000 rpm is equivalent to a 13,000 lb truck at normal gravity.

If you look inside an ultracentrifuge, you will find that the rotor (the thing that contains the samples) is sitting on a shaft. The shaft is rather small and actually wobbly. There is no way you could suspend a 13,000 lb truck from this shaft. So how does it work? It works because of symmetry. You always must have a sample directly across from the sample of interest that has the same overall mass. Thus, the two masses and the forces on them balance out and the shaft feels no torque. The moral of the story is that you must balance tubes for centrifuge runs. For ultracentrifuge runs, you must balance the tubes very, very carefully. I usually try to get the masses within about 0.03 grams for an ultracentrifuge run. Slower centrifuges you can use an accordingly less stringent balance procedure.

Rotors. There are many types of rotors, but most fall into one of three classes: fixed angle rotors, swinging bucket rotors and vertical rotors. Most of the time you will used a fixed angle rotor. Occasionally a swinging bucket or vertical rotor with be used, but not very often any form (swinging bucket allows the sample to swing out to the horizontal, giving the longest possible path of movement of the particles. The vertical rotors do the opposite -- they are used when a very short overall path of centrifugation is required.

Types of centrifugation applications. There are many ways in which centrifuges are used. More often than not they are used to sediment some material leaving the rest in solution. However, one can also use two other common applications for separating materials: equilibrium density sedimentation and kinetic density sedimentation. In the first case, the material is either layered on top of or mixed into some material that can either be preformed into a density gradient or will become a density gradient when it is spun at high speed. The centrifuge is then run until the material finds its place as a band of particular density within the tube. The kinetic density methods also generally involve long runs that allow the molecule to find a region of the medium with the same density and come to equilibrium. In kinetic density sedimentation, you do not run the gradient to the end. You start with a band of you sample on top of the tube and let it progress through the density gradient for some period of time.