Analytical centrifugation with preparative ultracentrifuges

ANALYTICALBIOCHEMISTRY

176,2@-216

(1989)

REVIEW Analytical Centrifugation Ultracentrifuges Allen

with Preparative

P. Minton

Laboratory of Biochemical Pharmacology, National Institute of Diabetes and Digestiue National Institutes of Health, Building 8, Room 226. Bethesda, Maryland 20892

and Kidne-v Diseases,

Various methods of quantitating solute gradients formed in the preparative ultracentrifuge are summarized and compared in the following section. Each of the subsequent sections reviews a particular type of analytical experiment: sedimentation equilibrium, sedimentation velocity, rate-zonal centrifugation, and isopycnic banding on a density gradient. Finally, the various methods used to determine sedimentation coefficients, to determine molecular weights, and to characterize intermolecular interactions are summarized and compared.

INTRODUCTION

For many years, the analytical ultracentrifuge has been a valuable tool for the characterization of the size and shape of macromolecules in solution and interactions between macromolecules. Currently available commercially produced analytical ultracentrifuges, such as the Beckman Model E, are difficult and expensive to maintain. Because these instruments do not incorporate recent developments in laboratory automation and computer-aided data acquisition and processing, performance of an experiment and processing of the raw data QUANTITATION OF SOLUTE GRADIENTS: to obtain the final result(s) desired by the investigator TECHNIQUES AND INSTRUMENTATION require time, patience, and substantial expertise. Use of The use of the preparative ultracentrifuge to perform the analytical ultracentrifuge has therefore substan- measurements conventionally performed with the anatially declined as simpler and more rapid chromatolytical ultracentrifuge requires that solute gradienbs graphic and electrophoretic methods for approximate formed at high gravitational force in the centrifuge be characterization of macromolecular size, shape, and in- preserved essentially intact during the process of bringteractions have come into widespread use, even though ing the rotor to a halt, unloading the sample tubes, and results obtained via these methods are considerably less measuring the solute gradient within each tube. Both accurate than those obtained from analytical ultracenconvection and diffusion can significantly degrade the trifugation. However, during the past 10 years methods gradient. Convection may be minimized through the use and instrumentation have been developed that permit of small centrifuge tubes and short sample columns, tomost of the measurements previously performed exclugether with the addition of a small amount (<5 mg/ml) sively with an analytical ultracentrifuge to be performed of a substance to the sample, sufficient to form a gentle rapidly, easily, and with comparable accuracy and precidensity gradient within the tube (3,4), but which does sion using a variety of commonly available preparative not react with the solute or otherwise affect its behavior. ultracentrifuges, ranging in size from the Beckman AirGradient decay via diffusion may be minimized by reducfuge to conventional floor models. Other recently devel- tion of the time required to quantitate the gradient and oped techniques permit new types of analytical data to by selecting conditions of centrifugation such that the be obtained using the preparative ultracentrifuge that solute gradient formed is no steeper than necessary to could not be obtained using the analytical ultracentriobtain the desired information (4,5). fuge. The primary objective of this review is to bring The classical method for determining the distribution these developments to the attention of the broader com- of solutes in a flat-top centrifuge tube is to puncture the munity of quantitative biochemists. tube at the bottom and collect drops in a fraction collecEmphasis is placed on novel techniques and/or applitor. The solute gradient existing prior to fractionation cations, and no attempt is made to cite routine use of is then quantitated through measurement of the solute concentration in each of the individual fractions. Variathe methods described here. The literature on analytical applications of the Beckman Airfuge has been pre- tions of this technique embodied in centrifuge tube fractionators currently marketed by Beckman Instruments viously reviewed by Pollet (1) and Howlett (2). 0003.2697/89 $3.00 Copyright icll989 by Academic Press, All rights of reproduction in any form

