# Differential centrifugation

Differential centrifugation

Differential centrifugation is a common procedure in microbiology and cytology used to separate certain organelles from whole cells for further analysis of specific parts of cells. In the process, a tissue sample is first homogenised to break the cell membranes and mix up the cell contents. The homogenate is then subjected to repeated centrifugations, each time removing the pellet and increasing the centrifugal force. Finally, purification may be done through equilibrium sedimentation, and the desired layer is extracted for further analysis.

Separation is based on size and density, with larger and denser particles pelleting at lower centrifugal forces. As an example, unbroken whole cells will pellet at low speeds and short intervals such as 1,000g for 5 minutes. Smaller cell fragments and organelles remain in the supernatant and require more force and greater times to pellet. In general, one can enrich for the following cell components, in the separating order in actual application:

• Whole cells and nuclei;
• Mitochondria, lysosomes and peroxisomes;
• Microsomes (vesicles of disrupted endoplasmic reticulum); and
• Ribosomes and cytosol.

## Theory

High g-force makes sedimentation of small particles much faster than Brownian diffusion, even for very small particles. When a centrifuge is used, Stokes' law must be modified to account for the variation in g-force with distance from the center of rotation.

$D = \sqrt{ \frac{18 \eta \, ln(R_f/R_i)}{( \rho_p - \rho_f) \omega^2 t} }$

where

• D is the particle diameter (cm)
• η is the fluid viscosity (poise)
• Rf is the final radius of rotation (cm)
• Ri is the initial radius of rotation (cm)
• ρp is particle density (g/ml)
• ρf is the fluid density (g/ml)
• ω is the rotational velocity (radians/s)
• t is the time required to sediment from Ri to Rf (s)

## Sample preparation

Before differential centrifugation can be carried out to separate different portions of a cell from one another, the tissue sample must first be homogenised. In this process, a blender, usually a piece of porous porcelain of the same shape and dimension as the container, is used. The container is, in most cases, a glass boiling tube.

The tissue sample is first crushed and a buffer solution is added to it, forming a liquid suspension of crushed tissue sample. The buffer solution is a dense, inert, aqueous solution which is designed to suspend the sample in a liquid medium without damaging it through chemical reactions or osmosis. In most cases, the solution used is sucrose solution; in certain cases brine will be used. Then, the blender, connected to a high-speed rotor, is inserted into the container holding the sample, pressing the crushed sample against the wall of the container.

With the rotator turned on, the tissue sample is ground by the porcelain pores and the container wall into tiny fragments. This grinding process will break the cell membranes of the sample's cells, leaving individual organelles suspended in the solution. This process is called homogenization. A portion of cells will remain intact after grinding and some organelles will be damaged, and these will be catered for in the later stages of centrifugation.

## Ultracentrifugation

The homogenised sample is now ready for centrifugation in an ultracentrifuge. An ultracentrifuge consists of a refrigerated, low-pressure chamber containing a rotor which is driven by an electrical motor capable of high speed rotation. Samples are placed in tubes within or attached to the rotor. Rotational speed may reach up to 100,000 rpm for floor model, 150,000 rpm for bench-top model (Beckman Optima Max-XP or Sorvall MTX150), creating centrifugal speed forces of 800,000g to 1,000,000g. This force causes sedimentation of macromolecules, and can even cause non-uniform distributions of small molecules.

Since different fragments of a cell have different sizes and densities, each fragment will settle into a pellet with different minimum centrifugal forces. Thus, separation of the sample into different layers can be done by first centrifuging the original homogenate under weak forces, removing the pellet, then exposing the subsequent supernatants to sequentially greater centrifugal fields. Each time a portion of different density is sedimented to the bottom of the container and extracted, and repeated application produces a rank of layers which includes different parts of the original sample. Additional steps can be taken to further refine each of the obtained pellets.

Sedimentation depends on mass, shape, and partial specific volume of a macromolecule, as well as solvent density, rotor size and rate of rotation. The sedimentation velocity can be monitored during the experiment to calculate molecular weight. Values of sedimentation coefficient (S) can be calculated. Large values of S (faster sedimentation rate) correspond to larger molecular weight. Dense particle sediments more rapidly. Elongated proteins have larger frictional coefficients, and sediment more slowly to ensure accuracy.

## Techniques

Equilibrium gradient centrifugation, also known as isopycnic density gradient centrifugation, is a type of centrifugation procedure widely used in biochemistry to separate molecules based on their isopycnic point (their buoyant density). It is achieved by spinning biological (or other) preparations at high g-force over long periods of time, in buffers or solutions containing a varying amount of a viscous molecule (e.g. 0.8 M/1.2 M sucrose step-gradient used in postsynaptic density isolation or a 20–50% linear sucrose gradient used in the purification of clathrin coated vesicles (CCVs).

