Velocities sedimentation

For sedimentation velocity experiments, angular velocities o are chosen to be so high that the diffusion term rD dc/dr) in Equation (9-93) is much smaller than the sedimentation term s jc3r c. A forced migration of 1 mol of molecules with the velocity dr/dt produces a resistance Fs.  

The proportionality constant fs is called the frictional coefficient. Additionally, an effective centrifugal force Fr acts on the molecule of hydrodynamic volume Vh. The force Fr is the resultant of the centrifugal field force V and the buoyancy VhP (o r due to the solvent 

5 values alone are not a measure of the molar mass, since the molar mass also depends on the frictional coefficient fs and the buoyancy term (1 — i 2 pi) (see Table 9-2). Frictional coefficients are determined by the shape and degree of solvation of the particles. 

The frictional coefficient can be eliminated by the following procedure. If frictional coefficients are equal for both sedimentation and diffusion, as is observed experimentally, then the Svedberg equation is obtained from the combination of Equation (9-96) with Equation (7-17)  

Another means of eliminating the frictional coefficient fs comes from viscosity measurements. According to Equation (7-19), the frictional coefficient fo is related to an asymmetry factor fA and the Stokes frictional 

The molecular sedimentation velocity is proportional to the centrifugal field,co r the proportionality coefficient is called the sedimentation coefficient 5  

The term s is defined here as the sedimentation velocity in a unit field  

A sedimentation coefficient of the value 1 x 10 s is called a Sved-berg unit(l S). 

Combination of equations (9-93)-(9-96) gives what is called the Lamm differential ultracentrifuge equation  

Since it is usually included with the Spinco E analytical ultracentrifuge (a commercially available instrument), we will first analyze the graph obtained with the Schlieren system. 

Assuming that the boundary is sharp and no diffusion occurs (which is usually the case for a homogeneous system), we have 

Now we divide the values of rb for the second, third, fourth, and fifth pictures (usually five pictures in a photographic plate taken at certain time intervals, e.g., 16 min) by the value of rb for the first picture to obtain the values 

With all the pertinent values available we can now calculate the sedimentation velocity coefficient directly by using Eq. (11.3)  

The unit of S is seconds or svedbergs (in honor of Theodor Svedberg, who was a pioneer in developing the untracentrifuge). One svedberg equals 1 x 10 s. 

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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. 

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. 

Factors Influencing Centrifugal Sedimentation. The sedimentation velocity of a particle is defined by equations I and 2. Each of the terms therein effects separation. 

The sequence, flocculation — coalescence — separation, is compHcated by the fact that creaming or sedimentation occurs and that this process is determined by the droplet size. The sedimentation velocity is monitored by the oppositely directed forces which form the buoyancy and the viscous drag of the continuous phase on the droplet ... 

For the same case of n = 1200 rpm and r = 0.5, we obtain u,/Ug = 800, whereas for the turbulent regime the ratio was only 28. This example demonstrates that the centrifugal process is more effective in the separation of small particles than of large ones. Note that after the radial velocity u, is determined, it is necessary to check whether the laminar condition. Re < 2, is fulfilled. For the transition regime, 2 < Re < 500, the sedimentation velocity in the gravity field is ... 

Partial etherification of the beech wood MGX with p-carboxybenzyl bromide in aqueous alkali yielded fully water-soluble xylan ethers with DS up to 0.25 without significant depolymerization the Mw determined by sedimentation velocity was 27 000 g/mol [400,401]. By combination of endo- 6-xylanase digestion and various ID- and 2D-NMR techniques, the distribution of the substituents was suggested to be blockwise rather than uniform. The derivatives exhibited remarkable emulsifying and protein foam-stabilizing activi-... 

Polysaccharide Polydispersity and Simple Shape Analysis by Sedimentation Velocity... 

With sedimentation velocity we measure the change in solute distribution across a solution in an ultracentrifuge cell as a function of time. An example of such a change is given in Fig. 2a for potato amylose [29]. 

Fig. 4 Sedimentation velocity g (s) profiles for starch polysaccharides using DCDT+. The profiles correspond to the radial displacement plots of Fig. 2. a Potato amylose, sample concentration 8 mg/ml in 90% in dimethyl sulphoxide. Rotor speed was 50 000 rpm at a temperature of 20 °C. b Wheat starch (containing amylose, left peak and the faster moving amylopectin, right peak), (total) sample concentration 8 mg/ml in 90% dimethyl sulphoxide. Rotor speed was 35 000 rpm at a temperature of 20 °C. From [29]...

One can see the M procedure has a parallel to either g (s) vs. s or c(s) vs. s in sedimentation velocity where the data are transformed from radial displacement space [concentration, c(r) versus r] to sedimentation coefficient space [g s) or c(s) versus s]. Here we are transforming the data from concentration space [concentration relative to the meniscus j(r) versus r] to molecular weight space [M r) versus r]. 

The carbohydrate has sites for ionic interaction (clusters of sialic acid or sulphate residues) and also hydrophobic interaction (clusters of hydrophobic methyl groups offered by fucose residues). Sedimentation velocity has been a valuable tool in the selection of appropriate mucoadhesives and in the characterisation of the complexes [ 138-143]. 

The approach is to first of all obtain mucin to a high degree of purity and to characterise the mucin and potential mucoadhesive. This is done by sedimentation velocity [g (s)j analysis and sedimentation equilibrium (M ) analysis—according to the procedures described above—together with SEC-MALLs [145,146]. 

G(S) and G(X) have been estimated by quantifying the effect on molecular size distributions inferred from sedimentation velocity, gel permeation chromatography, and dynamic light-scattering measurements [58]. 

The ribosomal subunits are defined according to their sedimentation velocity in Svedberg units (40S or 60S). This table illustrates the total mass (MW) of each. The number of unique proteins and their total mass (MW) and the RNA components of each subunit in size (Svedberg units), mass, and number of bases are listed. 

The various physical methods in use at present involve measurements, respectively, of osmotic pressure, light scattering, sedimentation equilibrium, sedimentation velocity in conjunction with diffusion, or solution viscosity. All except the last mentioned are absolute methods. Each requires extrapolation to infinite dilution for rigorous fulfillment of the requirements of theory. These various physical methods depend basically on evaluation of the thermodynamic properties of the solution (i.e., the change in free energy due to the presence of polymer molecules) or of the kinetic behavior (i.e., frictional coefficient or viscosity increment), or of a combination of the two. Polymer solutions usually exhibit deviations from their limiting infinite dilution behavior at remarkably low concentrations. Hence one is obliged not only to conduct the experiments at low concentrations but also to extrapolate to infinite dilution from measurements made at the lowest experimentally feasible concentrations. 

In the present chapter we shall be concerned with quantitative treatment of the swelling action of the solvent on the polymer molecule in infinitely dilute solution, and in particular with the factor a by which the linear dimensions of the molecule are altered as a consequence thereof. The frictional characteristics of polymer molecules in dilute solution, as manifested in solution viscosities, sedimentation velocities, and diffusion rates, depend directly on the size of the molecular domain. Hence these properties are intimately related to the molecular configuration, including the factor a. It is for this reason that treatment of intramolecular thermodynamic interaction has been reserved for the present chapter, where it may be presented in conjunction with the discussion of intrinsic viscosity and related subjects. 

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