1034
H. K. SCH.ICHJIAS
DETER;\IISLITIOS O F SEDIlIESThTIOS COSSTXXTS I S THE SHAIRPLESSUPERCESTRIFUGE H. E(. SCH.ICHXI-kS1 Depaitment of Anzvial a n d Plant Puthology, Rockefeller I i i s / i t u t c for Medical Research, 17' ~ n c e t o a.Yew , Jer scu X e c e i i ed S o u e m b e , 1 3 , 1Qd7 ISTRODUC T I O S
The high-speed centrifuge in recent year.; has become an invaluabie tool in many branches of colloid and biochemical research. In addition t o the technical improvements enabling the attainment of centrifugal fields ab high a5 500,000 times gravity, there have been developments in the optical methods used for study of the sedimenting material. The brilliant researches of The Svedberg and his collaborators (13) have culminated in the development of the ultracentrifuge. Centrifuges of another design have been developed b y Beams and coworkers ( 2 ) , Hauer and Picliels (l),and Wyclioff and Lagsdin (17) with the logical addition of a quantity-type rotor for centrifuging moderate quantities of liquids. The work of Stanley (12) has shonm this quantity-type rentrifuge to be of inestimable value in the isolation and purification of viruses. IIowever, the need for a less espensive centrifuge capable of continuous f l o ~operation and of sedinienting particles as small as the viruses resulted in investigations concerning the possibilities of the Sharples supercentrifuge. Hauser et a7. (5, 5) deyised an efficient procedure for fiactionating bentonite suspensions into several reasonably monodisperse fractions by utilizing the theory and equations deiived for the Sharples supercentrifuge. It was also demonstrated (5) that, irith very little effort, the size of a n-ell-defined fraction of particles could be evaluated. Success in quite a different field was experienced by Stanley (13, 14),~ v h o-ought a better method for the isolation of viruses on a large scale. I n vie\\ of the practical yalue of the Shnrples supercentrifuge in the purification of tobacco niosaic and influenza ~irubes.it seemed worthwhile to reexamine the tlieory of sedimentation in the supercentrifuge in an attempt to adapt it for the calculation of the sedimentation constants of those materials capable of being sedimented in fields of about 60,000 times gravity. An estimate of the reliability of the supercentrifuge method could then be made b y comparing the results 11-ith those obtained by direct measurement in the ultracentrifuge. THEORETICAL
Hauser and Reed (4) assumed that every particle in the bowl of the Sharples centrifuge is subjected to two velocity components, one perpendicular and the other parallel to the axis of rotation of the b o d . The first, whose magnitude is dependent on the centrifugal field, can be espressed quantitatively by a modified Stokes 1 a for ~ falling bodies; the second is proportional to the rate of f l o of ~ 1
Junior Researrh Fellow of the Sational Institute of Hralth.
material through the bov.1 and ran be defined by Se\vton's la\\- of T 1,-nder given experimental conditions the point a t which a particle hits the wall \vi11 lie a fiinctioii of the point of departure and the effective maw :mtl shape of t Iw pni'ticlc. This c;m lie expressed by
I-
=
F(S",???,., f )
(1)
\vliei.e 1- is the distance in centimeters from the t,op of the straightening vmes t,o the point ut which the particle settles, 'vic is the effective mass of the part'icle, f is the frictional coefficient' of the particle, arid Xo is t,lie distance from the itsis of rotation a t which sedimentation started (figure 1). The velocity rompoiient, in tlic .r direction can be espressed by t1.r ~ _H. lcW2.1. ~
(11
~
~~
f
I2)
1\.hcw iil is tlie angular Tyelocitj- of the centrifuge l i o i ~ lin i,;i(lian+ pt'r -w Intl. Ijeecl ($1~1, i'ollon-ing thc tiwtnient of Lamb (6)>foimd
tor the> i-elocity component puiallel to the axis of rotation.' 111 tlic pre-erit n-oik the lmvl ha5 the dimension.; I I I = 0.734 mi., Xs= 2.22 cm , and li = 1.11, and 'J,,,,, i* the rate of flon- of -oliitioii through the lion1 in milliliter- per miniitc. ,'ombniing equation\ 2 and 3 und integrating bctn een t h e limit< A = So.!/ = :ind 7 = I??. y = 1- lead5 t o equation 4:
n r t h c vclocity of flon- of licluid in a pipe of uniforiii circular section \ihc,rr>1 is tlic, I i ~ r i g of ~!~ tioii under consideration. (pl - p z ) is tlic prcssurc drop across t h a t soctiori, 7 is t!i(. \.ismosit?. of the medium, and -1 and R are c~onstantsof integration. In t h e case of fiow i n t i l ( , critrifugc bon-1 the treatmelit differs from t h a t of Lamb in t h a t the h u n d a r y conditioris or integration are t h o w of a cone-ciitric, shell of fluid rather t h a n a solid tube of fluid. Thf. ,onstants A and B are evaluntrd 11y tlic us? of tlic 1)oiuidar)- coritlitinri~.tli/,'tlt = 0 .r = '(2,
);(;id
d?/
hr
arross any scrt i n n ,
and
or t
cads
10
fliis
=
0 a t z = Iil. Cointiination of tlic, Irsulting equation
equation 3.