209 Inc. reserved

210

ALLEN

P. MINTON

and ISCO involve sealing the tube at the top and introducing an immiscible chase fluid from either above or below. The chase fluid is pumped continuously into the top or bottom of the tube, and the centrifuged solution is expelled from the opposite end into tubing leading to a spectrophotometric flow detector and/or a fraction collector. These methods work satisfactorily when the gradient of solute is extremely stable, as in the case of solute that has been banded isopycnically on a substantial density gradient. However, in the absence of a substantial density gradient, laminar and/or convective tlow during the process of tube evacuation and fraction collection lead to substantial loss of resolution (A. K. Attri and A. P. Minton, unpublished data). Methods for the fractionation of tube contents have been developed to avoid problems associated with continuous evacuation of the tube. Pollet et al. (3) used a precision microsyringe together with a micromanipulator to sequentially remove lo-p1 fractions starting from the top of a solution column in small cylindrical Airfuge tubes (5 X 20 mm). Each fraction so collected corresponds to a cylindrical lamina of solution within the tube that has a diameter of about 3.5 mm and a height of about 1 mm. At about the same time, Beckman Instruments subsequently introduced an Airfuge tube fractionator for the same purpose, which is simpler to use than the technique of Pollet et al. (3) but less precise. In 1986 Attri and Minton reported the development of an automated fractionator for small cylindrical quartz centrifuge tubes about the size of an Airfuge tube (6). Without significantly perturbing solute gradient(s) existing prior to fractionation, this device can separate and collect laminar fractions 0.1 mm high (volume, ca. 1~1) with a precision of better than ~2% (u). Attri and Minton (6) demonstrated that the automated fractionator provides concentration gradients of radiolabeled macrosolutes that are comparable in accuracy and resolution to those obtained for optically absorbing solutes using the uvvisible scanner of the analytical centrifuge. A nondestructive method for quantitating solute concentration gradients in small quartz centrifuge tubes was introduced in 1983 by Attri and Minton (4). A special holder was fabricated by means of which the optically transparent centrifuge tube may be placed in the sample compartment of a uv-visible spectrophotometer and elevated at constant velocity past a slit mask. The profile of absorbance versus time is automatically converted to a profile of absorbance (i.e., relative concentration) versus radial position in the centrifuge. This technique provides a resolution of 17 data points/mm tube height, almost twice that of the automated fractionator described above. The relative merits of fractionation and absorbance scanning as methods for quantitating concentration gradients have been previously discussed (6). Because of potentially greater resolution, accuracy, and speed, scan-

ning is the method tions are satisfied:

of choice when

the following

condi-

(a) The specialized equipment is available. At present it is not commercially produced,’ but detailed specifications, drawings, and copies of microcomputer software for instrument control, data acquisition, and data processing may be obtained from the author. (b) The solute or solutes to be quantitated possess absorbance maxima (or minima) in the uv or visible region obeying Beer’s law over the concentration range to be studied experimentally. (c) The loading concentration of the solute should have an absorbance between approximately 0.5 and 2.5 OD unit/cm at the scanning wavelength. (d) The solution to be studied contains no other substances with significant absorbance at the scanning wavelength. In addition to being useful when a scanning system is not available, the technique of centrifuge tube fractionation has several intrinsic advantages: (a) The technique of Pollet et al. (3) may be employed without any special instrumentation.’ (b) By specifically radiolabeling a target species to high activity, the gradient of concentration of that species may be measured at concentrations several orders of magnitude lower than those measurable by means of optical absorbance (3). Also, concentration gradients may be measured in solutions containing large amounts of substances that would interfere with an optical measurement. (c) Concentration gradients of each of several species centrifuged together may be obtained simultaneously by quantitating the amount of each species in each fraction via conventional analytical methods (chromatography, electrophoresis, specific color reactions, enzyme activity, etc.). SEDIMENTATION

EQUILIBRIUM

In 1978 Bothwell et al. (7) reported the first quantitative analysis of protein solutions centrifuged to sedimentation equilibrium in the 30” fixed angle Airfuge rotor (All0/30). A simple empirical relationship was found between the fraction of protein remaining in the top 50 ~1of a solution centrifuged to equilibrium, denoted by F, and the molecular weight of the protein. This relationship can be used (within specified limits) to estimate the molecular weights of unknown proteins. The analysis of ’ As of the date of writing, the automated scanner (4) and the automated fractionator (6) described here are being evaluated for possible commercial development by a manufacturer of scientific equipment and may be made available to the scientific community within the relatively near future. Further information may be obtained from the author.

