ANALYTICAL
BIOCHEMISTRY
Optimum
73, 78-92 (1976)
Conditions for High-Resolution Gradient Analysis’
R. W. ALLINGTON, M. K. BRAKKE, J. W. NELSON, C. G. ARON,AND B.A. LARKINS' Agricultural
Research Experiment
Service. Station;
U.S. Department oj’Agriculture; and Instrumentation Specialties Lincoln, Nebraska 68503
Nebraska Company,
Agricaltural
Received April 4, 1975; accepted February 10, 1976 The effect of experimental variables in the photometric scanning of centrifuged sucrose gradients on the apparent resolution was studied. Better resolution was obtained with a flow cell with a comparatively large diameter flow path that was designed for bulk flow than with a flow cell with a comparatively small diameter flow path that was designed for laminar flow. Degradation of resolution caused by an increase in the flow rate was more apparent with the laminar flow cell than with the bulk flow cell. The resolution increased as the illuminated volume of the flow cell decreased but was relatively insensitive to illuminated volume at the lower values tested. Resolution was determined by the number of pea polyribosomes resolved and the shape of their peaks and by the deterioration in shape of peaks given by zones of southern bean mosaic virus during repetitive scanning. It was found that resolution of ribosomal peaks is not a good quantitative method for characterizing instrumental performance.
Density-gradient centrifugation in sucrose gradients is widely used for analysis of macromolecules. Numerous procedures for analyzing centrifuged gradient columns have appeared (l-8). Many of these procedures give satisfactory results, as far as can be judged from published data. However, an accurate comparison of the different procedures is difficult for the following reasons. First, with the exception of Morton and Hirsch (4) and Morton (5), few authors have reported experimental comparisons of different systems or of variations in design of one system. Rather, ’ Cooperative investigations of the Agricultural Research Service, U.S. Department of Agriculture: the Nebraska Agricultural Experiment Station; and Instrumentation Specialties Co. of Lincoln. Nebr. Published with the approval of the Director as paper No. 3916, Journal Series, Nebraska Agricultural Experiment Station. Mention of a trademark or proprietary product does not constitute aguarantee or warranty of the product by the U.S. Department of Agriculture. nor does it imply its approval to the exclusion of other products that may also be suitable. 2 Respectively, President, Instrumentation Specialties Co.: Research Chemist, Agricultural Research Service, U.S. Department of Agriculture: Laboratory Director. Instrumentation Specialties Co.; Chemist, Instrumentation Specialties Co.; and Postdoctoral Fellow. School of Life Sciences, Purdue University, Lafayette, Ind.
78 Copyright All rights
0 197b by Academic Pres\, Inc. of reproduction in any form reserved.
HIGH-RESOLUTION
GRADIENT
ANALYSlS
79
results obtained with one system and one or two test preparations are given. Second, biological macromolecules are less than ideal as test materials. Their properties often vary in subtle ways from one preparation to another, and particularly from one laboratory to another. Third, the theory and practice of sucrose gradient centrifugation has not been developed to the point where actual resolution can be readily compared with that theoretically expected and the deviation expressed mathematically. Comparisons are subjective and conclusions may depend on the viewer. Schumaker and coworkers have made important advances in developing the theory of sucrose gradient centrifugation, especially for zonal rotors (9). One of the main practical results of this theory may be the ability to calculate diffusion coefficients from the observed zone width immediately after centrifugation (IO, 1 I), or from spreading of the zone in the gradient during storage after centrifugation. The feasibility of repeatedly analyzing gradients without destroying them or the suspended zones of macromolecules has been demonstrated (12,13). If diffusion coefficients are to be estimated, and if the best possible results from analysis based on sucrose gradient centrifugation are to be obtained, the analytical system must be carefully designed. Morton (5) reported that less mixing occurred when solutions of the same density were pumped through a 0.8 mm diameter tubing than when pumped through one of 1.6 mm diameter. On the basis of this result he designed a flow cell with small diameter pathways for analyzing density gradients which he claimed was superior to how cells with large diameter pathways. He did not, however, directly compare the two types of flow cells, as no density gradient was used. We report here a comparison of such cells for both single-pass and repetitive photometric scanning of gradients and the results of other variations in photometric scanning procedures for sucrose gradients. The accompanying paper (14) presents remarks on mathematical analysis of resolution. MATERIALS
AND METHODS:
I
Polyribosomes have been regarded as an ideal test sample for gauging the performance of analytical centrifugation methods (15). Therefore, they were used in this set of experiments. Replicate 5-ml gradients of 1, 1.5, 1.5, and 1 ml of 600, 450, 300, and 150 mg sucrose/ml of buffer, respectively, were layered in each tube and allowed to stand for 2 days. The buffer used for all polyribosome work was 0.01 M MgC&, 0.02 M KCl, and 0.04 M Tris-HCl, pH 8.5. Pea polyribosomes were prepared as described by Davies et al. (16) and used fresh or frozen. Either 1.40 or 1.80 A,,,,, units of polyribosome preparation in 70 ~1 of buffer were layered on top of each gradient; the amount being given in the pertinent figures. Six
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gradients in l/2 x 2 in. tubes were simultaneously centrifuged for 75 min at 45,000 rpm at 5°C in an SW-50.1 rotor in a Spinco L2-65B or L3-50 ultracentrifuge. Three gradients were scanned in one type of flow cell at various speeds. Afterwards the other three gradients were scanned in the other type of flow cell. Although the zones were in steep sucrose gradients, they diffusion-broadened perceptibly between the first and the last sets of scans. To prevent this broadening from producing a systematic error, one type of flow cell was used for the first three gradients in half the experiments, and the other type in the other half. Each comparison was repeated at least three times. The laminar flow cell system (Fig. 1) has a quartz 2-mm pathlength cell (obtained from Pyrocell Mfg. Co., Westwood, N.J.). The construction details have been published elsewhere (5), but an abbreviated description follows: The connecting tubing was 0.8 mm i.d. Tygon, 8 cm long. The coned fitting for the top of the centrifuge tube was constructed of Teflon, as were the flaired transition pieces that conduct the gradient from the 0.8 mm i.d. of the Tygon tubing to the 2 mm square cross section of the flow cell. The flow cell was masked on each face with a l.O-mm diam
DENSE CHASE SOLUTION
FIG. 1. Sectional view of laminar-flow analysis system. Dense chase solution is injected into the bottom of the l/2 x 2 in. centrifuge tube, thereby raising the centrifuged gradient and sample bands through the flow cell. The conduit leading from the cone over the centrifuge tube to the bottom of the flow cell has a diameter of 0.8 mm. Construction details are given in (5).
