ANALYTICAL BIOCHEMISTRY, 28,25-34 (1969)

A Transistor-Controlled Magnetic Densitometer

Designed for Small Sample Volumes

ROBERT GOODRICH, D. F. SWINEHART, M. J. KELLY, AND F. J. REITHEL

Department of Chemists, University of Oregon, Ezcgene, Oregon 97403

Received March 1,1968

The determination of the molecular weight of a protein or other large polymer by ultracentrifugal techniques requires a knowledge of the partial specific volume of the macromolecule. The measure- ment of this quantity involves the precise estimation of the densi- ties of a series of solutions. The partial specific volume, v*, then may be calculated by the relation:

v2 = ii (1 - (is)@.> (1)

where pe is the density of the solvent and c is a volume concentration (gm/ml). The fact that many purified proteins are available only in very small amounts dictates that the volumes of solution be kept small, 1 ml or less. This requirement makes density measure- ments with the requisite precision difficult and time consuming.

A reasonably satisfactory instrument for making such measure- ments has been described (1, 2) and has served as a point of departure for the development of the instrument described below.

The densitometer comprised an electronic servo system with feedback generated by an iron-containing glass buoy in the sample that moved relative to a sensing coil mounted around the sample container. The inductance in the sensing coil controlled the grid circuit of the detector. The latter was a tuned grid, tuned plate oscillator with a frequency of 2.5 megahertz. The sample container was mounted above the center of a solenoid.

The oscillator output was rectified and fed into the operational amplifier. The amplifier output controlled the current flow through the solenoid so that the buoy was maintained at a standard refer-

25

26 GOODRICH ET AL.

ence level determined by visual observation of the buoy with a 20X microscope. The voltage drop across high-precision resistors (R27, R28, Fig. 4) in series with the solenoid was measured. Potas- sium chloride solutions were used as standards. The calibration curve, used for interpolation, was fitted by least squares by a computer program.

MATERIALS AND METHODS

The solenoid1 was a random-wound coil of approximately 25,000 turns of 24 guage enameled copper wire and had about 10s ohms resistance. A 1 in. mandrel was used and the finished coil wrapped tightly with vinyl electrical tape. The coil was contained between l/s in. brass plates having r/ in. copper tubing soldered to the surface (both plates) for circulation of water for temperature con- trol. The solenoid was centered by brass tubing under a 3 in. ma- chined surface on the top plate. The glass sample container assembly was positioned on this surface over the perpendicular center line of the magnetic field.

Figure 1 is a diagrammatic view of the sample cell and container. The sample was contained in a cell (Fig. 1A) which held approxi- mately 0.5 ml and was 18 mm long with a 7 mm inside diameter. This cell was fused to a standard taper 29/26 male ground-glass joint. A small tube, opening at the top of the joint, was sealed in to provide a conduit for the wires of the sensing coil. This coil (0.35 ohm, 3 microhenries) consisted of 18 turns of 27 gage wire wound outside and around the top of the cell. It was covered with, and pro- tected from, the thermostat water by black vinyl electrical tape and General Electric RTV 102 silicone rubber cement. The constant- temperature chamber for the cell (Fig. lB, lC, 1D) was fabricated by sealing the female standard taper 29/26 joint into a 75 mm o.d. Pyrex tube with side arms for fluid circulation. The bottom of the tube was ground flat and in a manner to ensure a position of the cell axis normal to the brass plate.

Constant-temperature water flow was provided by a Lauda refrigeration unit, model K30, and circulating bath, model NSD8/25. Temperature control to -tO.OOl” was achieved by controlling the heater with a Hallikainen Thermotrol, model 1053. Water was pumped through the cell chamber directly from the circulator. The

1 The solenoid used was wound for us by Dr. D. V. Ulrich, Bridgewater College. Dr. Ulrich had previously constructed a densitometer with a cell on top of the solenoid instead of below it, and shared this information with us.

MAGNETIC DENSITOMETER 27

C

FIG. 1. Diagrammatic view of sample cell and container: (A) Side view cross-section of sample container-(a) position of sensing coil, (b) conduit for sensing coil wires. (B) Side view cross-section of constant-temperature chamber. (C) Top view of sample cell and container-(c) 18 mm Pyrex op- tically flat window. (D) Side view of sample cell and container showing Me- scope view port.

output flowed through a thermometer well, through the cooling coils for the solenoid, and back to the circular bath.

