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Correcting for cell tilt caused by differential expansion of rotors in the analytical ultracentrifuge
AXALYTICAL
BIOCHEMISTRY
CorrectFng
for of Rotors
6, 170-175
Cell Tilt
(1963)
Caused
in the Analytical LEE
From
Beckman
by Differential
Instwments,
Inc.,
Expansion
Ultracentrifuge
GROPPER Spinco
DilGion,
Palo
Alto,
Calijoka
Received November 14, 1962 INTRODUCTION In certain ultracentrifugal runs at high speeds, analysis of optical pat.terns is complicated by anomalies on the photographic plate. At times the photographic image of the bottom of the cell does not correspond to the actual cell bottom. This problem, however, is relatively minor as it can be remedied by using FC-43, an inert fluorochemical that will provide a false bottom for the cell (1). Ot,her and more serious complications involve the meniscus. In some cases, not only does the meniscus appear fuzzy, but its observed position does not correspond to the true meniscus position. Each of these anomalies is caused, in part, by light rays that are not parallel to the meniscus and boundary. The presence of light deviations in the cell can be inferred by using a mirrored window (2) in the cell and observing that the position of the reflected light source image changes as a function of speed. As the speed of the rotor increases, the reflected light source image moves in a centripetal direction. It has been assumed that this change in image position was caused by the wedging of the quartz window under the increased centrifugal force exerted at higher speeds. EXPERIMENTAL Several experiments? were undertaken in an attempt to determine the exact degree of wedging. One experiment employed a standard aluminum 4” single-sector cell assembly with a 12-mm centerpiece thickness. In this cell the standard lower window was replaced with a window that had been aluminized’ on one surface. The aluminized surface of the window was placed face down in the holder, away from the centerpiece; the centerpiece was filled with 0.5 cc of water. A centimeter scale was ‘Performed ‘Coated
by
on the Herron
Beckman Optical
Model Company,
E Analytical Ultracentrifuge. Los Angeles, California. 170
DIFFERENTIAL
EXPANSION
OF ANALYTICAL
171
ROTORS
then taped to the top of the light source and arranged in such a manner that part of the reflected image would fall on it. The light source was aligned so that at 5000 rpm the reflected light source image fell between the jaws of the light source. Rotor speed was then increased in increments of 5000 rpm and at each new speed the position of the reflect.ed image falling on the scale was recorded. Table 1 shows the position of the reflected light source image versus speed.
REFLECTED Speed
(rpm )
5,000 I0,000
15,000 30,000 25,000 :~o,ooo 35,000
IMAGE
TABLE 1 POSITION
VERSUS hfovement in centripetal
SPEED of source direction
image (mm)
0 0.75 0.75 1.00 1.35 1.50 1.75
The experiment was then repeated, but the window was reversed in its holder so that the aluminized surface faced the centerpiece. Because the position of the window had been reversed, it was expect.ed that the scale readings for this run would be the converse of those recorded for the first run. However, the readings for the two runs were identical. This indicated that the change in rcflectcd image position was not caused by the wedging of the quartz window. Three other possible phenomena were considered: (11 The rotational axis of the rotor was tilted due to an improperly leveled drive. ($2) Under the increased hydrostatic pressure at the bottom of the cell, the window had bowed. (31 The rotor was expanding differentially and causing the entire cell to tilt. To determine whether the rotational axis had shifted, the experiment was repeated with the UV optical system. If the axis had tilted, the reflected light source image would now move in the same direction as the reflected schlieren image, that, is, in a centrifugal direction when observed with the UV system. But the reflected image of the UV source moved in a ccntripetal direction, indicating that a tilt in the rotational axis was not t,he cause of the image shift. The bowing of the window was checked by placing the window in the top of the cell assembly. If the window was bowed, the reflected light source image would move in a centrifugal direction, or, in other words, in the opposite direction of the image noted when the window was in the
