Furth, A. and Moore, R. (1986). Self assembly of macromolecules, p.57. Open. University Press, Milton Keynes, UK. 3. Andrews, P. (1965). Biochem.I.,91.,22. 4.
Hydrodynamic properties of
proteins STEPHEN E. HARDING
L. Renaissanceof hydrodynamic techniques Sincethe first edition of this book, there has been somethingof a renaissance of hydrodynamic methods for the determination of the mass, quaternary structure, gross conformation, and interaction properties of proteins and other macromoleculesin solution. By 'hydrodynamic'(Greek for 'watermovement') techniques, we mean any technique involving motion of a macromoleculewith or relative to the aqueoussolvent in which it is dissolved or suspended.This therefore includesnot only gel filtration, viscometry,sedimentation (velocity and equilibrium), and rotational diffusion probes (fluorescenceanisotropy depolarization and electric-optical methods), but also 'classical'and 'dynamic' light scattering,which both derive from the relative motions of the macromolecularsolute in relation to the solvent. This definition also includes electrophoreticmethods (consideredin Chapter 8 and not covered here), which are powerful tools for separation, purification, and identificationof proteins,but also,with 'SDS' methodology,provide an estimate of polypeptidemolecularweight (seeChapter 1). The presentchapter therefore considers the hydrodynamic determination of 'molar mass' or molecular weight and quaternary structure (subunit composition and arrangement, self-associationphenomena, and polydispersity). It will also consider the measurementof protein conformation in dilute solution with particular reference to the use of the analytical ultracentrifuge, a technique although of considerableantiquity (70th birthday in 1993) that has been the centre of the revival of hydrodynamicmethodology. After a brief descriptionof the methodologyin eachcase,practical tips and advice about the measurementand analysiswill be provided-largely of the type not to be found in the manualsof commercialmanufacturers.The interestedreader can then find any other information neededfrom the latter and from the key referencesgiven.
Stephen E. Harding
2. Mass and quaternary structure measurement It is worth stressinghere that, unlike a polypeptidemassfrom sequenceanalysis or a protein structure from crystallographyor NMR, a hydrodynamicmassor a conformationis a 'soft' quantityasopposedto a'hard' one.That is to say,it will always come with a '+' and often with assumptions(about thermodynamic ideality, hydration, etc.). Although the molecular weight of an unglycosylatedpolypeptide can be determined to an accuracy of + 1 Da from sequenceinformation or from mass spectrometry (see Chapter 2), a similar precision cannot be obtained for glycosylated proteins becauseof polydispersity deriving from the variability of a cell's glycosylationprocess. Many proteins contain more than one non-covalently linked protein chain, particularly at higher concentrations.This can be uncoveredby carrying out analysesunder both native and denaturing conditions. An important role of hydrodynamic methods for mass analysisin protein chemistry is to give the molecular weight of the 'intact' or 'quaternary' structure and also to provide an idea of the strength of binding of these non-covalent entities through measurementof associationconstants.
2,7 Gel filtration and size exclusion chromatography The simplestmethod of measuringmolar massis gel filtration (1), commonly referred to as 'gel permeation chromatography'or now 'size exclusionchromatography' (SEC), sincethe chemicalinertnessof the separationmedium is assumed.Originally this was conceivedas a method for the separation and purification of macromolecules,but has developedover the years in its 'calibrated' form as a very popular method for measuringprotein molar masses both in native and dissociativeconditions. The separation medium is a cross-linked gel, traditionally cross-linked polysaccharideor polyacrylamide beads equilibrated with the appropriate buffer. The degree of cross-linkingdictates the separationrange of the gel: looser gels separatebigger molecules(see Chapter 1). Proper packing of columns requires some skill, and the user manuals as supplied by the commercial manufacturers are usually very comprehensive.The availability of HPLC versions makes the measurementparticularly attractive for protein chemists. Gel filtration or SEC depends on the principle that some of the space inside the gel particle is available to smaller molecules,but unavailable to larger molecules,which are excluded.Thus, when a solution is applied to a properly packed gel column (Figure la) only the dead space-between gel particles-is available to the excluded molecules,which therefore come off first when elution is commenced. The excluded molecules-the larger molecules-will thus have a smaller elution volume, V", and will elute first from the column (Figure 1b). Smaller macromolecules,having progressively 220
9: HydrodSmamicproperties of proteins (a)
buffer
-.€
(b)
applied protein solution
[, I to spectropholometer v or refractometer
elution volume elution volume V" V"
Figure 1. Principleof gel filtration and size exclusionchromatography.(a) Experimental set-up.(b) Exampleof an elution profile.Adaptedfrom ref. 2.
more and more spaceavailableto them as molecularweight decreases, are accordinglyeluted only at higher valuesof V". The separationis sometimes given in terms of the partition coefficient,Kuu,defined by: V": Vo + Ku,(Vt - Vo) t1] 'void 'total where Vo and V, are the volume' and volume' of the column, respectively.They are determinedfrom separateelutionsusingsolutespecies having partition coefficients of zero (totally excluded) and one (nonexcluded),respectively.Elution of proteinsas they emergefrom the column is usually monitored spectrophotometrically.If the buffer contains absorbing reagents,like ATP, azide,etc.,highly sensitivedifferential refractometersare now available,which are arguablypreferable now as the detection method of choice. All other things being equal, M, and V. are related empirically by the expression(1): V":A-BlognM,
tzl
where parametersA and B are properties of the column. This equation is valid only over the fractionation range of the gel; it also does not hold if other separation mechanismsare operating (a). To obtain M, of a protein molecule or mixture of molecules,the column is first calibrated by the use of standard proteins of known size. Linear regressionanalysisis then used to evaluateA and B; hence M, of the unknown protein can be found from its measured value of Iz". The calibration can only be applied within the fractionation range of the gel which depends on the pore size (Figure 2). Fractionation ability can be enhancedby running differing gel columns in 221
Stephen E. Harding
^
'
2tn
Glucogon
aro t90
Cytochrome Myoglobin ------i Chymotrypsinogen
o
5 r3o
Ovolbumin Molole dehydrogcnosa 0vomucoid+e 4 aal/ phospholose Bovine s€rum olbumin Glyceroldehyde 3Tronsterrin phosphole dehydrogenoso Loctopcroxidose/-\ _ . . Locloie dchydrog€nosr leluln+E \ Serumolbumindimer*j Aldolosc Ycost olcohol dehydrogenose Fumorose --o Cocruloolosmin ir-go1o1o.. Y'Globulins -/ P-Phycoerythrin q- Conorochin Fibrinogen+o
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-Goloclosidose -+ Ferrilin
Ureose o-Cryslollinz rn3
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Bluc rn6
weight, M"
Figure2. calibrationplot for proteinselutingfrom a sephadex G200column. From ref. 3.
series,a practice common with HPLC systemsbecauseof the much shorter elution times. Equation 2 is valid only for moleculesof similar shape and conformation. Thus calibration using globular protein standardswould be inappropriate for fibrinogen and asymmetric muscle proteins like myosin and titin and for heavily glycosylatedproteins. These calibration problems can be avoided by couplingan absolutemoiar massdetector(e.g.a light scatteringphotometer) downstreamfrom the column (seeSection2.5). The theory behindEquation2 is not rigorous,but, at leastfor globularproteins, it seemsto representthe data very well. For linear macromoleculesof limited stiffness,there appearsto be growing acceptancethat the separation is more a logarithmic function of the hydrodynamic volume of a macromolecule(- M,[n] where [q] is the intrinsicviscosityof a molecule)(seeSection 3) and its correspondinghydrodynamicor 'effective' radius, rg. This has culminated in a proposal for a 'universal calibration' (5). This may be more appropriate for proteins with disulfide bonds broken and in denaturing solvents, e.g. 6 M GdmCl. For such unfolded proteins, wider pore gels (such as Sepharose)are the most appropriateseparationmedium. The procedurefor gel filtration/ SEC analysisis given in Protocol 1.
2.2 Dynamic light scattering (DtS) The appearanceof simple to use fixed-angle (90') dynamic light scattering photometers has made DLS an increasinglypopular tool amongst protein 222
9: Hydrodynamic properties of proteins chemists.After certain assumptionsand approximations,largely involving an assumedspherical shape, remarkably reliable estimatesfor the mol. wt of globular proteins have been obtained(6). When used in isolation, this method is, like gel filtration, a relative one, requiring calibration using standard proteins of known mol. wt. For asymmetricproteins like fibrinogen and myosin, the single angle approximation fails, but extraction of mol. wt and related parametersis still possibleif a multi-angleinstrumentis used.Also, the primary parameter that comes from DLS measurementsis the translational diffusion coefficient, D (in units of cm2lsec).and it can be combined with results from sedimentation analysisin the analytical ultracentrifuge to determineM,more accurately(seeEquation9 in Section2.3.2). Protocol 1. Estimatingthe size of a protein by low-pressuregel filtration/SEC Equipment and reagents o Column, with optional reservoir to assist packing o G e l f i l t r a t i o n m a t r i x ( e . 9 . S e p h a d e xo f t h e appropriate grade) equilibrated with buffer a t t e m p e r a t u r ea t w h i c h a n a l y s i si s t o b e made
. Peristalticpump o M o l . w t c a l i b r a t i o ns t a n d a r d s o f s i m i l a r shape and other conformational properties to the protein to be characterized
Method M o u n t t h e e m p t y c o l u m n v e r t i c a l l y .w i t h t h e a i d o f a p l u m b - l i n e . Attach outlet tubing and fill the column with buffer, removing all dead space.Closeoutlet. 2. Packthe column with the matrix; pour in a thick gel slurry (preferably d e g a s s e d )i n a s i n g l e o p e r a t i o n ,a v o i d i n g a i r b u b b l e s a n d k e e p i n g the temperature approximatelyconstant.
