tion with addition products of benzene, and missing the fundamental concent of a CGaromatic nucleus) and makes a wrong statement' about the constitution of benzene (8). Therefore. at the time (March 1875)hesent ArthurHenninger the communication (6) for the Paris Chemical Society, van't Hoff should have not vet been in the nosition of writing Chapter 1V 7 , in whiih he applies the Gtrahedral atom to the Kekule and [.adenbum benzene models and fully and correctly examines, in te& of nonsuperimposable prismatic images, the disubstituted benzene derivatives (his reading of Ladenbur& idea). Assuming this logical reconstruction of events, it also follows that the part of Chapter I11 (7) where van't Hoff discusses the allene enantiomeric isomers in very general terms must have been conceived after reading the 1874 Le Be1 paper (3). Literature Cited
Rotterdam. 1887. 5. Paoloni, L. Alfi 111 Conue#%o Nolionole di Storin &lla F i s h : Palermo, 1982; pp 117-128. See alsoAm. Sci. 1987.75.230.
Leonello Paoloni Di~artimentodi Chimica Fisica Dell'Universita Via Archirafi, 20 90123 Palermo, Italy
Rate Zonal Sedimentation and lsopycnic Centrifugation To the Editor;
Turchi and Weiss ( I )have recently described a very useful sucrose density gradient experiment that can he carried out with undergraduate classes using minimal equipment and cultured yeast and bacteria that are then killed by addition of crystal violet. Then the dead cells are harvested. Their sedimentation on sucrose gradients is followed either by visually observing the movement of the blue color or by collecting fractions and measuring their absorbance at 550 nrenared nm. The sucrose eradients are s i m ~ l v . hv fillinea centrifuge tube 4 t h 25% sucrose solution, freezing it, and allowine it to thaw. thus formine a eradient from rouehlv 15% to 140%. A pestion students myght be asked is: %%; should this work, and what physical principles are involved? Turchi and Weiss ( 1 ) sueeested that this technioue is .... isopvcnic ccntnfugation, that is, the cells band according to their density. R u t we find this not to be s w r a t h e r this experiment demonstrates rate zonal centrifugation and the effect of d~ffcrentcell dimensions. The standard equation for sedimentation is
...
u = dr/dt =
798
&,- v,)a2r m
Journal of Chemical Education
-
Here w2ris the centrifugal force; pp and p, the densities of the cells and medium. resnectivelv: and n. the viscositv of the medium. Faster sedimkntation could be due to a larger cell d~ametertdJ or to a larger value of .0..r - .om - which would result in isopycnic banding only if pp were less than the highest p, (1.15 g/mL for 40% sucrose at 20 "C (2)). In practice both factors could he involved. In our hands the freezing and thawing procedure did indeed establish satisfactory 15% to 40% gradients. But, depending on the time and force of centrifugation, both yeast and E. coli pelleted-the yeast more rapidly. The diameter ofE. coli is about 0.6 Fm (3);S. cereuisiae, 3-5 pm (4) ~-,.
The same experiment can readily be extended to also demonstrate isopycnic centrifugation by use of denser gradients, most easily prepared by overlaying, from a pipet, progressively weaker sucrose solutions (from 90% to 55%) to make a gradient from about 87% to 47% (density from about 1.32 to 1.18 g/mL (2)). We thus obtained stationary bands while increasing d r or time. Bacillus subtilis is another useful oreanism to studv in addition to the yeast and E. coli sugge;ted by Turchi Hnd Weiss. Being Gram-positive,it absorbs crystal violet better than the Gram-negativeE. coli does. Its diameter, 1-1.5 Fm (3).is annreciahlv laraer than that of E. coli, and we found it to bakl a t a diameter of about 1.30 g/mL as opposed to less than 1.19 g/mL for E. coli. The S. cereuisiae formed three bands a t densities of about 1.26,1.29, and 1.30 g/mL, consistent with the existence of three populations (4).Thus, any difference in sedimentation rates between yeast and B. subtilis in lower sucrose concentrations must be due to difference in size. Exneriments with sucrose madients are instructive and inexpensive to perform. Thefcan be used, moreover, with the sameE. coli, B. subtilis, and S. cereuisiae preparations to demonstrate both rate zonal sedimentation and isopycnic banding -dependina . - on the sucrose concentrations of the gradients. Acknowledgements I am grateful to K. L. Manchester for much advice and encouragement in the performance of this work and to L. King of the Department of Microbiology for the growth of the micmorganisms. Literature Cited 1. Turehi, D. L.; Weiss, M. J. Cham E d u e 1988,65,170. 2. Gfi~th,0. M. Techniques ofPmpomfi"e Z o n d and ContinvovaFlW" Ulfmcontrifugotion; Beckman Instruments: Palo Alto,1919; p9.
3.Cmi"ksha"k,R.;hguia, J.P.;Marmio",B.P.;Swsin,R.H.AM~dimlM~mbrologv; Churchill: New Vork, 1975: pp428 and 449. 4. hdder, J.; Kreger-van Rij, N. J. W. The Yegeff,o Tarommie Study; North-Holland: Amsterdam, 1952; pp 131-132.
Dorota ~askowicz' Depanment of B ochernisf~y Un vers ly ofthe W rwatersrand ~ohannesburg, South Africa 'On leave from the Institute of Enzymology and Bioenergetics, University of Warsaw, Poland.