172
LEE
GROPPER
bottom of the cell. For the first of these experiments, the cell was filled with 0.5 cc of water. At speeds up to 15,000 rpm the reflected image shifted in a centripetal direction, but above 15,000 rpm the image began to shift in the opposite direction. This reversed shift resulted from the pressure gradient set up in the water. A second and very faint reflection (from the air space) was observed shifting in a centripetal direction even above 15,000 rpm. These results indicated that the window had not bowed. But to confirm this conclusion additional runs were made with the aluminized surface of the window at all four possible positions and with the cell half-filled with water, with the cell empty, and with the cell half-filled with FC-43. When the cell was half-filled with water and the aluminized window placed in the upper window holder, two images of the same relative intensity were noted moving in opposite directions. At 30,000 rpm the image from t.he air space moved 1.0 mm in a centripetal direct,ion; the image from the water moved 0.75 mm in a centrifugal direction. When an empty cell was run, the reflected image moved in much the same manner as the image of the air space observed previously. When the cell was half-filled with FC-43, the reflection from the FC-43 portion of the cell moved 5.75 mm farther than the image observed when the cell was half-filled with water. The increased shift with the FC-43 cell was expected, since FC-43 is more compressible than water and sets up a higher gradient. It was thus established that the light displacement in the cell was not caused by either a tilted axis of rotation or the bowing of the window. The remaining possibility to consider was that the rotor was stretching differentially and causing the entire cell to tilt. [Measurements of stretch in aluminum rotors have been given (3).] There are two possible causes of differential expansion, both related to the cell hole: (1) The differences in the inner diameter of the cell hole lead to a difference in the amount of support provided by the top and bottom of the cell hole. (9) Because of both the position of the metal cell support at the base of the cell hole and the weight of the screw ring, the cell’s center of gravity is not positioned on the rotor’s center plane of symmetry; thus there is a difference between the weights against the top and bottom of the cell hole. (1) Because the inner diameter at the bottom of the cell hole (where the cell seats) is smaller than that at the top of the cell hole, the bottom of the rotor is more or less reinforced. Consequently, under centrifugal force and the pressure of the cell, the top of the rotor could be expanding more than the reinforced bottom. To determine whether or not this difference in strength caused a differential expansion, almost all of the
DIFFERENTIAL
EXPANSION
OF
ANALYTICAL
ROTORS
173
metal cell support at the base of the hole was removed; only a small lip was left in order to keep the cell on the same plane in the rotor. And to maintain the same distribution of forces, the platform base of the rotor was removed. The experiments described above were then repeated and the results compared with those obtained from the experiments using a standard rotor. The results were almost identical and it was apparent that, even if the rotor was expanding differentially, the expansion could not be caused by differences in the support provided by the cell hole. (6) Because of both the position of the metal cell support and the weight of the screw ring, the cell’s center of gravity is above the rotor’s center plane of symmetry. Consequently, the weight against the top of the cell hole is greater than the weight against the bottom of the hole. To determine whether or not this could cause the rotor to expand differentially, the cell’s center of gravity was aligned with the center plane of the rotor by using a silvered (4) sapphire window and special window holder to weight down the bottom of the cell. In all runs made with the 12-mm aluminum cell correctly positioned in the rotor, there was no evidence of cell tilt. When this same cell was placed upside down in the rotor, the reflected light source image again moved in a centripetal direction. Addit,ional runs were made using other cell assemblies. These runs indicated that,, if the bottom of the cell is made too heavy, the cell’s center of gravity is brought below the center plane of the rotor and t.he cell tilts in the opposite direction, causing the reflected image to move in a centrifugal direction. It was also noted that, if sapphire windows are placed in both the upper and the lower window holders, they will offset to a large degree the relative weight of the screw ring and will reduce the cell tilt of a11 cells. RESULTS
