Rectangular Approximation for Concentration‐Dependent Sedimentation in the Ultracentrifuge
1.O. Lamm, Arkiv Math. Astron. Fysik 21B, 2 (1929).
2.H. Fujita, Mathematical Theory of Sedimentation Analysis (Academic Press Inc., New York, 1962).
3.H. Fujita, J. Chem. Phys. 24, 1084 (1956).
4.G. H. Weiss, J. Math. Phys. 5, 675 (1964).
5.G. H. Weiss, Nature 202, 792 (1964).
6.M. Mason and W. Weaver, Phys. Rev. 23, 412 (1924).
7.D. A. Yphantis and D. F. Waugh, J. Phys. Chem. 60, 623 (1956).
8.For studies with separation cells7 has been taken as the radius of the fractionation position, while in velocity experiments that are localized near the meniscus it appears useful to take since a choice of is equivalent to a choice of acting centrifugal field.
9.K. E. Van Holde and R. L. Baldwin, J. Phys. Chem. 62, 734 (1958).
10.The results for and agreed closely with evaluations of the Mason and Weaver6 equation for a closed cell. Several other obvious checks were also satisfactory, e.g., the distributions were Gaussian and showed the expected diffusion and displacement of the concentration gradient maximum for initial times when and the solutions always adhered to the appropriate boundary conditions [Eq. (6)]; for the solutions were in close agreement with the rectangular analog of the Gutfreund and Ogston11 equations: , where corresponds to any point in the plateau region. The parameter is bounded from below in this program by truncation error. This defect could readily be removed.
11.H. Gutfreund and A. G. Ogston, Biochem. J. 44, 163 (1949).
12.D. A. Yphantis, Biochemistry 3, 297 (1964).
13.D. A. Yphantis (to be published).
14.This similarity property of the rectangular approximation is not valid for the original Lamm equation.
15.D. A. Yphantis, J. Phys. Chem. 63, 1742 (1959).
16.It is interesting to note that the approximate solutions for sedimentation of ideal solutes near the meniscus given by Fujita and McCosham17 are essentially these ideal semi‐infinite solutions of Mason and Weaver, the only differences being the substitution of the variables for and of for and the presence of a multiplicative factor If be taken equal to then the two sets of solutions are indistinguishable for and
17.H. Fujita and V. J. McCosham, J. Chem. Phys. 30, 291 (1959).
18.Our calculations do not extend sufficiently far in (because of computational limitations to ) to allow us to say whether or not the nonideal distributions will become symmetrical in the limit of large However this appears likely from the behavior of solutions3 having this c dependence but without the meniscus perturbation.
19.G. Kegeles, J. Am. Chem. Soc. 74, 5532 (1952).
20.E. G. Pickels, W. F. Harrington, and H. K. Schachman, Proc. Natl. Acad. Sci. (U.S.) 38, 943 (1952).
21.R. J. Goldberg, J. Phys. Chem. 57, 194 (1953).
22.H. K. Schachman, Ultracentrifugation in Biochemistry (Academic Press Inc., New York, 1959).
23.M. Dishon, G. H. Weiss, and D. A. Yphantis (to be published).
24.G. M. Nazarian, J. Phys. Chem. 62, 1607 (1958).
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