determination of protein complex stoichiometry through multisignal

Analytical Biochemistry 407 (2010) 89–103

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Analytical Biochemistry

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Determination of protein complex stoichiometry through multisignalsedimentation velocity experiments

Shae B. Padrick a, Ranjit K. Deka b, Jacinta L. Chuang a, R. Max Wynn a,c, David T. Chuang a,c,Michael V. Norgard b, Michael K. Rosen a,d, Chad A. Brautigam a,*

a Department of Biochemistry, University of Texas, Southwestern Medical Center at Dallas, Dallas, TX 75390, USAb Department of Microbiology, University of Texas, Southwestern Medical Center at Dallas, Dallas, TX 75390, USAc Department of Internal Medicine, University of Texas, Southwestern Medical Center at Dallas, Dallas, TX 75390, USAd Howard Hughes Medical Institute, University of Texas, Southwestern Medical Center at Dallas, Dallas, TX 75390, USA

a r t i c l e i n f o

Article history:Received 20 May 2010Received in revised form 19 July 2010Accepted 20 July 2010Available online 25 July 2010

Keywords:Analytical ultracentrifugationSedimentation velocityPyruvate dehydrogenase complexArp2/3 complexHuman lactoferrin

0003-2697/$ - see front matter � 2010 Elsevier Inc. Adoi:10.1016/j.ab.2010.07.017

* Corresponding author. Fax: +1 214 645 5383.E-mail address: [email protected]

1 Abbreviations used: ITC, isothermal titration caloricentrifugation; SV, sedimentation velocity; LE, Lamm eqhE3, human dihydrolipoamide dehydrogenase; hE3Bhuman lactoferrin; IF, interferometric; EGTA, ethylenther)-N-N,N0 ,N0-tetraacetic acid; EDTA, ethylenediaminolet; rmsd, root mean square deviation; SE, sedimmultisignal SE.

a b s t r a c t

Determination of the stoichiometry of macromolecular assemblies is fundamental to an understanding ofhow they function. Many different biophysical methodologies may be used to determine stoichiometry.In the past, both sedimentation equilibrium and sedimentation velocity analytical ultracentrifugationhave been employed to determine component stoichiometries. Recently, a method of globally analyzingmultisignal sedimentation velocity data was introduced by Schuck and coworkers. This global analysisremoves some of the experimental inconveniences and inaccuracies that could occur in the previouslyused strategies. This method uses spectral differences between the macromolecular components todecompose the well-known c(s) distribution into component distributions ck(s); that is, each componentk has its own ck(s) distribution. Integration of these distributions allows the calculation of the populationsof each component in cosedimenting complexes, yielding their stoichiometry. In our laboratories, wehave used this method extensively to determine the component stoichiometries of several protein–pro-tein complexes involved in cytoskeletal remodeling, sugar metabolism, and host–pathogen interactions.The overall method is described in detail in this work, as are experimental examples and caveats.

� 2010 Elsevier Inc. All rights reserved.

Almost from the beginning of modern biochemistry, it has beenobvious that cells use large macromolecular complexes for criticaland diverse functions. Protein synthesis, DNA replication, fatty acidsynthesis, glucose metabolism, and a myriad of other processes arecarried out on large multicomponent complexes. As more genomesand proteomes are studied, more of such assemblies are discoveredand characterized. In studying a macromolecular complex, a funda-mental question always arises: what is the component stoichiom-etry? A host of different biophysical methods are available toaddress this question, including X-ray crystallography, nuclearmagnetic resonance, isothermal titration calorimetry (ITC),1 quan-titative gel electrophoresis, and the scattering of neutrons and oflight.

ll rights reserved.

du (C.A. Brautigam).metry; AUC, analytical ultra-uation; MSSV, multisignal SV;