AND
DISCUSSION
When the results of these experiments were compared, it was obvious that the rot,or was expanding differentially. This differential expansion was causing the cell to tilt with the result that light entered the solution at various angles to the normal, the angle being a function of the rotor used, the cell used, and rotor speed. Certainly, the displacement of light caused by cell tilt is much less than that caused by a gradient in the solution. Although correcting for cell tilt merely reduces the total magnitude of light displacement, it does enable the experimenter to achieve optimum experimental conditions. Cell tilt can be corrected in one of bwo ways. With certain cell assemblies, it can be eliminated by using a sapphire window in the bottom of the cell to align the cell’s center of gravity with the rotor’s center plane of symmetry, In other cases,cell tilt
174
LEE
GROPPER
can be corrected only by determining the differential expansion and then by repositioning the light source to compensate for the expansion at each speed. Once the image shift factor is established for a cell assembly run in a specific rotor at a certain speed, differential expansion can be det.ermined by relat’ing the shift to the distances from the top of the rotor to the bottom of the rotor and from the light source to the rotor. For the rotor shown in Table 1, for example, at 35,000 rpm the expansion at the top of the cell hole is 0.09 mm more than that at the bottom of the cell hole. In this case, therefore, if the light source is aligned at 5000 rpm, at 35,000 rpm light. will enter the solution at an angle of 2’. Using Snell’s law to correct for this angle, we would move the source 0.4 mm to the rear of the Model E. (At 35,000 rpm the observed meniscus position will be approximately 0.001 mm farther from the axis of rotation than the true meniscus position, This is caused by the shift in light rays as they travel through the tilted upper window.) Table 2 shows typical shifts in TABLE TYPICAL
SHIFTS
IN
SOURCE
Movement Speed
(rpm)
5,000 10,000 15,000 20,000 25,000 30,000 35,000 40 000 45,000 50,000 55,000
Rotor
0 0.05 0.30 0.55 0.60 0.70 0.80 1.00 1.05 1.20 1.30
I
Rotor
0 0.50 0.75 1.00 1.15 1.45 1.50 1.50 1.75 1.85 2.00
2
POSITION of murce II
WITH
VARIOUS
image in centripetal
Rotor
0 0 0 0.10 0.35 0.35
III
Rotor
ROTORS direction
IV
(mm)
Rotor
0 0 0.10 0.25 0.25 0.50 0.65
Rotor I, new titanium rotor. Rotor II, new analytical-D rotor. Rotor III, retired analytical-D rotor with over 1000 hr use. Rotor IV, B-hole analytical-G rotor, 5 yr old, Rith 500 hr use. Rotor V, analytical-D rotor with about 300 hr use. Rotor VI, analytical-D rotor with unknown number of hours. This use for over 7 yr; it exploded during this run at 57,000 rpm.
V
0 0.75 0.75 1.00 1.25 1.50 1.75
rotor
Rotor
VI-
0 0.15 0.25 0.35 0.50 0.60 0.90 1.00 1.25 1.60 2.25
had been
in
reflected light source image versus speed for several different rotors run with the 12-mm aluminum cell. In each case t,he cell was filled with 0.5 cc of water and an aluminized quartz window was placed in the lower window holder.
DIFFERENTIAL
EXPANSION
OF ANALYTICAL
ROTORS
175
SUMMARY
Because there is a difference in the weight applied against the top and bottom of its cell hole, an analytical rotor expands differentially. This differential expansion causes the cell to tilt so that light enters the solut,ion at various angles to the normal. Two procedures for dealing with cell tilt are described: the first eliminates cell tilt by correcting the disparity in weight; the second compensates for cell tilt by repositioning the light source. REFERENCES 1. GIMBURG, A., APPEL, P., AND SCHACHMAN, H., Arch. Biochem. Biophys. 65, 545 (1956). 2. TRAUTMAN, R., &o&n&. Biophys. Acta 28, 417 (1958). 3. SCHACHMAS, H., “Ultracentrifugation in Biochemistry.” Academic Press, New York, 1959. 4. STROM, G., “Procedures in Experimental Physics.” Prentice-Hall, New York, 1938.