HIGH-RESOLUTION
GRADIENT
ANALYSIS
81
ENTRIFUGE TUBE WITH DENSITY GRADIENT
DENSE CHASE SOLUTION
FIG. 2. Sectional view of bulk-flow analysis system. Dense chase solution is injected into the bottom of the l/2 x 2 in. centrifuge tube, as in Fig. 1. The conduit leading from the cone over the centrifuge tube to the bottom of the light path area of the flow cell has a diameter of 6.4 mm.
aperture. The illuminated volume was 1.6 ~1 and the volume inside the cell, corresponding to the height of the l-mm aperture, was 4 ~1. The system designed according to the bulk flow concept (Fig. 2) consists of a catalog No. 0085U “universal flow cell” with a collar to fit l/2 x 2 in. centrifuge tubes (ISCO, Lincoln, Nebr. 68505). A 6.4-mm diam conduit leads upward from the conical transition above the centrifuge tube to the bottom of the transition into the light path volume. The flow cell had an optical path length of 5 mm and horizontal slits 1 mm high. The total volume of liquid in the flow cell at the level of the light beam, 14 ~1, was illuminated. Cells with 2- and lo-mm light paths and slit heights of 2.8 mm as well as 1 mm were also tested. The absorbance measuring system was an ISCO Model UA-5 absorbance monitor with a Type 6 optical unit. The bulk flow cell clips directly into the Type 6 optical unit. A simple adaptor was made to hold the laminar style flow cell in the optical unit. The wavelength used was 254 nm. The cell used to evaluate laminar flow fractionation was built according to a laminar flow design which had been tested by Morton (5) and found to operate properly with narrow bore connecting passages. It is possible that the ISCO cell, being basically of bulk flow design, would not function properly if it were merely modified to narrow its connecting passages. Conversely a standard ISCO flow cell was used to evaluate bulk flow fractionation, rather than modifying the laminar flow cell to incorporate large bore connecting passages.
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The standard procedure was to inject dense sucrose solution into the bottom of the centrifuge tube at 0.5 or 0.6 ml/min by the tube piercing mode of operation of an ISCO Model 640 density-gradient fractionator. This apparatus has a rigid, cylindrical glass syringe barrel with a Delrin plunger head and an o-ring seal for injecting the chase solution rather than a plastic disposable syringe. The flexibility of the latter gives the plunger a stick-slip or chattering action and results in flow pulsations, while the former is free of this problem. Furthermore, the tapered shape necessary for manufacturing molded plastic syringes causes the flow rate to decrease slightly as the syringe plunger advances. Injection of the chase solution through a “dipstick” I8-gauge needle, inserted down through the top of the gradient, was also tested.
FIG. 3. Scanning patterns of S-ml gradient columns containing 1.3 A,,,,, units of pea polyribosomes centrifuged simultaneously for 75 min at 5°C. 45,000 rpm in the SW-50.1 rotor. Patterns A, B, C, and D were scanned with a bulk-flow type cell with a 5-mm light path with 14-~1 illuminated volume at rates of 0.2, 0.5, 1.0, and 2.0 mlimin, respectively. Pattern E was obtained with a bulk-type flow cell with a IO-mm light path and a 78-~1 illuminated volume at a flow rate of 0.5 ml/min. The chart speed was adjusted to maintain a similar length of pattern at different Bow rates. The arrow points to the ILmer. which was the highest polymer detected in D and E, whereas a Ih-mer is readily apparent in A and B with shoulders for 17-mer and 18-mer.
HIGH-RESOLUTION
GRADIENT
RESULTS: Effect of Experimental
83
ANALYSIS
I
Variables
It was found that patterns varied with the polyribosome preparations, and valid comparisons can be made only between patterns from the same preparation. For example, after centrifugation in the 112 x 2 in. tubes of the SW-50.1 rotor, 16 to 17 polyribosome peaks were resolved with the bulk flow system for one preparation (Fig. 3), but only 12 to 13 for another (Fig. 4). With the latter preparation and linear HO-600 mg sucrose/ml gradients, 16 peaks were detected after centrifuging for 6 hr at 25,000 rpm in the 5/8 x 4 in. tubes of the SW-27 rotors, 15 after centrifuging for 100 min at 35,000 rpm in the 9/16 x 2-l/2 in. tubes of the SW-41 rotor, and 12 after centrifuging for 50 min in the l/2 x 2 in. tubes of the SW-50.1 rotor. All subsequent experiments were done with the SW-50.1 rotor, even though it did not give best results, because shorter centrifugation times were
0
1
2 3 4 GRADIENT ML,
5
0
1
2 3 1 GRADIENT ,ML,
I
FIG. 4. Scans at 254 nm of pairs of simultaneously prepared and centrifuged pea polyribosome preparations. The left-half set of three was analyzed with the laminar flow system shown in Fig. I. The right-half set was analyzed with the bulk flow system shown in Fig. 2. Polyribosome preparations (70 ~1) were centrifuged in a 150-600 mg/ml sucrose gradient in an SW-50. I rotor for 75 min at 45,000 rpm, 5°C. Various instrumental sensitivities were used during scanning to make the patterns more directly comparable.
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RESE-RVOIR
LIGHT
CONED
CENTRIFUGE TUBE WITH DENSITY GRADIENT
PATH
FITTING
CENTRIFUGE TUBE WITH DENSITY GRADIENT DENSE CHASE SOLUTION
DENSE CHASE SOLUTION
5
-’
1
6
FIGS. 5 and 6. Sectional views of analysis flow systems adapted for multiple scanning. Reservoir tubes are attached above the flow cells with mirror-image symmetry (about the planes of the light paths) with respect to the centrifuge tubes below the light paths. Figure 5 is the laminar flow system, modeled after that shown in Fig. 1. Figure 6 is the bulk flow system, modeled after that shown in Fig. 2. Multiple scanning was accomplished by first injecting dense chase solution into the bottom of the centrifuge tube, which raised the gradient past the light path and up into the reservoir tube. Then the chase solution was withdrawn, lowering the gradient past the light path and back into the centrifuge tube.
