A sedimentation equilibrium method for determining molecular weights of proteins with a tabletop high speed air turbine centrifuge.

A technique has been developed for determining the molecular weights of proteins by sedimentation equilibrium in a tabletop, high speed, air turbine centrifuge. The small rotor containing six plastic tubes with a capacity of about 100 PI/tube can operate at lo5 rpm corresponding to centrifugal fields up to 1.6 x 10” times that of gravity. Molecular weights are determined by measuring the depletion of protein from the upper 40 ~1 of solution. The addition of dextran or the use of relatively concentrated protein solutions (5 mglml) provided a sufficiently high density gradient at the bottom of the tubes to stabilize the concentration distribution of protein during the deceleration of the rotor. Experiments with known proteins showed that the fractional depletion in the upper 40% of the tubes varied linearly with the exponential of the reduced molecular weight as predicted by the theoretical treatment. The preliminary empirical plot can be used for determining the molecular weights of other macromolecules. Although knowledge of the partial specific volume is required, this value can be estimated readily from the chemical composition. Since the method does not depend on transport properties, the results are not affected by the shape of the molecules. Only small amounts of material are needed and impure samples can be used if a specific biological assay is available. Accuracies of about 10% were obtained and improvements in the technique should lead to an enhancement in the precision.


SUMMARY
A technique has been developed for determining the molecular weights of proteins by sedimentation equilibrium in a tabletop, high speed, air turbine centrifuge.
The small rotor containing six plastic tubes with a capacity of about 100 PI/tube can operate at lo5 rpm corresponding to centrifugal fields up to 1.6 x 10" times that of gravity. Molecular weights are determined by measuring the depletion of protein from the upper 40 ~1 of solution.
The addition of dextran or the use of relatively concentrated protein solutions (5 mglml) provided a sufficiently high density gradient at the bottom of the tubes to stabilize the concentration distribution of protein during the deceleration of the rotor. Experiments with known proteins showed that the fractional depletion in the upper 40% of the tubes varied linearly with the exponential of the reduced molecular weight as predicted by the theoretical treatment.
The preliminary empirical plot can be used for determining the molecular weights of other macromolecules.
Although knowledge of the partial specific volume is required, this value can be estimated readily from the chemical composition.
Since the method does not depend on transport properties, the results are not affected by the shape of the molecules. Only small amounts of material are needed and impure samples can be used if a specific biological assay is available. Accuracies of about 10% were obtained and improvements in the technique should lead to an enhancement in the precision.
During the past 10 years, various empirical methods have been developed for determining the molecular weights of native proteins and the polypeptide chains produced by the addition of denaturants like guanidine hydrochloride or sodium dodecyl sulfate. Techniques such as gel chromatography (l-4), polyacrylamide gel electrophoresis (5), and electropho- resis on sodium dodecyl sulfate-polyacrylamide gels (6-8) generally yield reliable results, exhibit great sensitivity, and encompass a broad range of molecular weights. Although these methods require calibration with proteins of known molecular weight and in some instances there are marked departures from the empirically determined relationships, the techniques have proved invaluable for studies of proteins which are available only in microgram amounts. Moreover, the equipment required is simple and inexpensive.
The availability of a tabletop high speed centrifuge, known as the Airfuge, afforded an opportunity to develop an additional method for determining molecular weights. This paper presents a preliminary account of a sedimentation equilibrium technique for measuring molecular weights ranging from about lo4 to 1.5 x lo5 with small quantities of dilute solutions which are centrifuged at fields about 30,000 times that of gravity.
The method involves measurement of the fraction of protein remaining in the upper 40 ~1 of the solution (total volume of 100 yl) at the conclusion of the centrifuge experiment. Although presented here as an empirical technique, the method is based on the fundamental theoretical principles of sedimentation equilibrium (9) modified to account for the shape of the small tubes contained in the rotor and for the fractionation procedure invoked after equilibrium is attained.' A standard curve was obtained with proteins of known molecular weight and partial specific volume and it is seen that this empirical curve correlates approximately with calculated theoretical relationships.

GENERAL CONSIDERATIONS
The tabletop Airfuge is an air turbine centrifuge about 38 cm long, 28 cm wide, and 18 cm high and has an aluminum rotor which is only about 4 cm in diameter and contains six sample tubes. This rotor, which has turbine flutes machined into the bottom, is lifted and driven by ordinary laboratory compressed air so that it simulates a "spinning top" which rotates on a cushion of air. With readily available air pressures, the rotor attains its maximum operating speed of 100,000 rpm in about 30 s; at that speed the centrifugal field at the bottom of the tubes is slightly greater than 160,000 times that of gravity. For the sedimentation equilibrium experiments described here, special polyethylene tubes of lOO-~1 capacity were used instead of the standard cellulose propionate tubes which contain 175 ~1. These thicker walled, slightly tapered tubes, 2 cm in length and approximately 4 mm in diameter (inner), were chosen both to reduce the path of sedimentation and to minimize convective stirring during the deceleration of the rotor. The tubes are oriented at an angle of 18" relative to the axis of rotation and the positions of the for the other proteins, values of log F were determined from assays of enzyme activity. The values of molecular weight and partial specific volume of the various proteins used for calculating D are listed in Table I-S. The molecular weight scale at the top of the figure was calculated on the assumptions that all proteins had a partial specific volume of 0.73 ml/g and that the rotor speed was 42,000 'pm. For some proteins, several determinations were made and the vertical bars indicate the range of values of log F. The solid curve was drawn as a best fit through the experimental data and the dotted curve represents the theoretical curve based on the hypothesis that no reorientation of liquid occurred when the rotor was stopped (see "Supplementary Material").  Fig. 2A-S.