BIOCHEMISTRY
CorrectFng
for of Rotors
6, 170-175
Cell Tilt
(1963)
Caused
in the Analytical LEE
From
Beckman
by Differential
Instwments,
Inc.,
Expansion
Ultracentrifuge
GROPPER Spinco
DilGion,
Palo
Alto,
Calijoka
Received November 14, 1962 INTRODUCTION In certain ultracentrifugal runs at high speeds, analysis of optical pat.terns is complicated by anomalies on the photographic plate. At times the photographic image of the bottom of the cell does not correspond to the actual cell bottom. This problem, however, is relatively minor as it can be remedied by using FC-43, an inert fluorochemical that will provide a false bottom for the cell (1). Ot,her and more serious complications involve the meniscus. In some cases, not only does the meniscus appear fuzzy, but its observed position does not correspond to the true meniscus position. Each of these anomalies is caused, in part, by light rays that are not parallel to the meniscus and boundary. The presence of light deviations in the cell can be inferred by using a mirrored window (2) in the cell and observing that the position of the reflected light source image changes as a function of speed. As the speed of the rotor increases, the reflected light source image moves in a centripetal direction. It has been assumed that this change in image position was caused by the wedging of the quartz window under the increased centrifugal force exerted at higher speeds. EXPERIMENTAL Several experiments? were undertaken in an attempt to determine the exact degree of wedging. One experiment employed a standard aluminum 4” single-sector cell assembly with a 12-mm centerpiece thickness. In this cell the standard lower window was replaced with a window that had been aluminized’ on one surface. The aluminized surface of the window was placed face down in the holder, away from the centerpiece; the centerpiece was filled with 0.5 cc of water. A centimeter scale was ‘Performed ‘Coated
by
on the Herron
Beckman Optical
Model Company,
E Analytical Ultracentrifuge. Los Angeles, California. 170
DIFFERENTIAL
EXPANSION
OF ANALYTICAL
171
ROTORS
then taped to the top of the light source and arranged in such a manner that part of the reflected image would fall on it. The light source was aligned so that at 5000 rpm the reflected light source image fell between the jaws of the light source. Rotor speed was then increased in increments of 5000 rpm and at each new speed the position of the reflect.ed image falling on the scale was recorded. Table 1 shows the position of the reflected light source image versus speed.
REFLECTED Speed
(rpm )
5,000 I0,000
15,000 30,000 25,000 :~o,ooo 35,000
IMAGE
TABLE 1 POSITION
VERSUS hfovement in centripetal
SPEED of source direction
image (mm)
0 0.75 0.75 1.00 1.35 1.50 1.75
The experiment was then repeated, but the window was reversed in its holder so that the aluminized surface faced the centerpiece. Because the position of the window had been reversed, it was expect.ed that the scale readings for this run would be the converse of those recorded for the first run. However, the readings for the two runs were identical. This indicated that the change in rcflectcd image position was not caused by the wedging of the quartz window. Three other possible phenomena were considered: (11 The rotational axis of the rotor was tilted due to an improperly leveled drive. ($2) Under the increased hydrostatic pressure at the bottom of the cell, the window had bowed. (31 The rotor was expanding differentially and causing the entire cell to tilt. To determine whether the rotational axis had shifted, the experiment was repeated with the UV optical system. If the axis had tilted, the reflected light source image would now move in the same direction as the reflected schlieren image, that, is, in a centrifugal direction when observed with the UV system. But the reflected image of the UV source moved in a ccntripetal direction, indicating that a tilt in the rotational axis was not t,he cause of the image shift. The bowing of the window was checked by placing the window in the top of the cell assembly. If the window was bowed, the reflected light source image would move in a centrifugal direction, or, in other words, in the opposite direction of the image noted when the window was in the
172
LEE
GROPPER
