Current Protocols in Protein Science || Analytical Ultracentrifugation

UNIT 7.5Analytical UltracentrifugationAnalytical ultracentrifugation is the grand-

father of biochemical methods, with a 70-yearhistory of development and application (Sved-berg and Pederson, 1940; Schachman, 1959).Recently, the attention of protein scientists andmolecular biologists has been drawn to macro-molecular interactions, an area where analyti-cal ultracentrifugation excels, resulting in arenewed interest in this technology (Harding etal., 1992; Ralston, 1993; McRorie and Voelker,1993; Schuster and Laue, 1994). As this unitwill describe, analytical ultracentrifugation isone of the most powerful, though as yet under-exploited, techniques available to molecularbiology and biochemistry.

Two different but complementary methodsof sample analysis are possible using an analyti-cal ultracentrifuge: sedimentation velocity andsedimentation equilibrium (Table 7.5.1). Eachencompasses a range of techniques suitable forcharacterizing everything from crude mixturesto highly purified proteins. Sedimentation ve-locity provides such hydrodynamic informationas size, shape, and, when combined with diffu-sion measurements, molecular weight. Sedi-mentation equilibrium provides thermodynamicinformation about molecular weight, stoich-iometry, association energy, and nonideality.

Both sedimentation methods are understoodfrom first principles. Thus, no standards are

Table 7.5.1 Methods of Analytical Ultracentrifugation

Method Category Information obtained and notes

Velocity Direct fitting totransport equations

Modern way to obtain s (and the diffusioncoefficient) for a single solute. When combined withmolecular weight, s yields information concerningthe size and shape of the protein (Philo, 1994).

g(s)–particle sizedistribution analysis

Powerful method for analyzing complicatedmixtures of molecules. Holds promise for analyzingassociating systems (Stafford, 1992; Stafford, 1994).By increasing the gravitational field over the courseof an experiment, fractionation of incrediblycomplicated mixtures may be achieved (Mächtle,1988).

Differentialsedimentation

Sensitive means of detecting small (0.005%)differences in sedimentation due to conformationalchanges (Richards and Schachman, 1957).

Active enzymesedimentation

Means of characterizing an impure enzyme (Cohenet al., 1971) using a chromophoric assay andmonitoring the movement of color development asthe enzyme sediments.

Van Holde andWeischet extrapolation

Graphical means of removing the effects ofdiffusion, thus improving resolution of a pauci-disperse solution (Van Holde and Weischet, 1978).

Equilibrium Short-column analysis(750 µm, 15 µlsamples)

Useful for quick surveys of molecular weight,association properties, and nonideality (Yphantis,1960; Laue, 1992).

Longer-columnanalysis (3 mm, 110 µlsamples)

Provides higher precision than short-column; usefulfor low-molecular-weight solutes and analysis ofheterogeneity (Yphantis, 1964).

Miscellaneous Extinction coefficient Combines absorbance and refractive optical readingfor precise measurement of extinction coeffiecient.Sensitive test for sample homogeneity.

Tracer sedimentation Very sensitive and selective for characterizinginteractions between purified proteins.

Diffusion coefficient Obtained at low speed.

Contributed by Thomas M. LaueCurrent Protocols in Protein Science (1996) 7.5.1-7.5.9Copyright © 2000 by John Wiley & Sons, Inc. Supplement 4

7.5.1

Characteristics ofRecombinantProteins

required to interpret data and the same valuesshould be obtained for parameters (e.g., mo-lecular weight and s20,w) from preparation topreparation and from laboratory to laboratory.Of the two methods, sedimentation velocityprovides a greater degree of sample fractiona-tion, and it is uniquely suited to particle sizedistribution analysis (see Anticipated Resultsfor definitions and further discussions). Thestandardized sedimentation coefficient (s0

20,w;measured in Svedberg units, S) is a constant fora given molecule; it therefore is often used as aspecies descriptor (e.g., 30S subunit, 5S RNA).

The reasons behind the revival of analyticalultracentrifugation reveal many of its virtues.Fundamental information concerning samplepurity, native molecular weight, association en-ergies, and molecular size and shape are allreadily obtainable using this technique. Themethods are not fussy with regard to solventconditions, and can be applied to any sort ofprotein (fibrous or globular, large or small) overan enormous range of molecular weights (<100to >10,000,000 g/mol). Relatively small quan-tities of materials are required for analysis and,because the techniques are nondestructive,samples can be recovered afterwards. More-over, great experimental precision can be an-ticipated, even by a novice experimenter.