ANALYTICAL

APPLICATIONS

OF

Bothwell et al. (7) was extended to the case of interacting proteins by Clarke and Howlett (8). Two proteins were centrifuged together to sedimentation equilibrium in the AllO/ rotor, and the fraction of each remaining in the top 50 ~1 of solution (F, and FJ was measured by performing gel electrophoresis on a sample of this fraction and subsequently quantitating the amount of material in each band via densitometry. Models were formulated for the dependence of F, and Fz upon total protein concentrations and equilibrium association constants in the context of models for heteroassociation, and these models were fitted to the data to obtain best-fit values of association constants. In 1979 Pollet et al. (3) reported absolute molecular weight determinations of a variety of radiolabeled proteins via the conventional thermodynamic analysis of sedimentation equilibrium. As described above, these workers sequentially removed lo-p1 fractions from a column of solution previously centrifuged to equilibrium in the A110/30 rotor. As many as nine such fractions were obtained from a single tube. Given the dimensions and geometry of the rotor and tube, the mean radial distance in the centrifuge corresponding to each fraction, denoted by r, was calculated, and the relative concentration of labeled solute in each fraction was determined by gamma or scintillation counting as appropriate. In this fashion a set of data points { r’,c,,l) is obtained. According to the theory of sedimentation equilibrium (9), one may define an experimentally measurable parameter called the apparent weight-average molecular weight as M,,a = 2RT/[(

1 - Vp)w”]

X a! In c,,,/dr’,

[II

where w is the angular velocity of the rotor, Uis the partial specific volume of the solute whose gradient is being measured, p is the density of the solution, R is the molar gas constant, T is the absolute temperature, and c,,~ is the relative concentration of solute. If the tracer species is present as a single homogeneous species that sediments ideally, Mw,app is equal to the true molecular weight and is independent of concentration. When the data of Pollet et al. (3) were plotted in the form of In c,,i as a function of r’, a linear relationship was found, in agreement with the prediction of Eq. [ 11 for a single ideal macrosolute (Fig. 1). The molecular weight of each protein, calculated from Eq. [l] using the best-fit value of d In c,,,/dr’ obtained from the linearized plot of the data, was in satisfactory agreement with previously published results. This finding validates the assumption that reorientation of laminae of constant concentration during deceleration of the fixed angle rotor does not degrade the gradient formed in the centrifuge. The technique of fractionating solutions centrifuged to sedimentation equilibrium in a preparative centrifuge introduced by Pollet et al. (3) has been employed with

PREPARATIVE

I:LTRACENTRIFUGES

r

0

1.15

20

rkm) 1.20 125 1.30 1.35

40

so

Volume

(ul)

80

FIG. 1. The gradients of concentration of three proteins centrifuged to sedimentation equilibrium in a Beckman airfuge. Relative concentrations of each protein as a function of position are determined by tube fractionation followed by either measurement of radiolabel or enzymatic activity in each fraction, as described in Ref. (3). Figure reproduced from Ref. (3) with permission.

variations by a number of investigators to measure protein molecular weights and to characterize protein associations. We summarize below several studies that present special features. After equilibrating radioiodinated insulin with cultured lymphoblastoid cells, Pollet et aZ. (10) added disuccinimidyl suberate to covalently crosslink insulin to its cell membrane binding site (receptor). The membranes were then solubilized in detergent-buffer solutions of varying density; the density was varied by making up buffer with different proportions of H20, DzO, and Di80. The solutions of solubilized membrane protein were centrifuged to sedimentation equilibrium and the gradient of radiolabel was measured via fractionation and counting as described above. It was found, as expected, that the experimentally measured value of d In c,,,/dr’ varied with p. Assuming that Mw,app and Fare independent of the degree of isotopic substitution in the solvent, then a set of equations of the form of Eq. [l] (one for each value of p) may be solved for the best-fit values of Mw,app and Lcharacterizing the insulin-receptor-detergent complex. Assuming that Uis a weight-average of the (known or assumed) partial specific volumes of detergent and protein, the composition of the complex may be estimated, and on this basis the molecular weight of the insulin binding protein was estimated to be 310,000. Note that if the native form of the insulin receptor in the membrane were to exist as a heterooligomer of noncovalently linked polypeptide chains, this method would measure only the molecular weight of the insulinbinding subunit. Using an Airfuge, Howlett et al. (5) centrifuged trace amounts either [1”51]bovine serum albumin ( [‘251]BSA)2 ’ Abbreviations lin.

