Conservation of Signal: A New Algorithm for the Elimination of the Reference Concentration as an Independently Variable Parameter in the Analysis of Sedimentation Equilibrium

Abstract

The equation describing the radial distribution of a single solute species at sedimentation equilibrium in an ideal solution (Cantor & Schimmel, 1980) may be written in integrated form as

$$ w\left( r \right) = w\left( {{{r}_{{ref}}}} \right) \times \exp {\text{ }}\left[ {\frac{{M*{{\omega }^{{\text{2}}}}}}{{2RT}}\left( {{{r}^{2}} - {{r}_{{ref}}}^{2}} \right)} \right]{\text{ }} $$

((1))

where w(r) denotes the weight/volume concentration of the solute at radial position r, ω the angular velocity of the rotor, R the molar gas constant, T the absolute temperature, and r_ref an arbitrarily selected reference position. M* denotes the buoyant molecular weight of solute, defined as

$$ M* \equiv M\left( {1 - \bar{v}\rho } \right) $$

where M and v̄ respectively denote the molecular weight and partial specific volume of solute, and p denotes the density of solvent. The results of a sedimentation equilibrium experiment are ordinarily obtained as an experimental dependence of w (or, more properly, some measurable quantity that is proportional to w) upon r. Such data are customarily analyzed by fitting equation (1) to the data by the method of nonlinear least-squares (Johnson & Faunt, 1992) in order to obtain best-fit values of M* and w(r_ref). Note that only the best-fit value of M* is sought by the investigator; the presence of a second undetermined variable (the reference concentration) may, under certain circumstances, significantly reduce the precision with which the value of M* can be determined by least-squares fitting of the data. It has been pointed out on several occasions (Nichol & Ogston, 1965; Lewis, 1991; Hsu & Minton, 1991) that if w(r) is known over the entire length of the solution column, then the condition of conservation of mass may be utilized, together with the known loading concentration of solute, to eliminate the reference concentration w(r_ref) as an independently variable parameter. However, one may not always be able to obtain reliable data for w(r) over the entire length of the solution column, and in some experiments (particularly those involving unstable macromolecules) conservation of mass may not obtain over the duration of the experiment.