desired, and it has been more frequently used for polyribosomes than the other rotors. Polyribosome patterns also vary with other experimental conditions. Therefore, experiments were conducted to select conditions in which results would vary only slightly with minor variations in procedure. The slower the chase solution was introduced, the better was the polyribosome pattern, though 0.5 ml/min and 0.2 ml/min gave nearly identical patterns with the bulk flow cell (Fig. 3). Although 1 ml/min gave slightly poorer patterns, 2 ml/min gave considerably poorer ones. These results are consistent with those reported elsewhere for a laminar flow cell (5). Chart speeds were adjusted so that all scans being compared had nearly the same
HIGH-RESOLUTION
GRADIENT
ANALYSIS
85
length. A standard speed of 0.5 or 0.6 ml/min was used for all other comparisons reported. Nearly identical patterns were obtained with the ISCO flow cells with light paths of 10, 5, and 2 mm when 1 mm high horizontal slits were used (data not shown). Illuminated volumes were 28, 14, and 5.6 ~1 for the three cells, respectively. However, poorer results were obtained with a cell with a l-cm light path and a 2.8-mm slit (78 ~1 vol; Fig. 3). A cell with a 5-mm light path and l-mm slit was used for other comparisons reported. Identical results were obtained when the chase solution was introduced through the “dipstick” needle and through the standard bottom puncture method. The latter procedure was routinely used for other comparisons reported. Comparison of Flow Cells
The bulk flow cell with 5-mm path length and l-mm slits consistently gave perceptibly better polyribosome patterns than did the laminar flow cell used at the same scanning speeds, regardless of which cell was used first in analyzing the gradients of a particular centrifugation. A comparison of the pairs of patterns from the same polyribosome preparation and the same centrifugation shows that more peaks were consistently detected with the bulk flow cell than with the laminar (Fig. 4). The ratio of peak height to valley was greater with the bulk flow cell than with the laminar flow cell. Fewer peaks were detected in Fig. 4 than in Fig. 3 because a different polyribosome preparation was used. CRITIQUE OF METHOD
As noted earlier, variations from batch to batch of pea polyribosome preparations were greater than the difference observed in the scanning resolutions of the laminar and bulk flow systems being compared. For this reason alone, we feel that counting the number of observable polyribosome peaks is not a good quantitative measure of instrumental resolution. A further problem is that the absolute value of degradation of resolution with any given system cannot be determined; only the difference between two systems can be found. This method cannot enable one to attach a numerical value to instrumental performance. For these reasons, a second set of experiments was run using an experimental design that eliminated these variables. MATERIALS
AND METHODS:
II
In the second set of experiments the bulk flow system and the laminar flow system were compared with a multiple scanning method analogous to that reported earlier (12,13). Reservoir tubes were attached to the top
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ET AL.
of the flow cells of both systems in a manner symmetrical with the attachment of the centrifuge tubes below the flow cells. In each system, the diameter of the upper connecting conduit was the same as that of the lower conduit; 6.4 mm diam for the bulk flow system and 0.8 mm diam for the laminar flow system. In both systems, the upper reservoir tubes were equal in inside diameter to the centrifuge tubes. In each system, the cone fitting that connected the reservoir tube to the upper conduit was shaped like the cone fitting that connected the centrifuge tube to the lower conduit. The laminar flow system was constructed as reported earlier (3, with the added reservoir tube and connecting conduit being a mirror image of the flow system below the light path (Fig. 5). The bulk flow system was constructed the same as an IX0 catalog No. 0085U “universal flow cell” with a collar to fit a l/2 x 2 in. centrifuge tube, except that it was modified to be symmetrical about the light path. This flow cell had a path length of 5 mm and horizontal slits 1 mm high (Fig. 6). Purified southern bean mosaic virus (70 pg) was centrifuged for 90 min at 45,000 rpm at 5°C through linear 150-600 mg sucrose/ml gradients with the sucrose dissolved in 0.1 M, pH 7.0 phosphate buffer. RESULTS:
II
Tracings of multiple scans from the chart record of a 1.5 ml/min flow rate test of the laminar and bulk flow systems are shown in Fig. 7. The difference between the laminar and bulk flow results were consistant in every run and reflect the effect of the differing conduit diameters. The baselines were higher when the gradient was pumped down than when it was pumped up. This phenomenon was investigated further by scanning blank gradients with both systems. The shift in baseline was still present (Fig. 8). However, no baseline shift occurred with a solution of constant density was pumped up and down. We suggest that this baseline shift results from a cylindrical lens effect. When flow is upwards, an
FIG. 7. Typical multiple 254-nm scans of ca. 300~~1 SBMV zones. Run A used the laminar flow system shown in Fig. 5 and Run B used the bulk flow system shown in Fig. 6. Dense chase solution was injected into and withdrawn from the bottoms of the centrifuge tubes at a rate of 1.5 mYmin. The 5 ml gradients had 150-600 mg sucrose/ml and were both centrifuged in the same rotor for 90 min at 45,000 rpm. 5°C in an SW-50.1 rotor.
HIGH-RESOLUTION
GRADIENT
ANALYSlS
87
FIG. 8. Baseline shift at 254 nm due to flow reversal. Blank gradients of 150-600 mg sucrose/ml in 112 x 2 in. tubes were repetitively transported through flow cells at 1.5 ml/min. Scale factors are the same as in Fig. 7. Baseline shift with laminar flow style cell is shown in A and bulk Row style cell in B.
isodensity surface moving through the flow cell deforms upwards at its center because wall friction produces a downward force at the periphery of the gradient stream. As a result of this deformation, the center of the liquid in the light path has a higher refractive index than the liquid nearer the edges of the light path, thus producing a converging cylindrical lens. The opposite effect, and a diverging cylindrical lens, exists when the flow is downwards. Consequently, the light intensity reaching the photocell would be less for downwards flow than for upwards flow. This conclusion agrees with the observed results, that is, a higher baseline (less light) for downward flow than for upward. The deformation may be a displacement of the center of the gradient with respect to the periphery of the gradient. The magnitude of such a displacement would reach an equilibrium value when the stabilizing force of the density gradient equals the wall friction force. When these two forces reach equilibrium, the periphery would move at the same velocity as, but lag behind, the center. As the gradient leaves the top of the flow cell and enters the larger-diameter section of the reservoir, the stabilizing effect of the gradient would reflatten isodensity surfaces. An alternative possibility that would explain the cylindrical lens effect is the possible existance of a true velocity profile such as occurs with laminar flow. In such a case, the center of the density gradient would continuously and progressively advance ahead of the periphery to a point where the density gradient would not reorient perfectly as it leaves the flow cell and goes into the reservoir. Instead there would be a mixing effect related to the volume of the flow cell. In the cell used with the bulk flow system, mixing would be most likely to take place in the constricted region near the center of the cell. Here the wall friction will be greatest and the density gradient weakest. The volume of this constricted region is 400 ~1. It will be shown later in this paper that the amount of zone broadening per scan with the bulk flow system is 2.4 ~1, a very small fraction of the volume
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ET AL.
C
FIGURE
9.