### Equilibrium (isopycnic) sedimentation

Equilibrium sedimentation uses a gradient of a solution such as cesium chloride or sucrose to separate particles based on their individual densities (mass/volume). It is used as a purifying process for differential centrifugation. A solution is prepared with the densest portion of the gradient at the bottom. Particles to be separated are then added to the gradient and centrifuged. Each particle proceeds (either up or down) until it reaches an environment of comparable density. Such a density gradient may be continuous or prepared in a stepped manner. For instance, when using sucrose to prepare density gradients, one can carefully float a solution of 40% sucrose onto a layer of 45% sucrose and add further less dense layers above. The homogenate, prepared in a dilute buffer and centrifuged briefly to remove tissue and unbroken cells, is then layered on top. After centrifugation typically for an hour at about 100,000 x g, one can observe disks of cellular components residing at the change in density from one layer to the next. By carefully adjusting the layer densities to match the cell type, one can enrich for specific cellular components. Caesium chloride allows for greater precision in separating particles of similar density. In fact, with a caesium chloride gradient, DNA particles that have incorporated heavy isotopes (13C or 15N for example) can be separated from DNA particles without heavy isotopes.

Isopycnic centrifugation, also known as density gradient centrifugation or equilibrium sedimentation is a technique used to separate molecules on the basis of buoyant density. (The word "isopycnic" means "equal density".) Typically, a "self-generating" density gradient is established via equilibrium sedimentation, and then analyte molecules concentrate as bands where the molecule density matches that of the surrounding solution. To illustrate the process, consider the fractionation of nucleic acids such as DNA. To begin the analysis, a mixture of caesium chloride and DNA is placed in a centrifuge for several hours at high speed to generate a force of about 10^5 x g (earth's gravity). Caesium chloride is used because at a concentration of 1.6 to 1.8 g/mL it is similar to the density of DNA. After some time a gradient of the caesium ions is formed, caused by two opposing forces: diffusion and centrifugal force. The sedimenting particles (caesium ions) will sediment away from the rotor, and become more concentrated near the bottom of the tube. The diffusive force arises due to the concentration gradient of solvated caesium chloride and is always directed towards the center of the rotor. The balance between these two forces generates a stable density gradient in the caesium chloride solution, which is more dense near the bottom of the tube, and less dense near the top.

The DNA molecules will then be separated based on the relative proportions of AT (adenine and thymine base pairs) to GC (guanine and cytosine base pairs). An AT base pair has a lower molecular weight than a GC base pair and therefore, for two DNA molecules of equal length, the one with the greater proportion of AT base pairs will have a lower density, all other factors being equal. Different types of nucleic acids will also be separated into bands, e.g. RNA is denser than supercoiled plasmid DNA, which is denser than linear chromosomal DNA.

Sucrose gradient centrifugation is a type of centrifugation often used to purify enveloped viruses (with densities 1.1-1.2 g/cm³), ribosomes, membranes and so on. This method is also used to purify exosomes.[1] There are two methods - equilibrium centrifugation and non-equilibrium centrifugation.

Typically in equilibrium centrifugation, a sucrose density gradient is created by gently overlaying lower concentrations of sucrose on higher concentrations in a centrifuge tube. For example, a sucrose gradient may consist of layers extending from 70% sucrose to 20% sucrose in 10% increments (though this is highly variable depending on sample to be purified).

Alternatively, devices known as gradient mixers or gradient makers can be used to form a gradient. These devices consist of two chambers, containing solutions of differing concentrations, which are gradually mixed to create the gradient. These devices can be used to create linear, concave, convex and exponential gradients.

The sample containing the particles of interest is placed on top of the gradient and centrifuged at forces in excess of 150,000 x g. The particles travel through the gradient until they reach the point in the gradient at which their density matches that of the surrounding sucrose. This fraction can then be removed and analyzed. After it becomes known between which two layers the required fraction finally settles, a simplified setup with just these two layers may be used.

A similar technique is sucrose cushion centrifugation, in which a particle mixture is pelleted through a 20% sucrose layer, coming to rest at the interface with a 70% solution. This allows concentration of particles from a sample. Unlike standard centrifugation, which in effect crushes the particles against the bottom of the centrifuge tube, the sucrose cushion method causes no mechanical stress and allows the collection of morphologically intact particles[citation needed].

Non-equilibrium centrifugation is very similar to the equilibrium form, but the experiment is only run until a particular point. (These gradients can be called "velocity gradients"). Although particles with more density/less drag travel farther from the top surface, the run is ended before equilibrium is reached. The desired particle will be at a (hopefully known) set distance from the surface, and that band of the gradient is collected (sometimes called a "fraction").

Collection, once the run is ended, can be done by several methods. Perhaps the easiest way is for the sucrose solution to be eluted (drained)by puncturing the bottom of the tube and only the part with the desired protein or material is kept. It is also possible to suction the sucrose (gently, so as not to mix the layering formed during the centrifugation), dividing the suctioned material into successive "fractions". These can then be assayed by any of a number of means, to determine the distribution of the desired material, which allows you to choose the fractions containing this molecule/material.