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H. KAHLER .4ND B. J. LLOYD, JR.
(9) HAWSER, E. A.: Colloidal Phenomena. McGraw-Hill Book Company, Inc., New York (1939). (10) HENRI,V . : Caoutchouc & gutta-percha 3, 510 (1W). (11) HODGE,A. J., AND REES, A. L. G.:In preparation. (12) JAKUS,M. A.,AND HALL,C. E . :J. Biol. Chem. 167, 705 (1947). (13) PORTER, K.R.,AND HAWN,C. V. Z . : J . Exptl. Med. 90,225 (1949). (14) ROZSA,G . , SZENT-GYORGYI, A . , A N D WYCKOFF, R. W. G . : Biochim. et Biophys. Acta 3, 561 (1949). (15) USHER,F. L.: Proc. Roy. SOC.(London) A126, 143 (1929). (16) VERWEY, E. J. W., AND OVERBEEK, J . TH.G.:Theory of the Stability of Lyophobic CoZloids. Elsevier Publishing Company, New York (1948). (17) WAIJGH, D. F.:J. Am. Chem. Soc. 68, 247 (1946);70, 1850 (1948).
SEDIMENTATION OF POLYSTYRENE LATEX I N A SWINGING-TUBE ROTOR H . KAHLER AND B. J. LLOYD, JR. National Cancer Institute, National Institutes of Health, U.S.Public Health Service, Bethesda, Maryland
Received September 18,1960 INTRODUCTION
I n those cases where the concentration of a particulate component is too low to run in the optical analytical ultracentrifuge cell, fractionation by sampling, followed by analytical procedures on the samples, has been frequently utilized. Examples of this are the divided cell of Tiselius et al. (9),the divided inclined tube of Rosenfeld (6),the inverted capillaries of Bechhold and Schlesinger (l), and the angle tube with sucrose gradient used by Pickels ( 5 ) . The last method can be utilized to determine the concentrations throughout most of the tube. Obvious objections (4, 5 ) to the use of inclined tubes, however, prompted the authors to design a rotor somewhat similar to the Collatz “ECCO”rotor, with swinging tubes for horizontal sedimentation, since this procedure would come nearer to that utilized in the Svedberg cell. APPARATUS AND METHOD
A sketch of the rotor’ is shown in figure 1, in which small plastic tubes holding 1.5 ml. of fluid are slipped into stainless-steel jackets, which are in turn held in place by steel pins. The six-place steel frame for carrying the tubes slips on the central post of the duralumin rotor. When a t rest the tubes incline at an angle of 45’ with the vertical. After the material has been centrifuged for a time estimated to bring the boundary one-third to one-half of the way down the tube, the tubes are removed 1
Made by Fritz Linke, Charlottesville, Virginia
SEDIbIENTATION OF POLYSTYRENE LATEX
1345
from the rotor and then from the jackets by the device shown in figure 2. This tube puller is simply a bolt with the same thread as the threaded top of the plastic tube, and mounted so that a gentle pull can be exerted without shaking. The tubes are next fractionated by means of the sampler (figure 3), which is a 2-ml. or 5-ml. pipet sealed a t the tip with two or four holes drilled radially just above the tip. MATERIAL
In selecting a material to be used for checking the performance of the two types of rotors the qualities desired were homogeneity, stability, availability, and a known size and density. Dow latex 580 G lot 3584 is known from electron
Fig. 1. Horizontal rotor. Left: Side view shows 45' inclined surface for resting position of tubes. Right: Top view shows six stainless-steel jackets holding celluloid tubes in running position. Steel pins t in. in diameter pass through stainless-steel jackets and through notches in the tops of the celluloid tubes. Diameter of rotor, 6 in.; usual distance t o fluid meniscus, 4 00 cm. The bottom of the rotor is fitted with 81 steel shaft, the lower end of which fits in a flexible adjustable bearing filled u i t h oil
microscopy to be spherical, with a diameter of 2600 A. (3). Sharp, from centrifuge measurements, gives the density a! 1.054, the sedimentation constant as 1960, and the particle diameter as 2520 A. ( 7 ) . The low density of these particles restricts the use of stabilizing gradients to ,small values. In the case of a concentrated solution of a heavy proteinit density gradient a t the boundary is automatically formed, which is sufficient to induce stability or freedom from convection across the boundary. Convection may occur in the region above and below the boundary, where the density is nearly constant (5). However, for a material as light as latex, particularly for dilute solutions, the density gradient a t the boundary is insufficient to prevent convection across the boundary when the tubes are removed for handling. Under these circumstances an added density gradient is necessary for boundary preservation. The concentration of this latex could be conveniently determined by means
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E. KAHLER AND B. J. LLOYD, JR.
e
F FIG.2 FIG.3 FIG. 2. Tube puller. The stainless-steel jacket on being removed from the rotor is placed in block F and held in place by clip D. Bolt A is screwed into the plastic tube C. Table His racked down on B, removing the tube from the jacket. FIG.3. Sampler. The tubes in block G are racked up on B until the tip of the pipet F passes through the fluid meniscus. The fluid is then pulled u p into the sampler by,careful withdrawal of the syringe plunger a t E. The inset of the pipet tip is a t F, indicating that the fluid enters horizontally from the sides of the celluloid tubes. As fluid is pulled up, the table is racked up 80 that the tip of the pipet remains just below the meniscus.
of turbidity measurements with a commercial photoelectric instrument, which was calibrated for this purpose by measuring the turbidity of a series of dilutions of the original uncentrifuged material.