HIGH-RESOLUTION
GRADIENT
ANALYSIS
89
of the flow cell. Therefore the amount of mixing in the flow cell of the bulk flow system is negligible; so one can conclude that there exists only a temporary displacement of the center with respect to the periphery of the gradient, and not a true velocity profile. The nature of the flow inside the cell of the laminar flow system is not as clear, as the zone broadening per scan was found to be of the same order of magnitude as the total internal volume of the cell. To determine quantitatively the amount of resolution degradation per scan, we plotted the consecutive percent increases in peak width at halfheight for flow rates of 0.3,0.6, and 1.5 ml/min for both the laminar flow and bulk flow systems (Fig. 9). Each point shown is the average of data from two replicate runs. There was considerable scatter in the points for the laminar flow system at the two higher flow rates, because the rapid rate of peak degradation per scan made it difficult to determine the true baseline for each scan. For this reason, the lines indicating the degradation increase per scan for these two plots have slopes equal to the average slope of lines from the origin to the individual points. The remaining straight lines were drawn through the origins to produce the visible best fit with the data. Additionally, the difficulty in determining the exact baseline, because of the cylindrical lens effect, caused a noticeable shift in the data of the upwards scans with respect to the downwards scans. However, this effect averages out over the eight scans made in each run. The degradation per scan with respect to the flow rate is plotted for both the laminar and the bulk flow systems (Fig. 10). The points are the slopes of the respective straight lines in Fig. 9. The bulk flow system produced significantly less degradation per scan. The resolution with the bulk flow system was only slightly affected by flow rate, whereas the resolution with the laminar flow system initially degraded rapidly with increasing flow rate and then leveled out at a comparatively high value. DISCUSSION
Two passes through one-half of the system take place between successive peaks displayed in Fig. 7. For example, between the first and second peaks, the zone had passed upward from the flow cell into the reservoir tube, and then downward from the reservoir tube back to the flow cell. Therefore, the increase in the width of the zone when a gradient column
FIG. 9. Increases in peak width measured at half height with multiple scans of ca. 300~~1 SBMV zones. Multiple scans were made with the laminar flow system shown in Fig. 5 and the bulk flow system shown in Fig. 6. Two replicate runs were made with each system at each flow rate (A, 0.3; B, 0.6; and C, 1.5 mYmin). Points shown are averages of the two replicate runs. Odd numbered scans are in the upwards direction. The 5-ml gradients of 150-600 mg sucrose/ml were centrifuged in pairs for 90 min at 45,000 rpm, 5°C in an SW-50.1 rotor.
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is pumped through a flow cell once, as is usually done, should be half that indicated in Fig. 10. Based on this, the zone spreading on the initial scan with the bulk flow analysis process was about 0.8%, compared to about 7.3% with the laminar flow process. This is the zone spreading when the sample passes from the centrifuge tube and through the flow cell. An additional degradation may occur by the time that drops are collected. These figures are for a flow rate of 0.6 ml/min, which results in analysis time of approximately 9 min for an SW-50.1 tube, and apply to relatively wide (ca. 300 ~1) virus zones. Since the increase in zone width per scan was a linear progression, the zone broadenings at half-height during the initial scan may be calculated to be 22 ~1 for the laminar flow analysis process and 2.4 ~1 for the bulk flow process. The degree of broadening agrees with results obtained in the experiment with polyribosomes (Fig. 4). Consider the increasingly narrow peaks shown for the bulk flow process at the point where the peak widths at half height first begin to closely approach the widths of the valleys between peaks at half height, at about the 8-mer. This approach to equality implies a peak-to-peak separation of about 4a, where CTis the standard deviation, for a group of multiple Gaussian peaks (14). Here the full peak widths are about 90 ~1, and the laminar flow process peak-to-valley heights are slightly less than half that for the bulk-flow process. If the resolution
LAMINAR
BULK
L&-L__L_.LJ 0 06 FLOW
RATE
FLOW
SYSTEM
FLOW SYSTEM
0.9
12
1.5
mllmin
FIG. 10. Degradation of resolution per scan vs flow rate. Data points are the slopes of peak width broadening plotted against number of scans from Fig. 9. Zones of SBMV (300 pg) in a 1.50-600 mg/ml sucrose gradient were used. Degradation of resolution on the first scan of a centrifuged density gradient is half that plotted here (see text). First-scan degradations at the 0.6 ml/min flow rate may be expressed as zone spreadings of 22 ~(1 for the laminar flow system and 2.4 ~1 for the bulk flow system.
HIGH-RESOLUTION
GRADIENT
91
ANALYSIS
was 4a for the bulk flow process, this halving means that the resolution dropped to 3a for the laminar flow process (14). It can be shown that a spreading at half height of 2.4 ~1 on peaks 90 ~1 apart that are separated by 4.3 lo would produce the observed bulk flow resolution of 4~. A 22-~1 spread on these same 4.31~ peaks would reduce their separation to 2.94a, which is close to the observed value of 3~. A 2.4-~1 spread at half height was found for the first scan of a single virus zone when the bulk flow cell was used and 22 ~1 when the laminar flow cell was used. This agreement is closer than the recorder chart record can be read. If it were not for the possible existence of a “hump” in the baseline under the fine peaks, it would be more accurate to make this check on agreement by basing calculations on the ratio of peak-valley height to average height above baseline, instead of the method used. A hump is suspectea because the number of peaks observed varied with different preparations. Also the ratio of peak-valley height to height above baseline level was less than theoretical for peaks whose separations approach 4~ (14). For example, in Fig. 4D, assuming a flat baseline and noting that the S- through 12-mer peaks have roughly the same height, we calculate a separation of 2.4% for the S-mer peak from the ratio of peak-valley heights to heights above baseline. This calculated separation is clearly less than the actual separation of 4~. If the 8-mer peak were separated by only 2.4%, then the peak-valley heights of the 9- through 1 I-mer peaks do not bear the proper relation to their widths; they are much too high (14). Evidently the baseline is elevated under the 8-mer peak and rises even higher under the 9-, lo-, and 1 I-mer. A baseline hump could result from variable proportions of materials whose concentrations do not have the same periodicity as the polyribosomes in the perceptible peaks. This could be due, for example, to heterogeneity in the conformations of the polyribosomes or lack of ability of the centrifugation process to resolve polydisperse impurities. CONCLUSIONS
Based upon comparison, a bulk flow path with large flow passages provides better resolution than a laminar flow path with small flow passages. One should not infer from the results presented that we draw any additional conclusions as to the relative merits of the two apparatuses tested. However, we do draw further conclusions which are not based upon system comparison. These are that the effective illuminated flow cell volume should not exceed 28 ~1. and that polyribosome peaks do not provide a good quantitative measurement of instrumental resolution. REFERENCES 1. Brakke. 2. Herzog.
M. K. (1963)Ana/. Biochem. 5. 271. A., Lombaert, R.. and Hamers. R. (1966)
Anal.
Biochem.
14, 149.
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3. Leif, R. C. (1%8) Anal. Biochem. 25, 271. 4. Morton, B. E., and Hirsch, C. A. (1970) Anal. Biochem. 34, 544. 5. Morton, B. E. (1973) Anal. Biochem. 52, 421. 6. Hopkins, T. R. (1973)Anal. Biochem. 53, 339. 7. Liedtke, R.. and Moseback, K. 0. (1974) Anal. Biochem. 62, 377. 8. Bresch. H., and Meyer, H. (1973)Anal. Biochem. 53, 199. 9. Schumaker, V. N. (1967). Adv. in Biol. and Med. Phys. 2, 245. 10. HalsaIl, H. B., and Schumaker, V. N. (1970)Biochem. Biophys. Res. Commun. 39,479. 11. Halsall, H. B., and Schumaker, V. N. (1972) Biochemistry 11, 4692. 12. Brakke, M. K., and Van Pelt, N. (1968) Anal. Biochem. 26, 242. 13. Brakke, M. K., Ailington, R. W., and Langille. F. A. (1968) Anal. Biochem. 24, 30. 14. Allington, R. W. (1976) Anal. Biochem. 73, 93. 1.5. Nell, H. (1969) Annl. Biochem. 25, 130. 16. Davies, E., Larkins, B. A., and Knight, R. (1972) Plant. Physiol. 50, 581-584.