The disadvantages of sedimentation analy-sis are different for the velocity and equilibriummethods. Sedimentation velocity analysis re-quires relatively large sample volumes (450 µl)and, being a broad-zone method, exhibits poorsample fractionation when compared with vari-ous chromatographic and electrophoreticmethods (Table 7.5.2). Subtle changes readilyapparent upon electrophoresis may not be re-vealed by sedimentation. Another consequenceof the technique’s broad-zone nature is that onlythe slowest-sedimenting species can be exam-ined in a pure state; all other boundaries will becomposed of mixtures of components.

The interpretation of sedimentation equilib-rium data requires that highly purified proteinsbe used. For the analytical ultracentrifuge, rela-tively high concentrations of proteins (0.1 to1.0 mg/ml) are required for detection (Table7.5.3). Even if these criteria are met, compli-cated association schemes (e.g., highly non-ideal monomer:dimer:tetramer:octamer asso-ciations) are difficult to analyze in great detail.Finally, neither sedimentation velocity norsedimentation equilibrium is suitable for ki-netic analysis.

Even with these disadvantages, sedimenta-tion analysis compares favorably with alterna-tive methods (Table 7.5.2). There are threeclasses of methods that can be compared withsedimentation: (1) other primary methods(light scattering and osmotic pressure), (2)spectroscopic analysis for obtaining thermody-namic information, and (3) secondary methodsbuilt around electrophoresis and column chro-matography. Both light scattering and osmoticpressure are well-grounded in thermodynamicsand provide accurate estimates of molecularweight. However, neither affords any fractiona-tion of the solution and neither provides hydro-dynamic information equivalent to that fromsedimentation velocity. Both are subject toproblems with contamination (osmotic pres-sure from small particles and light scatteringfrom large ones), though this sensitivity can beuseful for detecting such contaminants. Finally,both require larger quantities and higher con-centrations of sample than does sedimentation.

Spectroscopic methods—e.g., fluores-cence, absorbance, circular dichroism (CD),nuclear magnetic resonance (NMR), and elec-tron spin resonance (ESR)—are often useful forexamining sample purity and for conductingbinding studies. For sample purity, these meth-ods are usually applied to detect the presenceof specific contaminants (e.g., detecting proteinin a DNA sample by absorbance). The concen-trations needed to conduct a study range fromquite low (fluorescence) to rather high (NMR).In addition to sample purity, spectroscopy oftenis used phenomenologically to monitor asso-ciations, including macromolecular interac-tions. Because of their respective sensitivities,the concentration range accessible to thesemethods is quite variable. All spectroscopicmethods suffer from certain common prob-lems. First, because they are phenomenologi-cal, it is not guaranteed that binding will leadto the production of an appropriate signal.Hence, it is possible for an interaction to occurthat gives rise to no measurable spectroscopicchange. Moreover, if the stoichiometry of bind-ing is >1, it is possible for different bindingevents to give rise to proportionately differentsignals. In these cases, the stoichiometry ofbinding will be nearly impossible to determineand estimates of the strength of binding may beseriously in error.

There are several chromatographic and elec-trophoretic methods available for makingmeasurements similar to those from sedimen-tation. These fractionate the sample and there-fore are extremely useful for detecting contam-

Supplement 4 Current Protocols in Protein Science

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AnalyticalUltracentri-

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Table 7.5.2 Alternative Analytical Methods

Class Method Notes

Primary methodsNo standards required; data interpre-tation grounded in physical firstprinciples; no sample fractionation.

Scattering Light and low-angle X-ray can yield molecularweight and radius of gyration. For mixtures, weight-average molecular weights and z-average radii areobtained. (Laue, 1995; Yphantis, 1964). Sensitive tolarge contaminants. Small cuvettes reduce samplevolume, but sensitivity is limited to relatively highconcentrations (>1 mg/ml). Particle scattering (e.g.,neutrons) is very expensive but yields details aboutparticular aspects of structure.

Osmotic pressure(other colligativemethods)

Useful for determining molecular weights of smallmolecules. For mixtures, number-average molecularweights are obtained. Sensitive to low-molecular-weight contaminants. Relatively high concentrations(>1 mg/ml) are required. Vapor pressure osmometersrequire small sample volumes.

Spectroscopic methodsPrimarily useful phenomenologi-cally; sample size and sensitivityvary from method to method; nosample fractionation.

Absorbance Useful for detecting particular contaminants. Simpleto use. Sensitivity to contaminants depends on theirextinction coefficient at the wavelength of interest.Changes in absorbance with binding can be used tomonitor macromolecular interactions with varyingsuccess.

