INVERSION FORMULAS FOR ELLIPSOID OF REVOLUTION MACROMOLECULAR SHAPE FUNCTIONS

Explicit relations linking ellipsoid of revolution shape parameters wi th the axial ratio (a/b) have been available for a long time, It is no t possible to directly invert these functions to give a/b as a functio n of the shape parameter, so in the past graphical or tabular interpol ation methods have been necessary. By the use of simple unconstrained polynomial expansions this restriction is no longer necessary. For the two salient hydration-dependent shape functions (P from the frictiona l ratio and nu from the intrinsic viscosity) and the four salient hydr ation-independent shape functions (beta and R, both from sedimentation and viscosity measurements, and Lambda and Il from combining viscosit y measurements with respectively fluorescence depolarization or thermo dynamic second virial coefficient measurements) the polynomial expansi on coefficients (to no more than seventh order) are given for the rang es 1.1 < a/b < 2.0, 2 < a/b < 10, and 10 < a/b < 100. The polynomial c oefficients give an excellent fit to the real data values, except for four uninteresting cases (where the shape function is too insensitive for practical use). (C) 1995 Academic Press, Inc.