BIOCHEMISTRY
Optimum
73, 78-92 (1976)
Conditions for High-Resolution Gradient Analysis’
R. W. ALLINGTON, M. K. BRAKKE, J. W. NELSON, C. G. ARON,AND B.A. LARKINS' Agricultural
Research Experiment
Service. Station;
U.S. Department oj’Agriculture; and Instrumentation Specialties Lincoln, Nebraska 68503
Nebraska Company,
Agricaltural
Received April 4, 1975; accepted February 10, 1976 The effect of experimental variables in the photometric scanning of centrifuged sucrose gradients on the apparent resolution was studied. Better resolution was obtained with a flow cell with a comparatively large diameter flow path that was designed for bulk flow than with a flow cell with a comparatively small diameter flow path that was designed for laminar flow. Degradation of resolution caused by an increase in the flow rate was more apparent with the laminar flow cell than with the bulk flow cell. The resolution increased as the illuminated volume of the flow cell decreased but was relatively insensitive to illuminated volume at the lower values tested. Resolution was determined by the number of pea polyribosomes resolved and the shape of their peaks and by the deterioration in shape of peaks given by zones of southern bean mosaic virus during repetitive scanning. It was found that resolution of ribosomal peaks is not a good quantitative method for characterizing instrumental performance.
Density-gradient centrifugation in sucrose gradients is widely used for analysis of macromolecules. Numerous procedures for analyzing centrifuged gradient columns have appeared (l-8). Many of these procedures give satisfactory results, as far as can be judged from published data. However, an accurate comparison of the different procedures is difficult for the following reasons. First, with the exception of Morton and Hirsch (4) and Morton (5), few authors have reported experimental comparisons of different systems or of variations in design of one system. Rather, ’ Cooperative investigations of the Agricultural Research Service, U.S. Department of Agriculture: the Nebraska Agricultural Experiment Station; and Instrumentation Specialties Co. of Lincoln. Nebr. Published with the approval of the Director as paper No. 3916, Journal Series, Nebraska Agricultural Experiment Station. Mention of a trademark or proprietary product does not constitute aguarantee or warranty of the product by the U.S. Department of Agriculture. nor does it imply its approval to the exclusion of other products that may also be suitable. 2 Respectively, President, Instrumentation Specialties Co.: Research Chemist, Agricultural Research Service, U.S. Department of Agriculture: Laboratory Director. Instrumentation Specialties Co.; Chemist, Instrumentation Specialties Co.; and Postdoctoral Fellow. School of Life Sciences, Purdue University, Lafayette, Ind.
78 Copyright All rights
0 197b by Academic Pres\, Inc. of reproduction in any form reserved.
HIGH-RESOLUTION
GRADIENT
ANALYSlS
79
results obtained with one system and one or two test preparations are given. Second, biological macromolecules are less than ideal as test materials. Their properties often vary in subtle ways from one preparation to another, and particularly from one laboratory to another. Third, the theory and practice of sucrose gradient centrifugation has not been developed to the point where actual resolution can be readily compared with that theoretically expected and the deviation expressed mathematically. Comparisons are subjective and conclusions may depend on the viewer. Schumaker and coworkers have made important advances in developing the theory of sucrose gradient centrifugation, especially for zonal rotors (9). One of the main practical results of this theory may be the ability to calculate diffusion coefficients from the observed zone width immediately after centrifugation (IO, 1 I), or from spreading of the zone in the gradient during storage after centrifugation. The feasibility of repeatedly analyzing gradients without destroying them or the suspended zones of macromolecules has been demonstrated (12,13). If diffusion coefficients are to be estimated, and if the best possible results from analysis based on sucrose gradient centrifugation are to be obtained, the analytical system must be carefully designed. Morton (5) reported that less mixing occurred when solutions of the same density were pumped through a 0.8 mm diameter tubing than when pumped through one of 1.6 mm diameter. On the basis of this result he designed a flow cell with small diameter pathways for analyzing density gradients which he claimed was superior to how cells with large diameter pathways. He did not, however, directly compare the two types of flow cells, as no density gradient was used. We report here a comparison of such cells for both single-pass and repetitive photometric scanning of gradients and the results of other variations in photometric scanning procedures for sucrose gradients. The accompanying paper (14) presents remarks on mathematical analysis of resolution. MATERIALS
AND METHODS:
I
Polyribosomes have been regarded as an ideal test sample for gauging the performance of analytical centrifugation methods (15). Therefore, they were used in this set of experiments. Replicate 5-ml gradients of 1, 1.5, 1.5, and 1 ml of 600, 450, 300, and 150 mg sucrose/ml of buffer, respectively, were layered in each tube and allowed to stand for 2 days. The buffer used for all polyribosome work was 0.01 M MgC&, 0.02 M KCl, and 0.04 M Tris-HCl, pH 8.5. Pea polyribosomes were prepared as described by Davies et al. (16) and used fresh or frozen. Either 1.40 or 1.80 A,,,,, units of polyribosome preparation in 70 ~1 of buffer were layered on top of each gradient; the amount being given in the pertinent figures. Six
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gradients in l/2 x 2 in. tubes were simultaneously centrifuged for 75 min at 45,000 rpm at 5°C in an SW-50.1 rotor in a Spinco L2-65B or L3-50 ultracentrifuge. Three gradients were scanned in one type of flow cell at various speeds. Afterwards the other three gradients were scanned in the other type of flow cell. Although the zones were in steep sucrose gradients, they diffusion-broadened perceptibly between the first and the last sets of scans. To prevent this broadening from producing a systematic error, one type of flow cell was used for the first three gradients in half the experiments, and the other type in the other half. Each comparison was repeated at least three times. The laminar flow cell system (Fig. 1) has a quartz 2-mm pathlength cell (obtained from Pyrocell Mfg. Co., Westwood, N.J.). The construction details have been published elsewhere (5), but an abbreviated description follows: The connecting tubing was 0.8 mm i.d. Tygon, 8 cm long. The coned fitting for the top of the centrifuge tube was constructed of Teflon, as were the flaired transition pieces that conduct the gradient from the 0.8 mm i.d. of the Tygon tubing to the 2 mm square cross section of the flow cell. The flow cell was masked on each face with a l.O-mm diam
DENSE CHASE SOLUTION
FIG. 1. Sectional view of laminar-flow analysis system. Dense chase solution is injected into the bottom of the l/2 x 2 in. centrifuge tube, thereby raising the centrifuged gradient and sample bands through the flow cell. The conduit leading from the cone over the centrifuge tube to the bottom of the flow cell has a diameter of 0.8 mm. Construction details are given in (5).
