Centrifugation sedimentation equilibrium

The centrifugal field in the sedimentation equilibrium experiment is the analog of the membrane in an osmometer. 

Sedimentation equilibrium Absolute requires only centrifuge measurements and partial specific volume of solute Time-consuming measurement and interpretation somewhat limited mol. wt. range 5... 

Finally, we consider the behavior of a solute in a solution in the cell subjected to the centrifugal field. At a suitable angular velocity, the tendency of the solute to sediment toward the bottom of the cell is countered by its tendency to diffuse backward toward the meniscus, because the concentration increases with increasing r, as indicated in Figure 2. 2 b). At some time, a sedimentation equilibrium is attained. A typical equilibrium concentration distribution is depicted in Figure 2. 2 b). Our aim is to find a quantitative analytical expression for this curve. 

Fig. 5. Sedimentation equilibrium analysis of hemopexin domain interactions. Mixtures of N- and C-domain were centrifuged to equilibrium at 25 C in the absence (upper panels) and presence (lower panels) of heme. Nonlinear fitting procedures were performed to obtain apparent values, and residuals of the fits are shown in the top portion of each panel (106).

Method by which the distribution of the concentration of the solute or dispersed component in a dilute solution or dispersion along the centrifuge cell is measured at sedimentation equilibrium, and the results are interpreted in terms of molar masses or their distribution, or both. 

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. 

It is our objective in this chapter to outline the basic concepts that are behind sedimentation and diffusion. As we see in this chapter, gravitational and centrifugal sedimentation are frequently used for particle-size analysis as well as for obtaining measures of solvation and shapes of particles. Diffusion plays a much more prevalent role in numerous aspects of colloid science and is also used in particle-size analysis, as we see in Chapter 5 when we discuss dynamic light scattering. The equilibrium between centrifugation and diffusion is particularly important in analytical and preparative ultracentrifuges. 

It might be noted that sedimentation equilibrium is approached very slowly however, techniques that permit equilibrium conditions to be estimated from preequilibrium measurements have been developed by W. J. Archibald. Equations (86) and (87) predict a linear semilogarithmic plot of c versus x or x2 for gravitational and centrifugal studies, respectively. The slope of such a plot is proportional to the mass of the particles involved. Remember that monodispersity was assumed in the derivation of these equations. If this condition is not met for an experimental system, the plot just described will not be linear. If each particle size present is at equilibrium, however, each component will follow the equations and the experimental plot will be the summation of several straight lines. Under certain conditions these may be resolved to give information about the polydispersity of the system. In any event, nonlinearity implies polydispersity once true equilibrium is reached. 

SDS-PAGE, presence of 2-mercaptoethanol [17] <15> 2 44000, SDS-PAGE, presence of 2-mercaptoethanol, high speed sedimentation equilibrium centrifugation of urea-treated enzyme [22] <2> 2 43195, calculated from sequence of cDNA [40] <5> 2 49000, SDS-PAGE [19] <14> 2... 

The sedimentation equilibrium experiment requires much smaller volumes of solution, about 0.15 ml. With six-hole rotors and multichannel centerpieces (41) it is potentially possible to do fifteen experiments at the same time. For situations where the photoelectric scanner can be used one might (depending on the extinct coefficients) be able to go to much lower concentrations. Dust is no problem since the centrifugal field causes it to go to the cell bottom. For conventional sedimentation equilibrium experiments, the analysis of mixed associations under nonideal conditions may be virtually impossible. Also, sedimentation equilibrium experiments take time, although methods are available to reduce this somewhat (42, 43). For certain situations the combination of optical systems available to the ultracentrifuge may allow for the most precise analysis of a mixed association. The Archibald experiment may suffer some loss in precision since one must extrapolate the data to the cell extremes (rm and r6) to obtain MW(M, which must then be extrapolated to zero time. Nevertheless, all three methods indicate that it is quite possible to study mixed associations. We have indicated some approaches that could be used to overcome problems of nonideality, unequal refractive index increments, and unequal partial specific volumes. 

An alternative method sometimes used to determine molecular weights of macromolecules is sedimentation equilibrium. In the previous example, using the Svedberg equation, the sample is rotated at a rate sufficient to sediment the particles. Here, the sample is rotated at a lower rate, and the particles sediment until they reach an equilibrium position at the point where the centrifugal force is equal to the frictional component opposing their movement (see Equation 7.6). The molecular weight is then calculated using Equation 7.12. 

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. 

By accelerating deposition with a slowly rotating ultracentrifuge, Stokes law [Eq. (4.1)] is modified in uniform circular motion to an equilibrium distribution along the axis of rotation (0 to x), as a function of solute mass (mt). At higher centrifugal velocities, sedimentation succeeds the equilibrium distribution. Sedimentation equilibrium and sedimentation velocity provide a means to determine M. 

Fig. 1. Sedimentation equilibrium (72). The concentration of adrenodoxin was 0.45 mg per ml. The centrifugation was performed at 44,770 r.p.m. for 20 hrs. The error bars correspond to an estimated uncertainty of 10 p. in the determination of the fringe displacement...

In a sedimentation equilibrium experiment the cell is rotated at a relatively low speed (typically 5000-10000 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 ot Mwand Mz, 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. 

With the liquid mobile phase off and the channel rotating at an appropriate speed, the sample mixture is injected into the channel. The channel is rotated in this mode for a relaxation or pre-equilibrium period that allows the particles to be forced towards the accumulation wall at approximately their sedimentation equilibrium position. Particles denser than the mobile phase are forced towards the outer wall. Diffusion opposite to that imposed by the centrifugal force causes the particles to establish a specific mean thickness near the accumulation wall as a function of particle mass. Liquid mobile phase is then restarted with a parabolic velocity front. Small particles are engaged by the faster moving central streamlines and are eluted first. Large particles near the wall are intercepted by the slower streamlines and are eluted later. Thus particles are eluted from the channel in order of increasing mass. 

Table 9-1. Characteristics of Sedimentation Velocity and Sedimentation Equilibrium Centrifugation...

Isopycnic or sedimentation equilibrium centrifugation involves allowing the sedimenting species to move through the gradient until they reach a... 

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