Fluorescence Very sensitive. Both luminescence and quenching offluorescence useful for detecting contaminants.Changes in fluorescence can be used to monitormacromolecular interactions with varying success.

Circular dichroism Not generally as useful as other spectroscopicmethods for detecting contaminants. Can be used tomonitor macromolecular interactions with varyingsuccess. Instrumentation expensive.

Nuclear magneticresonance, electronspin resonance

Not generally as useful as other spectroscopicmethods for detecting contaminants. Can be used tomonitor macromolecular interactions with varyingsuccess. Requires high concentrations of material andinstrumentation expensive.

Secondary methodsRequire standards for interpretation;can be particularly useful for detect-ing contaminants; most are used as“thin-zone” methods, which limitstheir usefulness in characterizing in-teractions.

Columnchromatography

Depending on column matrix, can be sensitive tosize, charge, or specific binding. In studying binding,useful qualitatively but less so for quantitative work.Fractionation can be excellent. Ability to measurecontaminants depends on detector used to monitoreffluent, but can be exquisitely sensitive. A modifieddetector in which the matrix is attached to thedetector is at the heart of the Pharmacia BiotechBiacore and related devices.

Electrophoresis Several methods based on electrophoretic mobilityexist (e.g., gel electrophoresis, capillary zonal electro-phoresis, and isoelectric focusing). Fractionation isusually superb; sensitivity depends on detector.Because of the high degree of sample fractionation,only limited, qualitative information aboutmacromolecular interactions is obtainable.

Current Protocols in Protein Science Supplement 4

7.5.3


inants. Most of these methods are now highlyrefined, are easy to use, and can examine a widerange of sensitivities. However, with regard tosample characterization, they are less rigorousthan sedimentation. This stems from the factthat all are secondary methods, requiring stand-ards for calibration and comparison. For exam-ple, gel permeation chromatography is oftenused to estimate molecular weights, radii, andstoichiometries. However, if a protein does notconform to the properties of the standards (e.g.,if the unknown is asymmetric and the standardsare all spherical), erroneous conclusions maybe reached with this approach. A second, morefundamental, problem arises when these meth-ods are used to examine macromolecular inter-actions. Both chromatography and electropho-

resis usually entail the monitoring of thin zonesof material. Because the concentration in thezone varies both spatially and with time, it isimpossible to relate the zone shape or positionto any association parameters in a rigorousfashion.

PLANNING AN EXPERIMENTThe principle measurement obtained in any

sedimentation experiment is the concentrationas a function of radial position. Knowledge ofthe concentration distribution, along with therotor speed and temperature, is needed to obtaina molecular weight or an s20,w. There are severalmeans of determining the concentration distri-bution (Table 7.5.3). Analyses may be con-ducted using either a preparative or an analyt-

Table 7.5.3 Methods of Solute Detection

Method of detection Usea Pb Ac Sd De Notes

Absorbance A, P G F G F Sensitivity depends on solute’s extinction coefficient.Discrimination depends on separation betweenabsorbances.

Refractive A E E G P Accuracy and precision cannot be matched by othertechniques. Method of choice for nonabsorbing solutes orbuffers that absorb in the UV.

Fluorescence P F F E E Specific labels can provide excellent sensitivity and superbdiscrimination, but the linearity of the concentrationdetermination is subject to several types of error.

Enzyme assay P, A F F E E Excellent discrimination and sensitivity. Can be used todetermine which form of an enzyme is active. Precisionand accuracy can be quite good or rather poor, dependingon the assay. A band sedimentation method for theanalytical ultracentrifuge works quite well, but requiresthat a suitable colorimetric assay be available.

Radiolabel P G F E E Superb discrimination and sensitivity can be attained.Accuracy of the concentration determination can rangefrom very good to very poor depending on the particularsof the radiolabeling.

