# Centrifugation

Centrifugation is a process which involves the application of the centrifugal force for the sedimentation of heterogeneous mixtures with a centrifuge, and is used in industrial and laboratory settings. This process is used to separate two miscible substances, but also to analyze the hydrodynamic properties of macromolecules.[1] More-dense components of the mixture migrate away from the axis of the centrifuge, while less-dense components of the mixture migrate towards the axis. Chemists and biologists may increase the effective gravitational force on a test tube so as to more rapidly and completely cause the precipitate (pellet) to gather on the bottom of the tube. The remaining solution (supernatant) may be discarded with a pipette.[citation needed]

There is a correlation between the size and density of a particle and the rate that the particle separates from a heterogeneous mixture, when the only force applied is that of gravity. The larger the size and the larger the density of the particles, the faster they separate from the mixture. By applying a larger effective gravitational force to the mixture, like a centrifuge does, the separation of the particles is accelerated. This is ideal in industrial and lab settings because particles that would naturally separate over a long period of time can be separated in much less time.[2]

The rate of centrifugation is specified by the angular velocity usually expressed as revolutions per minute (RPM), or acceleration expressed as g. The conversion factor between RPM and g depends on the radius of the centrifuge rotor. The particles' settling velocity in centrifugation is a function of their size and shape, centrifugal acceleration, the volume fraction of solids present, the density difference between the particle and the liquid, and the viscosity. The most common application is the separation of solid from highly concentrated suspensions, which is used in the treatment of sewage sludges for dewatering where less consistent sediment is produced.[3]

In the chemical and food industries, special centrifuges can process a continuous stream of particle-laden liquid.

Centrifugation is the most common method used for uranium enrichment, relying on the slight mass difference between atoms of U238 and U235 in uranium hexafluoride gas.[citation needed].

## Mathematical formulaEdit

The general formula for calculating the revolutions per minute (RPM) of a centrifuge is

${\displaystyle RPM={\sqrt {g \over r}}}$ ,

where g represents the respective force of the centrifuge and r the radius from the center of the rotor to a point in the sample.[4] However, depending on the centrifuge model used, the respective angle of the rotor and the radius may vary, thus the formula gets modified. For example, the Sorvall #SS-34 rotor has a maximum radius of 10.8 cm, so the formula becomes ${\displaystyle RPM=299{\sqrt {g \over r}}}$ , which can further simplify to ${\displaystyle RPM=91{\sqrt {g}}}$ .[5] the applied centrifugation field is square angular velocity in radians per sec .the radial distance o the particle from the axis;

The most common formula used for calculculating Relative Centrifugal Force (x g) is: RCF (x g) = 1.118 x Radius (mm) x (rpm/1000)²

Many clinical separations have historically been carried out at 3000 rpm. This is a somewhat arbitrary approach as the RCF applied is dependent upon the radius in a linear fashion - so a 10% larger radius means that a 10% higher RCF is applied at the same speed. To discover the RCF that you have been applying at 3000 rpm, the above formula can be simplified to:

[Short cut for 3000 rpm, with only a 0.62% error:] RCF (x g) = 10 x Radius (mm)

## Centrifugation in biological researchEdit

### MicrocentrifugesEdit

Microcentrifuges are used to process small volumes of biological molecules, cells, or nuclei. Microcentrifuge tubes generally hold 0.5 - 2.0 mL of liquid, and are spun at maximum angular speeds of 12,000–13,000 rpm. Microcentrifuges are small enough to fit on a table-top and have rotors that can quickly change speeds. They may or may not have a refrigeration function.

### High-speed centrifugesEdit

High-speed or superspeed centrifuges can handle larger sample volumes, from a few tens of millilitres to several litres. Additionally, larger centrifuges can also reach higher angular velocities (around 30,000 rpm). The rotors may come with different adapters to hold various sizes of test tubes, bottles, or microtiter plates.

### Fractionation processEdit

General method of fractionation: Cell sample is stored in a suspension which is:

1. Buffered - neutral pH, preventing damage to the structure of proteins including enzymes (which could affect ionic bonds)
2. Isotonic (of equal water potential) - this prevents water gain or loss by the organelles
3. Cool - reducing the overall activity of enzyme released later in the procedure
• Cells are homogenised in a blender and filtered to remove debris
• The homogenised sample is placed in an ultracentrifuge and spun in low speed - nuclei settle out, forming a pellet
• The supernatant (suspension containing remaining organelles) is spun at a higher speed - chloroplasts settle out
• The supernatant is spun at a higher speed still - mitochondria and lysosomes settle out
• The supernatant is spun at an even higher speed - ribosomes, membranes settle out

The ribosomes, membranes and Golgi complexes can be separated by another technique called density gradient centrifugation.