D, hE3-binding domain; hLF,e glycol-bis(2-amino-ethyle-

etetraacetic acid; UV, ultravi-entation equilibrium; MSSE,

Recently, there have been significant advances in the analysis ofanalytical ultracentrifugation (AUC) sedimentation velocity (SV)data for interacting biological systems [1–6]. By the term ‘‘interact-ing systems,” here we refer to biological macromolecules that bindeither to themselves (‘‘self-association”) or to a binding partner(s)(‘‘hetero-association”). Such systems may include the self- or het-ero-associations of proteins or nucleic acids. Many of these ad-vances are integrated into the software program SEDPHAT[1,3,4,6]. This program allows one to model kinetic Lamm equation(LE) solutions to the SV data directly via a global analysis of SVexperiments [4]. Although this approach is robust, it can be verycomputationally intensive. Alternatively, methods have been de-vised to use the information from the continuous distributionc(s) so as to obtain values from the SV data that may be fit to bind-ing isotherms. For example, the c(s) distribution may be integratedto obtain a signal average sedimentation coefficient of the interact-ing system. Proper conversion of these values using SEDPHAT al-lows one to determine the equilibrium association constant (KA)for a macromolecule or macromolecules exhibiting a self- or het-ero-association [3,6]. In the case of fast (i.e., koff > �10�3 s�1) het-ero-associations, Gilbert–Jenkins theory can be applied to valuesobtained from the integration of the fast and slow sedimentationboundaries manifested as peaks in the c(s) distribution [3,7]. This

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90 Multisignal sedimentation velocity experiments / S.B. Padrick et al. / Anal. Biochem. 407 (2010) 89–103

treatment allows one to estimate KA and the sedimentation coeffi-cient of the complex (scomplex). Although the above methods workwell, they assume prior knowledge of a stoichiometry, and knowl-edge of that quantity is important in designing the experimentsanalyzed in this way. Therefore, an experimental means of deter-mining the stoichiometry before performing other analyses is oftenessential.

In addition to those techniques enumerated above, Schuck andcoworkers have recently introduced the multisignal SV (MSSV)technique [1]. This methodology allows the experimenter to glob-ally model directly to multisignal SV data sets using convolutionsof LE solutions with ck(s) distributions, where ck(s) represents ac(s)-type distribution to which only one macromolecular compo-nent, k, contributes. As a consequence, one may determine the con-centrations of the components that comprise a cosedimentingcomplex. In this way, the stoichiometry of the components in ahetero-associating complex may be derived.

In our laboratories, determining such stoichiometries has beenof paramount concern. Our interest has been in characterizing pro-tein–protein hetero-associations. In this article, we describe threecases for which MSSV has been invaluable to determine the stoi-chiometries of the associations. The three systems are (i) humandihydrolipoamide dehydrogenase (hE3) binding to the hE3-bind-ing domain (hE3BD) of human E3-binding protein (hE3BP), (ii)Tp34 from Treponema pallidum binding to human lactoferrin(hLF), and (iii) the binding of domains from the Wiskott–Aldrichsyndrome protein (VCA) and cortactin (NtA) to a protein complexthat initiates the branching of actin filaments (Arp2/3). Informa-tion on the physiological import and implications of these pro-tein–protein interactions is detailed elsewhere [8–12].

In all of the cases delineated above, MSSV has performed well toreport on the stoichiometry of the proteins in their respective com-plexes. In this article, we detail, in a step-by-step fashion, how theMSSV method was used to confirm the stoichiometries of therespective protein assemblies. Features and caveats for the MSSVmethod are discussed.

Materials and methods

Theoretical underpinnings

The theoretical bases underlying the c(s) and MSSV methodshave been discussed extensively in the literature [1,13,14]; theyare only briefly recapitulated here. The observed signal from anSV experiment, a(r, t), may be represented as finite element solu-tions to the Lamm equation [v(s,D(s), r, t))] scaled by a continuous,differential concentration distribution called c(s) [14]:

aðr; tÞ ffiZ smax

smin

cðsÞvðs;DðsÞ; r; tÞds; ð1Þ

where r is the radius from the center of revolution, t is time, s is thesedimentation coefficient, and D(s) is the diffusion coefficient as afunction of s, calculated with the assumption of a single frictionalratio (i.e., the ratio of the species’ frictional coefficient, f, to the min-imum frictional coefficient for a species of identical mass, f0) for allsedimenting species.

If we consider an experiment in which there are K components(K > 1), and the SV data profiles are obtained at multiple signals(K = number of signals used), the profiles at one signal, ak(r, t)may by analogy be described by the equation

akðr; tÞ ffiXK

k¼1

ekk

Z smax ;j

smin ;jckðsÞvðs;DkðsÞ; r; tÞds; ð2Þ

where ck(s) represents the continuous distribution due to only onemacromolecular component k and ekk is the molar signal increment

of component k at wavelength k [1]. Note that only K componentscan be distinguished with this method (i.e., K 6K). The ‘‘signals”may be absorbance (Ak, where k is the wavelength) detection at agiven wavelength and data obtained using the Rayleigh interfero-metric (IF) system. For example, three solution components mightbe analyzed using A280, A250, and IF. Details on the practice of thismethodology are given in Results (see below).