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ANALYSIS
81
ENTRIFUGE TUBE WITH DENSITY GRADIENT
DENSE CHASE SOLUTION
FIG. 2. Sectional view of bulk-flow analysis system. Dense chase solution is injected into the bottom of the l/2 x 2 in. centrifuge tube, as in Fig. 1. The conduit leading from the cone over the centrifuge tube to the bottom of the light path area of the flow cell has a diameter of 6.4 mm.
aperture. The illuminated volume was 1.6 ~1 and the volume inside the cell, corresponding to the height of the l-mm aperture, was 4 ~1. The system designed according to the bulk flow concept (Fig. 2) consists of a catalog No. 0085U “universal flow cell” with a collar to fit l/2 x 2 in. centrifuge tubes (ISCO, Lincoln, Nebr. 68505). A 6.4-mm diam conduit leads upward from the conical transition above the centrifuge tube to the bottom of the transition into the light path volume. The flow cell had an optical path length of 5 mm and horizontal slits 1 mm high. The total volume of liquid in the flow cell at the level of the light beam, 14 ~1, was illuminated. Cells with 2- and lo-mm light paths and slit heights of 2.8 mm as well as 1 mm were also tested. The absorbance measuring system was an ISCO Model UA-5 absorbance monitor with a Type 6 optical unit. The bulk flow cell clips directly into the Type 6 optical unit. A simple adaptor was made to hold the laminar style flow cell in the optical unit. The wavelength used was 254 nm. The cell used to evaluate laminar flow fractionation was built according to a laminar flow design which had been tested by Morton (5) and found to operate properly with narrow bore connecting passages. It is possible that the ISCO cell, being basically of bulk flow design, would not function properly if it were merely modified to narrow its connecting passages. Conversely a standard ISCO flow cell was used to evaluate bulk flow fractionation, rather than modifying the laminar flow cell to incorporate large bore connecting passages.
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The standard procedure was to inject dense sucrose solution into the bottom of the centrifuge tube at 0.5 or 0.6 ml/min by the tube piercing mode of operation of an ISCO Model 640 density-gradient fractionator. This apparatus has a rigid, cylindrical glass syringe barrel with a Delrin plunger head and an o-ring seal for injecting the chase solution rather than a plastic disposable syringe. The flexibility of the latter gives the plunger a stick-slip or chattering action and results in flow pulsations, while the former is free of this problem. Furthermore, the tapered shape necessary for manufacturing molded plastic syringes causes the flow rate to decrease slightly as the syringe plunger advances. Injection of the chase solution through a “dipstick” I8-gauge needle, inserted down through the top of the gradient, was also tested.
FIG. 3. Scanning patterns of S-ml gradient columns containing 1.3 A,,,,, units of pea polyribosomes centrifuged simultaneously for 75 min at 5°C. 45,000 rpm in the SW-50.1 rotor. Patterns A, B, C, and D were scanned with a bulk-flow type cell with a 5-mm light path with 14-~1 illuminated volume at rates of 0.2, 0.5, 1.0, and 2.0 mlimin, respectively. Pattern E was obtained with a bulk-type flow cell with a IO-mm light path and a 78-~1 illuminated volume at a flow rate of 0.5 ml/min. The chart speed was adjusted to maintain a similar length of pattern at different Bow rates. The arrow points to the ILmer. which was the highest polymer detected in D and E, whereas a Ih-mer is readily apparent in A and B with shoulders for 17-mer and 18-mer.
HIGH-RESOLUTION
GRADIENT
RESULTS: Effect of Experimental
83
ANALYSIS
I
Variables
It was found that patterns varied with the polyribosome preparations, and valid comparisons can be made only between patterns from the same preparation. For example, after centrifugation in the 112 x 2 in. tubes of the SW-50.1 rotor, 16 to 17 polyribosome peaks were resolved with the bulk flow system for one preparation (Fig. 3), but only 12 to 13 for another (Fig. 4). With the latter preparation and linear HO-600 mg sucrose/ml gradients, 16 peaks were detected after centrifuging for 6 hr at 25,000 rpm in the 5/8 x 4 in. tubes of the SW-27 rotors, 15 after centrifuging for 100 min at 35,000 rpm in the 9/16 x 2-l/2 in. tubes of the SW-41 rotor, and 12 after centrifuging for 50 min in the l/2 x 2 in. tubes of the SW-50.1 rotor. All subsequent experiments were done with the SW-50.1 rotor, even though it did not give best results, because shorter centrifugation times were
0
1
2 3 4 GRADIENT ML,
5
0
1
2 3 1 GRADIENT ,ML,
I
FIG. 4. Scans at 254 nm of pairs of simultaneously prepared and centrifuged pea polyribosome preparations. The left-half set of three was analyzed with the laminar flow system shown in Fig. I. The right-half set was analyzed with the bulk flow system shown in Fig. 2. Polyribosome preparations (70 ~1) were centrifuged in a 150-600 mg/ml sucrose gradient in an SW-50. I rotor for 75 min at 45,000 rpm, 5°C. Various instrumental sensitivities were used during scanning to make the patterns more directly comparable.
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RESE-RVOIR
LIGHT
CONED
CENTRIFUGE TUBE WITH DENSITY GRADIENT
PATH
FITTING
CENTRIFUGE TUBE WITH DENSITY GRADIENT DENSE CHASE SOLUTION
DENSE CHASE SOLUTION
5
-’
1
6
FIGS. 5 and 6. Sectional views of analysis flow systems adapted for multiple scanning. Reservoir tubes are attached above the flow cells with mirror-image symmetry (about the planes of the light paths) with respect to the centrifuge tubes below the light paths. Figure 5 is the laminar flow system, modeled after that shown in Fig. 1. Figure 6 is the bulk flow system, modeled after that shown in Fig. 2. Multiple scanning was accomplished by first injecting dense chase solution into the bottom of the centrifuge tube, which raised the gradient past the light path and up into the reservoir tube. Then the chase solution was withdrawn, lowering the gradient past the light path and back into the centrifuge tube.