wiiti ttir' t>ilu:itioii
1036
H. I of flon betv een 40 and ZO nil. per minute I\ ith the recovery of approximately 80 per cent or more of the biological activity. His studies 11ere conducted at 50,000 R.P.M. .kccording to eqiiation (i the sedimcntntion constant of thc influenza
viruses would be ~boiitti30 S, 'l'lie most frequently reported values of t'lie m l i mentation constants of the strains of influenza virus lie between GOO and 700 S. ,Again, the results \vith the Sharples supercent,rifuge are in excellent, ab vecnienl n-it,h the value obtained by the reliable ult'racentduge technique. It is of interest, that, SIarkharn (8), following the approach of Bechhold Schlesinger (3) and of Sclilesinger (1I ), calculated the sediment,ation constant of tobacco mosaic virus on the basis of conlpletely stirred sedimentation. T1tLl;ing use of the formula for conrectire centrifuging,
he calculated values for the sedimentation constant
hich \\-ere in s a t m c t o r y
11
iigreement with those found by Lauffer ( 7 ) by means of the ultrncentrifiige. I n equation 9, !'t is the concentration of virus in the supernatant fluid at time t , ('0 is the initial concentration of virus, A is t'lie area of the internal surface of thc t)on-1 (279 cm.')), and T' is the volume of solution that has passed t,hrough the 11o1~1in the time t. -1s JIarliham pointed out', equation 9 applies t o the most iinf:ivoralde conditions for sedimentation, and the sedimentation constant n h e s derived fivm it should lie minimal. That they \\.ere, in fact,, larger than t,he accepted vnlue for tobacco mosaic virus could mean, :XY >larliham indicated, that there TVW some concentration gradient formation in the supernatant. I n that ciisc sec1iment:ition n-ould o c ~ u more r rapidly than expected and the values obtained by equation 9 should be high. Table 3 sliows the results obt,ained from the present. datii for the sedimentation cmstants on the basis of convectionless sedimentation as espressed by equation ii and under the conditions of convective centrifuging calculated by equation 9. I n all experiments except the last t'he values obtained on the basis of stirred sedimentation :we too high. The value, 8-1-0S , foi>thc sedimentation (*onstantof influenza virus is olitaincd hy the use of T*iBLE 3
the data oi Stanley ( L 2 : ~ i deqiintion 9. -Is in the case of most of tlic esperinients ivitli tolxwco mosaic Tinis, the sedimentation constant for influenz:i viriih calculutecl o:i the lial-is of convective centrifuging is t o o high. I n an :ittempt t o evaluate further the t i w theories for seclinicntation in the Sharples siipei'centrifiige the c~runulatiT-eiveiglit per rent curve was calculated in the follon.irip manner on thc l m i s of cwnvective ccntrifiiging:
(11I
sedimentation in the Sharples supercentrifuge on the basis of completc coriw(’tion was discussed and the results obtained 1 ,.its use u-ere presented. An a t tempt a t evaluating the relative cwntribution of convection \vas made by an analysis of the \\-eight’distribution of sediment along the wall of the centrifuge lion-1. The results indicated that the equations based on roni-ection-free sedimerit at ion yield values n-hich are in closer agreement n-ith experimental values. ‘I’he authoi. is indebted t o Dr. T I 7 , 11. Stanley of the Rockefeller Institute for Medical Research. Dr. 11. &I.Lauffer of the 1-nirersity of Pit,tsburgh, Dr. II-. ICauzmann of Princeton C-niversity, and Jlr. E. h.Hauser of the Massachusetts Institute of Technology for suggestions and valuahle disciissions during the preparation of this papei’. R F: FER E S C E S B.\L-ER,.J. I I . >. m u P I C K E I1:. .~G . . : J. Exptl. 1Icd. 64, 503 (1036 I . ( 2 ) BEAX, J . W .: Iicv. JIodern Phys. 10, 245 (1938). ( 3 ) DECHHOLU. H.. ASU PCHLESISGER.11.:13iochcm. %. 236, 386 (1931) . (4) HAUSER! E . -I,>.isu REEU.C . E . : .J. Phys. Cherii. 40, 1169 (19361. (5) I-IAL-SER, I