The sedimentation of discrete complexes of known stoichiome-try presents the experimenter with the opportunity for a powerfulconstraint on the above analysis [1]. If we represent the number ofsubunits k in a complex j as Sj

k , a new signal increment of the com-plex may be defined:

ejk ¼X

k

Sjk ekk; ð3Þ

which leads to a new model:

akðr; tÞ ffiX

j

Xjj ;k

Sjj

k ekk

Z smax ;j

smax ;jcðjÞj ðsÞvðs;DðsÞ; r; tÞds: ð4Þ

In this model, the continuous distribution is divided into j segments,and the distribution reports the abundance of only species withsedimentation coefficients between smin,j and smax,j and with thespectral composition of complex j. This treatment allows the anal-ysis of different expected complex stoichiometries in different seg-ments of sedimentation coefficient space.

Protein methods

The proteins used in this study were purified as described pre-viously [8,9,11,15]. Iron-free (apo-)hLF was used in this study. ThehLF/rTp34 experiments were undertaken in the presence of Zn2+,and there is evidence that both proteins bind to this cation[8,16]. The protein construct (XDD1) used to study the hE3-bindingproperties of hE3BD comprised residues 1 to 161 of hE3-bindingprotein. Bovine Arp2/3, purified from bovine thymus, had its nativesequence, whereas residues 421 to 502 of the VCA domain of hu-man Wiskott–Aldrich syndrome protein and residues 1 to 36 ofthe NtA domain of human cortactin were used.

For all SV experiments described in this article, a Beckman XL-Ianalytical ultracentrifuge (Beckman Coulter) was used. All experi-ments were performed in dual-sector, charcoal-filled Epon center-pieces (sandwiched between two sapphire windows) that hadbeen filled with 390 ll of sample in the sample sector and thesame volume of buffer without proteins in the reference sector.Assembled centerpiece housings were placed in an An60Ti rotoror in an An50Ti rotor and were centrifuged at 50,000 rpm untilall components apparently had sedimented to the bottom of thecell. Data from multiple signals were collected simultaneouslyusing the Beckman control software.

The hE3/XDD1 experiments were performed at 4 �C in 50 mMTris (pH 7.5). The samples were dialyzed against this buffer priorto their being loaded into the centrifugation cells. These proteinswere mixed and loaded into the experimental apparatus and thenallowed to equilibrate at the experimental temperature for 6 hprior to centrifugation. The Zn–hLF/Zn–rTp34 experiments wereperformed in a buffer composed of 20 mM Tris–HCl (pH 7.5),20 mM NaCl, and 300 lM Zn–acetate. Concentrated stocks of theproteins were diluted in this buffer just prior to cell loading; theywere allowed to equilibrate to the experimental condition (20 �C)for 2 to 4 h before centrifugation was initiated. The experimentsregarding Arp2/3, VCA, and NtA were carried out in a buffer com-posed of 5 mM Hepes (pH 7.0), 50 mM KCl, 1 mM MgCl2, and1 mM ethylene glycol-bis(2-amino-ethylether)-N-N,N0,N0-tetraace-tic acid (EGTA). The samples were treated the same as theZn–hLF/Zn–rTp34 samples.

Multisignal sedimentation velocity experiments / S.B. Padrick et al. / Anal. Biochem. 407 (2010) 89–103 91

Determination of fixed signal increments

The MSSV experiment requires that the molar signal increments(these are functionally equivalent to extinction coefficients and arehereafter represented by the symbol e) of all components beknown and fixed during the analysis for at least one of the signals.In our experiments, we calculate or determine the e values of allcomponents for one signal. In cases where one of the signals is sup-plied by the Rayleigh IF system, we usually assume that the e of aprotein (eIF) is directly proportional to its molar mass and, thus,may be easily calculated. The raw measurement of concentrationof protein measured by the Beckman interferometer is expressedin units of ‘‘fringes displaced,” DJ, which can be expressed as

DJ ¼ Dnl=k; ð5Þ

where Dn is the refractive index difference between the sample andreference sectors, l is the path length, and k is the wavelength of theincident radiation [17]. The quantity Dn is related to the concentra-tion of the protein by the relationship