Other P — — — — Any assay (RIA, ELISA, bioassay) that yields a signalproportional to the concentration may be used fordetermining molecular weight and s20,w. Of particularinterest are methods in which the sample is fractionated(e.g., by gels or HPLC) subsequent to sedimentation, whichallows detection of interactions between components inextremely complicated mixtures. Typically, the accuracy ofthese methods is not sufficiently high to allow furtheranalysis (i.e., determination of association constants).

aDesignates the instrument that may be used: A, analytical ultracentrifuge; P, preparative centrifuge with subsequent microfractionation. Where bothtypes of instruments may be used, the better of the two is listed first. In general, the analytical ultracentrifuge offers improved accuracy in thedetermination of radial position and concentration, which is necessary for determining accurate association constants and stoichiometries. The preparativecentrifuge offers lower cost and, in general, greater solute sensitivity and discrimination, but lower precision and accuracy.bPrecision of detection. Usually given as a standard error of replicates, the precision of a detection scheme may be very high, yet the accuracy may bepoor if systematic error is present. E, excellent; G, good; F, fair; P, poor.cAccuracy of detection. This depends on the lack of systematic errors (e.g., nonlinearity of the response of the detector with concentration).dSensitivity to solute.eDiscrimination between solutes.


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ical ultracentrifuge. It is worth taking a momentto consider which instrument will be most use-ful for elucidating a particular problem. To dothis, it is necessary to have a clear notion ofwhat information is being sought from the cen-trifugation experiment. If all that is needed is arough estimate of the molecular weight to con-firm a stoichiometry, then a preparative centri-fuge will be sufficient. On the other hand, ifassociation constants or accurate sedimenta-tion coefficients are needed, an analytical ul-tracentrifuge will be required.

The biggest difference between an analyti-cal and a preparative ultracentrifuge is the ana-lytical instrument’s ability to monitor the con-centration distribution as a sample is spinning.To do this, a special cell and rotor are used thatpermit light to pass through the sample. Lightsources and detectors are arranged to monitorthe cell contents throughout an experiment.Data acquisition is automated, and a large num-ber (500 to 2000) of data points are availableacross the cell (1.5 cm), yielding the high radialresolution needed for the analysis of interactingsystems. At present, absorbance and refractivedetection are available for the XLA analyticalultracentrifuge (Beckman), and prototype fluo-rescence optics are under development. Dataacquisition requires 5 to 30 sec per cell, and upto four cells may be used.

The ability to acquire data rapidly and withhigh radial resolution has led to improvementsin both sedimentation equilibrium and velocityanalysis. For sedimentation equilibrium, therehas been a resurgence of interest in short-col-umn methods (Yphantis, 1960; Laue, 1992),whose small sample volumes (15 µl), rapidequilibrium (typically ∼1 hr), and largethroughput (up to 16 samples simultaneously)are well-suited to addressing biochemical prob-lems. The development of time-derivative sedi-mentation velocity has improved the sensitivityof the refractive optical systems nearly 100-fold, and promises to revolutionize the range ofsystems suitable for sedimentation analysis.Experimental protocols in which the rotorspeed is accelerated over the course of an ex-periment (i.e., gravitational sweep sedimenta-tion) have been described (Stafford, 1992;Machtle, 1988) for analyzing and charac-terizing polydisperse samples. The fractiona-tion range and accuracy of this method farexceed those of any other technique presentlyavailable.

A good preparative ultracentrifuge (either afloor or tabletop model) may also be used foranalytical ultracentrifugation, as confirmed by

the long-time success of sucrose gradientanalysis. In many cases, these methods offergreat advantages because the sample is ana-lyzed after centrifugation by taking fractions(i.e., radial slices) from the centrifuge tube.Because of this, any detection scheme may beused to determine the concentration distribu-tion. This means that unparalleled sensitivityand selectivity are afforded by schemes that usethe preparative ultracentrifuge. Moreover, eachfraction may be further fractionated—e.g., byhigh-performance liquid chromatography(HPLC) or gel electrophoresis—yielding goodanalytical sedimentation data for complicatedmixtures. Detailed protocols for sedimentationvelocity and sedimentation equilibrium in apreparative ultracentrifuge are available, and asuperb microfractionator is available (fromBrandel) specifically for conducting sedimen-tation analyses (Attri and Minton, 1986).

However, it must be recognized that theinformation obtained from a preparative centri-fuge is a snapshot of the cell at the time ofdeacceleration (assuming no mixing occursduring deacceleration). This precludes the useof the elegant time-derivative methods thathave been developed for the analytical ma-chine. Moreover, the time delay between stop-ping the run and sampling the cell allows dif-fusion to distort the concentration gradient,leading to inaccuracy in its determination. Thisproblem becomes severe when steep gradientsare involved. In general, the radial resolutionfor the preparative techniques is not as high aswith the analytical ultracentrifuge.