The buoys used in the cell were made from Pyrex glass and each encased a small bit of soft iron. The iron used was HyMu 80 obtained from Carpenter Steel Company. A l/16 in. rod was ma- chined to 1 mm diameter and cut into 2.5 mm lengths. In order to restore the high permeability characteristic the pieces were an- nealed by heating to 1000°C in hydrogen (quartz tube) for 3-4 hours, cooIed slowly to 600°, and held at that temperature for 1 hour, then cooled rapidly to room temperature. Each iron bit was encapsulated in thin Pyrex and sealed in vacuum, leaving 2-3 mm of glass on one end. Glass bulbs (Fig. 2) were blown and an en- capsulated iron bit chosen to fit snugly was fitted into the stem of the bulb with about 1 mm extending into the bulb. The excess glass on the iron bit was then fused into the stem to seal the bulb.

The current required to position the buoy was determined by the difference between weight and buoyancy. Since each buoy had a range of about 0.025 gm/ml, a selection was necessary. Buoys were calibrated to a buoyancy slightly less than the least dense standard solution used. Fine calibration of the buoy necessitated hand-grind- ing a flat section on the tip. It was found to be very important to

28 GOODRICH ET AL.

--b I-- 0 GLASS m HY-MU80

FIG. 2. Buoy for density measurements.

use symmetrical buoys so that the iron cylinders were strictly vertical in the magnetic field. Failure to achieve this resulted in troublesome horizontal drift.

The sensing coil was coupled through coaxial RG50/U cable and a UG260/U connection to the detector circuit.

The detector circuit schematic may be seen in Figure 3. The output was fed into the amplifier, control, and measuring circuit complex shown in Figures 4 and 5. The active filter (Fig. 5) was placed in series with a Leeds and Northrup K3 potentiometer measuring circuit to reduce and dampen the noise, switching spikes, and parasitic oscillations. The 50K potentiometer was mounted on the front panel of the instrument with a locking control knob. Occasional checks for zero output of the operational amplifier, with the magnet circuit off, were necessary.

In operation the oscillator was tuned to maximum rectified sig- nal by peaking the plate (A), coupling (B) and grid capacitors (C) (Fig. 3). The grid capacitor (mounted on the front panel in our instrument) was then detuned to give maximum signal re- sponse to the movement of the buoy relative to the sensing coil. Magnet current must decrease when the buoy moves away from the sensing coil. Our circuit was most sensitive !when the buoy was pulled to the bottom of the cell by the position control giving a

MAGNETIC DENSITOMETER 29

solenoid current of 100 mA and a detector output current of about 7 .pA. This setting was checked for each sample.

The oscillator output was converted to a negative DC voltage which was applied across a 49.9 K resistor at a common junction with another resistor and the negative input of the operational amplifier. The output of the amplifier circuit (to the base of par- allel connected power transistors) controlled the current flow through the solenoid. This current was measured in terms of the potential across the 5 ohm high-precision resistors (R27 and R28) by a Leeds and Northrup K3 potentiometer using the 1.5 Volt scale. An Eppley standard cell was used for the reference voltage and a Leeds and Northrup constant-voltage supply provided a cur- rent of satisfactory stability for the potentiometer circuit. Stable readings on the 0.1 mV scale of a Kipp and Zonen microammeter (Microva AL4) were obtained but use of the 0.01 mV scale re- quired averaging of readings.

The telescope used to observe buoy movements was mounted to avoid vibration. All components near the densitometer were iron- free. The entire assembly was mounted free of mechanical or magnetic noise.

Concentration determinations of a precision comparable to that of the difference between the densities of the protein solutions and the dialyzate were required for all protein solutions.

All protein solutions were dialyzed for at least 48 hours with two changes of dialyzate (200: 1, dialyzate to sample). To check on possible losses of protein through defective dialysis bags the densities of dialyzate and original solvent were compared and no loss was detected. In order to remove denatured protein, bacteria, and dust from the stock solution and dialyzate before dilutions and density determinations were made, the solutions were passed through Millipore filters (0.45 p pore size). If this was not done a number of bubbles formed on the glass buoy causing erroneous density readings.