Dn ¼ dndc

cm; ð6Þ

where cm is the concentration of the protein (in mass units) and dn/dc is the specific refractive index increment of the protein. Assum-ing that proteins have a dn/dc of 1.86 � 10�4 L/g [17], and insertingthe value for k (the laser used in our Beckman XL-I has a wavelengthof 6.75 � 10�5 cm), we obtain

DJ ffi 2:75lcm: ð7Þ

To consider the concentration (c) in molar terms instead of massterms, it is necessary to introduce the molar mass of the protein(M) into this equation:

DJ ffi 2:75Mlc: ð8Þ

By setting eIF = 2.75M and assigning it units of fringes M�1 cm�1, aformulation similar to the familiar Beer–Lambert equation isderived:

DJ ffi eIFlc: ð9Þ

In practice, because the molar mass of the protein can usually becalculated from its amino acid sequence, we use

ekIF ¼ 2:75Mk

c ; ð10Þ

where Mkc ; is the calculated molar mass of component k. Therefore,

in a typical multisignal experiment using interferometry, the quan-tities DJ, l, and ek

IF are known and c is easily calculated.The above treatment works well for most proteins, and it was

used to determine eIF for hE3, XDD1, Arp2/3, VCA, and NtA(Table 1). However, the method assumes that the protein com-prises only amino acids. If a significant percentage of the mass ofthe protein is derived from posttranslational modifications (e.g.,

Table 1Fixed IF signal increments used in this study and empirically determined absorbancesignal increments for rTp34 and hLF.

Protein eIF (fringes M�1 cm�1) e280 (AU M�1 cm�1)

rTp34 65276.3a 31,645b

hLF 226,612a 91,254b

XDD1 51,326c –hE3 (homodimer) 289,759c –Arp2/3 615,516c –VCA 37185.5c –NtA 11281.0c –

a Refined in the MSSV experiment of Ref. [8].b Determined by Deka and coworkers [8].c Calculated using the known amino acid composition and Eq. (10).

glycosylation), the calculation of eIF is not as simple; accommoda-tions for the different IF signal increments of the heterogeneouschemical moieties must be made. Among the proteins studied inthis work, apo-hLF is known to be a glycoprotein. Therefore, in aprevious experiment [8], ek

IF was treated as an unknown for apo-hLF and, for consistency, for rTp34 as well. Instead of the abovetreatment, the e values for absorbance at 280 nm ðek

ABS280Þ weredetermined using the method of Pace and coworkers [18] for bothproteins. In brief, this method entails (i) measuring the absorbanceof chemically denatured protein, (ii) determining the concentra-tion of that protein using an extinction coefficient that is theweighted sum of the tabulated extinction coefficients of aminoacid chromophores, and (iii) measuring the absorbance of the na-tively folded protein and calculating its extinction coefficient basedon the known concentration of protein. The fixed ek

ABS280 values de-rived from these analyses are shown in Table 1.

Data analysis

All data were analyzed using SEDPHAT (version 7.22). By de-fault, SEDPHAT corrects all s values to standard conditions (s20,w);it is these values that are reported below. Time-invariant noise(all data sets) and radially invariant noise (IF data sets) featureswere calculated and subtracted from all of the data presented inthis article [19]. All values for buffer densities (q), buffer viscosities(g), and partial specific volumes (�m) of the proteins were estimatedusing SEDNTERP [20]. In the calculation of �m for hLF, a glycoprotein,the sugar moieties were ignored. To provide estimates for the buf-fer parameters in the Arp2/3 experiments, ethylenediaminetetra-acetic acid (EDTA) was substituted for EGTA in the SEDNTERPcalculations. For all ck(s) distributions presented in this article, Tik-honov–Phillips regularization was applied with a confidence levelof P = 0.70 [13]. In SEDPHAT, all SV data sets by default are assigneda ‘‘noise” level (re) of 0.01. This value is used in the calculation ofthe overall reduced chi-square (v2

r ), which is the goodness-of-fitstatistic that the program uses (see http://www.analyticalultracen-trifugation.com/sedphat/statistics.htm):

v2r ¼

1Ntot

Xe

XNe

i¼1

ðai;e � fi;eÞ2

r2e

; ð11Þ

where Ntot is the total number of data points in all data sets, Ne isthe number of data points in data set e, ai,e is the ith data point ofdata set e, and fi,e is the corresponding fitted point. Theoretically,re should be set to the expected error of data acquisition. Examina-tion of Eq. (11) shows that data sets with a large number of datapoints will dominate the statistic and, thus, perhaps unduly influ-ence parameter refinement. In our cases, Ne for the IF data is typi-cally three to four times that in the absorbance data sets.Therefore, we compensated for this imbalance by dividing re forthe absorbance data sets by approximately

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiNIF=Ne

p. The interested

reader is referred to the above website for an expanded discussionon this topic. The distributions were normalized such that the areaunder a peak yields its total concentration.