The concentration of protein needed for anexperiment depends on what question is beingaddressed. If one merely seeks the molecularweight or sedimentation coefficient of a solute,then any convenient concentration may beused. However, if one is interested in knowingthe association state of a sample under particu-lar conditions (e.g., at concentrations found invivo, or in an assay), the choice of detectionscheme may become critical. In this case, onemust work out what concentration is neededand what detection schemes are suitable for theconcentration range, and match this to an entryin Table 7.5.3. It is essential to realize that anyexperimental protocol must examine the sedi-mentation behavior over a range of concentra-tions to take account of thermodynamicnonideality (sedimentation equilibrium) andhydrodynamic effects (sedimentation velocity;Laue et al., 1992).

The stability and accuracy of the tempera-ture is a critical experimental parameter. The


7.5.5


XLA ultracentrifuge can be operated at tem-peratures between 0° and 40°C. Although thisis convenient for most biochemical work, thereare some studies (e.g., thermal denaturation)where a wider range is desired. In this case, oneis limited to using an appropriately configuredpreparative centrifuge. Regardless of the tem-perature used, temperature stability is impor-tant in preventing convection. The accuracy ofthe temperature measurement is also important,particularly for sedimentation velocity analy-sis, where adjustment of a measured sedimen-tation coefficient (s) to standard conditions(20°C and water; the s20,w) must be made.Methods for making these adjustments are wellestablished and have been automated (Laue etal., 1992).

The rotor speed should be chosen carefully,as the gravitational field (g) increases as itssquare (g = ω2r, where ω = π × rpm/30 and r isthe rotor radius). Different criteria are used tochoose the rotor speed for sedimentation veloc-ity and for sedimentation equilibrium analyses.For a sedimentation velocity experiment, twooptions can be considered: (1) gravitationalsweep, in which the rotor speed is increasedperiodically throughout the experiment, and (2)s, where a single rotor speed is chosen for theanalysis. Gravitational sweep is particularlyuseful for the initial characterization of a sys-tem where it is useful to get a general idea ofhow broad the particle size distribution is. Inthis method, the rotor is accelerated to a lowspeed (e.g., 3000 rpm) and several (six to ten)concentration distributions are collected to de-termine if there are any fast-moving bounda-ries. Next, the rotor speed is accelerated two-fold, and data collection again undertaken. Thisprocess is continued until the maximum rotorspeed (60,000 rpm) is attained, followingwhich data are acquired until all boundarieshave sedimented at least three-quarters of theway down the cell. Using this scheme, a samplecan be “scanned” for the presence of an extraor-dinarily broad range of particle sizes (fromgreater than 1000S to ∼1S).

The second method of analysis acquires dataat a fixed rotor speed. This is useful for samplesthat have one or only a few types of proteinswith similar sizes (within an order of magni-tude). If one is trying to resolve two proteins ofsimilar size, the highest rotor speed that allowsa sufficient quantity of data to be obtainedshould be used (i.e., such that the fastest bound-ary takes ∼30 min to travel the length of thecell). The time-derivative data analysis routineswork best with large numbers of data sets

closely spaced in time, so data should be ac-quired frequently throughout a run.

Multiple rotor speeds should be used forsedimentation equilibrium analysis. Choosingappropriate rotor speeds is relatively simple ifthe molecular weight of the largest species isknown (rpm ≈ 2 × 106 √M−1 ), and a practicalscheme for choosing an initial rotor speed isavailable for other cases. Low speeds are usefulfor detecting aggregates and high speeds areuseful for detecting proteolytic fragments. Ingeneral, rotor speeds should be used that keepthe reduced molecular weight, σ, between 2 and12. An estimate of σ can be calculated from themolecular weight:

σ = M(1 − ν__

ρ) ω2⁄RT

where ν__

is the partial specific volume (∼0.72ml/g is a good rough estimate), ρ is the solventdensity (1 g/ml for the dilute aqueous buffersusually used in biochemistry), ω is the rotorangular velocity (see above), R is the gas con-stant (8.31 × 107 erg/mol o), and T is the absolutetemperature. Even a crude estimate of σ willsuffice. The range of rotor speeds used in ananalysis should vary σ over a 4-fold or greaterrange, if possible. The experimental protocolshould involve incrementing rather than decre-menting the rotor speed, as (because of diffu-sion) it takes much longer for a rotor to reachequilibrium when approaching it from a higherspeed. There are many other practical tips forchoosing the rotor speed, estimating σ, anddesigning an appropriate experimental proto-col (Ralston, 1993; Laue, 1992).

