A modified fixed-volume mixer for extended sucrose density gradients

.4NALYTIC.%L

HlOCH!AMISTRY

A Modified

41, 365-371 (1(3i1)

Fixed-Volume Sucrose Density s. H. NEFFl

Laboratory

for

Mixer for Gradients

Extended

CT.I,. MEEKER?

AND

Qurtntitntive Biology, Coral Garbles, Florida,

Univewity SUl2,$

of dliccnli,

Received August 20, 1970

No11 (1) and Kidby (2) have described fixed-volume gradient mixers which can produce a column of sucrose solution or acrylimide gel having an exponential variation of density with respect to the length of the column. These are convenient and inexpensive devices to build and use because the variation of density is dependent only on the amount of fluid which has passed through the mixer; thus, a precise punlping mechanism is not necessary. The density variation with length can be made linear (2) or convex (I), provided the less dense portion of the column is produced first. If the more dense portion is produced first, the gradient will have a less desirable concave variation of density with length, as shown by the lower curve of Fig. 1. It is experimentally more feasible to produce a sucrose gradient by allowing the more dense fluid to drain to the bottom of the cell rather than floating the less dense fluid to the top, since in the latter case a tube must be inserted through the gradient to the bottom of the cell and the gradient is likely to be disturbed when the tube is removed. For this reason we have modified t’he design of Kidby’s mixer so that we may produce a gradient with a more desirable variation of density with column length while depositing the more dense portion of the gradient first. Figure 2 presents a schematic drawing of our modified gradient mixer. The main mixing reservoir containing fluid with the desired maximum sucrose concentration is preceded by a small reservoir which initially contains nonzero concentration. Fluid with zero sucrose concentration is pumped continuously into the first reservoir, and an equal amount with continuously decreasing concentration leaves the main reservoir and is deposited in the ultracentrifuge cell. The effect of the small reser* Present Address: Department of Physics, Earlham College. Richmond. Indiana 47374. ’ Present Address: Department of Biology, Sacramento State College. Sarramento. California 95819. 365

FRACTION

OF

CELL

LENGTH

FIG. 1. Theoretical 50-1576 gradients that should be formed by single-chambered mixer depositing more dense material first (lower curve), and two-chambered device of a = 3. A linear gradient is also shown for comparison.

voir is to prevent the concentration from decreasing too rapidly with distance from the bottom of the cell. Mathematically we let yl and V, represent the volume and concentration of sucrose in the small reservoir, y and V similar quantities for the large reservoir, and yz the concentration of material entering the small reservoir. Further, let a = V/V, > 1.

2. Diagram

FIG.

Then the equations deposited, w, are:

of two-chambered

mixer.

governing the change in concentration d!Jl/dV = (yz - J/l)(U/V) dy/dv

If we let y3 = 0, then

= (y -

!J1)(1/V)

with volume (1) (2)

FIXED-\‘OLCME

GRADIENT

where y10 is the initial concentration Using (3) in (2)) we obtain:

MIXERS

of solution

367 in the small reservoir.

(4) It is technically convenient for yl,,, = yo. In this case the concentration will exceed the linear value at the top of the cell, and will be less than the linear value near the bottom. The extent to which this function differs from one with linear change in density can be minimized by proper choice of a. We have found that a good choice of a is a = 10R

where R is the ratio of the desired concentration at the top of the cell to that at the bottom. Once a has been chosen, V may be found by solution of the following:

where in this case w. represents the total volume of the cell to be filled. Equation (5) is a one-step iteration of (4), with y,,) = y0 and R = ~(v~)/y”. Further iterations are not necessary if R < a/10. In Fig. 3

368

KEFF

AND

MEEKER

we present values for vo/V for a = 2 through 5 and R = 0.1 through 0.5. Also included is a curve for a = 00 which gives v,,/V for a single reservoir device. A design procedure for obtaining the values of 8, and V needed to build a two-chambered mixer, given R and vO, would be as follows: 1. Let a = 10R. 2. Find v,/V from Fig. 3 for the given values of a and R (or evaluate 2J1,/V using equation (5) ) . 3. Then V = v,/ (vJV) , and V, = V/a. For example, using this procedure for a 50-15s gradient, we would obtain the following values for R = 0.3 and v,~ = 11.4 ml: a = 3,/vo/V = 1.61. Therefore V = 7.08 ml and V, = 2.35 ml. The theoretical curve for a gradient formed using a device of these dimensions is also presented in Fig. 1. It appears to be a considerable improvement over the single-reservoir device, having a standard deviation of 5% from the linear curve compared with 11% for the singlereservoir curve. In general, we find the same kind of improvement for values of R greater than 0.2-the larger R, the more linear the curve. For R less than 0.2, however, the predicted curves are so nonlinear that gradients made with such a device might not be suitable for density gradient centrifugation. METHODS