Results

The methodology

Proteins are made up of 20 different amino acids, but only asmall subset of these act as chromophores. The chromophoric ami-no acids are tryptophan, tyrosine, and phenylalanine; the disulfidelinkage of a cystine also absorbs light in the ultraviolet (UV) range.With the exception of 100% identical homologs, each protein has aunique sequence of amino acids and, thus, has the potential topossess a unique chromophoric signature. This phenomenon can

http://www.analyticalultracentrifugation.com/sedphat/statistics.htm

http://www.analyticalultracentrifugation.com/sedphat/statistics.htm

Fig. 1. Conventional c(s) distribution. Conventions established in this figure hold forall other figures except where noted. (A) Simulated sedimentation velocity data andfit. In the upper part, the individual data points are represented as open circles; theyform the characteristic sigmoid shape that describes one point in time (i.e., a ‘‘scan”)during the experiment. The inflection point of this feature moves from left to rightas time progresses. The x axis shows the radius from the center of rotation. The yaxis in the upper part shows the magnitude of the signal. For clarity, only everysixth data point used in the data analysis is shown. Also, only every third scan usedto analyze the data is shown. The fit to these data using the c(s) distribution in panelB is shown as a solid line. The lower part of the figure shows the residuals as afunction of radius, where the residual is equal to the y value of a given data pointminus the y value of the fitted data point. The data were simulated using a singlesignal (k1) to include two species (A and B) with identical hydrodynamiccharacteristics (5 S, 77,081 Da) but different concentrations: [A] = 5 lM;[B] = 2 lM; eA

k1 ¼ eBk1 ¼ 100;000 M�1 cm�1. (B) The c(s) distribution that best

describes these data. On the x axis is the s20,w of the simulated species used forthe fit, and on the y axis is the normalized population of material present for eachspecies. This distribution describes the data well, but no spectral discriminationbetween the two proteins is afforded.


manifest in several ways. For example, proteins often differ in themass/chromophore ratios. A small protein with many tryptophanresidues would have a much different mass-to-UV extinction ratiothan a large protein with one tyrosine residue. Furthermore, tyro-sine and tryptophan have significantly different UV absorptionprofiles. If we represent the signal increment at wavelength k nmas eABSk (in units of signal M�1 cm�1, which are assumed through-out the text), proteins with different tryptophan-to-tyrosine ratioswill have significantly different eABS280/eABS250 ratios. When neces-sary, unique absorption features can be introduced to proteins bymodifying them with a chromophoric label. The signals measuredby the Beckman XL-I are directly proportional to the protein con-centration; the magnitude of the interference signal is proportionalto eIF, which is dependent on the protein’s molar mass (see Eqs.(5)–(10)), and the magnitude of the absorbance signal is propor-tional to ek, which is dependent on the number of chromophoricamino acids present in the protein.

The conventional c(s) distribution, as implemented in SEDFIT,has as its units signal per Svedberg (S). For example, an experimentcarried out using IF would have a c(s) distribution with units offringes/S. If only one component k were present and its IF incre-ment ðek

IFÞ were known, it would be straightforward to convertthese units to concentration/S. In the general sense, this distribu-tion is termed a ck(s) distribution for the single component k.

Consider now the case in which two components, A and B, arepresent and have the same molar masses and sedimentation coef-ficients. If data using only one signal, k1, were collected for an SVexperiment containing these two components, there is no way tocalculate the concentrations of the individual components presentin the single c(s) or ck(s) peak without additional information evenif eA

k1 and eBk1 were known (Fig. 1). However, if data from two sig-

nals, k1 and k2, were collected and the ratios eAk1=eA

k2 and eBk1=eB

k2

were significantly different, the data could be analyzed globallyto distinguish between the two cosedimenting proteins. Two over-lapping distributions, cA(s) and cB(s), could be calculated simulta-neously from such data (Fig. 2). In the cA(s) distribution, the dataare globally modeled using just the characteristic extinction prop-erties (i.e., the spectral signature) of protein A. The cB(s) distribu-tion would do the same with the spectral signature of protein B.SEDPHAT is capable of simultaneously optimizing both the cA(s)and cB(s) distributions to the k1 and k2 data, allowing determina-tion of the correct concentrations of the cosedimenting proteins(Fig. 2).

