Ultracentrifugation

In analytical ultracentrifugation (Lebowitz, Lewis, and Schuck 2002 Scott, Harding, and Rowe 2006), the sample suspension is rotated at high speed with simultaneous 

FIGURE 10.3 (a) Examples of high-pressure size-exclusion chromatograms for a variety of 

In a sedimentation velocity experiment, the stationary sedimentation velocity u is measured and the sedimentation coefficient, s, is obtained by 

The molecular weight is related to s through the Svedberg equation (valid at infinite dilution)  

Jacob et (d. (Jl) used 4-step ammonium sulfate fractionation of hog gastric mucosal extracts, followed by ultracentrifugation, to obtain high-potency intrinsic factor-active materials (Table 5). The intrinsic factor-containing fraction precipitated between 39 and 47% ammonium sulfate saturation was active at a 1-mg level. About 90% sedimented with a constant of 1.78-1.82 S. Other heavier components formed only about 

Material Processing method Sedimentation constant ( 20. w) Paper electrophoretic pattern Non- hexos- amine hex- oses Hex- osa mine Fu- cose Sialic acid Intrinsic factor activity 

Precipitate, D Fourth step of the ammonium sulfate precipitation at 47% saturation 1.82 (90%) 4.32(10%) 6 components (4 anodic and 2 cathodic) 4.47 2.55 0.59 0.68 Very high at 1.0 mg level on isotope assay 

Low molecular wt. fraction, a-2 Ultracentrifugation of 4 ammonium sulfate precipitates C-F obtained at 39-69% saturation 0.78 6 components incl. 4 anodic (fast, intermediate, and slow) and 2 cathodic (in traces) 3.20 1.87 0.45 1.23 Questionable or weak at 2.0-4.0mg level on isotope assay 

The size and shape of macromolecules in solution can be studied using two techniques termed equilibrium and velocity ultracentrifugation. These techniques use an ultracentrifuge to rotate solutions of macromolecules and place them under a centrifugal force to study their physical properties. The size and shape of the macromolecules can then be determined from the solution physical properties. The ultracentrifuge is equipped for direct measurement of the solution as it spins at high speed. 

At high speeds greater than 40,000 rpm in the ultracentrifuge, macromolecules settle towards the rotor periphery. Under these conditions the sedimentation coefficient s, is determined from the speed of sedimentation divided by the angular acceleration. The sedimentation coefficient is related to molecular weight using Equation (4.15). 

Using M and s from ultracentrifugation experiments Dt can be calculated and compared to Dt determined from quasi-elastic light scattering. 

Values of M and s determined by analytical ultracentrifugation are given in Table 4.4 for some biological macromolecules. From these values we can get an idea of the shape factor for a given biological macromolecule. 

Measurements of the sedimentation behaviour of polymer molecules in solution can provide a considerable amount of information, e.g. hydrody- 

In a sedimentation equilibrium experiment the cell is rotated at a relatively low speed (typically 5000-10 000 rpm) until an equilibrium is attained whereby the centrifugal force just balances the tendency of the molecules to diffuse back against the concentration gradient developed. Measurements are made of the equilibrium concentration profiles for a series of solutions with different initial polymer concentrations so that the results can be extrapolated to c = 0. A rigorous thermodynamic treatment is possible and enables absolute values oi and to be determined. The principal restriction to the use of sedimentation equilibrium measurements is the long time required to reach equilibrium, since this is at least a few hours and more usually is a few days. 

The sedimentation velocity method involves rotating the solution cell at 

In many instances, average molar masses and their ratios (i.e. polydisper-sity indices) are insufficient to describe the properties of a polymer and more complete information on the molar mass distribution is required. One way of obtaining this information is to separate (i.e. fractionate) the polymer into a number of fractions each of which has a narrow distribution of molar mass. The weight and molar mass of each polymer fraction are determined and enable the molar mass distribution to be constructed in the form of a histogram. However, such procedures are rarely used nowadays because much more rapid and powerful methods of size-exclusion chromatography (Section 3.17) are available for determining molar mass distributions. Nevertheless, fractionation itself is still practised, often for purposes of purification, and will be considered here in some detail because it introduces the important topic of phase-separation behaviour of polymers. 

The simplest procedure for polymer fractionation is to dissolve the polymer at low concentration in a poor solvent and then to bring about stepwise phase separation (i.e. precipitation ) of polymer fractions by either changing the temperature or adding a non-solvent. The highest molar mass species phase separate first and so the fractions are obtained 

An alternative ED method in 96 well plate format has been reported by Kariv et al. (2000). The authors used a disposable equilibrium dialyser with a 10 KDa ultrathin membrane, co-developed with Amika Corp. (Columbia MD USA). The binding of three well-studied drugs, propranolol, paroxetine and losartan with low, medium, high binding properties, respectively were tested to validate the method. The data of free fraction correlated with the published values determined by conventional ED. 

The vertical design of 96 well dialyze block of Banker et al. (2003) allows the robotic system the access to the sample and dialysate site. The dialysis block with partially separated bars is reusable. The validity of the system was tested with ten different standard compounds, in comparison to standard ED, and literature data. 

To equalize the osmotic pressure and therefore to attenuate the volume shift, dextran 2.5 % (w/v) was added to the dialysate (Lima et al. 1983). However, this approach is inconvenient for high throughput. That the test compounds show no affinity to dextran has to be proven in an additional experiment. 

