# Appendix F: Centrifugation

The single most important advance in the use of centrifugal force to separate biologically important substances. was the coupling of mechanics, optics and mathematics by T. Svedberg and J.W. Williams in the 1920's. They initiated the mathematics and advanced the instrumentation. 1 to a point where it was possible to prove that proteins were large molecules that could be weighed in a centrifuge. 2. In honor of that work, the value for a molecule's (or organelle's) sedimentation velocity in a centrifugal field is known as its Svedberg constant or S value for short.

The instrumentation has progressed quite far since the early work of Svedberg and Williams. Today, any technique employing the quantitative application of centrifugal force is known as ultracentrifugation. The design of the basic instruments, the rotors and the optical systems for measurement are too extensive to cover in this volume. For our purposes, we will concentrate on two types of rotor, and a few selected parameters to be measured.

### ROTORS

Table F.1. Rotor Characteristics

Rotors for a centrifuge are either fixed angles , swinging buckets , continuous flow, or zonal, depending upon whether the sample is held at a given angle to the rotation plane, is allowed to swing out on a pivot and into the plane of rotation, designed with inlet and outlet ports for separation of large volumes, or a combination of these. Figure F.1 demonstrates the characteristics of each of these.

Fixed angles generally work faster; substances precipitate faster in a given rotational environment, or they have an increased relative centrifugal force for a given rotor speed and radius. They also have few (or no) moving parts on the rotor itself and thus have virtually no major mechanical failures, other than potential metal stress, which all rotors undergo. These rotors are the work-horse elements of a cell laboratory, and the most common is a rotor holding 8 centrifuge tubes at an angle of 34 ° C from the vertical (such as the Sorvall SS-34 rotor or the Beckman JA-20). Figure F.1 presents a cross- sectional diagram of the Sorvall SS-34.

Swinging bucket rotors (also known as horizontal rotors) have the advantage that there is usually a clean meniscus of minimum area. In a fixed angle rotor, the materials are forced against the side of the centrifuge tube, and then slide down the wall of the tube. This action is the primary reason for their apparent faster separation, but also leads to abrasion of the particles along the wall of the centrifuge tube. For a swinging bucket, the materials must travel down the entire length of the centrifuge tube and always through the media within the tube. Since the media is usually a viscous substance, the swinging bucket appears to have a lower relative centrifugal force, that is it takes longer to precipitate anything contained within. If, however, the point of centrifugation is to separate molecules or organelles on the basis of their movements through a viscous field, then the swinging bucket is the rotor of choice. Moreover, if there is a danger or scraping off an outer shell of a particle (such as the outer membrane of a chloroplast), then the swinging bucket is the rotor of choice. Most common clinical centrifuges 1 have swinging buckets. Since the buckets are easy to interchange, this type of rotor is extremely versatile. Its major drawback is the number of moving parts which are prone to failure with extended use.

Nearly all cell biology laboratories will have several examples of fixed angle and horizontal rotors. While the sample volumes of these rotors can be significant, they are limiting. To overcome this limitation, a continuous flow centrifuge can be used. Limnologists often employ such a device to separate plankton from gallons of lake water. Cell biologists employ zonal rotors for the large scale separation of particles on density gradients. Zonal rotors can contain up to 2 liters of solution and can work with tissue samples measured in ounces (or even pounds). The rotors are brought up to about 3000 RPM while empty, and the density media and tissues are added through specialized ports. This type of rotor has a distinct preparative advantage over the gradient capacity of more typical rotors.

### ROTOR TUBES

In using either a fixed angle or swinging bucket rotor, it is necessary to contain the sample in some type of holder. Continuous and zonal rotors are designed to be used without external tubes.

For biological work, the tubes are divided into functional groups, made of regular glass, Corex glass, nitrocellulose, or polyallomer. Regular glass centrifuge tubes can be used at speeds below 3,000 RPM, that is in a standard clinical centrifuge. Above this speed, the xg forces will shatter the glass.

A special high speed glass with the tradename of Corex (Corning Glass Works) has been developed to handle speeds up to 15-18,000 RPM. These tubes can be used in most routine cell organelle preparations, if, and only if, the proper adapters are also used within the centrifuge rotors. These tubes are relatively expensive (about \$3.50 each) and should never be used for any purpose other than the centrifuge. Any tubes with scratches or chips should be disposed of immediately. These high- speed glass tubes will shatter above 18,000 RPM.

For work in the higher speed ranges, centrifuge tubes are made of plastic or nitrocellulose. Preparative centrifuge tubes are made of polypropylene (sometimes polyethylene) and can withstand speeds up to 20,000 RPM. These tubes should be carefully examined for stress fractures before use. A tube with a fracture will hold fluids before centrifugation, but the cracks will open under centrifugal force.