Experimental considerations

As in all sedimentation experiments, the first concern is theexperimental design. Many considerations, including rotor speed,buffer choice, and temperature, are general for an SV experimentand are addressed elsewhere [21]. Also, before the experiment be-gins, an assessment of its feasibility should be performed. Forexample, if researchers studying a two-component system planto use IF and A280 as the two signals to monitor sedimentation, theyshould calculate the ratio of kIF to e280 for both components. Themethod is completely dependent on divergent signal increment ra-tios for the spectral discrimination of the components. For this rea-son, as a rule of thumb, we suggest that the ratios be at least 20%different before proceeding (although even this may be insufficient[see below]). The choice of wavelength is also important. To mini-mize the effect of the wavelength inaccuracy in the Beckmanmonochromator, wavelengths away from any steep slope in themacromolecule’s absorption spectrum should be chosen. Often, itis convenient to choose a wavelength close to an absorbance max-imum or minimum, which fits the above criterion. Notably, not allproteins have an absorbance maximum at 280 nm; indeed, for hE3(studied below), there is an absorbance maximum at 274 nm.

The concentrations chosen for the components are critical. Toobtain the proper stoichiometry, the complex must be fully occu-pied. For example, in a two-component system, it is advantageousto include one component at a large molar excess over the otherand well in excess of the dissociation constant; mass action willthen favor a fully occupied complex. If the components are differ-ently sized, it is convenient to include the smaller of the two inmolar excess. This strategy allows the assumption that all of thefaster sedimenting material is complexed. There are limitationson the amount of molar excess that may be employed. It is unde-sirable for the signal due to the complex to be less than 10-foldover the intrinsic noise of data acquisition, which is generally0.005 signal units for both data acquisition systems. Furthermore,the absorbance optical system is inaccurate above optical densitiesranging from 1.0 to 1.5. Finally, very high protein concentrationsmay induce hydrodynamic nonideality in the samples, compromis-ing the quality of the data analysis. In practice, the concentration atwhich nonideality becomes a hindrance to the analysis is difficult

Fig. 2. Two-signal MSSV experiment. For these simulated data, the signalincrements for protein A were 100,000 and 50,000 M�1 cm�1 for signals k1 andk2, respectively. For protein B, the increments were 100,000 and 80,000 M�1 cm�1

for signals k1 and k2, respectively. (A) Data and global fit for signal k1. (B) Data andglobal fit for signal k2. The y axis of the upper part was put on the same scale as thatin panel A to emphasize the difference in the magnitude of the signals collected atthe two different wavelengths. (C) The cA(s) (solid line) and cB(s) (dashed line)distributions that best describe the data in panels A and B. Integrating the peaks inthese distributions returns the proper concentrations of the components, that is,R s max

s min cAðsÞds ¼ 5 lM andR s max

s min cBðsÞds ¼ 2 lM.


to predict; we avoid concentrations much greater than 1 mg/ml.The choices of concentrations, therefore, require a careful balancebetween mass action and physical and instrumentationlimitations.

For a hetero-associating system with K components, at leastK + 1 centrifugal cells must be prepared and centrifuged: one foreach component and at least one for the mixture of components.There are notable exceptions to this rule (see Arp2/3 discussionbelow). Furthermore, the centrifuge’s control software must be

programmed to collect more than one signal from each cell.Currently, the control software for the Beckman XL-I is capable ofcollecting up to four signals per cell. One data set may come fromthe Rayleigh interferometer, and the other three may be absor-bance data collected at three different wavelengths using theradially scanning spectrophotometer. At least as many signals ascomponents must be collected (with a notable exception [seeArp2/3 discussion below]). It is essential that the reference buffersbe identical to the sample buffers, and buffer components thatabsorb at the subject wavelengths should be avoided if possible.The IF system is exquisitely sensitive to all buffer mismatches;because osmolytes such as glycerol are difficult to match well, theyshould be avoided.

