262 H. K. SCHACHMAN AND R. C. WILLIAMS 



dependence the more serious will be the sharpening effect. For tobacco 

 mosaic virus (Schachman, 1951b) and deoxyribonucleic acid (Peacocke and 

 Schachman, 1954) this self- sharpening leads to hypersharp boundaries and 

 to the misleading impression that the material is homogeneous. Finally the 

 boundary is distorted by the existence of the Johnston-Ogston effect (1946). 

 Because a given molecule sediments more slowly in the presence of other 

 components than it does while sedimenting alone, there is an apparent en- 

 hancement in concentration of the slower moving species, with a concomitant 

 reduction in the apparent amount of the more rapidly sedimenting com- 

 ponents. It is tliis effect which often leads to marked errors in the analysis 

 of mixtures of two components. In the absence of complications, the area 

 under the curve (with schlieren optics) is a measure of the concentration of 

 the component responsible for the bomidary. However, the existence of the 

 Johnston-Ogston effect complicates the analyses and special treatments are 

 necessary. 



The demonstration of homogeneity is a laborious task but the theory and 

 techniques for such an experimental investigation are now available. Several 

 factors must be included in a rigorous test. Not only must there be a single, 

 symmetrical boundary throughout the experiment, but also the concentra- 

 tion of the sedimenting substance must vary in accord with the radial dilu- 

 tion equation which accomits for the cell shape and the varymg centrifuga] 

 field (Trautman and Schumaker, 1954). AU of the sedimenting material in 

 the solution must be accounted for by the moving boundary. Depending 

 upon the optical system employed, different procedures are available for 

 this test. The concentration evaluated from the ultracentrifuge patterns 

 should agree within a few per cent with that obtained by chemical analysis. 

 A single boundary should be observed under a variety of experimental con- 

 ditions. This test, of course, may be limited by the stability range of the 

 virus. As a prerequisite to more detailed investigations of the boundary 

 shape, the sample should be examined at a series of concentrations to 

 ascertain whether corrections are necessary for artificial bomidary sharpen- 

 ing (Fujita, 1956). Through the application of absorption optics with ultra- 

 violet light, solutions at sufficiently low concentrations may be employed so 

 that tliis complication is avoided. If the change in sedimentation coefficient 

 across the boundary proves to be negligible, the boundary spreading can be 

 analyzed directly in terms of the standard deviation of the bomidary curve. 

 As a criterion of homogeneity the plot of the standard deviation versus time 

 should be linear. This is equivalent to finding that the apparent diffusion 

 coefficient, evaluated individually from each ultracentrifuge pattern, does 

 not vary with time. Most systems have sufficient change in sedimentation 

 coefficient across the boundary, however, that such a test is illusory and 

 corrections for self-sharpening are mandatory (Schachman, 1951b). For these 