DISCUSSION
As seen in Table I, the stabilizing density gradient formed from the sedimentation of dextran T40 (or proteins) at about 5 mg/ml was sufficient to prevent significant stirring during the deceleration of the rotor and the sampling procedure.
Moreover, in accordance with theory (see "Supplementary Material"), the fraction of protein remaining in the upper 40 ~1 of the solutions was almost linearly dependent on the exponential of the reduced molecular weight (Fig. 2).

Molecular Weight Determinations with a Tabletop Centrifuge
The accuracy of the molecular weight determinations depends on a number of factors. First is the assay for measuring the fraction of protein in the supernatant relative to the initial solution. Second is the use of appropriate experimental conditions so that the values of F approach neither unity nor zero. This point is illustrated by the results in Fig. 2. For cytochrome c, the value of F was about 0.7; hence for smaller molecules, F would be closer to 1.0 and experimental errors in determining the concentrations of the initial solution and the supernatant would lead to much more uncertainty in the evaluation of F. Similarly, for proteins with molecular weights about 105, the values of F are about 0.01 and errors in measuring the small amount of protein in the supernatant would lead to inaccurate values of F. A third factor influencing the accuracy of the molecular weight determinations is the calibration curve itself. This method like gel chromatography and polyacrylamide gel electrophoresis requires knowledge of the molecular weights of the proteins used as standards. The proteins should be homogeneous and have no tendency to aggregate or dissociate. Only one speed, 42,000 rpm, was employed for the experiments summarized in Fig. 2 and the results encompassed proteins with molecular weights ranging from lo4 to 1.5 x 105. Greater precision could be obtained with two calibration curves, one for the smaller proteins at higher centrifugal fields so that the values of F were lower and the other for larger proteins at lower fields and correspondingly higher values of F. A reasonable assessment of the accuracy obtainable is derived from the experiments with peroxidase; in these studies F was 0.29 2 0.05 for initial concentrations of enzyme varying from 0.05 to 1 mg/ml. According to the calibration curve in Fig. 2, the molecular weight of peroxidase is 41,000 2 3,000; hence an uncertainty of about 17% in F corresponds to an error in M of less than 10%.
In the experiments described above, the 40-~1 samples were removed manually without the use of any special device for lowering the pipette as liquid was being withdrawn. Some experimental error can be attributed to imprecision in the removal of the samples and this technique could be improved through the use of a vertical rack for adjusting the height of the pipette. The accuracy in measuring F depends on the technique used for the determination of concentrations. Generally, enzyme assays are less precise than spectral determinations of concentration.
But one of the principal advantages of the technique is its potential for molecular weight determinations of biologically active proteins even before they are purified. In this regard, it is analogous to gel chromatography and electrophoresis on polyacrylamide gels where the location of the component is based on assays for biological activity. The techniques differ, however, in that the transport methods require only the location of the species for the empirical determination of molecular weights, whereas the sedimentation equilibrium method requires quantitative assays of the amount of the active component in the supernatant and original solution. If the value of F is in the correct range, the measurement of concentration need not be extremely accurate; for F = 0.1, an error of 30% would lead to only a 10% error in the estimation of the molecular weight.
According to theoretical treatments for sedimentation equilibrium (g-111, the depletion of macromolecules from the upper fraction of the solution depends on the partial specific volume as well as the molecular weight. For most proteins the partial specific volume, 0, is about 0.725 ml/g (see range of values in Table I-S). When the value of v is not available experimentally, it can be calculated with excellent precision from the amino acid composition (12) or it can be assumed to be 0.725 ml/g. In an analogous way, the value of v can be estimated satisfactorily from the chemical composition of nucleic acids, polysaccharides, glycoproteins, or lipoproteins.
In the experiments conducted thus far there appeared to be no complications resulting from the use of dextran T40 to create the stabilizing density gradient. Interactions between some macromolecules and dextran T40 may occur and in those cases misleading results would be obtained. For the experiments reported here the solutions of protein contained the dextran T40 throughout the entire tube. It is possible to layer the protein solution over a small volume of the more dense dextran T40 which is placed in the bottom of the tubes. In this way, problems stemming from interactions may be reduced. Alternatively, tubes containing some type of constriction at the bottom might help to reduce convective stirring during the deceleration of the rotor.
Just as in conventional sedimentation equilibrium experiments, the technique described here would provide useful information about the heterogeneity of the macromolecules through experiments at different speeds. Variations of M with rotor speed would indicate heterogeneity or interacting systems.
With the existing rotor and stator, it is difficult to operate at speeds below 40,000 rpm. Hence, determinations of molecular weights greater than about 1.5 x loj are difficult. Some modification in the Airfuge to circumvent this problem is needed. In contrast, it is possible to determine the molecular weights of very small proteins readily since the maximum centrifugal force available is so great. It should be emphasized that the molecular weights are not affected by the shape or hydration of the sedimenting material since the technique is based on the theory of sedimentation equilibrium. With improvements stemming from greater experience, the method promises to be a useful adjunct to the transport techniques used so widely for determination of molecular weights. The method is founded on well understood physical principles. Improvements in the theoretical treatment beyond the preliminary description presented under "Supplementary Material" should further enhance its value. In principle, the method presented here could be used for determining the molecular weights of unfolded polypeptide chains in guanidine HCl or sodium dodecyl sulfate solutions.