THE PHYSICAL PROPERTIES OF INFECTIVE PARTICLES 2G7 



d. The Transient States during the Approach to Sedimentation Equilibrium. 

 During the past five years there has been vigorous activity in developing 

 procedures for molecular weight determinations during the approach to 

 sedimentation equilibrium. All of these efforts are based upon the investiga- 

 tions of Archibald (1947) aimed at securing mathematical solutions of the 

 differential equation describing sedimentation in the ultracentrifiige. 

 Although the detailed mathematical solutions are not of much practical 

 value at present, Archibald emphasized that the limiting (or boundary) 

 conditions themselves provided the basis for an ultracentrifugal method for 

 the direct determination of molecular weights. The net transport of solute 

 across any given surface in the ultracentrifuge can be expressed as the 

 difference in the fluxes due to sedimentation and diffusion. At equilibrium 

 the net flux is equal to zero everywhere in the cell. To acliieve this equili- 

 brium state throughout the cell, as already noted, very long time periods 

 are required. However, at the two end surfaces of the cell the net flux is 

 equal to zero for all times. This is a consequence of the fact that the cell is 

 closed and the macromolecules cannot cross the meniscus from the air 

 bubble nor can they leave the aqueous solution at the bottom. To be sure, 

 the concentration does decrease at the meniscus (and increase at the cell 

 bottom), but the concentration gradients change accordiiDgly and there is 

 no transport of solute across the two end surfaces. When these relations are 

 expressed in mathematical terms and the equations rearranged we find 



RT idcldx)^ 

 M = = ^ ' ' (27) 



(1 — Yp)oji^ ^mPm 



The subscript, m, in Equation 27 refers to the meniscus and a corresponding 

 equation can be written for the cell bottom. It should be noted that these 

 relationships are derived by a thermodjTiamic treatment as well. Like the 

 equations presented earlier, these refer to ideal solutions containing only 

 two components. Extrapolation procedures are required in order to obtain 

 values of the concentration gradient, dcjdx, at the two ends of the cell. 

 The corresponding concentrations are evaluated by calculation procedures 

 which, though tedious, yield reliable values. 



For homogeneous materials the molecular weights calculated for the top 

 and bottom of the ceU should be the same. Thus the results secured from the 

 two ends of the ceU provide some measure of the homogeneity of the sedi- 

 menting material. Evidence of gross heterogeneity is obtained readily by 

 this method, but it does not possess the sensitivity inherent in the sedimen- 

 tation velocity method. The success and scope of the method have been so 

 great that a vast amomit of data has been accumulated already by its 

 application. As yet this method has not been employed successfully with 

 viruses. However, recent technical improvements which permit operation of 