Plum et al. (1999) showed the applicability of a step-wise ED for the plasma binding determination of the two strong adhesive 125I-labeled proteins insulin aspart and insulin detemir. 

Bowers WF, Fulton, Thompson J (1984) Ultrafiltration vs equilibrium dialysis for determination of free fraction. Clin Pharmacokinetic 9(Suppl l) 49-60 Brprs O, Jacobsen S (1985) pH lability in serum during equilibrium dialysis. Br J Clin Pharmacokinetic 20 85-88 Henricsson S (1987) Equilibrium Dialysis in a Stainless Steel Chamber Measurement of the Free Plasma Fraction of Cyclosporin. Pharmacy and Pharmacology Communications 6(10) 447-450 

FIGURE 3.18 Response to selected detectors as a function of retention volume for myoglobin (dissolved in PBS buffer at a pH of 6.9). The three detectors are the RI = refractive index signal, LS = lightscattering signal, and DP = differential pressure transducer (viscosity signal). (Courtesy of Viscotek, Houston, TX. With permission.) 

The rate of sedimentation is defined by the sedimentation constant 5, which is directly proportional to the polymer mass m, solution density p, and specific volume of the polymer V, and inversely proportional to the square of the angular velocity of rotation o), the distance from the center of rotation to the point of observation in the cell r, and the fractional coefficient /, which is inversely related to the diffusion coefficient D extrapolated to infinite dilution. These relationships are shown in the following equations in which (1 — Vp) is called the buoyancy factor since it determines the direction of macromolecular transport in the cell. 

The sedimentation velocity determination is dynamic and can be completed in a short period of time. The sedimentation equilibrium method gives quantitative results, but long periods of time are required for centrifugation at relatively low velocities to establish equilibrium between sedimentation and diffusion. 

Some 30 years ago the analytical ultracentrifuge played an important part in characterising weight-average MWD, size distribution, and density distribution in polymers. This technique was displaced by SEC. However, with improvements in instrumentation, ultracentrifuge methods are to some extent making a comeback. 

Machtle and Klodwig [209] have reported on improvements in instrumentation in the analytical centrifuge technique, including an eight-cell interference optics multiplexer and an eight-cell Schlieren optics multiplexer, both based on the same light source, a modulable laser, and a titanium rotor with a maximum speed of 60,000 rpm. 

Sedimentation methods have also been applied to PS [210], polyglycols [211], and 

Because molar mass is so important for the identification of a molecule and the determination of its structure, we need to discuss sophisticated and accurate methods for its determination. 

In a gravitational field, heavy particles settle toward the foot of a column of solution by the process called sedimentation. The rate of sedimentation depends on the strength of the field and on the masses and shapes of the particles. Spherical molecules (and compact molecules in general) sediment faster than rodlike or extended molecules. For example, DNA helices sediment much faster when they are denatured to a random coil, so sedimentation rates can be used to study 

Case Study 11.1 The structure of DNA from X- ray diffraction studies 423 

Checklist of key concepts 465 Checklist of key equations 466 Discussion questions 467 Exercises 467 

1 (a) An ultracentrifuge head. The sample on one side is balanced by a blank diametrically opposite, (b) Detail of the sample cavity the top surface is the inner surface, and the centrifugal force causes sedimentation toward the outer surface a particle at a radius r experiences a force of magnitude mcem.  

At reasonably low concentrations (to avoid associations) and moderate rotor speeds, sedimentation of macromolecules follows a series of well-defined relations. For nucleic acids, UV optics may be conveniently used to measure the rate of sedimentation with time. At an angular velocity, w, the distances Xi and Xg (in cm) traveled at times h and t2 (in seconds) are related to the observed sedimentation coefficient Sobs. This result may be normalized to correspond to the density of water at 20° as follows  

Since the viscosity of the solute is implicated in these equations, the sedimentation coefficient is not a priori a measurement of molecular weight it is also influenced by shape, flexibility, solvatation, etc., of the solute. Therefore, standards of known molecular weight are generally run with the sample (or in a parallel experiment) to calibrate the measurements. 

In order to avoid many of the technical difficulties of sedimentation in homogeneous media (convection, associations, etc.), a continuous density gradient is often used. After a sedimentation run in a buffered gradient, established before the run in the centrifuge tube, a hole is punched in the bottom of the tube, and the solution collected drop by drop. Monitoring is by absorption, determination of radioactivity and enzyme activity, etc., and, frequently, a marker of known molecular weight is added to the solution. 

As shown later in Section 13.4 of Chapter 13, the drag force on an isolated sphere can be written in terms of the Stokes-Einstein equation as 

On multiplying both sides of Eq. (8.5.3) by Avogadro s number, the molecular weight M of the sphere can be derived as 

instead of a single particle, a large number of particles are dropped into the tube, then, in the absence of particle-particle interactions, the mass flux of spheres at any cross section is given by 

As time proceeds, spheres build up at the bottom of the tube, and the tendency to equalize concentrations causes a diffusive flux of spheres upward in the tube. The magnitude of the flux is given by Pick s law (see Chapter 13) as follows  

These techniques work well provided that the polymer solution is such that the assumptions made in deriving either the Svedbeig equation or Eq. (8.5.9) remain valid. This is possible for biological molecules (such as proteins and nucleic acids) that act like relatively compact and rigid spheres in solution. They 

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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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