There are two stages of separation with centrifuges. The first stage takes advantage of the difference in the terminal velocities of different particles as determined by Stoke's law:
vt = 2R2(ps-p)a/(9µ)where vt is the terminal velocity of the particle, R the radius of the particle, a the centrifugal acceleration of the centrifuge, µ the viscosity of the medium, ps the density of the particle, and p the density of the medium. From the above equation, it is apparent that the terminal velocity is a function of the particle radius and density. Thus, on the average, bigger and heavier particles will travel through the medium faster and settle at the bottom of a centrifuge tube in a shorter time. Because a typical mixture of cell homogenate contains organelles of varying sizes and densities, as well as shapes, they can be separated according to the sedimentation speed. The decrease in the sedimentation time in a centrifuge over gravitational settling is mainly due to the considerable increase in the variable a in Stoke's equation.
In the study of cell organelles, different fractions of the subcellular particles are routinely separated with a centrifuge. It was by this type of isolation technique that mitochondria were discovered to be responsible for the entire tricarboxylic acid cycle and ribosomes accountable for protein biosynthesis.
In a typical separation scheme, an isotonic 0.25-0.35M sucrose solution is mixed with cells. The mixture is placed in a bead homogenizer, an ultrasonic cell disrupter, or a simple kitchen blender and the cell membranes are broken to spill out the cell contents. The resulting mixture of subcellular organelles can be placed in a centrifuge and spun at 1000g for 10 minutes. Intact cells and heavy nuclei are collected at the bottom of the centrifuge tube as a pellet. After the supernatant is further centrifuged at 10,000g for 20 minutes, subcellular particles of intermediate terminal velocities such as mitochondria, lysosomes, and microbodies may be collected. The smaller and lighter particles (ribosomes, endoplasmic reticulum fragments, cell membranes, and microsomes) can be further separated from the supernatant of the preceeding stage by centrifugation at 100,000g for 60 minutes. The final supernatant may be considered to be the soluble portion of the cell cytoplasm. Notice the increasingly longer time and especially the exponentially increasing centrifugation speed required to effect separation. The last speed is achievable in an ultracentrifuge. This mode of separation is commonly called differential centrifugation.
Each fraction obtained through differential centrifugation contains quite a few different types of organelles which have similar sedimentation velocities, i.e. similar values of R2(ps-p). Because this factor is a combination of both the size and the density, the fraction can be further separated based on density alone irrespective of the sizes. This second stage can be accomplished by a process known as density gradient centrifugation.
The density gradient may be established naturally by simply placing sucrose crystals at the bottom of a test tube. The sugar dissolves in the solution and diffuse toward the top. However, the time required to establish a sugar gradient in this manner is unacceptably long, and the process is not well regulated. A more practical method of establishing a density gradient is by placing layer after layer of sucrose solutions of different concentrations, thus, densities, in a test tube, with the heaviest layer at the bottom and the lightest layer at the top. The cell fraction to be separated is placed on top of the layer. A particle will sink if the density of the particle is higher than that of the immediate surrounding solution. It will continue to sink until a position is reached where the density of the surrounding solution is exactly the same as the density of the particle. A centrifuge can be highly helpful to accelerate this process of reaching the quasi-equilibrium point; however, unlike the differential centrifugation technique used during the first stage of cell separation, the length of centrifugation for this second stage does not matter too much, as long as the system is permitted to come to quasi-equilibrium.
Size and density of some typical organelles* ---------------------------------- Organelle diameter Density (µm) (g/cm3) ---------------------------------- Nuclei 5-10 1.4 Mitochondria 1-2 1.1 Ribosomes 0.02 1.6 Lysosomes 1-2 1.1 ---------------------------------- *Carolina Tips, Nov. 1, 1973.In the following steps, organelles are substituted by colored plastic beads to demonstrate separation according to the particle density in a density gradient.