used: BSA,

bovine

serum

albumin;

CaM,

calmodu-

212

ALLEN

1.05

115

1.25

r

lcmi

1.35

"

1.2

1.6

1-6

rz

fd)

1.8

FIG. 2. Concentration gradients of [‘2”I]BSA obtained via centrifugation to sedimentation equilibrium in the presence of unlabeled BSA at loading concentrations of 5 (triangles), 40 (circles), and 80 mg/ml (squares). Figure reproduced from Ref. (5) with permission.

or [‘251]Cu1-acid glycoprotein to equilibrium in the presence of varying concentrations of unlabeled BSA. They found that the apparent weight-average molecular weight of each labeled protein, calculated from the observed value of d In cJcir2, decreased monotonically with increasing BSA concentration (Fig. 2). Such behavior is characteristic of nonideal solutions and may be attributed to repulsive intermolecular interactions between the labeled species and itself (if present at sufficiently high concentrations) or the labeled species and other unlabeled species in the solution (11,12). Using the Airfuge, Husain et al. (13) centrifuged trace amounts of radiolabeled calmodulin (CaM) to sedimentation equilibrium in the presence of either dextran or BSA at a concentration of 5 mg/ml in buffers of low and moderate ionic strength. They reported that in low ionic strength buffer, the apparent weight-average molecular weight of CaM in BSA is almost twice that in dextran, or in either species at moderate ionic strength. The difference was attributed to the formation of a CaMBSA complex in low ionic strength buffer.3 As part of a study of the physical properties oflipoprotein lipase, Osborne et al. (14) performed parallel sedimentation equilibrium experiments in analytical and preparative ultracentrifuges. Optical scanning of the equilibrium gradient in the analytical ultracentrifuge revealed the presence of a heterogeneous distribution of sedimenting species which was attributed to the presence of both reversibly and irreversibly formed lipase oligomers. The tube centrifuged to equilibrium in a swinging bucket rotor was fractionated in a manner similar to that employed by Pollet et al. (3), and each of the

P. MINTON

fractions was assayed for lipase activity. The gradient of active enzyme obtained in this fashion was consistent with a single species of molecular weight equal to the smallest significant component of total protein, establishing that lipase oligomers detected by absorbance scanning of the equilibrium gradient (and by size exclusion chromatography) were enzymatically inactive. In 1983 the automated scanner (4) was introduced, permitting investigators to collect data on relative solute concentration versus radial distance in a centrifuge tube with a resolution 17 times greater than previously possible. Subsequent introduction of the automated fractionator (6) permitted the quantitation of gradients of radiolabeled proteins with comparable resolution. The benefits are twofold: the gradient may be measured to correspondingly greater precision, leading to enhanced precision of the result, and/or a substantially shorter (23x) column may be centrifuged, leading to a severalfold reduction in the centrifugation time required to attain sedimentation equilibrium. Using quartz centrifuge tubes together with appropriate adaptors, a variety of proteins have been centrifuged to sedimentation equilibrium in the A110/30 fixed angle Airfuge rotor (4), the SW-41 swinging bucket rotor for conventional preparative centrifuges (4,6), and, most recently, the TLS-55 swinging bucket rotor for the Beckman TL-100 benchtop ultracentrifuge (15) (Fig. 3). Molecular weights, calculated automatically within moments of scanning a centrifuge tube or completing scintillation counting of radiolabeled fractions, are in good agreement with literature values. Since the automated scanner assays the absorbance gradient of solute rapidly and nondestructively, one can easily scan and then fractionate the contents of a single centrifuge tube. Such a procedure would facilitate comparisons of the respective gradients of absorbance and,

I

I 60

I 61

62

63

64

r* (cm’)

3 This hypothesis cannot be confirmed until additional concentration dependence studies are performed. In the absence of significant concentrations of added electrolyte, the ionic strength of the 5 mg/ml BSA solution is substantially larger than that of the 5 mg/ml dextran solution; the difference in ionic strength alone could contribute significantly to differences in the sedimentation equilibrium of CaM in the two solutions.