In general, conducting an experiment withan analytical ultracentrifuge is very simple. Theusual cause of difficulty is the sample, either interms of its purity (for experiments trying toextract thermodynamic details) or its behavior(for previously uncharacterized biochemicalsystems). Problems often encountered foreither sedimentation velocity or sedimentationequilibrium, along with suggestions for resolv-ing them, are discussed in Table 7.5.4.

ANTICIPATED RESULTSDifferent, yet complementary, information

is obtained from sedimentation velocity andsedimentation equilibrium experiments. Forsedimentation velocity, the rate of movementof the boundary yields the sedimentation coef-ficient, s. Straightforward adjustment of thismeasured value provides s20,w, the expectedsedimentation coefficient for the molecule if itwere sedimented in pure water at 20°C (Laueet al., 1992). A second adjustment is made by


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measuring the sedimentation coefficient of theboundary at several different protein concen-trations, then extrapolating the values of s20,w

to zero protein concentration to get s020,w. For

a nonassociating protein, s020,w decreases with

increasing concentration; this decrease occursgradually if the protein is spherical (by ∼1%per mg/ml) and more strongly if it is asymmet-ric. In addition to gaining insight into the shapeof a protein, there are three reasons for adjustingto standard conditions. First, s0

20,w is a practi-cal, descriptive constant for a protein that canbe used to compare preparations made underdifferent conditions or in different laboratories.

Second, determination of s020,w provides a first-

principle means of detecting changes in thehydrodynamics of the protein (see below).Third, an increase in s0

20,w with increasingconcentration is a useful diagnostic for massaction association of a protein.

Sedimentation velocity is also useful forcharacterizing more complicated mixtures ofmolecules (Stafford, 1992). In these cases sedi-mentation coefficient profiles are obtained. Forsamples containing only a few boundaries (pau-cidisperse samples), appropriate extrapolationof the data to infinite time provides higherprecision and improved resolution of the

Table 7.5.4 Troubleshooting Guide for Analytical Ultracentrifugation

Problem Possible cause Solution

Velocity methodNo boundary or very broad bound-ary

Convection May be caused by thermal instability ormechanical instability (rotor vibration)

Sample heterogeneity (aggregates orfragments)

Clean sample by gel filtration

Loss of sample to cell walls Use centerpiece made of differentmaterial.

Interacting system (concentration-dependent; may show pressuredependence)

Analyze by sedimentation equilibrium

Too few data points; boundaryreaches base in <30 min

Rotor speed too high Shake cell and rerun at lower rotor speed

Boundary that moves too slowly Rotor speed too low Shake cell and rerun at higher rotorspeed

Presence of proteolytic fragments Fractionate sample by gel filtrationImproper sample dialysis Buffer component not equilibrated in

sample and reference channels

Equilibrium methodDecrease in molecular weightwith increased concentration

Nonideality; little dependence of rotorspeed on molecular weight

Use a nonideal model in nonlinear leastsquares analysis; extrapolate to zeroprotein concentration. Information aboutmolecular size and charge available.

Sample heterogeneity; molecularweight also decreases with increasedrotor speed

Fractionate sample

Increase in molecular weight withincreased concentration, but littlechange as rotor speed is varied

Mass-action association Characterize by nonlinear least-squaresanalysis

Somewhat higher molecularweight than expected; slow loss ofmaterial

Slow aggregation; flocculantformation (data are often noisier thanusual; inconsistent molecular weightsare obtained from one sample to thenext)

Use sedimentation velocity analysis todetect this as a fast boundary or slopingplateau concentration. Only cure is tofind buffer conditions that stabilizeprotein solubility. For intracellularproteins, be sure a reducing agent (2-ME or DTT) is present.

Somewhat lower molecularweight than expected

Proteolysis (e.g., molecular weightdrops with time)

Use protease inhibitors in sample;refractionate by gel filtration.

Improper dialysis of sample prior toanalysis

Be sure sample and reference buffers areat dialysis equilibrium prior to run. Usecentrifugal gel filtration for rapidequilibration.


7.5.7


boundaries (Van Holde and Weischet, 1978;Stafford, 1994).

In addition to s020,w, the Stokes radius, RS,

of a particle may be obtained from sedimenta-tion analysis (Laue et al., 1992). Models can beapplied in which RS is analyzed in terms ofeither the extent of hydration or the degree ofasymmetry (Laue et al., 1992). Such analysesoften provide the first insight into the shape ofa protein.