1347
SEDIMENTATION OF POLYSTYRENE LATEX RESULTS
A . The inclined tube or angle rotor These tests were made to see how the conventional rotor would compare with the new rotor. The angle rotor used carried tubes holding 5 m.! and inclined a t 30" with the vertical. In sampling these tubes a 5-ml. sampling pipet was used, taking fractions of 0.6 ml. Usually seven fractions were taken. The tubes were filled with latex 580 G at a concentration of 0.007 per cent. In figure 4a is shown the distribution of latex in the seven fractions with no glycerol added, and with glycerol added to make a uniform 9 per cent solution. I
'
'
1
a 0
'
1
"1
i A 0.0% GLYCERINE
Q~~YCERINE NO GLYCElllHL
0 0.3% GLYCLRIWE
O0l0O
90
-
eo
, 1
l 'o0 1
2
FRACTION
3
4
a
g
7
FRACTION
a b FIG.4a. 30' angle rotor, no density gradient. Latex centrifuged in 0.9 p e r cent sodium 9 per cent glycerol (A). Conchloride solution ( 0 )and in 0.9 per cent sodium chloride
+
centrations are observed values. Fractions are 0.6 ml. each in volume. Radial distances of fractions are 0.132 cm. X fraction number plus meniscus distance. Speed of rotor, 120 R . P . S . Total time = 19.0 min., including acceleration and deceleration equivalents. No boundary after sampling. Fio. 4b. Same run as 4a, other tubes containing glycerol density gradients. Glycerol concentrationat top of tubeqis 0 per cent, a t bottom of tubes 3 per cent ( 0 )and 9 per cent
(A).
There is no indication of a sedimentation boundary in either case, and there is little material sedimented from the tubes containing 9 per cent glycerol 0.9 per cent sodium chloride, p = 1.024. In figure 4b, the same experiment, is shown the distribution when a glycerol density gradient was produced in the tubes. I n one case the glycerol concentration varied from 0 per cent at the top of the tube to 3 per cent at the bottom, while in the other case it varied from 0 per cent a t the top to 9 per cent a t the bottom. Both these tubes show boundaries near the middle fraction, but from the known homogeneity of the latex these boundaries are obviously too diffuse.
'+
B. Swinging-tube rotor The tubes holding 1.5 ml. were sampled in 0.2 ml. per fraction, similar fractions from several tubes being pooled for turbidity measurements. In figure 5 are
1348
H. IiAHLER AND B. J. LLOYD, JR.
shown the results of three different experiments performed under different conditions. The concentrations in the tubes with no density gradient shov no evidence of a boundary. This is probably due to convection. The concentrations with density gradients of glyerol give a sharper boundary than was obtained with the angle rotor. The shape of the plateau region is very sensitive to convection and stirring of material from the bottom sediment.
100 X
0
0
90
Ic
,
,
0
A o
/
I
/
,
0.5% GLYCERINE 3% GLYCERINE NO GRADIENT 0.9% GLYCERINE
i
4
BO
70 60
50 40
30 20 IO ' 0 1
2
3
4
5
6
7
FRACTION
FIG.5. Horizontal swinging-tube rotor. A : no density gradient; solvent, 0.9 per cent saline 3 per cent glycerol; no boundary after sampling: fractions are 0.2ml. each; time, 25.0 min.; speed, 120 R.P.S. 0 : glycerol density gradient 0 per cent a t top t o 9 per cent a t bottom; speed, 120 R . P . s . ; time, 25 min. 0 :glyceroldensitygradient0 percent t o 5 percent; speed, 120 R.P.s.; time, 31.5 min.