Nitrocellulose are inexpensive and used for most ultracentrifugation. They are meant to be used only once and then discarded. Repeated use increases the chance of tube collapse due to internal molecular stress within the tube walls. There is no way to pre-determine this, so it is best to always use a new tube for ultracentrifugation. Nitrocellulose also becomes less flexible with age, and the purchase date for all tubes should be noted. Tubes older than 1 year should be discarded. A centrifuge tube is inexpensive when compared to the loss of time and materials for a typical ultracentrifuge run.

Polyallomer tubes are re-usable, more expensive, and slippery. Molecules will slide down the walls of these tubes more easily, and thus are the tubes of choice for precipitation centrifugations. They are also more chemically inert.

### RELATIVE CENTRIFUGAL FORCE

Figure F.2. Nomogram for R.C.F.

Modern day ultracentrifuges can generate forces in excess of 300,000 times that of gravity, forces sufficient to overcome the very cohesion of most molecules (including the metal of the rotor). The force is usually given as some value times that of gravity.

The centrifugal force is dependent upon the radius of the rotation of the rotor, the speed at which it rotates, and the design of the rotor itself (fixed angle, vs swinging bucket). Rotor speed and design can be held constant, but the radius will vary from the top of a centrifuge tube to the bottom. If a measurement for the radius is taken as the mid-point, or as an average radius, and all forces are mathematically related to gravity, then one obtains a relative centrifugal force, labeled as xg. Centrifugation procedures are given as xg measures, since RPM and other parameters will vary with the particular instrument and rotor used. Relative Centrifugal Force is a constant that is independent of the apparatus used.

Figure F.2 presents a Nomogram for calculation of R.C.F. for a given radius and RPM. A simple formula for calculating this value is:

RCF = 1.12r (RPM/1000)
where r = radius in millimeters
RPM = revolutions per minute

The difficulty with using the formula is establishing the value for r. Typically, there are three r values given (by the manufacturer) for a rotor: the maximum, minimum and average r. These correspond to the distances from the center of rotation to the bottom, top and middle of the sample tube.

If the density and viscosity of the medium are known, as well as the density of a given particle, then the time needed to completely sediement a particle can be determined by the formula:

T = ((D-L)/(D+L))*(N/(d(g-p)S))
where T = time in minutes
D = radial distance in cm for r
L = radial distance to meniscus
N = viscosity of the fluid medium
g = density of the fluid medium
p = density of the particle to sediment
d = diameter of the particle in cms.
S = rotational velocity in RPM

### ROTOR COMPARISONS

When separating a particle, it is convenient to be able to compare one rotor's design characteristics with those of a differing rotor. A procedure may be given as centrifuging for 20 minutes at 15,000 RPM in a Sorvall SS34 rotor. The problem then becomes one of how do you equate that to a Beckman JA-20 rotor?

Working with the maximum RCF for each rotor, the conversion can be made with the following equation:

t = (t x RCF) / RCF
where t = run time needed for the Beckman rotor t = run time specified in the procedure
RCF = RCF of JA-20 rotor at maximum speed
RCF = RCF specified in the procedure
(calculated if procedure in RPM)

This equation can be altered somewhat to be even more useful. The efficiency of rotors can be compared for any given task. Each rotor is given a value for k (the clearing constant, or clearing factor), which is an estimate of the time (in hours) required to pellet a particle of known sedimentation coefficient at the maximum speed of the rotor. 4 The lower the value of k, the shorter the time required to sediment a given particle. The relationship is given by

t = k / s ¸
k = clearing factor expressed in hour-Svedbergs
s ¸ = Sedimentation Coefficient in water at 20 ° C
expressed in Svedbergs

It is possible to compute k, but it is easiest to use the manufacturers values, which can be looked up in tables such as those in Table F.1.

k =(253,300)[ln(r/r)]/(Rotor angular velocity/1000)

Using tabulated k values, however, the comparison of rotors is even easier, as the equation above becomes

t = kt / k
where the t and k values are the time and k factor for each rotor.

By substituting this equation, you can also determine the time of centrifugation for any change in rotor speed. 5

For a Sorvall SS-34, for example, at 20,000 RPM (k=402), the time required to sediment a particle of100 S, in water at 20 ° C is calculated by:

t = 402/100or 4.02 hours (4 hrs, 1 min)

Table F.2 presents the k values for the Sorvall SS-34 rotor and for the Sorvall GSA rotor. Since these two rotors will be used throughout the remainder of the course, reference should be made to this table in any future centrifugation work, when another rotor is substituted.