FIG. 3. Linearized plots of gradients of native y-globulin (circles) and [‘%]y-globulin (squares) centrifuged together to sedimentation equilibrium. The centrifuge tube was optically scanned prior to fractionation and subsequent scintillation counting. The slopes of the two best-fit straight lines, which should be proportional to molecular weight, agree to within 1.5%. Figure reproduced from Ref. (6).

ANALYTICAL

APPLICATIONS

OF

PREPARATIVE

say, enzyme activity, facilitating analyses comparable to that of Osborne et al. (14) summarized above. Comparisons between the equilibrium gradients of absorbance and radiolabel could also facilitate the characterization of heteroassociations between a labeled macrosolute and a second unlabeled (but optically absorbing) macrosolute. In 1987, Attri and Minton (16) described an automated method for accurately measuring the quantity of each of two macrosolutes, respectively labeled with 3H and 14C, as a function of position in a centrifuge tube at sedimentation equilibrium. They demonstrated that with this method it is possible to accurately measure the molecular weights of each of two differently labeled proteins in a mixture, even when one is present at a much higher concentration than the other, and even when the molecular weights of the two proteins are comparable. Such determinations are prohibitively difficult if one is constrained to measure only the sum of the concentrations of the two macrosolutes, as in a conventional optical experiment. The potential of the dual label method for the characterization of heteroassociations is obvious, but has not yet been exploited. Most recently, Muramatsu and Minton (17) performed extensive measurements of the sedimentation equilibrium of three globular proteins, BSA, aldolase, and ovalbumin, over a very large range of concentrations (ca. l-200 mg/ml) in phosphate-buffered saline. A trace amount of protein labeled with the chromophore fluorescein isothiocyanate was present in all solutions at constant concentration; only the concentration of unlabeled protein was varied. The centrifuge tubes were scanned at a wavelength maximum of the label (493 nm) to facilitate measurement of the relative concentration of the protein as a function of radial position over a wide

213

IJLTRACENTRIFUGES

I

I

I

I

1

I

5.8

6.0

6.2

6.4

6.6

6.8

r (cm)

FIG. 5. Absorbance gradient of BSA after centrifugation for 180 min at 35K rpm and 20°C in a TLS-55 swinging bucket rotor. The leftmost vertical line (AI represents the position of the meniscus, and the rightmost vertical line (B) represents the weight-average position of the trailing boundary of sedimenting protein. Figure reproduced from Ref. (151.

concentration range. At lower concentrations all three proteins behaved as ideal macrosolutes with molecular weights characteristic of the native protein (monomer for BSA and ovalbumin, homo-tetramer for aldolase). At concentrations exceeding about 20 mg/ml, substantial deviations from this behavior were observed. In the case of BSA, the deviations may be ascribed entirely to nonideal behavior arising from volume exclusion (ll), whereas in the casesof aldolase and ovalbumin, substantial self-association at high protein concentrations must be invoked in addition to volume exclusion (11) in order to account for the observed dependence of apparent weight-average molecular weight upon total protein concentration (Fig. 4). SEDIMENTATION

VELOCITY

AND

DIFFUSION

In 1984 an automated method for determining the sedimentation coefficient of macromolecules with a preparative centrifuge was described by Attri and Minton (18). A centrifuge tube initially containing a uniform concentration of solute is centrifuged at high angular velocity until the meniscus is depleted of solute. The tube is subsequently scanned, and the position of the meniscus and the weight-average position of the trailing boundary of solute are automatically calculated as described in Ref. (18) (Fig. 5). From these two positions, the known rotor geometry, and known angular velocity profile of the centrifuge run, the sedimentation coefficient is automatically calculated.4 The automated analysis of velocity exFIG. 4. Apparent weight-average molecular weight of ovalbumin as a function of protein concentration. Data (filled circles) show combined effects of self-association at moderate concentration and nonideality at high concentration. Upper pair of dashed curves indicates estimates of actual weight-average molecular weight, corrected for nonideality according to Ref. (11). Figure reproduced from Ref. (17).