In our application, a 50-15s gradient was formed within an SW-41 centrifuge tube of volume 11.4 ml. As pointed out above, this particular gradient requires mixing volumes of 2.35 ml for the smaller chamber and 7.08 ml for the larger. These chambers were fashioned from disposable plastic syringe tips (2) cut from 30 ml and 50 ml syringes, respectively, and fixed with epoxy cement to the bottom of disposable plastic culture dishes as illustrated in Fig. 2. The output from the smaller chamber was led to the larger mixing reservoir through a short length of polyethylene catheter tubing. The input t’o the smaller chamber was a No. 26 hypodermic needle pushed through the side of the syringe tip and the output nipple was fitted with a No. 20 needle. The input to the larger chamber consisted of another No. 20 needle and the final output was a No. 18 needle fitted with another short length of catheter tubing leading to the centrifuge tube to be filled. Mixing was accomplished by magnetic stirring bars in each chamber. The total cost of t,he components was $5.85 exclusive of the magnetic stirring motors. In use, both mixing chambers were filled through the input to the

smaller chamber with 50% (w/v) sucrose made up in HERS3 buffer (3). HERS buffer was then injected through the system by hand using a 20 ml hypodermic syringe at a rate slow enough and steady enough to prevent significant disturbance of tho gradient. being formed. An 11.4 ml gradient can easily be formed in this way in less than 10 min. Gradients were allowed to stand overnight at 2°C before use. Gastrulae from the sea urchin Echinottlet~r luclrnter served as the test material. The embryos were washed twice in an isotonic salt solution (NaCl, 0.53 M; KCl, 0.03 M) by hand centrifugation and were homogenized in 1.5 vol HERS buffer. The homogenates were centrifuged at 12,500g for 15 min and 0.2 ml of the resulting supernatant was layered on each gradient. These gradients were then centrifuged at 39,000 rpm in a Beckman SW-41 rotor at 4” for 80 min. Gradients were scanned at 260 nm as described in (3). For refractive index determinations, the mixing chambers were filled with 30% sucrose and drop fractions were collected from the output catheter as 10 ml of distilled water was injected. The refract& indices were read on t,he Amcriran Optical model 10402 Goldberg refractometer and the readings were converted to per cent sucrose. RESULTS

AND

DISCUSSION

Figure 4 presents the measured concentration of sucrose solution produced by our 2-stage device as a fuuction of the total volume of fluid which has passed through the reservoir; in this case the initial sucrose concentration was 30%. The results indicate a nearly linear gradient,

FRACTION

OF

CELL

LENGTH

FIG. 4. Comparison of theoretical and measured concentrations of sucrose produced by two-chambered mixer as function of total volume of fluid that has passed through mixing reservoir. ‘O.OlM

Tris., 0.43M

KCl,

0.018M

MgCX,

pH

7.8.

370

KEFF

AND

MEEKER

which, at the top of the tube, would be more linear thau theory would predict,. The major deviation from linearity occurs in the bottom 1 ml of the tube, where the gradient flattens, as predictctl by theory. In scparation experiments, this region is less important, since relevant species need not reach this portion of the cell. Although the linearity of a gradient is important, the crucial test of a gradient maker is whet,her or not it gives well-resolved reproducible peaks. We made four similar gradients with end points of 50% and 15% sucrose solution and then centrifuged through them the sea urchin embryo material described above. A scan of one of the gradients after centrifugation is presented in Fig. 5. The results show sharp, symmetrical peaks,

I

I 1

I 2

01sT~NcE

I 3

FROM

I 4

TOP

(ARBITRARY

I 5

I 6

I 7

UNITS)

FIG. 5. Test of two-chambered mixer: profile (OD2,,) of an SW-41 N-1576 sucrose density gradient layered with sea urchin gastrula material and centrifuged at 39,000 rpm for 80 min.

demonstrating the presence of ribosomal subunits, monosomes, and six classes of polysomes in the homogenate. The resolution and separation compare favorably in this respect with previous results obtained with similar material centrifuged in linear gradients prepared with a Technicon proportioning pump (3). As a measure of the reproducibility of our gradients, we found that for the four similar gradients the same peaks were observed, and in every case the positions of the peaks were repeated to within 2% of the total migration distance. We consider these results ample proof of the reliability of this device in producing gradients that give consistently reproducible results.

FIXED-VOLCME

GRADIENT

371

MIXERS

ACKNOWLEDGMENT This work was supported in part. by NIH Grant GB-7709 to R. M. Iverson.

Training

Grant HD00187

and NSF

REFERENCES 1. NOLL, H., Nature 215, 360 2. KIDBY, D. K., Anal. Biochem. 3. IVERSEN, R. M., AND COHEN,

(1967). 34, 478

(1970).

G. H., in “The Cell Cycle” (G. M. Padilla, G. L. 14’hitson. and I. L. Cameron, eds.), p. 299. Academic Press, New York, 1969.