Sedimentation-equilibrium method

The purple protein is reddish in solutions and purple in the ammonium sulfate precipitate. The molecular weight is 39,000 by the sedimentation equilibrium method. The purple protein is brightly red-fluorescent, but the fluorescence characteristics cannot be related to the luminescence of Latia (Fig. 6.1.5 Shimomura and Johnson, 1968c). 

It is essential that the solution be sufficiently dilute to behave ideally, a condition which is difficult to meet in practice. Ordinarily the dilutions required are beyond those at which the concentration gradient measurement by the refractive index method may be applied with accuracy. Corrections for nonideality are particularly difficult to introduce in a satisfactory manner owing to the fact that nonideality terms depend on the molecular weight distribution, and the molecular weight distribution (as well as the concentration) varies over the length of the cell. Largely as a consequence of this circumstance, the sedimentation equilibrium method has been far less successful in application to random-coil polymers than to the comparatively compact proteins, for which deviations from ideality are much less severe. 

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. 

In the sedimentation equilibrium method, the solution is allowed to come to equilibrium. When this happens, the analysis becomes very similar to that described in the previous section for gravitational fields, with the gravitational work mgdh replaced by mu2rdr, where u is the angular velocity of the centrifuge (in rad sec-1) and r is the distance from the center of the centrifuge. The final result is an equation similar to (12.21)... 

In the sedimentation-equilibrium method a lower centrifugal field is applied and the processes of sedimentation and diffusion are brought to equilibrium [13]. In this case the governing equation contains sedimentation equilibrium concentrations of species at different positions from the axis of rotation, but one does not need to know D. It should be pointed out that sedimentation and diffusion are more complicated when the species are electrically charged. This is because the smaller counterions sediment at a slower rate than do the colloidal-sized species. This creates an electric potential gradient that tends to speed up the counter-ions and to drag the colloidal species. The reverse effect occurs for diffusion. 

Conventional Sedimentation Equilibrium Method) Although separating compounds is the most important use of a preparative ultracentrifuge, the determination of a molecular weight is the most important function of the analytical ultracentrifiige. Several equations are used to determine the molecular weight, but one that is convenient is ... 

The sedimentation equilibrium method does not require an independent measurement of the diffusion coefficient, in contrast to the sedimentation-velocity method. However, the time required for complete equilibrium to be established is so long that the method is often inconvenient to use, especially if the molecular weight is greater than 50 000. 

In order to overcome this drawback, a modification to the sedimentation-equilibrium method was proposed in 1947 by the Canadian physicist William J. Archibald At the top meniscus of the cell, and at the bottom of the ceil, there can be no net flux, so that the sedimentation-equilibrium equations must hold at these sections at all times. Therefore, shortly after the ultracentrifuge is brought to its top speed, concentrations in these special sections can be determined, and M calculated from (11.89). This modification of the sedimentation-equilibrium method greatly increases its applicability. 

Sedimentation equilibrium methods measure the concentration gradients of molecules in solution when spun at high speed in a centrifuge. Samples are held in special cells in the rotor, with optically flat clear windows and, in current instruments, several samples (including controls) may be run simultaneously. The concentration gradient, as a function of radius (r), is measured using UV/visible absorbance, fluorescence or refractive index methods, using optical systems mounted outside the rotor. 

Unlike sedimentation equilibrium methods, measurement of sedimentation rates - how fast the molecules fall in the centrifugal field -can give information about both macromolecular shape and the size. These methods use relatively high centrifugal forces and measure the concentration profiles within the centrifuge tube (cell) as a function of time. 

In the sedimentation equilibrium method, a lower centrifugal field is maintained for a period of time in such a way that sedimentation is balanced by diffusion and M equilibrium distribution of polymer is established in the cell. Although M and Mz are easily determined, the length of time of the experiment is a disadvantage. In contrast to light scattering, this method is not affected by dust particles, and no calibration is needed. The molecular weight distribution may be obtained from the sedimentation velocity data, but not without mathematical difficulties... 

Two approaches are in vogue for determination of molecular weights through centrifugation, the sedimentation velocity method and the sedimentation equilibrium method, the former being more popular. A third method, the approach to equilibrium method is also used. 

The sedimentation equilibrium method, in which diffusion plays an equally important role. This is done at a relatively low speed, for example, 12,000 rpm. 

J-600 essentially as described previously [3]. Sedimentation equilibrium was performed at 20 °C in a Beckman analytical ultracentrifuge model XL-A. Molecular weights and partial specific volumes of the peptides were determined by the H2O/D2O sedimentation equilibrium method [6]. All the measurements were carried out in 10 mM Tris-HCl (pH 7.5) with or without 10 mM NaCl. 

A completely different nonstandard technique to obtain a first overview of the equation of state was recently proposed by Addison et al. [269], whereby a gravitation-like potential is applied to the system, and the equilibrium density profile and the concentration profile of the center of mass of the polymers is computed to obtain the osmotic equation of state, fii this sedimentation equilibrium method one hence considers a system in the canonical MVT ensemble using a box of linear dimensions L x L x H, with periodic boundary conditions in x and y directions only, while hard walls are used at z = 0 and at z = H. An external potential is applied everywhere in the system ... 

However, if one is interested only in a rough overview of the behavior of the model, without precise characterization of these jumps and the location of the transition, the sedimentation equilibrium method (Sect. 3.2) is a conceptually simple and straightforward alternative (Fig. 14). 

In the sedimentation velocity method a high ultracentrifugal field (up to about 400 OOOg) is applied and the displacement of the boundary set up by sedimentation of the colloidal particles is measured from lime to time. In the sedimentation equilibrium method, the colloidal solution is subjected to a mueh lower centrifugal field, until sedimentation and diffusion (mixing) tendencies balance one another and an equilibrium distribution of particles throughout the sample is attained. 

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