4 Equation [3.7] of this relation is

of Ref.

(18) contains

an error.

The

correct

version

214

ALLEN

matically calculated from the change in the slope of the boundary. The sedimentation coefficient, diffusion coefficient, and molecular weight, calculated from

30

A

: 0

_---_

4*-k.

20

it4 = RTI(1

; 8

P. MINTON

10

0 I

13.4

I

13.8

14.2

14.6

- Up, x so/Do,

where so and Do are respectively the values of the sedimentation and diffusion coefficients in the limit of low concentration, are in good agreement with literature values. As many as four such determinations may be made concurrently in a total elapsed time (including centrifugation) of under 2 h.

r (cm)

FIG. 6. Radiolabel gradient of [iz51]BSAafter centrifugation for 125 min at 30.5K rpm and 20°C in a SW-41 swinging bucket rotor. The open circle represents the position of the meniscus, and the vertical line represents the weight-average position of the trailing boundary of sedimenting protein. Figure reproduced from Ref. (6).

periments was subsequently generalized (6) to permit such experiments to be carried out using the microfractionator as well as the scanner5 (Fig. 6). Precise determination of the meniscus position using either the scanner or microfractionator requires that the aqueous solution be overlaid with a small amount of light, immiscible oil. Because of surface effects, the oil-water interface does not reorient upon rotor deceleration; hence velocity experiments can be carried out only in swinging bucket rotors. In 1987, Muramatsu and Minton (19) described an automated method for determination of the diffusion coefficient of macrosolutes, based upon the observed rate of boundary spreading in a quartz centrifuge tube. They demonstrated that the method can be used in conjunction with a sedimentation velocity measurement to simultaneously measure the sedimentation and diffusion coefficients of a macrosolute. A simple device was described by means of which an aliquot of buffer may be gently layered onto a column of protein solution in a centrifuge tube, resulting in a narrow, symmetric boundary. The centrifuge tube is scanned prior to and after the conclusion of centrifugation (Fig. 7). The weight-average boundary position and slope of the boundary at its midpoint are automatically determined as described in Refs. (16) and (18). The sedimentation coefficient is automatically calculated from the change in weight-average boundary position, and the diffusion coefficient is auto-

ANALYTICAL

RATE-ZONAL

Centrifugation of a narrow zone of solute through a medium containing a density gradient sufficient to stabilize the zone has been a useful method for measuring the sedimentation coefficient of macromolecules and macromolecular assemblies for many years (20) and is probably the first widespread analytical application of the preparative ultracentrifuge. Recently this technique has been extended to the study of interactions between macromolecules (21). The principle of the method is as follows: A zone of macromolecule (“substrate”) is applied to the top of solution containing a uniform concentration of a smaller reactant (“ligand”) and a gradient of some presumably inert substance such as sucrose or glycerol used to maintain a small density gradient. As the substrate sediments through the tube, it is in equilibrium with ligand at the ligand’s loading concentration; if the ligand is a smaller macromolecule (also sedimenting), the zone of substrate will be within the plateau region of the ligand for the duration of the experiment. If the interaction between substrate and ligand results in the formation of one or more complexes having a sedi1.00

0.75

-

0.50

13.65

Only the printed equation was erroneous; sedimentation coefficients calculated in Ref. (18) and subsequent publications using this method (6,15-17) were calculated using the correct relation given above. 5 Traditional methods of tube fractionation (such as those described in Refs. (3) and (20)) lack the resolution required to adequately quantitate the position and shape of a trailing boundary of solute.