Equilibrium sedimentation provides ther-modynamic information about a sample. Ana-lyzed in the simplest way, the data can be usedto obtain the molecular weight. For a mixtureof molecules, various average molecularweights (number, weight, and z) may be calcu-lated (Yphantis, 1964; Laue, 1995). By meas-uring the molecular weight in a denaturingsolvent (e.g., 6 M guanidine⋅HCl; APPENDIX 3A)and in a physiological solvent , thestoichiometry of the native molecule can read-ily be determined (Laue, 1992). More detailedanalysis of the concentration distributions canprovide energies of assembly and nonidealitycoefficients (McRorie and Voelker, 1993).

TIME CONSIDERATIONSFor a typical run with the XLA ultracentri-

fuge involving three cells per rotor, samplepreparation and cell loading requires ∼1 hr. Forsedimentation velocity analysis, a run requires∼2 hr (once the rotor is at the desired tempera-ture). Gravitational sweep analysis requiressomewhat longer. The time required to conducta sedimentation equilibrium analysis is dis-cussed below. In any case, operation of thecentrifuge, including data acquisition, is com-pletely automated. After the run, sample recov-ery and cell cleaning require ∼1 hr. For maxi-mum efficiency, it is worthwhile to have twocomplete sets of cells so that one may becleaned and loaded while the other is being run.Data analysis for sedimentation velocity ex-periments is computerized and rather straight-forward, and usually requires <1 hr.

The time required to conduct a sedimenta-tion equilibrium experiment depends a greatdeal on the particulars of the experimentalsetup. The number of samples that can be ana-lyzed simultaneously depends on the choice ofcenterpieces, so that up to sixteen samples maybe analyzed simultaneously. Cell loading stillonly requires ∼1 hr. The time needed to reachsedimentation equilibrium depends on the sol-vent viscosity, the diffusion coefficient of theprotein, and the distance between the meniscusand the base of the solution column. In general,

the time increases linearly with the viscosity,as the cube root of the molecular weight, andas the square of the column height of the solu-tion. Shorter solution columns can be accom-modated in any of the centerpieces. For a typi-cal aqueous buffer and a 50,000-molecular-weight protein, the time needed to reachequilibrium is ∼9 hr for a 3-mm solution col-umn (∼110 µl of sample) and ∼1 hr using a shortcolumn centerpiece (∼15 µl of sample). Be-cause a typical experimental protocol requiresequilibrium at three or four rotor speeds, a full1 or 2 days are needed to complete data acqui-sition.

Computer programs have automated equi-librium data analysis. Even so, the time neededto analyze equilibrium data depends on thelevel of detail of the scrutiny. If only an averagemolecular weight is required, this can be ac-complished in a few minutes. On the otherhand, determination of both the stoichiometryand energetics of a self-associating protein mayrequire several days of analysis if no previouscharacterization has been done. Both the levelof detail required to answer a biological ques-tion and the experience of the researcher willaffect the time needed to complete an analysis.

For either velocity or equilibrium sedimen-tation, there are no time-critical steps once thecentrifuge run has started. Zealots often begindata analysis during the centrifuge run. Al-though this is not strictly necessary, it is par-ticularly useful when examining a previouslyuncharacterized system as it allows adjustmentof the experimental conditions to maximize thequality of the data.

Methods using a preparative centrifuge canhandle a larger number of samples in a run(depending on which rotor is used). Likewise,the time required for preparation will vary,though it will be on the same order of magnitudeas for the XLA. Unlike with the XLA, dataacquisition is not fully automated in that theradius of each fraction must be calculated onthe basis of its volume and the sample-tubegeometry (Attri and Minton, 1986). Likewise,assaying the fractions may or may not requireconsiderable time.

HELP FOR THE NOVICEIt is widely recognized that undertaking

sedimentation analysis for the first time can bea daunting task. Fortunately, the most difficultparts—including data acquisition, data analy-sis, and data interpretation—have been auto-mated. Commercial computer programs forthese tasks are available from Beckman Instru-


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ments. In addition, there is an Internet bulletinboard ([email protected]) where ana-lytical sedimentation is discussed and a widevariety of computer programs are available freeof charge. Often, though, it is not the processof conducting analytical ultracentrifugationthat is a problem for biochemists, but rathertheir uncertainty about the solution physicalchemistry of proteins. Fortunately, the cadre ofresearchers working with the ultracentrifugewelcome the opportunity to help newcomers tothe field. For further information contact theauthor by e-mail at [email protected].

LITERATURE CITEDAttri, A.K. and Minton, A.P. 1986. Technique and

apparatus for automated fractionation of the con-tents of small centrifuge tubes: Application toanalytical ultracentrifugation. Anal. Biochem.152:319-328.