3. Close off the the column without trapping any air; repeat with any a d d i t i o n a cl o l u m n st h a t a r e t o b e u s e d i n s e r i e s . 4. Attach peristalticpump to the first column, and run through at least t h r e e c o l u m n v o l u m e so f b u f f e rt o e n s u r ee q u i l i b r a t i o n( c h e c kt u b i n g j o i n t s f o r l e a k s ! ) .T h e m a x i m u m f l o w r a t e w i l l d e p e n d u p o n t h e matrix (see manufacturers'specifications); typically, it is in the range 0.2-6 ml/min. 5 . Attach a UV recorder downstream from the last column. To monitor most proteins, set the monitoring wavelength to 278 nm or, if the buffer is sufficiently transparent, to 210-230 nm, which will give greater sensitivity. 6. Measurethe absorbancebaselineof the buffer. 7 . Inject samples of the mol. wt standards on to the column and measuretheir V".
223
Stephen E. Harding Protocof 1.
Continued
8. Calibratethe column by plotting V" versus mol. wt for the standards. 9. Injectthe test protein and measureits V" under the same conditions. 10. Estimatethe mol. wt of the test protein from its V" and the calibration c u r v ef o r t h e c o l u m n . 1 1 . W a s h t h e c o l u m n w i t h t h r e e v o l u m e so f b u f f e r . 12. lf the column is to be used again at a later time, keep buffer flowing s l o w l y t h r o u g h i t ; o r i n c l u d ea n a n t i - m i c r o b i aal g e n t ,s u c h a s s o d i u m azide.and store it in the cold.
2.2.1 Principle The principle of DLS experimentsis very simple (Figure 3a) and is basedon the high intensity, monochromaticity,collimation, and coherenceof laser light. Laser light is directedon to a thermostattedprotein solution,and the intensity is recorded at either a single or multiple anglesusing a photomultiplier/photodetector.The intensities recorded will fluctuate with time caused by Brownian diffusive motions of the macromolecules;this movement causes a 'Doppler' type of wavelengthbroadening of the otherwise monochromatic light incident on the protein molecules.Interferencebetweenlight at these wavelengthscausesa 'beating' or fluctuation in intensity in much the sameas a listener perceivesa radio station with superpositionof other radio stations at nearby frequencies.How rapid the intensityfluctuates(nsecto psectime intervals) dependson the mobility or diffusivity of the protein molecules.A purpose-builtcomputer, known as an autocorrelator,'correlates'or interprets these fluctuations. It does this by evaluating a 'normalized intensity autocorrelationfunction'1t(z))as a function of the 'delay time', r (in the range of milli- to microseconds). The decayof the correlation,g(z)(r) as a function of t, averagedover longer time intervals (usually minutes) can then be used,by an interfaced PC or equivalent, to obtain the value of D. Larger and/or asymmetric particles that move more sluggishly will have slower intensity fluctuations,slower decayof f{z) ft) with r, and hencesmaller D values compared to smaller and/or more globular particles. The delay time r itself is the product of the 'channel number' b (taking on all integral values between1,and 64,or up to 128or 256 dependingon how expensivethe correlator) and a user-set'sample time', r,; its value is typically - 100 nsec for a rapidly diffusing protein of low mol. wt (e.g. about 20000) and increasingup to millisecondsfor microbes.In the past,rrwas selectedby trial and error, but now modern data acquisitionsoftwareusually doesthis automatically. For sphericalparticles, a single term exponential describesthe decay of f with r: ttz)(r)*1-"-Dk' t 224
t3l
9: Hydrodynamic properties of proteins
(b) o.o -0.5 -t.o I
-1.5 c
-2.0 -2.5
T+,
-3.0 0
1
0
2
0
3
0
4
0
5
0
6
0
ChonneL number
Figure 3. Principleof dynamic light scattering.(a) Experimentalset-up. (b) Normalized - 1.1 autocorrelationdecay plotforthe protein assemblydynein (in 40 mM NaCl).D02e,* x 10-7cm?sec;M, (trom Equation9) - 2.5 x 106.From ref. 7. where k is the Bragg wave vector whose magnitude
is defined by:
{4rrnDrlsin (0/2) t4l n is the refractive index of the medium, 0 the scattering angle, and X the wavelengthof the incident light. Equation 3 can be reasonablyapplied to quasi-spherical particleslike globular proteins or spheroidalprotein assemblies (Figure3b). k:
225
Stephen E. Harding 2.2.2 Fixed,-angle(90") DLS photometer For globular proteins and spheroidalassemblies,applicationof Equation 3 at only a single fixed-angleis usually sufficient.Low anglesare usually avoided becausethey magnify problems due to any contaminationwith dust or other supramolecularparticles:an angle of 90" is normally used.For a given laser power at a given protein concentration,the smaller the protein the lower the intensityof scatteredlight, and hencethe longer the averagingrequired to give a sufficient signal.A commercialinstrument is availablebasedon this single fixed-angleprinciple (6) (Figure4a).lts operationis describedin Protocol2. To obtain mol. wt information from the value of D, a calibrationcurveof log D versuslog M, is produced,basedon globular protein standardsand known as an 'MHKS' (Mark-Houwink-Kuhn-Sakurada) scalingrelation (8) (Figure 4b).It is assumedthat the samerelation holds for the unknown protein. Protocol2. Measuringthe diffusioncoefficientand approximate molecularweight of a globularproteinby fixeda n g l eD L S Equipment o Fixed-angle DLS photometer, such as the P r o t e i nS o l u t i o n s8 0 1 i n s t r u m e n t . Sterile syringe with appropriate filter, 0 . 1 - 0 . 4 5p m , d e p e n d i n g u p o n t h e s i z e o f the orotein . D e i o n i z e dd, i s t i l l e dw a t e r
o Sample of protein in an appropriate buffer a n d c l o s et o t h e o p t i m a l c o n c e n t r a t i o n( f o r the Protein Solutions 801 instrument, 2 m g / m l f o r a 3 0 k D a p r o t e i n ,p r o p o r t i o n a l l y less for larger proteins)
Method 1. Inject water or buffer, via a 0.1 pm filter. into the warmed-up DLS photometerto obtain the clean water count rate. 2. Inject the sample in the same way, using the appropriatefilter, and measurethe count rate. 3. lf the count rate is below the manufacturer'sthreshold. check the i n s t r u m e n ta l i g n m e n to r i n c r e a s et h e p r o t e i nc o n c e n t r a t i o n . 4. Use the instrument'ssoftware to obtain the diffusion coefficientand, w h e r e a p p r o p r i a t e ,t h e i n - b u i l t c a l i b r a t i o nt o o b t a i n d i r e c t l y t h e approximatemol. wt. 5. Rinseand dry the flow cell of the photometer.
Figure 4. Single-angledynamic light scattering.(a) Photometer DynaPro 801 (courtesyof ProteinSolutionsLtd.)incorporatesa 20 mW infrared(780nm) semiconductorlaser.Photons scatteredat an angle of 90" are collectedby a lens and conductedto an avalanche photodiodevia an optical fibre; this producesa single electricalpulse for each photon received and these are stored and correlated by an integral computer. The optical bench
226
9: Hydrodynamic properties of proteins (a)
(b) r.r I
0.9
0.8
b0 n^ 0.5
1.00
1.20
4.10
1.60
4.80
5.00
5,20
5.10
5.60
5.80
5.00
log16M. measuresonly 25 x 5 x 5 cm (6). (b) Double logarithmiccalibrationplot of rx versus M, for: 1, thyroglobulin;2,apoferritin;3,lgG; 4, yeast alcoholdehydrogenase;5,hexokinase; 7. horsealcoholdehydrogenase;8, 6, amyloglucosidase; transferrin;9,bovineserum album i n ; 1 0 ,h a e m o g l o b i n1; 1 ,h e x o k i n a sseu b u n i t ;1 2 ,o v a l b u m i n 1 ; 3 ,c a r b o n i ca n h y d r a s e ; 1 4 , chymotrypsinogen; 15,myoglobin;16,lysozyme;17,ribonuclease A. From ref.6.