### UltracentrifugationsEdit

Ultracentrifugation makes use of high centrifugal force for studying properties of biological particles. Compared to microcentrifuges or high-speed centrifuges, ultracentrifuges can isolate much smaller particles, including ribosomes, proteins, and viruses. Ultracentrifuges can also be used in the study of membrane fractionation. This occurs because ultracentrifuges can reach maximum angular velocities in excess of 70,000 rpm. Additionally, while microcentrifuges and supercentrifuges separate particles in batches (limited volumes of samples must be handled manually in test tubes or bottles), ultracentrifuges can separate molecules in batch or continuous flow systems.

In addition to purification, analytical ultracentrifugation (AUC) can be used for determination of the properties of macromolecules such as shape, mass, composition, and conformation. Samples are centrifuged with a high-density solution such as sucrose, caesium chloride, or iodixanol. The high-density solution may be at a uniform concentration throughout the test tube ("cushion") or a varying concentration ("gradient"). Molecular properties can be modeled through sedimentation velocity analysis or sedimentation equilibrium analysis. During the run, the particle or molecules will migrate through the test tube at different speeds depending on their physical properties and the properties of the solution, and eventually form a pellet at the bottom of the tube, or bands at various heights.

Density gradient centrifugation Is considered one of the more efficient methods of separating suspended particles. Density gradient centrifugation can be used both as a separation technique and as a method of measuring the densities of particles or molecules in a mixture.[6] A tube, after being centrifuged by this method, has particles in order of density based on height. The object or particle of interest will reside in the position within the tube corresponding to its density.[7]

Linderstorm-Lang, in 1937, discovered that density gradient tubes could be used for density measurements. He discovered this when working with potato yellow-dwarf virus.[6]

This method was also used in Meselson and Stahl’s famous experiment in which they proved that DNA replication is semi-conservative by using different isotopes of nitrogen. They used density gradient centrifugation to determine which isotope or isotopes of nitrogen were present in the DNA after cycles of replication.[7]

Nevertheless, some non-ideal sedimentations are still possible when using this method. The first potential issue is the unwanted aggregation of particles, but this can occur in any centrifugation. The second possibility occurs when droplets of solution that contain particles sediment. This is more likely to occur when working with a solution that has a layer of suspension floating on a dense liquid, which in fact have little to no density gradient.[6]

### Differential CentrifugationEdit

Differential Centrifugation is a type of centrifugation in which one selectively spins down components of a mixture by a series of increasing centrifugation forces. This method is commonly used to separate organelles and membranes found in cells. Organelles generally differ from each other in density in size, making the use of differential centrifugation, and centrifugation in general, possible. The organelles can then be identified by testing for indicators that are unique to the specific organelles.[8]

## Other applicationsEdit

• Separating chalk powder from water
• Removing fat from milk to produce skimmed milk
• Separating particles from an air-flow using cyclonic separation
• The clarification and stabilization of wine
• Separation of urine components and blood components in forensic and research laboratories
• Aids in separation of proteins using purification techniques such as salting out, e.g. ammonium sulfate precipitation.[9]

## HistoryEdit

By 1923 Theodor Svedberg and his student H. Rinde had successfully analyzed large-grained sols in terms of their gravitational sedimentation.[10] Sols consist of a substance evenly distributed in another substance, also known as a colloid.[11] However, smaller grained sols, such as those containing gold, could not be analyzed.[10] To investigate this problem Svedberg developed an analytical centrifuge, equipped with a photographic absorption system, which would exert a much greater centrifugal effect.[10] In addition, he developed the theory necessary to measure molecular weight.[11] During this time, Svedberg’s attention shifted from gold to proteins.[10]

By 1900, it had been generally accepted that proteins were composed of amino acids; however, whether proteins were colloids or macromolecules was still under debate.[12] One protein being investigated at the time was hemoglobin. It was determined to have 712 carbon, 1,130 hydrogen, 243 oxygen, two sulfur atoms, and at least one iron atom. This gave hemoglobin a resulting weight of approximately 16,000 dalton (Da) but it was uncertain whether this value was a multiple of one or four (dependent upon the number of iron atoms present).[13]

Through a series of experiments utilizing the sedimentation equilibrium technique, two important observations were made: hemoglobin has a molecular weight of 68,000 Da, suggesting that there are four iron atoms present rather than one, and that no matter where the hemoglobin was isolated from, it had exactly the same molecular weight.[10][11] How something of such a large molecular mass could be consistently found, regardless of where it was sampled from in the body, was unprecedented and favored the idea that proteins are macromolecules rather than colloids.[12] In order to investigate this phenomenon, a centrifuge with even higher speeds was needed, and thus the ultracentrifuge was created to apply the theory of sedimentation-diffusion.[10] The same molecular mass was determined, and the presence of a spreading boundary suggested that it was a single compact particle.[10] Further application of centrifugation showed that under different conditions the large homogeneous particles could be broken down into discrete subunits.[10] The development of centrifugation was a great advance in experimental protein science.

