Ultracentrifuges

The rotor of the ultracentrifuge is spun at speeds of up to 60 000 rpm in a vacuum to minimize air drag [75-77]. It may be used, therefore, to measure the size distribution of ver fine particles. McCormick [78], for example, describes its use for determining the size distribution of polystyrene (0.088 d 0.511) pm and Brodnyan [79] uses it for determining emulsion particle size. It has also been used in combination with light scattering for polymer size distribution determination [80]. 

In a round-robin test series Mueller [81] found the ultracentrifuge to be the most satisfactory size analysis method for the sub-pm range a sample containing nine monodisperse components with 10% diameter difference being resolved. 

An analytical ultra-centrifugation technique has been used in combination with a scanning optical absorption system for particle size distribution determination. The system was demonstrated for colloidal plulimim 0.4 to 2) nm and unstabilized zinc (4-9) nrn during particle growth [82], A review of examples of colloid analysis of nanosize particles by ultracentrifugation with a focus on multicomonent mixtures has been published.[83] 

This is claimed to be the first fractionating analytical technique with almost atomic resolution. 

Sedimentation techniques are widely used for partiele size analysis since the determined size distribution relates to unit operations such as classification. The distribution also relates to many end-use properties 

To determine the molecular weight of lactoglobulin from measurements on sedimentation equilibrium in an ultracentrifuge. 

The sedimentation equilibrium of lactoglobulin, dissolved in an aqueous buffer, was studied in an ultracentrifuge at 20.0 °C by K. O. Pedersen (Biochem, J. 1936, 30, 967). By an optical method he measured the concentration gradient. By integrating and kno ing the total quantit of solute he evaluated the concentration c at various distances. r from the axis. At a rotational rate of 182.8 rev/s he obtained the results given in table 1. 

The fundamental equation for the sedimentation equilibrium of a dilute solution in a centrifugal field may be written 

The technique of direct determination of dc/dx is especially powerful when applied to a solute which is not homogenous with respect to molecular weight. 

The sedimentation eoefficient is defined as the sedimentation velocity in a unit force 

For a given polymer-solvent system, the sedimentation eoefficient is dependent on temperature, pressure and polymer concentration. For obtaining thermodynamic data from sedimentation eoefficients, one additionally has to measure the diffusion coefficient. This ean be made with an ultraeentrifuge in special diffusion cells or with dynamic light scattering based on the theory of Pecora. Nearly all diffusion coefficients have been measured by this method sinee it became available in 1970. The determination of sedimen- 

Equation [4.4.52] is strictly valid for monodisperse polymers, i.e., one single component 2. For polydisperse polymers, different averages were obtained for the sedimentation and the diffusion coefficient, which depends on the applied measuring mode and the subsequent calculations. The averages of M2 correspond with averages of D and s and are mixed ones that have to be transformed into the desired common averages - for details please see Refs.  

Sedimentation-diffusion equilibrium in an ultracentrifuge gives also a virial series  

Equation [4.4.53] is again valid for monodisperse polymers only. Polydisperse polymers lead to apparent molar mass averages and to averages of the virial coefficients which have to be transformed into the desired common averages by appropriate calculation meth- 

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Apart from tliese mainstream metliods enabling one to gain a comprehensive and detailed stmctural picture of proteins, which may or may not be in tlieir native state, tliere is a wide variety of otlier metliods capable of yielding detailed infonnation on one particular stmctural aspect, or comprehensive but lower resolution infonnation while keeping tlie protein in its native environment. One of tlie earliest of such metliods, which has recently undergone a notable renaissance, is analytical ultracentrifugation [24], which can yield infonnation on molecular mass and hence subunit composition and their association/dissociation equilibria (via sedimentation equilibrium experiments), and on molecular shape (via sedimentation velocity experiments), albeit only at solution concentrations of at least a few tentlis of a gram per litre. 

Schuster T M and Toedt J M 1996 New revolutions in the evolution of analytical ultracentrifugation Curr. Opinion Ceii. Bioi. 6 650-8... 