227
Stephen E. Harding Other approximations and practical requirements with the operation of this type of fixed-angleinstrument have to be made: (a) Solutions must be as free as possiblefrom dust and supramolecular aggregates. This requirementis met by injection of the sampleinto the (scrupulouslyclean)scatteringcell via a Millipore filter(s) of appropriate size(0.1-0.45pm). (b) The diffusion coefficient is a sensitivefunction of temperature and the viscosity of the solvent. The log D versus log M, calibration must be made under the sametemperature(kept constantduring the measurement) and solventviscosityconditions. (c) The diffusion coefficient measuredat a single concentrationis an apparent one,Duoo,becauseof non-idealityeffects(finite volume and charge). These effects becomevanishinglysmall as the concentration approaches zero. The approximation is made-usually reasonablyfor proteins-that Dupp= D, or that any non-idealityeffectsare the sameasfor the calibration standards. Despite these approximations,the values of diffusion coefficients and M, obtainedin this way have been remarkablyreliable.For non-globularproteins, however, the log D versus log M, calibration becomes invalid and Equation 3 no longer applies;resort has then to be made to an instrument with a multi-angle facility. 2.2.3 Multi-angle instruments Measurementsusing multi-angle equipment (Figure 5a) are more timeconsuming, and the instrur,nentationlarger and more expensive.Data analysisis also more complicated.Equation 3 no longer applies, largely becauseof the added complication of rotational diffusion effects. These effects vanish, however, as the scatteringangle 0 approacheszero. It is therefore possibleto use Equation 3 in terms of an apparentdiffusion coefficientDuoo,with contributionsfrom both concentrationand rotational diffusion effects.D,oo is measuredat severalanglesand extrapolatedback to zero angleto give D if concentrationeffectsare negligible.If, however,concentrationdependenceeffectsare suspected,a double extrapolationcan be performedon the sameplot (calleda'Dynamic Zimm plot') of Duootozero angleand to zero concentration(10).The commoninterceptgivesthe 'ideal' (in a thermodynamicsense)diffusion coefficient,D0. Becausethis quantity is not only an intrinsic property of the protein but also of the viscosity,1, and the temperatureof the buffer, it has to be correctedto standardconditions (viscosityof pure water at 20'C, I2s.*), either before or after the extrapolation(11):
Doro,*:Do(n/n o.i Q1293.15). 224
tsl
9: Hydrodynamic properties of proteins
WET FILTER
DRY FILTER
CELL EYPASS OUTIfT TUBE
Figure5. Multi-angleDLS.(a) PhotometerMalvern Instruments4700system in our laboratory. A, 15 mW He-Ne laser; B, water-bath,goniometer;C, photomultipliers/amplifier discriminator;D, autocorrelator;E, PC. (b) schematic of speciallyconstructedcuvette designedto minimizethe dust problem.From ref. 9.
Stephen E. Harding The sizeof a protein, as representedby its equivalenthydrodynamicradius, by the Stokesequation: rs, is relatedto Du2s,* rH: ksTl (6Tn s,* Do2r,*)
t6l
where ks is Boltzmann'sconstant.To obtain an absolutemeasureof M, of a protein from D02s,*,without assumptionsconcerningthe shapeof the protein, requires combination with the sedimentationcoefficient frorn the analytical ultracentrifuge,as describedin Section2.3. Somemodern softwareattempts to evaluate M, directly from the diffusion coefficient; this should be treated with somecaution. 2.2.4 Fwther notes (a) For multi-angle measurements,preferencesvary in terms of the type of cuvettesused.Squarecuvettesare optically more reliable, but cell corners are obviously prohibited. Cylindrical cuvettes,if used, should be of the wide diameter type (> 2 cm) to avoid internal and stray reflections. (b) Scrupulousattention to sampleand cuvette clarity is mandatory,particularly for macromoleculesof M, < I}s. which give low scatteringsignals, and if low anglesare employed,where the effectsof supramolecularcontaminants are at their maximum. Specialcuvette filling arrangementsare usedfor clarification purposes(Figure 5b). (c) The angularextrapolationof Duoocan provide an estimatefor the rotational diffusioncoefficient,albeit to a lower precisionthan conventional methods(fluorescence depolarization,electricbirefringence). (d) If the protein is polydisperseor self-associating, the logarithmicplot of the type shown in Figure 3b will tend to be curved, and the corresponding diffusion coefficient will be a z-average(12). The spreadof diffusion coefficients is indicated by a parameter known as the 'polydispersity factor' (12) which most softwarepackagesevaluate. (e) Various computer packagesare available from the commercialmanufacturer for data acquisitionand evaluation.In our laboratory,we prefer to acquirethe data in ASCII format usingthe data capturesoftwareof the commercialmanufacturer and then use our own in-houseroutine 'PROTEPS' (S. E. Harding, J. C. Horton, and P. Johnson,unpublisheddata) for the evaluationof diffusion coefficientsand polydispersityfactors. (f) More advancedroutines are available,such as 'CONTIN', designedfor the study of heterogeneoussystemsby going beyond the use of polydispersity factors and inverting the autocorrelation data directly to give distributionsof particlesize.Thesemethodshavebeenrecentlyreviewed (13). (g) DLS is particularly valuable for the investigation of changesin macromolecularsystemswhen the time-scaleof changesis minutes or hours, and not secondsor shorter(14). 230
9: HydrodSmamicproperties of proteins (h) For chargedmacromolecularsystems,DLS provides a useful tool for monitoring electrophoreticmobilities (1-5),and commercialinstrumentation is availablefor this purpose.
2.3 Sedimentation velocity in the analytical ultracentrifuge Combination of the sedimentationcoefficient,,!, from sedirnentationvelocity with the diffusion coefficient, D, from DLS gives an absolute value for the mol. wt of a protein, without assumptionsabout conformation. This method for mol. wt measurementwas given by T. Svedberg(16), the founder of the analytical ultracentrifuge:a techniquewhich is now undergoingsomethingof a renaissancewith the launch of a new commercial instrument (Figure 6a) (17). The basic principle of the technique is as follows: a solution of the protein is placed in a specially designedcell with sector-shapedchannel and transparent end windows (Figure 6b). This in turn is placed in an appropriately balanced rotor and run in high vacuum at the appropriate speed (typically 50000-60000r.p.m. for a protein of M,104 to 10s,lower speedsfor larger molecules). A light source positioned below the rotor transmits light via a monochromator or filter through the solution and a variety of optical components.The moving boundary is recorded at appropriate time intervals, either on photographic film, on chart paper, or as digital output fed directly into a PC. Measurementof the rate of the movement of the boundary (per unit centrifugal field) enablesevaluationof the sedimentationcoefficient.For an introduction, see ref. 11; for the state of the art, see two recent books (18,19). 2.3.1 Optical systems Threeprincipleopticalsystemscan be employed: o absorbance(in the range20o-700nm) o 'Schlieren'(refractiveindex gradient) o Rayleighinterference The simplest systemis the absorbancesystem,and it is used in the Optima XL-A analyticalultracentrifugeavailablecommercially,so it will be described here. Use of the other optical systemsrequires more specialistknowledge, and the interestedprotein chemistneedsreally to consult an expert. Examplesof sedimentingboundariesrecordedusing absorptionopticsare shown in Figure 7, using a highly purified preparation of an enzyme (Figure 7a) and a heterogeneouspreparation of a DNA binding protein (Pf1) with a macromolecular component and a fast moving aggregate(Figure 7b). The procedurefor obtaining suchdata is describedin Protocol 3. 237
Stephen E. Harding
(a) BeckmanOptima XL-A in our laboraFigure6. Modern analyticalultracentrifugation. tory, equippedwith scanningabsorptionoptics,with full on-line data captureand analysis. The rotor is stable down to : 1000 rev. min, permitting the analysis of large macromolecularassemblies.(b) Componentsof an analyticalcell (12 mm optical path length).
232
9: Hydrodynamic properties of proteins (a)
Msoln
Figure 7. sedimentationvelocity diagrams obtained using scanning absorption optics. (a) Methylmalonylmutase,0.7 mg/ml. Monochromatorwavelength295 nm; scan interval 9 min; rotor speed 44000 r.p.m.;temperature20oC;measureds2e= (7.14 + 0.04)5. (b) Gene 5 DNA-bindingprotein,0.7 mg/ml. Monochromatorwavelength,27g nm; scan interval,S min; rotor speed,40000 r.p.m..temperature,20oC;measureds0zo,*: (35.5 + 1.4)S(fasterboundary)and (2.6 + 0.1)S(slowerboundary).