For dry weight determinations protein solutions twere trans- ferred with a micrometer syringe (1.0 ~1 per division) to aluminum boats of 25 mm diameter and a capacity of 1.2 ml. Volumes were varied from 0.500 to 0.900 ml to check reproducibility. The boats containing the samples to be weighed were placed in a vacuum desiccator over P,O, for 24 hours or until the boats contained only a white residue. They were then placed on a Cahn model RG automatic recording vacuum electrobalance and evacuated to a pres- sure of approximately 4 p until constant weight was achieved. For

30 GOODRICH ET AL.

FIG. 3. Detector circuit (Lancaster and Jackson). Oscillator capacitors are silver mica. The Nuvistor socket is Cinch SNS or crimp mount 13365. The metal film resistors are l/8 W unless specified. Connections x and y to power supply (see Fig. 4).

the final weighing the system was returned to atmospheric pres- sure with air filtered through an absorption tube containing acti- vated silica gel. About 3 minutes was required for the balance to stabilize. Duplicate measurements were made on the dialyzate using the same procedure and the dry weight of protein was ob- tained by difference.

Dry weights of at least two samples in a series of concentrations were measured and all other samples were diluted from a stock solution of protein, using the micrometer syringe, into stoppered 2 ml volumetric flasks and kept at 5.0°C until needed.

RESULTS

Calibration of the magnetic densitometer required the use of a standard with a density known to sufficient accuracy under a variety of conditions. Solutions of potassium chloride satisfied this requirement. Values of the density of solutions of the salt were taken from the “International Critical Tables” (3) and a plot of these values vs. concentration was fitted by least squares by an equation which <was quadratic in the concentrations. Solutions of known concentrations were prepared from recrystallized, pulver- ized, and dried reagent-grade potassium chloride and their densi-

MAGNETIC DENSITOMETER 31

FIG. 4. Amplifier, control, and measuring circuitry: (A’) input from detec- tor; (B’) operational amplifier, Union Carbide H6010 ; (C’) active filter (see Fig. 6).

Rll 24.9K z4

0.0068 mf R12 49.9K 100 mf 450 V DC R13 49.9K Cl5 100 mf 450 V DC R14 lK-10 turn pot. Ll 8H R15 1M (feedback) Q4 2N2925 R16 24.9K

%YlY DTS413

R18 24.9K IN626 R20 2.4K CR2 N2863 RCA R21 50K pot. CR3-6 IN1696 R22 510 ohms 1W 5y0

Zl pri. 115V sec. 208V

R24 1K 0 to 50 pA R25 51 ohms 1W 5% M2 0 to 100 mA R26 51 ohms 1W 5oj, SPST switch R27\ 5 ohms each 1W WireWound 2 SPST switch R281 25 PPM/C=’ 1% 3 pos. rotary R29 120K 2W 5% Et 1.5A R30 pilotlamp assy. PG2 Amphenol 160-S connector R31 0.75 ohm PG3 MS3102A-14S-9P connector R32 1.5 ohms PG4 MS3102A-14S-7S connector Cl1 75 pf

Resistors are metal film, s W, 1 y0 except where noted.

ties calculated from the quadratic relation. Then E, the potentio- meter reading of the solenoid support current, was measured for each standard solution.

32 GOODRICH ET AL.

i 24.SK 24.SK COM

B’ - OUT 2 POT A

To PO3

FIG. 5. Active filter: (B’) operational amplifier, Union Carbide H6010; (A.B-PG3) see Figure 4.

It can be shown that

P - Pw = g + PB - pw (21

where p=density of solution,

p,,=density of water.

pB=density of the buoy, and

k,= solenoid constant.

pw was left in the equation for manipulative convenience. The constants in this equation were calculated by least squares from the observed values of E. The precision of the fit is shown in Table . 1.

The globular protein p-lactoglobulin A ;Was used to test the relia- bility of the instrument. Pentex Inc. lot No. 5 was used without further purification. Approximately 50 mg of protein was dis- solved in 3 ml of 0.1 M NaCl and dialyzed against 0.1 M NaCl. The results from two separate runs are presented in Table 2.

The partial specific volume calculated from the results in Table 2 was 0.748+0.002 and the density of the dialyzate was 1.003841 at 2O.OO”C.