### ROTOR SAFETY

There are a number of safety precautions that must be adhered to when using any centrifuge and rotor.

Rotor Failure:

All rotors are subject to stress and with time will undergo metal fatigue. This is a given, and consequently, a detailed history of the rotor use should be kept. This is usually not done with clinical centrifuges, but is an absolute for an ultracentrifuge rotor.

EVERY USE OF AN ULTRACENTRIFUGE ROTOR MUST BE RECORDED IN THE CENTRIFUGE LOG. ABSOSLUTELY NO EXCEPTIONS!

After a period of use, each rotor will in turn be derated , that is its maximum RPM will be lowered. The Beckman rotors may contain optical speed control rings at their base - be sure they are present, and clean before use. These devices will strobiscopically monitor the maximum speed that a rotor can be used at. They are replaced as the rotor is derated.

By far the most common cause of rotor failure is corrosion stress. Salts, highly alkaline detergents and of course corrosive acids and alkali's will cause decomposition of the coatings on aluminum rotors, which in turn will concentrate stress and eventually result in cracks and total rotor failure. Titanium rotors are more corrosion resistant, but more expensive. Ultracentrifuge rotors are expensive (in excess of \$6,000 each on average) and can be potentially hazardous. At the forces generated in an ultracentrifuge, a rotor failure is the equivalent of a small bomb.

### THEREFORE THE FOLLOWING RULES MUST BE OBSERVED.

1. Before running a centrifuge, check the classification decal on the centrifuge to ensure that the rotor is safe to use in the centrifuge at hand.

2. Never use an alkali detergent on a rotor (most are highly alkaline - be sure to check before use).

3. Always clean and completely dry the rotor after every use. Any spilled materials, especially salts and corrosive solvents must be removed immediately with running water. Fixed angle rotors are stored upside down, to drain after thorough cleaning and rinsing. Swinging buckets have only the buckets cleaned and dried, and stored inverted and with the caps removed. NEVER immerse the rotor portion of a swinging bucket rotor. Inevitably the linkage pins will rust, as it is virtually impossible to remove all fluids from them.

4. Be especially careful not to scratch the surface of a rotor or bucket. Use plastic brushes only. Normal wire brushes will scratch the anodized surface of aluminum rotors which will increase the likelihood of corrosion. The anodized layer is extremely thin and is the main defense against corrosion of an aluminum rotor.

5. Always use the proper centrifuge tube. Glass tubes are used in clinical centrifuges only. High Speed Corex tubes can be used up to 15,000 RPM (in SS34 rotor) IF there are no scratches or imperfections in the glass, and if the proper rubber or plastic adapter is employed. All ultracentrifugation use employs nitrocellulose or polyallomer tubes. Nitrocellulose ages and will collapse in a strong centrifugal field if old.

6. Always fill the centrifuge tubes to the proper level. (usually full to within 1/2 inch of the top). The tubes are thin walled and will collapse if improperly filled.

7. Always balance the rotor properly. Use a precision scale for most work. Always balance the tube with a medium that is identical to that being centrifuged, i.e. do not balance an alcohol solution with water, or a dense sucrose solution with water only -- the distribution of the densities will be incorrect. For swinging buckets, be sure the buckets are weighed with their caps in place, that the seals are intact and that the caps are secure. Be careful in the placement of tubes within a rotor to ensure proper balance - check the manufacturers guides for complex rotors that hold multiple tubes.

8. Ensure that the rotor is properly seated within the centrifuge. For swinging buckets, ensure that they are hanging properly - Double or Triple check! For preparative rotors, be sure the rotor cover is in place and properly screwed down, where appropriate. NEVER use a rotor without its lid, when one is supplied - the screw actually holds the rotor to the motor shaft.

9. Check that the centrifuge chamber is clean, defrosted and that all membranes or measuring devices are intact and functional (Beckman speed and temperature controls) and that the lid is securely closed.

10. Adjust acceleration rates, deceleration rates, temperature and RPM controls as appropriate. Set brake on or off as appropriate and check vacuum level where appropriate.

11. Start the centrifuge and set the timer. Do not attempt to open the centrifuge until the rotor has come to a complete stop.

12. Before opening the centrifuge, record the appropriate information in the centrifuge log.

Note: If properly balanced and used, the rotor should accelerate smoothly and with a constant change in the pitch of the motor sound. Any vibrations, or unusual sounds should cause the cessation of operation IMMEDIATELY by the operator. NEVER leave the centrifuge until you are certain that it has reached its operating speed and is functioning properly. All rotors go through a minor vibration phase when they first start. There will be a minor flutter when the rotor reaches this vibration point - do not confuse this with a serious vibration caused by imbalance. If in doubt, halt the centrifuge and get assistance.