Protocol3. Sedimentationvelocitymeasuredwith an analytical ultracentrifuge with scanningabsorptionoptics detectionsystem Equipment o BeckmanOptima XL-A ultracentrifuge
Method 1. Concentration requirements for the protein. This depends on the extinction coefficient of the protein (see Chapter 10). The lower the protein concentration the better, since it minimizes problems of thermodynamic non-ideality.For proteins of average absorbanceat 280 nm (: 500 ml/g/cm),concentrationsas low as 0.2 mg/ml are possible with 12 mm optical path length cells. This can be made even
233
Stephen E. Harding Protocol 3.
Continued
lower if the buffer is transparent and the peptide bond wavelength c a n b e u s e d ( 2 1 0 - 2 3 0n m ) . F o r a b s o r b a n c ev a l u e s > 3 , s h o r t e r p a t h l e n g t hc e l l sn e e dt o b e e m p l o y e d( t h e m i n i m u m i s a b o u t 3 m m ; b e l o w t h i s , c e l l w i n d o w p r o b l e m s b e c o m e s i g n i f i c a n t )',o f f - m a x i m a 'w a v e lengths used (with caution), or, more desirably, a different optical system used (interferenceor Schlieren). lf possible,work with an aqueous 2. Choosethe appropriatebuffer/solvent. solventof sufficientlyhigh ionic strength(> 0.05M) to provideadequate s u p p r e s s i o no f n o n - i d e a l i t yp h e n o m e n ad e r i v i n gf r o m m a c r o m o l e c u l a r charge effects (see below). lf denaturing/dissociatingsolvents are used, appropriate centre-piecesneed to be used (e.9. of the 'Kel-F' type; BeckmanInstruments). 3 . L o a d t h e s a m p l e i n t o t h e c e l l . D o u b l e s e c t o rc e l l s a r e u s e d w i t h t h e protein solution (0.2-O.4ml) in one sector and the referencebuffer or solvent in the other;the latter is filled to a slightly higher levelto avoid c o m p l i c a t i o n cs a u s e db y t h e s i g n a lc o m i n g f r o m t h e s o l v e n tm e n i s c u s : the scanningsystem subtractsthe absorbanceof the referencebuffer f r o m t h a t o f t h e s a m p l e .E l e c t r o n i cm u l t i p l e x i n ga l l o w s m u l t i p l e h o l e rotors to be used,so that severalsamplescan be run at a time. 4. C h o o s e t h e a p p r o p r i a t et e m p e r a t u r e .T h e s t a n d a r d t e m p e r a t u r ea t which sedimentationcoefficientsare quoted is now 20"C (sometimes 2 5 " C ) . l f t h e p r o t e i n i s t h e r m a l l y u n s t a b l e( a s e d i m e n t a t i o nv e l o c i t y run can take between one and a few hours), temperaturesdown to about 4"C can be used without difficulty. 5 . C h o o s et h e a p p r o p r i a t es p e e d .F o r a s m a l l g l o b u l a r p r o t e i n o f s e d i mentation coefficient- 2 Svedbergs(S, where 1S : 10-13sec), a rotor s p e e d o f 5 0 0 0 0 r . p . m . w i l l g i v e a m e a s u r a b l es e t o f o p t i c a l r e c o r d s a f t e r s o m e h o u r s . F o r l a r g e r p r o t e i n s y s t e m s ( e . g . 1 2 5 g l o b u l i n so r 3 0 S r i b o s o m e s )s, p e e d so f < 3 0 0 0 0 r . p . m .c a n b e e m p l o y e d . 6. Measure the sedimentation coefficient, s. The sedimentation coefficient, s, is defined by the rate of movement of the boundary per unit centrifugalfield: s : (drldtlla2r,where r is the radial position of the boundary at time f, and c,ris the angular velocity in radians/sec (o : r.p.m. x 2r'160l.Commercialsoftware is availablefor identifying t h e c e n t r eo f t h e s e d i m e n t i n gb o u n d a r y( s t r i c t l yt h e ' 2 n d m o m e n t ' o f the boundary is more appropriate;practicallythere is no real difference). Personal choices vary, but we find the most satisfactory method-if requiringa little more effort-is: (a) To plot out the boundaries (recorded at appropriate time interv a l s ) u s i n g a h i g h r e s o l u t i o np r i n t e r o r p l o t t e r a n d g r a p h i c a l l y d r a w a l i n et h r o u g ht h e u s e r - i d e n t i f i ebdo u n d a r yc e n t r e s .
234
9: Hydrodynamic
properties of proteins
(b) Then use a graphicstablet to recapturethe central boundary posit i o n s a s a f u n c t i o no f r a d i a lp o s i t i o n . C o m p u t e r r o u t i n e s s u c h a s X L A - V E L( H . C o l f e n a n d S . E . H a r d i n g , u n p u b l i s h e dd a t a )y i e l d t h e s e d i m e n t a t i o nc o e f f i c i e nat n d a c o r r e c t i o n t o t h e l o a d i n gc o n c e n t r a t i o n f o r a v e r a g er a d i a ld i l u t i o nd u r i n g t h e r u n ( c a u s e db y t h e s e c t o rs h a p eo f t h e c e l l c h a n n e l s ) . 7. Correctthe resultsto standardconditions.For each protein concentration used, correct the sedimentationcoefficient,s, to standaro conditions of buffer/solventdensity and viscosity(water at20"C, p2q,*and 12s.*respectively): s2o,*: s(rtllzo,*){(1 - vp2s.*) lfi - nfll Vl where p is the density of the solvent. Knowledge of a parameter known as the 'partial specificvolume', v (essentiallythe reciprocalof t h e a n h y d r o u sm a c r o m o l e c u l adr e n s i t y )i s n e e d e d t; h i s c a n u s u a l l yb e obtainedfor proteinsfrom amino acid composition data, or measured with a precisiondensity meter (20).Typicallyfor proteins, v is close to 0 . 7 3m t / 9 . 8. Extrapolateto zero protein concentration.Plot s2s,*versus concentrat i o n ( c o r r e c t e df o r r a d i a ld i l u t i o n )a n d e x t r a p o l a t e( u s u a l l yl i n e a r l y )t o zero concentration(Figure8) to give a parameter,sOzo.* which can be directly related to the frictional propertiesof the macromolecule(the s o - c a l l e d' f r i c t i o n a lr a t i o ' )a n d f r o m w h i c h s i z ea n d s h a p e i n f o r m a t i o n can be inferred.lf the protein is very asymmetric or solvated,plotting 1/szo.w versus concentrationgenerally gives a more useful extrapolation. The downward slope of a plot of s2q,*V€rsusconcentrationis a result of non-idealitybehaviourand is characterizedby the parameter k" in the equation: s2o.*: dro.* {t-k c). t8l The value of k", which reflectsnon-idealityeffects of the system, will depend on the size. shape, and charge of the protein. lf the solvent used is of a sufficientionic strength,chargeeffectscan be suppressed.
2.3.2 Evaluation of molecular weight The molecular weight, M,, can be found by combination of s02e.* with D02e.* usingthe Svedbergequation: - r pzo.*)}. M,: (soro,*lDozo,*) {R Te tel An accurate estimate for v as described above is normally required, since errorsare tripled for proteins;e.g.an error of + Lo/oin v resultsin an error of + 3Yo in M.. This means that care has to be made if the protein is glycosylated,sincethe i of carbohydratgis typically 0.6 mVg. For a heterogeneoussystem,su2s,*will be a weight averageand D026.*a 235
Stephen E. Harding 8,5
u 8.0 (u { t.) X
s
/.v
6.5
c (m9'zmL) Figure8. Sedimentationcoefficienteo.* Ersa function of concentrationfor a rat lgE antibody. Measuredd26,*: 17.92 + 0.06)5.
z-average:the M, calculatedwill also be a weight average(12), thus distinguishingit from the M, obtainedby osmometry(2I), which is a number average. A further approximateestimatecan be obtained simply by combiningruzo,* with k"(22):
5 M, : (6.n"tro.*soro.*)1 l(3fl|afl.l(k,l2r)-(r,lr)ll0s
[10]
where v. is a specific volume allowing for hydration of the protein; since (t,/t) in Equation 10 is usually small in comparison with (.k,l2n),only an approximate estimate is needed. This method has given reliable estimates for standardprotein moleculesof known mol. wt. The parameterk. is itself valuable for shapemeasurement.The form of the concentration-dependence systems(23), althoughsedican also be used as an assayfor self-associating mentationequilibriummethodsare usuallysuperior(seeSection2.4). 2.3.3 Limitations Sedimentationvelocity is not so convenientfor evaluatingthe molecular weights of proteins in denaturing/dissociatingsolvents,since their sedimentation coefficientsare much smaller,due to greater frictional forces:s values of < 15 are difficult to measurewith any precision becauseof the upper limit of rotor speed (60000 r.p.m.). If these solventsare used, care has to be expressedconcerninginertnessof the cellsused.