bottom of the cell. For the first of these experiments, the cell was filled with 0.5 cc of water. At speeds up to 15,000 rpm the reflected image shifted in a centripetal direction, but above 15,000 rpm the image began to shift in the opposite direction. This reversed shift resulted from the pressure gradient set up in the water. A second and very faint reflection (from the air space) was observed shifting in a centripetal direction even above 15,000 rpm. These results indicated that the window had not bowed. But to confirm this conclusion additional runs were made with the aluminized surface of the window at all four possible positions and with the cell half-filled with water, with the cell empty, and with the cell half-filled with FC-43. When the cell was half-filled with water and the aluminized window placed in the upper window holder, two images of the same relative intensity were noted moving in opposite directions. At 30,000 rpm the image from t.he air space moved 1.0 mm in a centripetal direct,ion; the image from the water moved 0.75 mm in a centrifugal direction. When an empty cell was run, the reflected image moved in much the same manner as the image of the air space observed previously. When the cell was half-filled with FC-43, the reflection from the FC-43 portion of the cell moved 5.75 mm farther than the image observed when the cell was half-filled with water. The increased shift with the FC-43 cell was expected, since FC-43 is more compressible than water and sets up a higher gradient. It was thus established that the light displacement in the cell was not caused by either a tilted axis of rotation or the bowing of the window. The remaining possibility to consider was that the rotor was stretching differentially and causing the entire cell to tilt. [Measurements of stretch in aluminum rotors have been given (3).] There are two possible causes of differential expansion, both related to the cell hole: (1) The differences in the inner diameter of the cell hole lead to a difference in the amount of support provided by the top and bottom of the cell hole. (9) Because of both the position of the metal cell support at the base of the cell hole and the weight of the screw ring, the cell’s center of gravity is not positioned on the rotor’s center plane of symmetry; thus there is a difference between the weights against the top and bottom of the cell hole. (1) Because the inner diameter at the bottom of the cell hole (where the cell seats) is smaller than that at the top of the cell hole, the bottom of the rotor is more or less reinforced. Consequently, under centrifugal force and the pressure of the cell, the top of the rotor could be expanding more than the reinforced bottom. To determine whether or not this difference in strength caused a differential expansion, almost all of the
DIFFERENTIAL
EXPANSION
OF
ANALYTICAL
ROTORS
173
metal cell support at the base of the hole was removed; only a small lip was left in order to keep the cell on the same plane in the rotor. And to maintain the same distribution of forces, the platform base of the rotor was removed. The experiments described above were then repeated and the results compared with those obtained from the experiments using a standard rotor. The results were almost identical and it was apparent that, even if the rotor was expanding differentially, the expansion could not be caused by differences in the support provided by the cell hole. (6) Because of both the position of the metal cell support and the weight of the screw ring, the cell’s center of gravity is above the rotor’s center plane of symmetry. Consequently, the weight against the top of the cell hole is greater than the weight against the bottom of the hole. To determine whether or not this could cause the rotor to expand differentially, the cell’s center of gravity was aligned with the center plane of the rotor by using a silvered (4) sapphire window and special window holder to weight down the bottom of the cell. In all runs made with the 12-mm aluminum cell correctly positioned in the rotor, there was no evidence of cell tilt. When this same cell was placed upside down in the rotor, the reflected light source image again moved in a centripetal direction. Addit,ional runs were made using other cell assemblies. These runs indicated that,, if the bottom of the cell is made too heavy, the cell’s center of gravity is brought below the center plane of the rotor and t.he cell tilts in the opposite direction, causing the reflected image to move in a centrifugal direction. It was also noted that, if sapphire windows are placed in both the upper and the lower window holders, they will offset to a large degree the relative weight of the screw ring and will reduce the cell tilt of a11 cells. RESULTS