CENTRIFUGATION

13.65

14.05

14.25

r (cm)

FIG. ‘7. Trailing boundary of BSA measured by absorbance scanning before and after centrifugation (circles and squares, respectively) in an SW-41 rotor at 30K rpm for 52 min at 20°C. Figure reproduced from Ref. (19).

ANALYTICAL

APPLICATIONS

OF

PREPARATIVE

mentation coefficient(s) significantly different from that of free substrate, the sedimentation velocity of the substrate zone will be observed to depend upon the loading concentration of ligand. If the reactants are in rapid equilibrium with the complex(es), then the observed sedimentation velocity will be a weight-average quantity reflecting the mass fraction of each of the substrate species in the zone. Using this technique Siegel and Schumaker (21) and Lakatos (22) characterized equilibrium associations between subcomponents of complement protein Cl. The rate-zonal method of measuring association equilibria is especially useful when it can be established that only one ligand-substrate complex is formed: under these conditions the measured sedimentation velocities of the zone in the presence of limiting high and low concentrations of ligands suffice to unambiguously characterize both species present in the sedimenting zone at intermediate levels of ligand. The presence of intermediate complexes that cannot be independently characterized complicates quantitative analysis of the results, as the sedimentation coefficient of each of the intermediate complexes becomes an undetermined parameter in any model for the dependence of zone sedimentation velocity upon ligand concentration. ISOPYCNIC

BANDING

ON

A DENSITY

GRADIENT

Prior to the advent of rapid methods for the nucleic acid sequencing, density determination in the analytical ultracentrifuge via isopycnic banding on a density gradient was frequently used to characterize the purine-pyrimidine composition of nucleic acids. While this particular application is no longer useful, accurate determination of changes in the density of macromolecules can still be used to monitor the progress of reactions not readily followed by other analytical methods. Using the automated centrifuge tube scanner (4) to quantify the equilibrium positions of bands on a self-forming density gradient, Attri and K. Minton (23) demonstrated that if a density standard is included in the tube, the absolute density of an unknown band may be automatically and precisely calculated from known physical-chemical properties of the gradient-forming solute and the relative radial positions of the standard and unknown bands. This technique was used by Love et al. (24) to measure the extent of covalent interstrand crosslinking in d(GT),/d(CA), as a function of the dose of ultraviolet light to which this polynucleotide was exposed under a variety of experimental conditions. The formation of the crosslinked species was monitored by the appearance of a band in a Cs,SO, gradient having a buoyant density between those of the dissociated strands of the starting material. COMPARISON Measurement

preparative

OF ALTERNATIVE of sedimentation

ultracentrifuge,

TECHNIQUES coefficient. Using a

the sedimentation

coefl-

ULTRACENTRIFUGES

215

cient may be measured either via a conventional highspeed meniscus depletion experiment (18) or via a ratezonal experiment (20). The precision of the measurement is limited by the precision with which the distance of migration of the weight-average position of the trailing boundary (in the depletion experiment), or the weight-average position of the sedimenting zone (in the rate-zonal experiment), may be determined. If the investigator is limited to standard methods of large centrifuge tube fractionation (see, for example, Ref. (20)), then solute migration of at least 2 cm is needed if the final position of the trailing boundary or band is to be determined to within 25%. The duration of centrifugation needed to obtain the requisite migration will be of the order of 6-7 h for a solute with a sedimentation coefficient of ca. 5 S. Using the automated microfractionator or scanner and small centrifuge tubes, the sedimentation coefficient of the same solute may be determined to within ?3% with a centrifugation time of under 2 h (18). Measurement of molecular weight. Using the preparative ultracentrifuge, the molecular weight of a macrosolute may be determined via measurement of the gradient at sedimentation equilibrium or by the simultaneous determination of sedimentation and diffusion coefficients. As demonstrated by Pollet et al. (3), sedimentation equilibrium experiments may be performed reasonably rapidly, i.e., on a time scale of 1 to 2 days, using small centrifuge tubes and a fixed angle rotor. The resolution afforded by manual fractionation is sufficient for determination of equilibrium gradients, provided that they are not too steep. The accuracy, precision, and ease of determination is enhanced by use of the automated scanner and/or fractionator. Determination of molecular weight by simultaneous measurement of the sedimentation and diffusion coefficients requires the use of an optical scanner and an artificial boundary forming device (19). Moreover, the solute must be pure, or at least the only solute present absorbing light at some wavelength in the visible or uv. If these conditions are met, then the molecular weight may be determined to better than +5% within 2 h. Characterization of macromolecular self- and heteroassociations. Noncovalent macromolecular associations