2.4 Sedimentation equilibrium
The 'sedimentation-diffusion' method for giving the mol. wt, although an absolute method, is rather inconvenient in that it requires two sets of measurements.A simpler method is to use one measurementby sedimentation 236
9: Hydrodynamic properties of proteins equilibrium, and it is probably the method of choice for mol. wt determination of intact protein assemblies,and for the investigationof interacting systemsof proteins(24). The sameinstrument and optical system(s)for sedimentation velocity are used,the principal differencesbeing: o the much lower rotor speedsemployed e the longer run times o the shorter solution (and buffer) columns in the ultracentrifuse cell: hencethe smaller amount of material required Sedimentation equilibrium, unlike sedimentation velocity, gel filtration, and dynamiclight scattering,is not a transportmethod. In a sedimentation equilibrium experiment, the rotor speed is chosen to be sufficiently low so that the forces of sedimentationand diffusion on the macromolecularsolute become comparable and an equilibrium distribution of solute is attained. This equilibrium can be establishedafter a period of 2 to 96 hours, depending on the macromolecule,the solvent,and the run conditions.Sincethere is no net transport of solute at equilibrium, the recording and analysisof the final equilibrium distribution (Figure 9) will give an absoluteestimate of the
o) o " ^ (E .cl
8os
lt
6.0
o.z
o.4
o.o
7.0
7.2
Radius(cm) Figure 9. sedimentation equilibrium profiles for B-lactoglobulinB. Absorption optics, with wavelength280 nm. Rotor speed. 15000 r.p.m.;temperature,20"C.A multichannel cell (12 mm opticalpath length)was used allowingthree solution/solventpairs,with 0.12 m l i n t h e s o l v e n tc h a n n e l sa n d 0 . 1 0 m l i n t h e s a m p l ec h a n n e l sT. h e i n i t i a lp r o t e i nc o n centrationswere 0.1 mg/ml (inner profile);0.2 mg/ml (middle);0.3 mg/ml (outer).Only absorbances< 1.5 could be used with the outer channel;this difficultycould have been overcome by using a longer wavelength.with the inner channel,the signal could have been increasedby using a far-UVwavelength(210-230nm).
237
Stephen E. Harding protein massand associatedparameters,sincefrictional (i.e. shape)effects are not involved. Protocol 4 reters only to the absorption system-because of its simplicity and availability-for recording the equilibrium distribution of solute in the ultracentrifuge cell. The most accurate method is, in fact, the interference system, but it requires considerable more expertise to operate correctly (11,18,19).
Protocol4. Measuringthe sedimentation/equilibrium profileof a protein Equipment o As in Protocol 3
Method Choosethe appropriateconditions.These are similar to those applying to sedimentationvelocity lsee Protocol3). As with sedimentation velocity, a temperatureof 4oC can be used without difficulty.Sample volume requirements are lower than for sedimentation velocity: 0 . 1 - 0 . 2m l g i v e s a c o l u m n l e n g t h o f a b o u t 0 . 1 - 0 . 2m m w i t h 1 2 m m c e l l s .T h e l o n g e rt h e c o l u m n ,t h e g r e a t e rt h e p r e c i s i o na n d t h e m o r e informationthat can be extracted.The shorter the column, the quicker e q u i l i b r i u m w i l l b e r e a c h e d( 2 7 ) , w h i c h m a y b e i m p o r t a n t i f m a n y samples need to be run and/or the protein is relativelyunstable.
2. Load the sample in the cell as in Protocol 3. As with sedimentation v e l o c i t y ,m u l t i p l ec e l l s c a n b e r u n s i m u l t a n e o u s l yi n m u l t i h o l er o t o r s and electronically multiplexed. Further, because of the shorter c o l u m n s n e e d e df o r s e d i m e n t a t i o ne q u i l i b r i u m ,s p e c i a lm u l t i c h a n n e l celfs containingthree sample/solventpairs can be used (Figure9). So, for a four-hole ultracentrifugerotor (with one hole needed for the counterpoisewith referenceslits for calibratingradial positions in the c e l l ) ,n i n e s o l u t i o n sc a n b e r u n s i m u l t a n e o u s l yE. i g h t - h o l er o t o r s a r e now available.
3. Choosethe appropriaterotor speed. 4. Run the rotor until equilibrium is reaahed,when scans separatedby s u f f i c i e n tt i m e a r e i d e n t i c a l .S m a l l e r m o l e c u l e sg e t t o e q u i l i b r i u m faster than larger ones. Less than 24 h are required for molecules of M,< 104;farge,slower diffusing molecules take 48-72 h. The time to e q u i l i b r i u mc a n b e d e c r e a s e db y i n i t i a l' o v e r s p e e d i n g 'i ,. e . r u n n i n ga t higher speed for a few hours before setting to the final equilibrium speed. lt may, in some applications, be desirable to use shorter columns (as short as 0.5 mm); although the accuracyof the measure-
234
9: Hydrodynamic properties of proteins 'short column' method offers the advantage ments will be lower, this o f r e a c h i n ge q u i l i b r i u mi n a f e w h o u r s . 5 . Record the equilibium profile. The parameter measured is the absorbanceof the protein,A, as a function of the radial distancefrom the centreof the rotor, r. lf scanningabsorptionopticsare used,equilibrium patternssuch as Figure9 can be read directlyinto an attachedPC. 6. M e a s u r et h e a b s o r b a n c eb a s e l i n e .l f t h e p r o t e i n sa r e n o t t o o s m a l l , after the final equilibrium pattern has been recorded,the rotor is run for a short time at a higher speed(up to 60000 r.p.m.or the upper limit for the particularcentre-piece)to depletethe solution-or at least t h e m e n i s c u s r e g i o n - o f s o l u t e : t h e r e s i d u a la b s o r b a n c eg i v e s t h e baselineabsorbanceof the solvent.With small proteins,careful dialysis of the protein solution versus the referencesolvent before the run may be necessary. 7 . C a l c u l a t et h e m o l e c u l a rw e i g h t . T h e a v e r a g es l o p e o f a p l o t o f I n A versus f ,Gigure l?alwillyield M,: M , : ( o t nA l d f l x 2 R T l $ - i p l a 2 .
1111
As with Equation 9, an accurate estimate for the partial specific volume 7 is required;p is the density of the solvent. 8. Analyse for heterogeneity.For a non-associating,monodispersesystem, the plot of In A versus I will be linear (Figure 1lbl;for a heterog e n e o u sp r o t e i n ( c o n t a i n i n gi n t e r a c t i n go r n o n - i n t e r a c t i n sg p e c i e so f different molar mass),it will be curved upwards.This situation occurs with self-associatingsystems (see below) and with mixed solute or heavily glycosylatedprotein systems such as mucus glycoproteins.In this casethe data can be treated in one of two ways: ( a ) A n a v e r a g es l o p e i s m e a s u r e dT . h i s y i e l d s ,a s w i t h E q u a t i o n9 , t h e weight averagemol. wt, M*. For strongly curving plots or for syst e m s w h e r e t h e c e l l b a s e l i n ei s n o t c l e a r l yd e f i n e d ,a p r o c e d u r e that uses a function known as Mx (25,2d is useful. ( b ) L o c a ls l o p e s ( u s i n g a s l i d i n g s t r i p p r o c e d u r e()2 8 ) a l o n g t h e I n A versus I curve can be obtained to give what is called 'point' weight averagemol. wts, M*(r), as a function of either radial position (or the equivalent local concentrationor absorbance).This procedureis particularlyusefulfor the investigationof self-association phenomena and other types of heterogeneity;it also provides a method for extractingthe z-averagemol. vvt,M,: { M * ( r : c e l l b a s e )- M * ( r : m e n i s c u s ) } M,: -
base) Wt: meniscus)A(meniscus)} {WV-- cellbase)A(cell [12] The ratio M,/M* can be usedas an index of the heterogeneity of the sample and, for non-interactingsystems, is a measure of the 235
Stephen E. Harding Protocol 4.