Cohen, R. and Mire, M. 1971. Analytical-band cen-trifugation of an active enzyme-substrate com-plex. 1. Principle and practice of the centrifuga-tion. Eur. J. Biochem. 23:267-275.

Harding, S.E., Rowe, A.J., and Horton, J.C. 1992.Analytical Ultracentrifugation in Biochemistryand Polymer Science. Royal Society of Chemis-try, Cambridge.

Laue, T.M., Shah, B., Ridgeway, T.M., and Pelletier,S.L. 1992. Computer-aided interpretation ofsedimentation data for proteins. In AnalyticalUltracentrifugation in Biochemistry and Poly-mer Science (S.E. Harding, A.J. Rowe, and J.C.Horton, eds.) pp. 90-125. Royal Society ofChemistry, Cambridge.

Laue, T.M. 1992. Short Column SedimentationEquilibrium Analysis for Rapid Characterizationof Macromolecules in Solution. Technical Infor-mation DS-835. Beckman Instruments, PaloAlto, Calif.

Laue, T.M. 1995. Sedimentation equilibrium as athermodynamic tool. Methods Enzymol.259:427-452.

Mächtle, W. 1988. Coupling particle size technique.A new ultracentrifuge technique for determina-tion of the particle size distribution of extremelybroad distributed dispersions. Die Angew. Mak-romol. Chem. 162:35-52.

McRorie, D.K. and Voelker, P.J. 1993. Self Associ-ating Systems in the Analytical Ultracentrifuge.Beckman Instruments, Fullerton, Calif.

Philo, J.S. 1994. Measuring sedimentation, diffu-sion and molecular weights of small moleculesby direct fitting of sedimentation velocity con-centration profiles. In Modern Analytical Ul-tracentrifugation: Acquisition and Interpretationof Data for Biological and Synthetic PolymerSystems (T.M. Schuster and T.M. Laue, eds.) pp.156-170. Birkhauser, Boston.

Ralston, G. 1993. Introduction to Analytical Ul-tracentrifugation. Beckman Instruments, Fuller-ton, Calif.

Richards, E.G. and Schachman, H.K. 1957. A dif-ferential ultracentrifuge technique for measuringsmall changes in sedimentation coefficient. J.Am. Chem. 79:5324-5325.

Schachman, H.K. 1959. Ultracentrifugation in Bio-chemistry. Academic Press, New York.

Schuster, T.M. and Laue, T.M. 1994. Modern Ana-lytical Ultracentrifugation: Acquisition and In-terpretation of Data for Biological and SyntheticPolymer Systems. Birkhauser, Boston.

Stafford, W.F. III. 1992. Boundary analysis in sedi-mentation transport experiments: A procedurefor obtaining sedimentation coefficient distribu-tions using the time derivative of the concentra-tion profile. Anal. Biochem. 161:70-79.

Stafford, W.F. III. 1994. Sedimentation boundaryanalysis of interacting systems. In Modern Ana-lytical Ultracentrifugation: Acquisition and In-terpretation of Data for Biological and SyntheticPolymer Systems (T.M. Schuster and T.M. Laue,eds.) pp. 119-137. Birkhauser, Boston.

Svedberg, T. and Pederson, K.O. 1940. The Ul-tracentrifuge. Clarendon Press, Oxford.

Van Holde, K.E. and Weischet, W.O. 1978. Bound-ary analysis of sedimentation-velocity experi-ments with monodisperse and paucidisperse sol-utes. Biopolymers 17:1387-1403.

Yphantis, D.A. 1960. Rapid determination of mo-lecular weights of peptides and proteins. Ann.N.Y. Acad. Sci. 88:586-601.

Yphantis, D.A. 1964. Equilibrium ultracentrifuga-tion of dilute solutions. Biochemistry 3:297-317.

KEY REFERENCESHarding et al., 1992. See above.

Excellent book containing descriptions of many ofthe modern methods of analytical ultracentrifuga-tion.

Schachman, 1959. See above.

Classic work describing many useful methods stillused today.

Schuster and Laue, 1994. See above.

Up-to-date collection of methods for analytical ul-tracentrifugation.

Svedberg and Pederson, 1940. See above.

A classic work that is still relevant in that it providessome of the clearest descriptions available of ana-lytical centrifugation.

INTERNET RESOURCESwww.bbri.harvard.edu/rasmb/rasmb.html

Web site for most recent programs and discussiongroup on analytical ultracentrifugation.

Contributed by Thomas M. LaueUniversity of New HampshireDurham, New Hampshire


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