+
SEDIMENTATION CONSTANT OF LATEX 580 G The main object of this study mas to see how reliably the sedimentation constant could be determined by these methods. A number of runs were made on solutions so dilute that there would be no appreciable difference between the values obtained and the value a t infinite dilution. The actual runs were made a t 25"C., the temperature of the centrifuge being controlled by recirculating water. The mean value for five determinaJions was Szo = 2155. For a spherical parti$e this leads to a diameter of 2642 A. with a standard deviation of about 100 Ab The difference between this value and the electron-microscopic value of 2600 A. is therefore not significant. The conclusion seems warranted from these figures that the use of a swingingtube rotor followed by the sampling technic outlined should give the sedimentation constant to within 5 per cent, excluding errors in density and bioassay, for such particles as viruses. T H E EFFECT O F SOLVENT GRADIEhTS UPON CONCENTRATION O F SEDIMENTING MATERIAL
The concentration of sedimenting material in a cell in which it was assumed that no convection occurred has been calculated in detail (8). In the case of no
SEDIMENTATION O F POLYSTYRESE LATEX
1349
diffusion, the concentration e l in the part of the cell where it was constant (the plateau region) was shown to be c1 = co(s>’
where co is the original concentration, and 2 0 and me the positions at the times 0 and t. This equation was derived for a sector-shaped cell. I t is valid for a cylindrical tube of any cross-sectional shape, since the concentration change is determined solely by the radial direction and velocity change of sedimentation, excluding convection and rdntry of particles from the malls of the cell. In the following example, for simplicity, the cell is imagined to have parallel vertical walls for the sides and parallel horizontal walls for the top and bottom, the results applying equally well to a cylindrical tube of circular cross-section.
FIG.6. Illustrating the Bow of N particles from annulus A Dt o A t . Particles originally outside of e limits are thrown down a t the walls of the tube without contributing t o concentration in .4t. Any side convection carrying particles outside of angle e limits reduces the concentration in At by side-wall sedimentation.
With a gradient in density and viscosity an additional change in concentration is produced, owing to an added change in velocitywith distance of the sedimenting particles. Consider a group of N particles sedimenting radially with arbitrary velocity occupying an annulus of volume hrd dro (figure 6), where h is the height of the cell, e is the angle in radians, t o is the radial distance from the axis, and dro = uo dt; then co =
N -
htoOva dt
In the next time interval these particles occupy the annulus of volume hrlOal dt, and finally for the annulus a t time t the volume is hrtOvt dt.
Thus the concentration ratio after time t is proportional to the geometric factor due to spreading of the particles at right angles to the tube axis and to the inverse velocity ratio a t the two positions (for parallel motion c f / c o = vo/ul). The velocity ratio at the two positions as determined by centrifugal force is n / r 1and its dependence upon the viscosity q and density p of the medium can be obtained from rll (1 - VPO) 70 ( I - VPf)
TO/T(
1350
€ KAHLER I. AND B. J. LLOYD,
JR.
Vis the partial volume of the material. The subscripts on 7 and p refer to positions in the cell, giving
In time t the boundary moves from ro to r t . In other parts of the tube the distance moved b y any particle group can be approximated from the velocityradial distance graph constructed from assumed values of 7 and p in different parts of the centrifuge tube. I n the experiment illustrated in figure 5 (circles) the correction factor (rO/r,)z amounted to 0.71, while the gradient correction ?r (1 70
- Vm)
( I - VPl)
amounted to 1.13. ct/co for the plateau region was 0.71 X 1.13 = 0.80. Calculations for other parts in the tube showed that the concentration for particles starting 1.07 cm. from the meniscus was increased to only 0.81, indicating that the plateau is practically constant for the caw of a uniform gradient in the solvent medium. In the majority of experiments performed the experimentally measured concentrations in the plateau region were lower than the calculated values. This suggests that convection towards the sides of the straight-walled centrifuge tubes is responsible for 'an increased removal of material from the solution by means of side-wall sedimentation. BUMMARY
I n the absence of a density gradient, convection destroyed the sedimentation boundary. With a material of low density the conventional angle rotor gives boundaries too diffuse for satisfactory determination of sedimentation even with superimposed density gradients. On the other hand, the swinging-tube rotor described gave a sedimentation constant for polystyrene latex which leads to a particle diameter not significantly different from the electron-microscopic value. It was shown that the relative concentration of the material in the plateau region can be estimated by multiplying the usual corrections by a gradient correction factor. The observed concentrations were too low, suggesting side-wall sedimentation due to lateral convection during centrifugation. REFERENCES (1) BECHHOLD, H.,AND SCHLESINGER, M . : Biochem. 2. 236, 387 (1931). (2) FRIEDEWALD, W.F., AND PICKELS, E. G.: J. Exptl. Med. 79, 301 (1944). (3) GEROULD, C. H . : J . Applied Phys. 21, 183 (1950). (4) KINOSITA, K.:J. Colloid Sci. 4, 525 (1949). (5) PICKELS, E.G . : J. Gen. Physiol. 26, 341 (1943). (6) ROSENFELD, M.:Rev. Sqi. Instruments 18, 154 (1942). (7) SHARP,D.G.: J . Applied Phys. 21, 71 (1950). (8) SVEDBERG, T.,A N D PEDERSEN, K. : The Ultracentrifuge. Oxford University Press, London (1940). (9) TISELIUS, A., PEDERSEN, K. O., AND SVEDBERG, T . : Nature 140, 848 (1937).