DISCUSSION

The above results indicate that the instrument described is satisfactory for the determination of apparent partial specific volumes of proteins and other polymers to better than 0.5% pre- cision. The value reported here for p-lactoglobulin A is in reason- able agreement with the value 0.743+0.005 calculated at 20°C re- ported by McKenzie et al. (4). The discrepancy between the density

MAGNETIC DENSITOMETER 33

TABLE 1 Calibration of Buoy at 2O.OO”C in KC1

E’,o V2 Difference,

ID/ml ( x 109

0.0000 0.04091 0.99824 0.99824 0.0 0.3966 0.11549 1.00077 1.00076 1.0 0.6260 0.15892 1.00223 1.00223 0.0 1.0757 0.24384 1.00511 1.00510 1.0 1.5215 0.32890 1.00796 1.00798 -2.0 1.7581 0.37376 1.00948 1.00950 -2.0 2.0896 0.43666 1.01161 1.01162 -1.0 2.6302 0.53812 1.01508 1.01506 2.0 3.2414 0.65537 1.01902 1.01902 0 4.2265 0.84333 1.02538 1.02538 0

a Average deviation in E for three separate measurements was i 0.0001 V. h The values in this column were calculated from the relation p = 0.998237 +

0.00637268 + 0.00001179Cz, where C (concentration) is obtained by the least-squares fit of data from reference 3.

e Values calculated from equation 2 using the least-squares constants: kl = 29.560 f 0.002, pi - pu, = -0.00139 f 0.00001.

TABLE 2 6-Lactoglobulin A in 0.1 M NaCl at 20.00”C

COIlCMltdiOll,~ gm pmtein/lOO ml

E. V Density, gm/ml

1 0.0362 0.41402 1.00403 1.00399 2 0.0724 0.41477 1,00405 1.00408 3 0.0774 0.41725 1.00412 1.00410 4 0.1127 0.41880 1.00416 1.00418 5 0.1445 0.42265 1.00427 1.00426 6 0.1448 0.42240 1.00427 1.00426 7 0.2597 0.43220 1.00455 1.00455 8 0.3621 0.44100 1.00481 1.00481 9 0.5011 0.45166 1.00513 1.00515

10 1.1275 0.50092 1.00672 1.00671

a Samples 1, 2, 6, and 8 are from a separate experimental run and were included to demonstrate reproducibility.

* Concentrations were determined to better than 1% precision on duplicate dry weights.

= A plot of density vs. concentration was fit with a straight line by least squares yielding a slope of 0.2488 i 0.0022 and an intercept of 1,00390. The values in this column were calculated from this line to show precision of the fit.

34 GOODRICH ET AL.

of the dialyzate and the intercept of the density vs. concentration curve suggests a preferential interaction (5) which merits further study.

It is important to point out that the concentrations reported may be slightly high if true dry weight was not achieved by the method used. Preliminary experiments have not indicated such an error but Hunter (6) has reported differences in dry weights by various methods.

ACKNOWLEDGMENTS

The transistor circuitry was designed by H. Lancaster and T. Jackson, Berkeley, and assembled by California Electronics Mfg. Co., Alamo, California. Drs. D. W. Kupke and J. W. Beams and their respective associates at the University of Virginia were of greatest assistance at several stages in the construction. Dr. J. E. Robbins was instrumental in initiating the project and S. L. Lowe was most helpful in preparing the computer program for our calculations. The technical assistance of Gerrit de Wilde was invaluable. This work was supported by NSF Grant GB-2513.

REFERENCES

1. BEAMS, J. W., AND CLARKE, A., Rev. Sci. Znstr. 33,750 (1962). 2. ULRICR, D. V., KUPKE, D. W., AND BEAMS, J. W., Proc. N&Z. Acud. Sci. 52,

349 (1964). 3. “International Critical Tables.” McGraw-Hill, New York, 1933. 4. MCKENZIE, H. A., SAWYER, W. H., AND SMITH, M. B., Biochem., Biophys.

Acta 147, ‘73 (1967). 5. BARNETT, L. B., AND BULL, H. B., Amh. Biochem. Biophys., 88,328 (1960). 6. HUNTER, M. J., J. Phys. Chem. 70,3285 (1966).