Finally, some information regarding the character of the inter-action between the two proteins is desirable. In general, MSSVworks best with proteins that associate tightly (i.e., KA > 105 M�1

for a two-component hetero-association) and with a slow kineticoff-rate (i.e., koff < 10�3 s�1). Associations that do not meet thesecriteria can be studied using MSSV, but they require a large molarexcess of one or more of the components to fully populate the com-plex [1]. To obtain information concerning koff, it is recommendedthat the experimenter study the interaction at various concentra-tions using SV and analyze the data using the c(s) distribution.The appearance of the distribution is diagnostic of the koff [7,21].For an A + B M AB system, a slow koff would yield three stationaryc(s) peaks that change heights as the component concentrationschange. For a fast koff, two peaks would usually be observed: onerepresenting a free component and the other representing thereaction boundary [7]. The apparent position and height of thereaction boundary peak would change based on the populationsof complex and free components [7,22]. Simulations [1] haveshown in the case of a fast koff that, unless one of the componentsis present at a large molar excess, the observed molar ratio of thecosedimenting species corresponds to the molar ratio of thereaction boundary, not the complex. For difficult cases, such aswhen the sedimentation coefficient of the complex (scomplex) isapproximately equal to that of one (or both) of the components,we recommend using a large molar excess of one of the compo-nents and at least two concentrations of the component in excess.We note that the method is not dependent on scomplex being thefastest sedimenting species, but this is usually the case.

General features of the analysis

An MSSV analysis of a two-component hetero-associating sys-tem (e.g., A + B M AB) usually comprises three steps. In the firststep, a global SV analysis using at least two signals is performedon a sample that contains only component A. In this analysis, typ-ically, for one of the signals (signal k1 in the following notation),the signal increment of A ðeA

k1Þ is known, either through calculation(i.e., via Eq. (10) or a program such as SEDNTERP) or throughempirical determination (e.g., amino acid analysis or absorptionmeasurements under denaturing and native conditions [18]). Thesignal increments for A (eA

k2; eAk3, etc.) with respect to the other sig-

nals (signals k2, k3, etc.) are unknown; obtaining their best-fit val-ues is the goal of this step. The value of eA

k1 is held constant in theanalysis, and the data from all signals are globally fit with a singlecA(s) distribution while concurrently allowing the unknown signalincrements to refine to their optimal values. In essence, knowledgeof eA

k1 and the total amount of signal allows the program to calcu-late the concentration of A. Because all other signals come from theidentical sample, [A] is known and the unknown signal incrementscan be varied until the best global fit to the data is obtained. Once asatisfactory global fit to the data is reached, the refined values ofeA

k2 and the like are noted for future use. Contrary to traditionalc(s), which has units of signal per Svedberg, cA(s) (and, more


generally, ck(s)) has units of concentration per Svedberg. An impor-tant consequence of this difference is that the area beneath a peakin a cA(s) distribution is equal to [A].

The second step in the analysis is similar to the first step. Theonly difference is that the global analysis is carried out for thesedimentation of protein B alone, not protein A. Again, the refinedvalues of eB

k2 and the like are noted for use in the third step.In the third step, the fixed and refined increments are applied to

the global analysis of sedimentation data obtained from a mixtureof A and B. In this case, no signal increments are allowed to refine(hyper- or hypochromicity cannot be accommodated in this type ofanalysis). We always initially analyze such a system by fitting thedata with two ck(s) distributions, cA(s) and cB(s), which have thesame range of s values. In parts of the distribution that show cosed-imentation of the two components, the distributions are integratedto determine the molar concentrations of the respective compo-nents. The ratio of these molar concentrations is equal to the molarratio of proteins in the complex. From the observed sedimentationcoefficient of the complex, an estimate of the overall complex sizecan be made and the stoichiometry of the complex can be derived.Further analyses using assumed fixed stoichiometries are possibleand are detailed below.

The MSSV analysis affords the experimenter the opportunity totest the statistical validity of constraints on the model. For exam-ple, if the data obtained as above point to a certain complex stoi-chiometry (e.g., 1:1), a stoichiometric constraint can be added tothe analysis for pertinent s value ranges. In essence, the followingquestion is posed: given the quality of the data, the accuracy of therefined extinction coefficients, and the assumptions inherent in theck(s) model, does the addition of a stoichiometric constraint cause astatistically significant degradation of the quality of the fit? If thisquestion is answered negatively, we may say that the queried com-plex stoichiometry is consistent with the data given our statisticalcriterion. A positive answer should cause the experimenter tocarefully evaluate whether the constraint can be consideredcorrect or not.

All of the tools necessary for this test are present in SEDPHAT.The quality of the unconstrained fit (obtained in the third step) isassessed in SEDPHAT with a global reduced v2ðv2

r Þ. We call thev2

r arising from the best fit v2b. Fits with a stoichiometric constraint

in place result in a higher v2 value, here called the ‘‘test v2” or v2t .