desired, and it has been more frequently used for polyribosomes than the other rotors. Polyribosome patterns also vary with other experimental conditions. Therefore, experiments were conducted to select conditions in which results would vary only slightly with minor variations in procedure. The slower the chase solution was introduced, the better was the polyribosome pattern, though 0.5 ml/min and 0.2 ml/min gave nearly identical patterns with the bulk flow cell (Fig. 3). Although 1 ml/min gave slightly poorer patterns, 2 ml/min gave considerably poorer ones. These results are consistent with those reported elsewhere for a laminar flow cell (5). Chart speeds were adjusted so that all scans being compared had nearly the same
HIGH-RESOLUTION
GRADIENT
ANALYSIS
85
length. A standard speed of 0.5 or 0.6 ml/min was used for all other comparisons reported. Nearly identical patterns were obtained with the ISCO flow cells with light paths of 10, 5, and 2 mm when 1 mm high horizontal slits were used (data not shown). Illuminated volumes were 28, 14, and 5.6 ~1 for the three cells, respectively. However, poorer results were obtained with a cell with a l-cm light path and a 2.8-mm slit (78 ~1 vol; Fig. 3). A cell with a 5-mm light path and l-mm slit was used for other comparisons reported. Identical results were obtained when the chase solution was introduced through the “dipstick” needle and through the standard bottom puncture method. The latter procedure was routinely used for other comparisons reported. Comparison of Flow Cells
The bulk flow cell with 5-mm path length and l-mm slits consistently gave perceptibly better polyribosome patterns than did the laminar flow cell used at the same scanning speeds, regardless of which cell was used first in analyzing the gradients of a particular centrifugation. A comparison of the pairs of patterns from the same polyribosome preparation and the same centrifugation shows that more peaks were consistently detected with the bulk flow cell than with the laminar (Fig. 4). The ratio of peak height to valley was greater with the bulk flow cell than with the laminar flow cell. Fewer peaks were detected in Fig. 4 than in Fig. 3 because a different polyribosome preparation was used. CRITIQUE OF METHOD
As noted earlier, variations from batch to batch of pea polyribosome preparations were greater than the difference observed in the scanning resolutions of the laminar and bulk flow systems being compared. For this reason alone, we feel that counting the number of observable polyribosome peaks is not a good quantitative measure of instrumental resolution. A further problem is that the absolute value of degradation of resolution with any given system cannot be determined; only the difference between two systems can be found. This method cannot enable one to attach a numerical value to instrumental performance. For these reasons, a second set of experiments was run using an experimental design that eliminated these variables. MATERIALS
AND METHODS:
II
In the second set of experiments the bulk flow system and the laminar flow system were compared with a multiple scanning method analogous to that reported earlier (12,13). Reservoir tubes were attached to the top
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of the flow cells of both systems in a manner symmetrical with the attachment of the centrifuge tubes below the flow cells. In each system, the diameter of the upper connecting conduit was the same as that of the lower conduit; 6.4 mm diam for the bulk flow system and 0.8 mm diam for the laminar flow system. In both systems, the upper reservoir tubes were equal in inside diameter to the centrifuge tubes. In each system, the cone fitting that connected the reservoir tube to the upper conduit was shaped like the cone fitting that connected the centrifuge tube to the lower conduit. The laminar flow system was constructed as reported earlier (3, with the added reservoir tube and connecting conduit being a mirror image of the flow system below the light path (Fig. 5). The bulk flow system was constructed the same as an IX0 catalog No. 0085U “universal flow cell” with a collar to fit a l/2 x 2 in. centrifuge tube, except that it was modified to be symmetrical about the light path. This flow cell had a path length of 5 mm and horizontal slits 1 mm high (Fig. 6). Purified southern bean mosaic virus (70 pg) was centrifuged for 90 min at 45,000 rpm at 5°C through linear 150-600 mg sucrose/ml gradients with the sucrose dissolved in 0.1 M, pH 7.0 phosphate buffer. RESULTS:
II
Tracings of multiple scans from the chart record of a 1.5 ml/min flow rate test of the laminar and bulk flow systems are shown in Fig. 7. The difference between the laminar and bulk flow results were consistant in every run and reflect the effect of the differing conduit diameters. The baselines were higher when the gradient was pumped down than when it was pumped up. This phenomenon was investigated further by scanning blank gradients with both systems. The shift in baseline was still present (Fig. 8). However, no baseline shift occurred with a solution of constant density was pumped up and down. We suggest that this baseline shift results from a cylindrical lens effect. When flow is upwards, an
FIG. 7. Typical multiple 254-nm scans of ca. 300~~1 SBMV zones. Run A used the laminar flow system shown in Fig. 5 and Run B used the bulk flow system shown in Fig. 6. Dense chase solution was injected into and withdrawn from the bottoms of the centrifuge tubes at a rate of 1.5 mYmin. The 5 ml gradients had 150-600 mg sucrose/ml and were both centrifuged in the same rotor for 90 min at 45,000 rpm. 5°C in an SW-50.1 rotor.
HIGH-RESOLUTION
GRADIENT
ANALYSlS
87
FIG. 8. Baseline shift at 254 nm due to flow reversal. Blank gradients of 150-600 mg sucrose/ml in 112 x 2 in. tubes were repetitively transported through flow cells at 1.5 ml/min. Scale factors are the same as in Fig. 7. Baseline shift with laminar flow style cell is shown in A and bulk Row style cell in B.
isodensity surface moving through the flow cell deforms upwards at its center because wall friction produces a downward force at the periphery of the gradient stream. As a result of this deformation, the center of the liquid in the light path has a higher refractive index than the liquid nearer the edges of the light path, thus producing a converging cylindrical lens. The opposite effect, and a diverging cylindrical lens, exists when the flow is downwards. Consequently, the light intensity reaching the photocell would be less for downwards flow than for upwards flow. This conclusion agrees with the observed results, that is, a higher baseline (less light) for downward flow than for upward. The deformation may be a displacement of the center of the gradient with respect to the periphery of the gradient. The magnitude of such a displacement would reach an equilibrium value when the stabilizing force of the density gradient equals the wall friction force. When these two forces reach equilibrium, the periphery would move at the same velocity as, but lag behind, the center. As the gradient leaves the top of the flow cell and enters the larger-diameter section of the reservoir, the stabilizing effect of the gradient would reflatten isodensity surfaces. An alternative possibility that would explain the cylindrical lens effect is the possible existance of a true velocity profile such as occurs with laminar flow. In such a case, the center of the density gradient would continuously and progressively advance ahead of the periphery to a point where the density gradient would not reorient perfectly as it leaves the flow cell and goes into the reservoir. Instead there would be a mixing effect related to the volume of the flow cell. In the cell used with the bulk flow system, mixing would be most likely to take place in the constricted region near the center of the cell. Here the wall friction will be greatest and the density gradient weakest. The volume of this constricted region is 400 ~1. It will be shown later in this paper that the amount of zone broadening per scan with the bulk flow system is 2.4 ~1, a very small fraction of the volume
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C
FIGURE
9.
HIGH-RESOLUTION
GRADIENT
ANALYSIS
89
of the flow cell. Therefore the amount of mixing in the flow cell of the bulk flow system is negligible; so one can conclude that there exists only a temporary displacement of the center with respect to the periphery of the gradient, and not a true velocity profile. The nature of the flow inside the cell of the laminar flow system is not as clear, as the zone broadening per scan was found to be of the same order of magnitude as the total internal volume of the cell. To determine quantitatively the amount of resolution degradation per scan, we plotted the consecutive percent increases in peak width at halfheight for flow rates of 0.3,0.6, and 1.5 ml/min for both the laminar flow and bulk flow systems (Fig. 9). Each point shown is the average of data from two replicate runs. There was considerable scatter in the points for the laminar flow system at the two higher flow rates, because the rapid rate of peak degradation per scan made it difficult to determine the true baseline for each scan. For this reason, the lines indicating the degradation increase per scan for these two plots have slopes equal to the average slope of lines from the origin to the individual points. The remaining straight lines were drawn through the origins to produce the visible best fit with the data. Additionally, the difficulty in determining the exact baseline, because of the cylindrical lens effect, caused a noticeable shift in the data of the upwards scans with respect to the downwards scans. However, this effect averages out over the eight scans made in each run. The degradation per scan with respect to the flow rate is plotted for both the laminar and the bulk flow systems (Fig. 10). The points are the slopes of the respective straight lines in Fig. 9. The bulk flow system produced significantly less degradation per scan. The resolution with the bulk flow system was only slightly affected by flow rate, whereas the resolution with the laminar flow system initially degraded rapidly with increasing flow rate and then leveled out at a comparatively high value. DISCUSSION
Two passes through one-half of the system take place between successive peaks displayed in Fig. 7. For example, between the first and second peaks, the zone had passed upward from the flow cell into the reservoir tube, and then downward from the reservoir tube back to the flow cell. Therefore, the increase in the width of the zone when a gradient column
FIG. 9. Increases in peak width measured at half height with multiple scans of ca. 300~~1 SBMV zones. Multiple scans were made with the laminar flow system shown in Fig. 5 and the bulk flow system shown in Fig. 6. Two replicate runs were made with each system at each flow rate (A, 0.3; B, 0.6; and C, 1.5 mYmin). Points shown are averages of the two replicate runs. Odd numbered scans are in the upwards direction. The 5-ml gradients of 150-600 mg sucrose/ml were centrifuged in pairs for 90 min at 45,000 rpm, 5°C in an SW-50.1 rotor.