Note that this method of standardizing D values makes no allowance for the possibility that a molecule may change size, shape, or solvation with changes in temperature. In the next section we shall survey the behavior of polymeric materials in an ultracentrifuge. We shall see that diffusion coefficients can be... 

Since the radial acceleration functions simply as an amplified gravitational acceleration, the particles settle toward the bottom -that is, toward the circumference of the rotor-if the particle density is greater than that of the supporting medium. A distance r from the axis of rotation, the radial acceleration is given by co r, where co is the angular velocity in radians per second. The midpoint of an ultracentrifuge cell is typically about 6.5 cm from the axis of rotation, so at 10,000, 20,000, and 40,000 rpm, respectively, the accelerations are 7.13 X 10, 2.85 X 10 , and 1.14 X 10 m sec" or 7.27 X 10, 2.91 X 10, and 1.16 X 10 times the acceleration of gravity (g s). 

The ultracentrifuge has been used extensively, especially for the study of biopolymers, and can be used in several different experimental modes to yield information about polymeric solutes. Of the possible procedures, we shall consider only sedimentation velocity and sedimentation equilibrium. We shall discuss these in turn, beginning with an examination of the forces which operate on a particle setting under stationary-state conditions. 

Figure 9.13 Location of sedimentation boundary after various times in an ultracentrifuge (a) c versus r and (b) dc/dr versus r.

We have emphasized biopolymers in this discussion of the ultracentrifuge and in the discussion of diffusion in the preceding sections, because these two complementary experimental approaches have been most widely applied to this type of polymer. Remember that from the combination of the two phenomena, it is possible to evaluate M, f, and the ratio f/fo. From the latter, various possible combinations of ellipticity and solvation can be deduced. Although these methods can also be applied to synthetic polymers to determine M, they are less widely used, because the following complications are more severe with the synthetic polymers ... 

The sedimentation boundary of an enzyme preparation in an aqueous buffer at 20.6 C was measured after various times in an ultracentrifuge at 56,050 rpm. The following results were obtained ... 

Fig. 2. Ultracentrifugal pattern for the water-extractable proteins of defatted soybean meal in pH 7.6, 0.5 ionic strength buffer. Numbers above peaks are approximate sedimentation coefficients in Svedberg units, S. Molecular weight ranges for the fractions are 2S, 8,000—50,000 7S, 100,000—180,000 IIS, 300,000—350,000 and 15S, 600,000—700,000 (9). The 15S fraction is a dimer of the IIS protein (10).

Albumin. Investigation iato the safety of bovine plasma for clinical use was undertaken ia the eady 1940s ia anticipation of wartime need (26). Using modem proteia chemistry methods, including electrophoresis and ultracentrifugation, it was shown that most of the human adverse reactions to blood substitutes were caused by the globulin fraction and that albumin was safe for parenteral use. Human albumin is now used extensively as a plasma expander ia many clinical settings. 

Light scatteting and gel-permeation chromatography (qv) can be used to measure the weight-average mol wt, whereas ultracentrifugation can provide a measure of the -average mol wt. 

Deoxyribonucleic acid (from plasmids). Purified by two buoyant density ultracentrifugations using ethidium bromide-CsCl. The ethidium bromide was extracted with Et20 and the DNA was dialysed against buffered EDTA and lyophilised. [Marmur and Doty J Mol Biol 5 109 1962 Guerry et al. J Bacteriol II6 1064 1973.] See p. 504. 

Lipoproteins (from human plasma). Individual human plasma lipid peaks were removed from plasma by ultracentrifugation, then separated and purified by agarose-column chromatography. Fractions were characterised immunologically, chemically, electrophoretically and by electron microscopy. [Rudel et al. Biochem J 13 89 1974.]... 

Toyopearl HW-75 resin, with pores larger than 1000 A, have been used in place of ultracentrifugation steps for the purification of plasmid DNA. Ultracentrifugation is a time-consuming process and requires expensive chemicals, such as cesium chloride. Toyopearl HW-75 resin provides superior separation performance for plasmid DNA and also provides high yields (54). 

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