266 H. K, SCHACHMAN AND R, C. WILLIAMS 



Improvements are still needed, liowever, in the construction of damping 

 devices to eliminate vibration and precession of the rotor at speeds as low 

 as 500 r.p.m. When these improvements are realized, sedimentation equili- 

 brium experiments with viruses will become routine. 



The equations describing the concentration distribution in an ultra- 

 centrifuge cell in which equilibrium is attained can be derived either from 

 thermodynamics or from consideration of the transport of material by 

 sedimentation and diifusion. That such distribution fmictions can be deduced 

 from thermodynamics constitutes the major appeal of the sedimentation 

 equilibrium method. The shape, permeability, and hydration of the solute 

 are irrelevant to a determination of the molecular weight, for the thermo- 

 dynamic description of a system at sedimentation equilibrium does not 

 involve these factors. For homogeneous materials in solution sufficiently 

 dilute that concentration effects are negligible, the molecular weight is calcu- 

 lated from a plot of log c versus x- according to 



2i2T dine 



M = = TT-Z7 25) 



(1 - FpK ^(^") 

 Equation 25 is useful for ultracentrifuge experiments employing ultraviolet 

 absorption optics or the Rayleigh interferometer. This equation can be 

 used in a different form when schlieren optical systems are used. Alterna- 

 tively the molecular w^eight can be calculated from data expressing the con- 

 centration gradient as a function of distance: 



M= ^^f >''-- (26) 



(1 — 7p)a>2 d{x^) 



It should be noted that these equations are restricted to two-component 

 systems. As in the sedimentation velocity and light-scattering method 

 complications are introduced when large amounts of a third component are 

 present in the solution. Neglect of possible preferential interactions between 

 the solute and one of the components of the solvent can lead to serious errors 

 in molecular weight determinations. This is also the situation with the novel 

 sedimentation equilibrium method involving sedimentation and flotation 

 of macromolecules in a density gradient formed by the distribution of a 

 solute of low molecular weight (Meselson et al., 1957). 



Some information regarding heterogeneity is also provided by sedimenta- 

 tion equilibrium experiments, but it should be noted that this method is not 

 nearly as sensitive as the sedimentation velocity teclmique. If solutions 

 exhibit concentration effects, as is often the case particularly with elongated 

 macromolecules, experiments at different concentrations are necessary. The 

 data are then used for extrapolation to infinite dilution. 