Continued
y f a s y s t e m ;t h i s i s p a r t i c u l a r l yr e l e v a n t o i n h e r e n tp o l y d i s p e r s i t o the study of heavilyglycosylatedsystems. 9 . E x a m i n ew h e t h e r a n y a p p a r e n th e t e r o g e n e i t yi n m o l . w t i s d u e t o association of the protein. lf the system is self-associatingor i n v o l v e d i n ' h e t e r o l o g o u s 'a s s o c i a t i o n ( i . e . c o m p l e x f o r m a t i o n ) , either the In A versus I plot or the M*(r) versus A plot can be used to measurethe stoichiometryand strength of the interaction.There are s e v e r a lc o m m e r c i a sl o f t w a r ep a c k a g e sa v a i l a b l e , ' a n da r e c e n ta r t i c l e h a s r e v i e w e dt h r e e u s i n g t h e d i m e r i z i n gB - l a c t o g l o b u l ians a m o d e l system for self-associations(29). Methods are also availablefor distinguishing betweenself-associating and non-interactingmixtures. 1 0 . C o n s i d e rn o n - i d e a l i t yF. o r l a r g e rm a c r o m o l e c u l e(sM , > 1 0 5 )s, u c h a s protein assembliesand heavilyglycosylatedsystemsand/or for more concentratedsolutions,non-ideality(throughmacromolecular exclusion and any unsuppressed charge effects) may become significant, w h i c h w i l l t e n d t o c a u s e d o w n w a r d c u r v a t u r ei n t h e I n A v e r s u s I plots. This can obscure heterogeneity phenomena, and the two effects (non-idealityand heterogeneity)can occasionallycancel to g i v e a l i n e a rp l o t t h a t c a n b e m i s l e a d i n gt;h i s c a n b e a v o i d e db y r u n n i n g a t m o r e t h a n o n e i n i t i a l p r o t e i nc o n c e n t r a t i o nl.f t h e s a m p l e i s not significantlyheterogeneous,a simple extrapolationfrom a single experiment of point (apparent) mol. wt to zero concentration ( a b s o r b a n c ec) a n b e m a d e , t o g i v e t h e i n f i n i t ed i l u t i o n ' i d e a l ' v a l u e (in general,reciprocalsare usually plotted asin Figure 77)(30).Altern a t i v e l y ,s e v e r a ls e d i m e n t a t i o ne q u i l i b r i u me x p e r i m e n t sp e r f o r m e d at different initial concentrationsand extrapolation of 'whole cell' molecularweights, M*,uro,to zero concentrationare necessary. 'Software currently availablefrom the commercial manufacturer tends to reouire an assumeo model prior to the analysis (ideal monomer, self-association,non-ideal self-association,etc.). We find two other general packages,not requiring assumed models, of use.These are: ( a ) M S T A R ,w r i t t e n i n - h o u s e( 2 6 ) a n d n o w a v a i l a b l ef o r P C ( H . C c j l f e na n d S . E . H a r d i n g , unpublished data), which evaluates M.,"oo (using the M* functionl, M,,urv or Mn,"ro land also M,,"oo,if the data are of sufficientlyhigh quality) versus ror A. (b) XLAse. which evaluates M*,,r, and M.."ee(M. D. Lechner, Universitdt Osnabrtick,unpubl i s h e dd a t a ) . After these model-independentanalyses have been performed, resort is then made to tne more specialist packages (self-association,polydispersity, etc.). There exists now a highly useful e-mail system called RASMB for the exchange of software and other matters concerning analytical ultracentrifugation (RASMB database; W. F. Stafford, stafford€edu. harvard. eri . bbri).
2.5 Classical light scattering This is another powerful absolutemethod for the determination of mol. wts of intact macromolecules,and it is particularly suited to the study of large 240
9: Hydrod5mamic properties of proteins (a)
t o a.5 0.0 a
-0.5
.t
1/
-
I
J
-1 0
f
ll
t'
,t
- 1 . 1 I'
-2.0 .n -'6.o
0.2
o.6
0.4
o.B
?
: (b) L
I 4
T 2
tsl
F
X I
Fl
I 0 O E
o.6 a 4 0.2 0
1.0
A Figure 10. Sedimentationequilibrium data analysisfor human lgM.,.Phosphatebuffer pH 6.8; ionic strength,0.1M; protein concentration,- 0.6 mg/ml. Scanningwavelength, 278 nm; rotor speed, 5000 r.p.m.;temperature.20"C. (a) Log absorbanceversus radial displacementsquared plot. € - G - 8l(8 - a2)where r is the radial displacementat a given point in the solute distribution and a and b the correspondingpositions at the meniscusand cell base,respectively.From M* analysis(25,26). of this data, M,: (1.00+ 0.02)x 106.(b) Plot of point average(apparent)M,versus local concentration(expressed in absorbanceunits) in the solute distribution.Apart from noise near the meniscusthere is no trend in the data, confirming a monodisperse,nearly ideal system. Adapted from ref.26.
247
Stephen E. Harding 0.200
tr
0.195 0.190
r-
F
0.185 0.180 0.175 0.170
1.0
1.5
2.5
c (mg/ml) Figure 11. Plot of the reciprocalpoint (apparent)averagemolecularweight as a function of focaf concentrationfor turnip yellow mosaicvirus. The measuredM, (trom extrapolation to zero concentration)is (5.8 + 0.2) x 106.Adaptedfrom ref. 30.
macromolecularassemblies,up to a maximum of 50 x 706M;, beyond this the simple theory (known as the 'Rayleigh-Gans-Debye'approximation) breaksdown. By'classical'light scattering(asopposedto DLS) we meanthe total or time-integratedintensityof light scatteredby a macromolecularsolution compared with the incident intensity for a range of concentrations and/or angles.Although a more rapid and, in principle, more convenient alternative to either the sedimentation-diffusionmethod or sedimentation equilibrium, the application of classicallight scattering has until relatively recently sufferedgreatly from the 'dust problem', namely all solutions/scattering cells having to be scrupulouslyclear of dust and supramolecularparticles, particularly for the analysisof proteins of mol. wt < 50000; unlike for DLS, except for small proteins, measurementsat low angles(where dust problems are their greatest) are mandatory. This has resulted in many casesin the requirementfor unacceptablylarge amountsof purified material: experiments on incompletelypurified solutionshavebeen of little value. Two developmentshave made the technique now worthy of serious con(31): siderationby protein scientists (a) The use of laserlight sources,providing high collimation,intensity,and monochromaticity. (b) The couplingof SEC-HPLC systemson-line to a light scatteringphotometer via the incorporation of a flow cell. These facilitate considerablythe analysisof mixtures of proteins and, more signiflcantly,provide a very effective on-line 'clariflcation' systemfrom dust and supramolecularcontaminants.An example of such a set-up is given in Fisure 12. 242
9: Hydrodynamic properties of proteins
GPC COLUMNS
DAWN MODE- F GPC DETECTOR
A/D INTERFACE
"x,till8l,Figure 12. Multi-anglelaser light scatteringcoupled to size exclusionchromatography (a) Experimentalset-up in our laboratory.A, Dawn-F(WyattTechnology); (SEC-MALLS). B, HPLCpump; C, refractiveindex detector;D, two SEC columns in series;E, interfaced PCsystem.(b) Schematic(courtesyof Wyatt Technology).
2.5.L Principle The intensityof light scatteredby a protein solutionis measuredas a function of angle with a light scatteringphotometer (Figure 12a). For solutionsof macromoleculesor macromolecularassemblies,the basic equation for the angulardependenceof light scatteringis the Debye-Zimm relation: + 2Bc) KctRs* {1 + (16n2Rnzt3tz1sin' [(e/2)]][(11M,)
[13]
where it is assumedthat the secondvirial coefficient B (in units of ml mol g-2) is sufficientto representnon-ideality(i.e. third and higher order terms are 243
Stephen E. Harding assumedto be negligible); c is the protein concentration.Rr is the Rayleigh excessratio-the ratio of the intensityof excesslight scattered(comparedto pure solvent)at an angle0 to that of the incidentlight intensity(a cosOcorrection term is necessaryif unpolarizedlight is used).K is an experimental constantdependenton the squareof the buffer or solventrefractiveindex, the squareof the refractive index increment (dn/dc in ml/g, analogousto the partial specificvolume for proteins,and with a value of about 0.19ml/g for proteins),and the inversefourth power of the incident wavelength,\. The parameterR, is usuallyreferred to as the 'radius of gyration' of the macromolecule,and is usefulfor conformationstudies(seeSection3). If the macromolecular solute is heterogeneous,M, will, as with sedimentation-diffusion and sedimentationequilibrium,be a weight average,M*. Equation 13 is valid for particlesof maximumdimension< }' (i.e.M,< 50 x 106). Normally, a double extrapolationto zero scatteringangleand to zero protein concentrationis necessary.using a procedureknown as a Zimm plot (32).However: (a) For particlesof dimensions< L/20 (i.e. M,< 50000),the angularterm in Equation 13 is small 1i.e. sin2(e/2): 0) and no angular dependence measurementsare in principle necessaryto obtain M, (although this comesat a price:R, cannotbe measuredif a conventionallight sourceis used,althoughit can be measuredusing electromagneticradiation of a lower wavelength-namelyX-ray and neutronscattering(33)). (b) More significantly,if the concentrationis small enough(< 0.5 mg/ml for proteinsand protein assemblies), the concentrationterm in Equation 13 is small (i.e. Bc - 0), and only an angularextrapolationis necessary. This is usually the situation with modern photometersdesignedwith a flow cell for couplingon-lineto an SEC system(31):after dilution throughthe column,the effectivescatteringconcentrationis usually < 0.5 mg/ml. In thesecases,Equation 13 becomes: KctRs- (7tM,){7+ (16+ Rs2t3\2) sin2t(0/2)l}
[14]
For the specialcaseof globularproteinsof M,< 50000,the term Kc/Rsis approximatelyequal to IlM, and no angular extrapolationis necessary.In this case,a large scatteringangle (90') is normally chosen,since at lower anglesthe greaternoise/signalratio is much more seriouscomparedwith the casefor largerscatterers. To a further approximation: RslKc- M,{1.-(1Gr2 Rr2l3t21sin2 [(e/2)]].