AND
DISCUSSION
When the results of these experiments were compared, it was obvious that the rot,or was expanding differentially. This differential expansion was causing the cell to tilt with the result that light entered the solution at various angles to the normal, the angle being a function of the rotor used, the cell used, and rotor speed. Certainly, the displacement of light caused by cell tilt is much less than that caused by a gradient in the solution. Although correcting for cell tilt merely reduces the total magnitude of light displacement, it does enable the experimenter to achieve optimum experimental conditions. Cell tilt can be corrected in one of bwo ways. With certain cell assemblies, it can be eliminated by using a sapphire window in the bottom of the cell to align the cell’s center of gravity with the rotor’s center plane of symmetry, In other cases,cell tilt
174
LEE
GROPPER
can be corrected only by determining the differential expansion and then by repositioning the light source to compensate for the expansion at each speed. Once the image shift factor is established for a cell assembly run in a specific rotor at a certain speed, differential expansion can be det.ermined by relat’ing the shift to the distances from the top of the rotor to the bottom of the rotor and from the light source to the rotor. For the rotor shown in Table 1, for example, at 35,000 rpm the expansion at the top of the cell hole is 0.09 mm more than that at the bottom of the cell hole. In this case, therefore, if the light source is aligned at 5000 rpm, at 35,000 rpm light. will enter the solution at an angle of 2’. Using Snell’s law to correct for this angle, we would move the source 0.4 mm to the rear of the Model E. (At 35,000 rpm the observed meniscus position will be approximately 0.001 mm farther from the axis of rotation than the true meniscus position, This is caused by the shift in light rays as they travel through the tilted upper window.) Table 2 shows typical shifts in TABLE TYPICAL
SHIFTS
IN
SOURCE
Movement Speed
(rpm)
5,000 10,000 15,000 20,000 25,000 30,000 35,000 40 000 45,000 50,000 55,000
Rotor
0 0.05 0.30 0.55 0.60 0.70 0.80 1.00 1.05 1.20 1.30
I
Rotor
0 0.50 0.75 1.00 1.15 1.45 1.50 1.50 1.75 1.85 2.00
2
POSITION of murce II
WITH
VARIOUS
image in centripetal
Rotor
0 0 0 0.10 0.35 0.35
III
Rotor
ROTORS direction
IV
(mm)
Rotor
0 0 0.10 0.25 0.25 0.50 0.65
Rotor I, new titanium rotor. Rotor II, new analytical-D rotor. Rotor III, retired analytical-D rotor with over 1000 hr use. Rotor IV, B-hole analytical-G rotor, 5 yr old, Rith 500 hr use. Rotor V, analytical-D rotor with about 300 hr use. Rotor VI, analytical-D rotor with unknown number of hours. This use for over 7 yr; it exploded during this run at 57,000 rpm.
V
0 0.75 0.75 1.00 1.25 1.50 1.75
rotor
Rotor
VI-
0 0.15 0.25 0.35 0.50 0.60 0.90 1.00 1.25 1.60 2.25
had been
in
reflected light source image versus speed for several different rotors run with the 12-mm aluminum cell. In each case t,he cell was filled with 0.5 cc of water and an aluminized quartz window was placed in the lower window holder.
DIFFERENTIAL
EXPANSION
OF ANALYTICAL
ROTORS
175
SUMMARY
Because there is a difference in the weight applied against the top and bottom of its cell hole, an analytical rotor expands differentially. This differential expansion causes the cell to tilt so that light enters the solut,ion at various angles to the normal. Two procedures for dealing with cell tilt are described: the first eliminates cell tilt by correcting the disparity in weight; the second compensates for cell tilt by repositioning the light source. REFERENCES 1. GIMBURG, A., APPEL, P., AND SCHACHMAN, H., Arch. Biochem. Biophys. 65, 545 (1956). 2. TRAUTMAN, R., &o&n&. Biophys. Acta 28, 417 (1958). 3. SCHACHMAS, H., “Ultracentrifugation in Biochemistry.” Academic Press, New York, 1959. 4. STROM, G., “Procedures in Experimental Physics.” Prentice-Hall, New York, 1938.