## SourcesEdit

• Harrison, Roger G., Todd, Paul, Rudge, Scott R., Petrides D.P. Bioseparations Science and Engineering. Oxford University Press, 2003.
• Dishon, M., Weiss, G.H., Yphantis, D.A. Numerical Solutions of the Lamm Equation. I. Numerical Procedure. Biopolymers, Vol. 4, 1966. pp. 449–455.
• Cao, W., Demeler B. Modeling Analytical Ultracentrifugation Experiments with an Adaptive Space-Time Finite Element Solution for Multicomponent Reacting Systems. Biophysical Journal, Vol. 95, 2008. pp. 54–65.
• Cole, J.L., Hansen, J.C. Analytical Ultracentrifugation as a Contemporary Biomolecular Research Tool. Methods and Reviews, 1999/2000.
• Howlett, G.J., Minton, A.P., Rivas, G. Analytical Ultracentrifugation for the Study of Protein Association and Assembly. Current Opinion in Chemical Biology, Vol. 10, 2006. pp. 430–436.
• Dam, J., Velikovsky, C.A., Mariuzza R.A., et al. Sedimentation Velocity Analysis of Heterogeneous Protein-Protein Interactions: Lamm Equation Modeling and Sedimentation Coefficient Distributions c(s). Biophysical Journal, Vol. 89, 2005. pp. 619–634.
• Berkowitz, S.A., Philo, J.S. Monitoring the Homogeneity of Adenovirus Preparations (a Gene Therapy Delivery System) Using Analytical Ultracentrifugation. Analytical Biochemistry, Vol. 362, 2007. pp. 16–37.

## ReferencesEdit

1. ^ Garrett, Reginald H.; Grisham, Charles M. (2013). Biochemistry (5th ed.). Belmont, CA: Brooks/Cole, Cengage Learning. p. 111. ISBN 9781133106296.
2. ^ Frei, Mark. "Centrifugation Basics". Sigma-Aldrich. Retrieved 10 May 2016.
3. ^ Article on "Centrifugation" retrieved on 15 October 2013 from http://www.lenntech.com/library/clarification/clarification/centrifugation.htm
4. ^ Ballou, David P.; Benore, Marilee; Ninfa, Alexander J. (2008). Fundamental laboratory approaches for biochemistry and biotechnology (2nd ed.). Hoboken, N.J.: Wiley. p. 43. ISBN 9780470087664.
5. ^ Ballou, David P.; Benore, Marilee; Ninfa, Alexander J. (2008). Fundamental laboratory approaches for biochemistry and biotechnology (2nd ed.). Hoboken, N.J.: Wiley. p. 235. ISBN 9780470087664.
6. ^ a b c Brakke, Myron K. (April 1951). "Density Gradient Centrifugation: A New Separation Technique". J. Am. Che. Soc. 73 (4): 1847–1848. doi:10.1021/ja01148a508.
7. ^ a b Oster, Gerald; Yamamoto, Masahide (June 1963). "Density Gradient Techniques". Chem. Rev. 63 (3): 257–268. doi:10.1021/cr60223a003.
8. ^ Ballou, David P.; Benore, Marilee; Ninfa, Alexander J. (2010). Fundamental Laboratory Approaches for Biochemistry and Biotechnology (seconde ed.). University of Michigan: John Wiley & Sons, Inc. p. 213. ISBN 978-0-470-08766-4.
9. ^ Ballou, David P.; Benore, Marilee; Ninfa, Alexander J. (2008). Fundamental laboratory approaches for biochemistry and biotechnology (2nd ed.). Hoboken, N.J.: Wiley. pp. 238–239. ISBN 9780470087664.
10. Van Holde, K. E. (1998). Analytical ultracentrifugation from 1924 to the present: A remarkable history. Chemtracts – Biochemistry and Molecular Biology. 11:933-943
11. ^ a b c Svedberg, T. (1927). The Ultracentrifuge Nobel Lecture
12. ^ a b Tanford, C., and Reynolds, J. 2001. Nature’s robots: A history of proteins. Oxford University Press. pp. 303-305
13. ^ Simoni, D. S., Hill, R. L., and Vaughan, M. (2002). The structure and function of hemoglobin: Gilbery Smithson Adair and the Adair equations. The Journal of Biological Chemistry. 277(31): e1-e2