Archibald method sedimentation equilibrium

Note The use of the term approach to sedimentation equilibrium for Archibald s method is discouraged, since it has a more general meaning. 

Evaluation of Mweq. Sedimentation Equilibrium Experiments and the Archibald Method. At constant temperature the condition for sedimentation equilibrium is that the total potential jZi for each associating species i (i = A, B, or AnBw) be constant at every radial position r in the solution column of the ultracentrifuge thus... 

Analysis by the Archibald Method or by Sedimentation Equilibrium Experiments at Different Speeds. Instead of using Mweq here, one uses Mwa, the apparent weight-average molecular weight. For the Archibald experiment one obtains Mwa,t at rm or r6 by the application of Equations 13-16. The extrapolation of Mwa>t to zero time gives Mwo. For sedimentation equilibrium experiments at different speeds, one can evaluate Mwa by two different methods here one uses either Equations 17 or 18. For a mixed association such as A + B AB, the basic sedimentation equilibrium equation can be written as... 

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. 

Received January 17, 1972. Work supported by grants GM 15551 and GM 17611, National Institutes of Health. It is based on the MS theses submitted by Allen H. Pekar (nonideal, sedimentation equilibrium experiments and Archibald method) and by Peter J. Wan (light scattering) to the Graduate School of the Illinois Institute of Technology. 

CR, cryoscopic method DV, diffusion constant and intrinsic viscosity EB, ebullioscopic method EG, end-group titration IV, intrinsic viscosity-molecular weight relationship in other solvents LS, light scattering MV, melt viscosity-molecular weight relationship OS, osmotic pressure PR, analysis of polymerization rate SD, sedimentation and diffusion constants SE, sedimentation equilibrium (Archibald s method) SV, sedimentation constant and intrinsic viscosity [see Eq. (72)]. 

Values kindly determined by Mr. D. M. Brown and Prof. E. L. Smith on a sample prepared in this laboratory. The values have been obtained, respectively, by the Archibald method of sedimentation equilibrium and by sedimentation-diffusion, assuming a partial specific volume of 0.721 for the protein. 

Figure 3 a) Molecular weight determination by equilibrium ultracentrifugation b) Comparison of molecular weights determined by the Archibald method and by sedimentation equilibrium. 

It often takes an inconveniently long time for sedimentation equilibrium to be established. In 1947 the Canadian physicist William J. Archibald developed a method based on the approach to sedimentation equilibrium. The so-called Archibald method now is used commonly by biologists and biochemists. For details of the various methods used for studying sedimentation the student is referred to Chapter 11 and to texts listed at the end of this chapter. The interested reader is also referred to a useful new technique in sedimentation studies, density gradient centrifugation (see... 

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. 

Methods for the weight-average molecular weight, M LS, light scattering SA, approach to the sedimentation equilibrium (Archibald s method). 

Archibald suggested that we need focus only on the top and the bottom of the cell during the process of equilibrium sedimentation to determine molecular weight we do not have to wait for equilibrium to be reached. Hence, the method is also called approach to equilibrium. Equation (11.4) can be rearranged for... 

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