[1s]
2.5.2 SEC-MALLS An example of a multi-angle laser light scatteringphotometer (MALLS) coupledto SEC is illustratedin Figure12.The photometeris the DAWN-F system(Wyatt Technology).The angular scatteringenvelopeis measured simultaneouslyby an array of photodiodes, unlike the moving photomulti244
9: Hydrodynamic properties of proteins plier system used by multi-angle dynamic light scattering photometers (Figure5a). Equations14 or 15 are used,or Equation 13 if the term Bc is significantand is known. From Equations 13-15,it is clear that it is necessary to have also a concentrationdetector,as well as the MALLS detector;this is normally a highly sensitivedifferential refractometer, also equipped with a flow cell (seecorner of Figure 12). For proteins,the principle value of this method is that it allows on-line clarification of the material from supramolecularaggregates.The method is, however,most valuablefor the analysisof mixturesor for polydisperseheavily glycosylatedprotein systemssuchasmucusglycoproteins,sinceit provides weight-average massesand massdistributionswithout recourseto calibration standardsrequired by SEC (Section2.1). Protocol 5 and Figure 13 describe the variousstagesof analysis. Protocol5.
SEC-MALLSanalysis
Equipment . SECchromatography apparatus(see Profo- . Light scattering photometer, which must c o l 1 l . aA p u l s e - f r e eH P L Cp u m p i s e s s e n b e c a l i b r a t e d( b u t n o t i n a p r o t e i n s t a n t i a l . A g u a r d f i l t e r u p s t r e a mi s d e s i r a b l ea, s dards sense), usually with a strong i s p r e - f i l t e r i n gs o l u t i o n st h r o u g h a n a p p r o R a y l e i g h( i . e . m a x i m u m d i m e n s i o n< V 2 0 ) p r i a t eM i l l i p o r ef i l t e r { e . 9 .0 . 2 2p m ) . F o r t h e scatterersuch as toluene, whose scattering p r o p e r t i e s a r e k n o w n ( 3 1 ) . C a l i b r a t i o ni s D a w n - Fs y s t e m ,a - 1 0 0 p l m i c r o i n j e c t i o n l o o p i s d e s i r a b l eA . c o l u m n b y - p a s so p t i o n necessarvbecausethe ratio of the intensican be installed if fract;onationis not t i e s o f t h e s c a t t e r e da n d i n c i d e n tb e a m s i s required (namely the Zimm plot or full u s u a l l yv e r y s m a l l ( - 1 0 - 6 ) . b a p p l i c a t i o no f E q u a t i o n 1 3 i s d e s i r e df o r a r a n g eo f l o a d i n gc o n c e n t r a t i o n s ) .
Method 1 . D e t e r m i n ea c c u r a t e l yt h e d e l a y i n e l u a n tv o l u m e o r t i m e b e t w e e nt h e light scatteringphotometer and the concentration(refractiveindex or UV absorbance)detector,so that the Kc/Reterm in Equations 13-15 can be synchronized. 2 . R e c o r d t h e S E C e l u t i o n p r o f i l e u s i n g t h e c o n c e n t r a t i o nd e t e c t o r (refractometer)and the light scattering.Only the 90' light scattering signal is shown in Figure 13. 3. Subject each elution volume V" as it passesthrough the detectorsto measurementof Kc/R,over the range of the angular scatteringenvel o p e .T h e r e s u l t i n g ' D e b y ep l o t ' ( E q u a t i o n1 5 )y i e l d st h e m o l a r m a s s o f e a c hv o l u m e e l e m e n t . 4. Calibratethe column in terms of log,'sM, versus V". 5 . D e t e r m i n et h e w e i g h t - a v e r a g em o l e c u l a rw e i g h t s ( a n d o t h e r d e r i v e d averagessuch as the number and z-averages)and plot a relativemass distribution. 6 . D e t e r m i n et h e r e f r a c t i v ei n c r e m e n t ,d n / d c ( 3 5 ) .l t s v a l u e i s n o r m a l l y 245
Stephen E. Harding Protocof 5.
Continued
in the rangeof 0.18to 1.19ml/g for proteins,but can be as low as 0.15ml/gfor heavilyglycosylated proteins. ' C h o o s e S E Cc o l u m n s a s a p p r o p r i a t e M . o l e c u l e sl i k e t h e g l y c o p r o t e i ne x a m p l eo l F i g u r e 1 3 a r e a t t h e u p p e r l i m i t o f r e s o l u t i o nb y g e l c o l u m n s .F o r l a r g e rp a r t i c l e so, t h e r m e t h o d so f s e p a r a t i o n ,o n - l i n e t o t h e M A L L S d e t e c t o r b a s e d o n f i e l d f l o w f r a c t i o n a t i o na r e n o w a v a i l a b l e (36,37). D F o rs i m u l t a n e o u sm u l t i - a n g l ed e t e c t i o nt,h e d e t e c t o r sh a v e t o b e n o r m a l i z e dt o a l l o w f o r t h e differing scattering volumes as a function of angle and the differing responsesof the detect o r s . T h i s i s u s u a l l yp e r f o r m e du s i n g a s o l u t i o no f a m a c r o m o l e c u l eo f k n o w n M , ( g e n e r a l l y< 5 0 0 0 0 )o r f o r a s o l u t i o no f a l a r g e rm a c r o m o l e c u l e w h o s e B ni s k n o w n ( e . g .T - 5 0 0D e x t r a n ) .
3. Shape measurement Although the main thrust of this chapterhas been on the estimationfrom hydrodynamicmeasurementsof the molecular weight of a protein in its native state,the hydrodynamicparametersof a protein are also dependent upon the shapeof the molecule.For mol. wt measurement, this canbe a complication,althoughit can be overcomeby combiningthe sedimentationand diffusion coefficients (Equation 9), each of which are affected similarly by the shape.Alternatively, transport methods can be avoided altogetherby usingeither of the thermodynamicequilibrium-based techniquesof sedimentation equilibriumand classicallight scattering. On the other hand,hydrodynamicmethodsprovide information about the macromolecularshape.There is the complication that the hydrodynamic shapeparametersobtainedalso dependupon the extent of hydration of the protein (i.e. the amount of aqueoussolventchemicallybound or physically entrapped),which is very difficult to measurewith any real precision.A further problem is that the more complicatedthe shapemodel used,the greater the number of independent parameters needed to specify the model uniquely.For example,to specifyuniquely the radius of a sphericalmodel requires only one parameter;for the axial ratio of an ellipsoid of revolution (i.e. an ellipsoidwith two equal axes),two parametersare needed;for a general triaxial ellipsoid,with three unequalaxes,three parametersare needed (38). All of these approachesare known as 'whole-body'approaches.The most complexway of representingshapeis 'hydrodynamicbead modelling', where the protein structure is approximated as an array of spherical beads (39). Problemsof the uniquenessof any suchmodel are considerable,however, and this form of modellingis best usedfor choosingbetweenplausible structures(e.g.subunit arrangementsin a multisubunitprotein, such as the angle between the two Fab arms of an antibody molecule) or for refining a crystallographicor NMR structure to dilute solution conditions. Segmental flexibility can also,in principle,be modelledusingthis latter approach. 246
9: Hydrodynamic properties of proteins The choiceof hydrodynamicshapeparametersis wide: (a) The 'Perrin' frictional ratio (from the sedimentationor diffusion coefficients). (b) The various rotational frictional ratios or relaxation times (from fluorescencedepolarization or electro-optic measurements). (c) The viscosityincrement(from measurementof the intrinsicviscosity). (d) The concentration-dependence of the sedimentationcoefficient. (e) The radiusof gyrationfrom solutionX-ray scattering(or for proteinsof M, > 50000,from classicallight scattering). (f) The molecularco-volumeof the protein (from measurements of the nonideality parameterB in osmoticpressure,sedimentationequilibrium,or classicallight scatteringmeasurements). The viscosityand rotationalfriction parametersare amongthe more sensitive but canbe correspondingly more difficult to measure.The hydrationproblem is most effectively dealt with by combining two parameters to give 'hydration-independent'shapeparameters. Whereasthe extractionof mol. wt informationis relativelystraightforward, the extractionof shapeinformation is generallynot, and the detailsare outside the scopeof this chapter.The interestedreader is referred to a recent articlethat examinesin detail the variousapproachesand providesthe necessaryreferences(8). Sufficehere to mention somePC softwarealgorithmsfor hydrodynamicconformationanalysisusingeither the simpler'whole-body'or the'hydrodynamicbead' algorithms.