may be characterized by measuring the variation of the sedimentation coefficient of a labeled macrosolute as a function of the concentration of a second, unlabeled macrosolute that remains in equilibrium with the labeled solute throughout the duration of centrifugation (21,22). Both self- and heteroassociations may be studied, depending upon whether the labeled and unlabeled species are identical or different. Such experiments must be conducted at low macromolecular concentrations to assure that the sedimentation coefficients of each of the individual sedimenting species are independent of concentration. As mentioned above, some uncertainty is en-

216

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P. MINTON

countered in the analysis if the labeled species can exist in more than two significant states of association. Sedimentation equilibrium experiments can provide an experimentally determined dependence of the apparent weight-average molecular weight of a macrosolute upon its total concentration. The observed dependence may then be compared with the predictions of alternative model association schemes, in order to discriminate between them and to evaluate equilibrium association constants appearing in the most likely association scheme or schemes (17). The recently introduced dual label method for simultaneous quantitation of the gradients of each of two species (16) centrifuged in a mixture holds promise for quantitative characterization of heteroassociations with unprecedented precision.

3. Pollet, R. J., Haase, B. A., and Standaert, M. L. (1979) J. Biol. Chem.254,30-33. 4. Attri, A. K., and Minton, A. P. (1983) Anal. Biochem. 133, 142152. 5. Howlett, G. J., Dickson, P. W., Birch, H., and Schreiber, G. (1982) Arch. Biochem. Biophys. 215,309-318. 6. Attri, A. K., and Minton, A. P. (1986) Anal. Biochem. 152, 319328. 7. Bothwell, M. A., Howlett, G. J., and Schachman, H. K. (1978) J. Biol.

Chem.

253,2073-2077.

8. Clarke, R. G., and Howlett, G. J. (1979) 195,235-242. 9. Schachman, H. (1959) Ultracentrifugation demic

Press,

10. Pollet, Chem.

Biochem.

Biophys.

in Biochemistry,

Aca-

New York.

R. J., Haase, 256,12118-12126.

11. Chatelier,

Arch.

B. A., and Standaert,

M.

R. C., and Minton,

A. P. (1987)

R. C., and Minton,

A. P. (1987)

L. (1981)

Biopolymers

J. Biol. 26,

507-

524. CONCLUSION

Most of the experiments traditionally carried out using the analytical centrifuge may now be performed with comparable accuracy and precision, and with significantly greater ease and rapidity, using a variety of preparative ultracentrifuges. Moreover, the recently developed high-resolution microfractionator permits concentration gradients of analytical quality to be obtained when optical methods of quantitation are either inappropriate or unfeasible.

12. Chatelier, 1113. 13. Husain,

A., Howlett,

Biopolymers

G. J., and Sawyer,

26,1097-

W. H. (1985)

Anal.

Bio-

J. C., Jr., Bengtsson, G., Lee, N. S., and Olivecrona, Biochemistry 24,5606-5611.

T.

chem.145,217-221. 14. Osborne, (1985)

15. Muramatsu, N., and Minton, A. P. (1988) Beckman TL-100 News 3,1-3. 16. Attri, A. K., and Minton, A. P. (1987) Anal. Biochem. 162,409419.

17. Muramatsu,

N., and Minton,

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ACKNOWLEDGMENTS I acknowledge the invaluable contributions of Arun K. Attri, Nobuhiro Muramatsu, and James V. Sullivan to the analytical methods and instrumentation developed in our laboratory. I thank Susan Lakatos and Marc S. Lewis for critically reading and commenting upon preliminary drafts of this review.

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