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is pumped through a flow cell once, as is usually done, should be half that indicated in Fig. 10. Based on this, the zone spreading on the initial scan with the bulk flow analysis process was about 0.8%, compared to about 7.3% with the laminar flow process. This is the zone spreading when the sample passes from the centrifuge tube and through the flow cell. An additional degradation may occur by the time that drops are collected. These figures are for a flow rate of 0.6 ml/min, which results in analysis time of approximately 9 min for an SW-50.1 tube, and apply to relatively wide (ca. 300 ~1) virus zones. Since the increase in zone width per scan was a linear progression, the zone broadenings at half-height during the initial scan may be calculated to be 22 ~1 for the laminar flow analysis process and 2.4 ~1 for the bulk flow process. The degree of broadening agrees with results obtained in the experiment with polyribosomes (Fig. 4). Consider the increasingly narrow peaks shown for the bulk flow process at the point where the peak widths at half height first begin to closely approach the widths of the valleys between peaks at half height, at about the 8-mer. This approach to equality implies a peak-to-peak separation of about 4a, where CTis the standard deviation, for a group of multiple Gaussian peaks (14). Here the full peak widths are about 90 ~1, and the laminar flow process peak-to-valley heights are slightly less than half that for the bulk-flow process. If the resolution
LAMINAR
BULK
L&-L__L_.LJ 0 06 FLOW
RATE
FLOW
SYSTEM
FLOW SYSTEM
0.9
12
1.5
mllmin
FIG. 10. Degradation of resolution per scan vs flow rate. Data points are the slopes of peak width broadening plotted against number of scans from Fig. 9. Zones of SBMV (300 pg) in a 1.50-600 mg/ml sucrose gradient were used. Degradation of resolution on the first scan of a centrifuged density gradient is half that plotted here (see text). First-scan degradations at the 0.6 ml/min flow rate may be expressed as zone spreadings of 22 ~(1 for the laminar flow system and 2.4 ~1 for the bulk flow system.
HIGH-RESOLUTION
GRADIENT
91
ANALYSIS
was 4a for the bulk flow process, this halving means that the resolution dropped to 3a for the laminar flow process (14). It can be shown that a spreading at half height of 2.4 ~1 on peaks 90 ~1 apart that are separated by 4.3 lo would produce the observed bulk flow resolution of 4~. A 22-~1 spread on these same 4.31~ peaks would reduce their separation to 2.94a, which is close to the observed value of 3~. A 2.4-~1 spread at half height was found for the first scan of a single virus zone when the bulk flow cell was used and 22 ~1 when the laminar flow cell was used. This agreement is closer than the recorder chart record can be read. If it were not for the possible existence of a “hump” in the baseline under the fine peaks, it would be more accurate to make this check on agreement by basing calculations on the ratio of peak-valley height to average height above baseline, instead of the method used. A hump is suspectea because the number of peaks observed varied with different preparations. Also the ratio of peak-valley height to height above baseline level was less than theoretical for peaks whose separations approach 4~ (14). For example, in Fig. 4D, assuming a flat baseline and noting that the S- through 12-mer peaks have roughly the same height, we calculate a separation of 2.4% for the S-mer peak from the ratio of peak-valley heights to heights above baseline. This calculated separation is clearly less than the actual separation of 4~. If the 8-mer peak were separated by only 2.4%, then the peak-valley heights of the 9- through 1 I-mer peaks do not bear the proper relation to their widths; they are much too high (14). Evidently the baseline is elevated under the 8-mer peak and rises even higher under the 9-, lo-, and 1 I-mer. A baseline hump could result from variable proportions of materials whose concentrations do not have the same periodicity as the polyribosomes in the perceptible peaks. This could be due, for example, to heterogeneity in the conformations of the polyribosomes or lack of ability of the centrifugation process to resolve polydisperse impurities. CONCLUSIONS
Based upon comparison, a bulk flow path with large flow passages provides better resolution than a laminar flow path with small flow passages. One should not infer from the results presented that we draw any additional conclusions as to the relative merits of the two apparatuses tested. However, we do draw further conclusions which are not based upon system comparison. These are that the effective illuminated flow cell volume should not exceed 28 ~1. and that polyribosome peaks do not provide a good quantitative measurement of instrumental resolution. REFERENCES 1. Brakke. 2. Herzog.
M. K. (1963)Ana/. Biochem. 5. 271. A., Lombaert, R.. and Hamers. R. (1966)
Anal.
Biochem.
14, 149.
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3. Leif, R. C. (1%8) Anal. Biochem. 25, 271. 4. Morton, B. E., and Hirsch, C. A. (1970) Anal. Biochem. 34, 544. 5. Morton, B. E. (1973) Anal. Biochem. 52, 421. 6. Hopkins, T. R. (1973)Anal. Biochem. 53, 339. 7. Liedtke, R.. and Moseback, K. 0. (1974) Anal. Biochem. 62, 377. 8. Bresch. H., and Meyer, H. (1973)Anal. Biochem. 53, 199. 9. Schumaker, V. N. (1967). Adv. in Biol. and Med. Phys. 2, 245. 10. HalsaIl, H. B., and Schumaker, V. N. (1970)Biochem. Biophys. Res. Commun. 39,479. 11. Halsall, H. B., and Schumaker, V. N. (1972) Biochemistry 11, 4692. 12. Brakke, M. K., and Van Pelt, N. (1968) Anal. Biochem. 26, 242. 13. Brakke, M. K., Ailington, R. W., and Langille. F. A. (1968) Anal. Biochem. 24, 30. 14. Allington, R. W. (1976) Anal. Biochem. 73, 93. 1.5. Nell, H. (1969) Annl. Biochem. 25, 130. 16. Davies, E., Larkins, B. A., and Knight, R. (1972) Plant. Physiol. 50, 581-584.