3.1 Computer programs for conformational analysis For ellipsoid modelling,we have in-housea suite of algorithmsthat have been transferredfrom mainframeFORTRAN to PC (BASIC and FORTRAN). ELLIPS1 (40) evaluatesthe axial ratio for prolate and oblate ellipsoidsfor a user-specified value of a hydrodynamicparameter.It is basedon polynomial approximationsto the full hydrodynamic equations,but the accuracyof this approximationis normally well within the precision of the measurement. ELLIPS2 usesthe full hydrodynamic equationsfor general triaxial ellipsoids to specifythe set of hydrodynamicparametersfor any given value of the axial ratios.ELLIPS3 and ELLIPS4 carry out the reverseprocedure,using a variety of graphicalcombinationsof hydration-independent triaxial shapefunctions. Elsewhere,the routinesHYDRO and SOLPRO developedby J. Garciade la Torre and colleagues(4I,42) are particularly useful for the applicationof bead models;to facilitateits application,a front-end algorithm (A to B) has beenconstructedto enableTRV to predict the set of hydrodynamicparameters for a given set of crystalstructureco-ordinates(O. Byron, PhD dissertation,1992,Universityof Nottingham,UK). 247
Stephen E. Harding
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Figure 13. Extractionof mol. wt distributionof a high mol. wt glycoprotein(a pig gastric mucin preparation'581') using SEC-MALLS.(a) Elution profile recordedusing the concentration(refractiveindex)detector(lower profile,lighter dots) and the MALLS detector (only 90" detectionshown).The negativeand positivepeaksat high elution volume correspondto salt elution.(b) 'Debye'plot for a specificvalue of %. (c) Absolute logarithmic calibrationplot showing clearlythe 'range'ofthe gel. (d) Mol. wt distribution.The commercial manufacturerssoftware was used for all the analyses:(a-c) ASTRA, (d) EASI. F r o mr e f . 3 4 .
References 1. Ackers,G. (1975).In Theproteins(3rd edn) (ed. H. Neurathand R. L. Hill), Vol. 1, p. 1. AcademicPress,New York. 2. Furth, A. and Moore, R. (1986).Self assemblyof macromolecules, p.57. Open UniversityPress,Milton Keynes,UK. 3. Andrews,P. (1965).Biochem.I.,91.,22. 4. Barth,H. G. (1980). I. Chromatogr.Sci.,18,409. 5. Dubin, P. L. and Principi, J. M. (1989).Div. Polym. Chem.Am. Chem. Soc. Preprints,30,400. 6. Claes,P., Dunford, M., Kennedy,A., and Vardy, P. (1992).In Laser light scattering in biochemistry(ed. S. E. Harding, D. B. Sattelle,and V. A. Bloomfield), p. 66.Royal Societyof Chemistry,Cambridge,UK. 7. Wells,C., Molina-Garcia,A. D., Harding,S. E., and Rowe,A. J. (1990).J. Muscle Res.Cell Motil., l1., 344. 245
Stephen E. Harding 8. Harding,S.E. (1995).Biophys.Chem.,55,69. 9. Sanders,A. H. and Cannell,D. S. (1980).ln Light scatteringin liquidsand macromolecularsolutions(ed. V. Degiorgio,M. Corti, and M. Giglio), p. 173.Plenum, New York. 10. Burchard,W. (1992).ln Laser light scatteringin biochemistry(ed. S. E. Harding, D. B. Sattelle,and V. A. Bloomfleld),p. 3. Royal Societyof Chemistry,Cambridge,UK. 11. Van Holde, K. E. (1985).Physicalbiochemistry(2nd edn), p. L10.PrenticeHall, EnglewoodCliffs,New Jersey. 12. Pusey,P. N. (1974).In Photon correlation and light beatingspectroscopy(ed. H. Z. Cumminsand E. R. Pike),p. 387.Plenum,New York. 13. Johnsen,R. M. and Brown, W. (1992).ln Laser light scatteringin biochemistry (ed. S. E. Harding, D. B. Sattelle,and V. A. Bloomfleld),p.77. Royal Societyof Chemistry,Cambridge,UK. 14. Harding,S. E. (1986).Biotech.Appl. Biochem.,8,489. 15. Langley,K. H. (1992).It Laser light scatteringin biochemistry(ed. S. E. Harding, D. B. Sattelle,and V. A. Bloomfield),p. 151.Royal Societyof Chemistry,Cambridge,UK. 16. Svedberg,T. and Pedersen,K. O. (1940). The ultracentrifuge.Oxford University Press. 17. Giebler, R. (1992).ln Analytical ultracentrifugationin biochemistryand polymer science(ed. S. E. Harding,A. J. Rowe, and J. C. Horton), p. 16.Royal Societyof Chemistry,Cambridge,UK. 18. Harding, S. E., Rowe, A. J., and Horton, J. C. (ed.) (1992).Analytical ultracentrifugation in biochemistryand polymer science.RoyalSocietyof Chemistry,Cambridge,UK. 19. Schuster,T. M. and Laue, T. M. (1994). Modern analytical ultracentrifugation. Birkh?iuser, Boston. 20. Kratky, O., Leopold,H., and Stabinger,H. (1973).InMethodsin enzymology(ed. C. H. W. Hirs and S.N. Timasheff),Vol. 27D,p.98. AcademicPress,New York. 21. Tombs, M. P. and Peacocke,A. R. (1974). The osmoticpressureof biologieal macromolecules.Oxford University Press,Oxford. 22. Rowe, A. J. (1992).In Analytical ultracentrifugationin biochemistryand polymer science(ed. S. E. Harding,A. J. Rowe,and J. C. Horton), p. 394.Royal Societyof Chemistry,Cambridge,UK. 23. Gilbert, L. M. and Gilbert, c. A. (1973).ln Methods in enzymology(ed. C. H. W. Hirs and S. N. Timasheff),Vol. 27,p.273.AcademicPress,New York. 24. Schachman, H. K. (1989).Nature,341.,259. 25. Creeth,J. M. and Harding,S. E. (1982).J. Biochem.Biophys.Methods,7,25. 26. Harding, S. E., Horton, J. C., and Morgan, P. J. (1992).ln Analytical ultracentrifugationin biochemistryand polymer science(ed. S. E. Harding,A. J. Rowe, and J. C. Horton), p. 275.Royal Societyof Chemistry,Cambridge,UK. 27. Correia, J. J. and Yphantis, D. A. (1992).In Analytical ultracentrifugationin biochemistryand polymerscience(ed. S. E. Harding,A. J. Rowe, and J. C. Horton), p. 231.Royal Societyof Chemistry,Cambridge,UK. 28. Teller, D. C. (1973).ln Methods in enzymology(ed. C. H. W. Hirs and S. N. Timasheff),Yol.27D, p. 346.AcademicPress,New York. 29. Joss,L. A. and Ralston,D. B. (1995).Anal Biochem.,in press.
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30. Harding,S. E. and Johnson,P. (1985).Biochem.J.,231,549. 31. Wyatt, P. J. (1992).In Laserlight scatteringin biochemisty(ed. S. E. Harding,D. B. Sattelle,and V. A. Bloomfleld),p. 35. Royal Societyof Chemistry,Cambridge, UK. J. Wiley & Sons,New 32. Tanford, C. (1961).Physicalchemistryof mauomolecules. York. 33. Perkins, S. J. (1994). ln Microscopy, optical spectroscopyand mauoscopic techniques(ed. C. Jones,B. Mulloy, and A. H. Thomas),p. 39. Humana Press,New Jersey. 34. Jumel,K., Fiebrig,I., and Harding,S.E.(1995).Int. J. Biol. Macromol.,18,133. 35. Huglin, M. B. (ed.) (1972). Light scatteringfrom polymer solutions. Academic Press.New York. 36. Arner, E. C. and Kirkland, J. J. (1992). ln Analytical ultracentrifugationin biochemistryand polymer science(ed. S. E. Harding,A. J. Rowe, and J. C. Horton), p. 209.Royal Societyof Chemistry,Cambridge,UK. 37. Adophi, U. and Kulicke,W. M. (1996).Polymer,in press. (ed. S. E. 38. Harding,S. E. (1989).In Dynamicpropertiesof biomolecularassemblies Harding and A. J. Rowe),p. 32.Royal Societyof Chemistry,Cambridge,UK. 39. Garcia de la Torre, J. (1989).ln Dynamic properties of biomolecular assemblies (ed. S. E. Harding and A. J. Rowe),p. 3. Royal Societyof Chemistry,Cambridge, UK. 40. Harding,S. E'.,Horton, J. C., and Ccilfen,H. (1996).Eun Biophys."I.,in press. 41. Garcia de la Torre, J., Navarro, S., Lopez-Martinez,M. C., Diaz, F. G., and Lopez-Cascoles, J. J. (1,994). Biophys.J.,67,530. 42. Garciade la Torre, J., Carrasco,B., and Harding,S. E. (1996).Eur. Biophys.J.,in press.
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