The answer to the question posed above depends on whether v2t

exceeds another v2 value called the ‘‘critical v2” or v2c;1r. The exper-

imenter can determine vc,1r using an F statistic calculator availablein SEDPHAT. To arrive at vc,1r, SEDPHAT uses the formula

v2c;1r ¼ v2

bFal;m; ð12Þ

where Fal;m is the (1 � a) one-sided F statistic with l and m degrees of

freedom, l = m = the number of data points being fitted, anda = 0.683. Thus, our criterion for statistical significance is a changethat worsens the fit by more than 1r. Constrained fits with v2

t lessthan or equal to v2

c;1r are accepted as statistically indistinguishablefrom the best fit, and the answer to the above question is no. Con-versely, constrained fits with v2

t above v2c;1r are considered as statis-

tically worse, and the answer to the above question is yes. Inpractice, the following steps are performed. First, the experimentermakes note of v2

b for the best unconstrained fit. Second, the v2c;1r is

calculated using SEDPHAT’s statistical calculator. Third, the stoichi-ometry of the components is constrained in relevant s value ranges,which are typically greater than sA or sB. For example, components Aand B can be constrained to be in 1:1 complexes in a given s valuerange. Fourth, a new fit is performed in the presence of the con-straint. Fifth, v2

t is compared with v2c;1r and the question of statisti-

cal significance is answered using the criteria delineated above. We

routinely use this method to check whether the derived stoichiom-etry is justified by the data.

A constrained fit with v2t > v2

c;1r does not automatically invali-date the stoichiometric constraint. It is possible that the constraintis correct, but it causes a slightly ‘‘worse” fit. For cases wherev2

t > v2c;1r, we suggest calculating a rejection v2, v2

c;2r. This valueis calculated exactly as in Eq. (12) except that a = 0.95. Ifv2

t > v2c;2r, the stoichiometric constraint is unlikely to be correct.

If v2c;1r < v2

t < v2c;2r, the constraint might be valid, but it results in

a statistically ‘‘worse” fit by our definition. In such a case, caveatsshould be acknowledged (e.g., deficits in the spectral resolution,the quality of refined extinction coefficients, or the degree of satu-ration of binding sites), and information from other experiments(e.g., repetitions of the experiment at different concentrationsand stoichiometries derived from other biophysical methods)may come to bear on the validity of the constraint.

A straightforward example

To illustrate the steps outlined above, we reanalyzed one dataset that, among others, was used to confirm the stoichiometry ofa complex comprising human E3-binding domain (here calledXDD1) and human dihydrolipoamide dehydrogenase (called hE3)[10]. Two crystal structures had established that the stoichiometryof the complex is 1:1 [11,12], but this finding was challenged in theliterature [23,24].

First, we analyzed the sedimentation of hE3 alone. This proteinis a constitutive dimer; our construct had a calculated molar massof 105,367 Da. The mass of FAD, which is noncovalently bound tohE3, was neglected in our calculations. Sedimentation data wereacquired using both IF and absorbance optics (Fig. 3A and B,respectively). We chose 276 nm because it was close to an absor-bance maximum for hE3 (274 nm) and a plateau in the absorbanceof XDD1 (not shown). In our previous analysis of these data [10],we fixed the meniscus of the IF data because it tended to refineto unrealistic values. However, in the current work, we have re-moved this constraint. We find that refinement of the meniscusis more stable in newer versions of SEDPHAT. A small percentage(�9%) of the protein is present as higher order aggregates. Previ-ously, these were modeled with a few species having sedimenta-tion coefficients close to 15 S. Here we explicitly treat thoseaggregates as a continuous distribution of species sedimenting be-tween 10.1 and 50 S (insets of Fig. 3C and F). Therefore, there aretwo ‘‘segments” of s values considered: one from 0.2 to 10 S anda second from 10.1 to 50 S. Each is allowed to have a separate over-all frictional ratio (fr). In our experience, the fr values refine to thesame values obtained from a conventional c(s) analysis, and signif-icant variance between the conventional and MSSV approachesindicates a problem with the latter analysis. According to Eq.(10), ehE3

IF ¼ 289;759 fringes M�1 cm�1. This value was fixed inthe analysis. As a first substep in this analysis, we fixed the valuesof all nonlinear parameters except that of ehE3

ABS276 (e.g., the samplemenisci, fr values). This methodology allowed the efficient approx-imate refinement of ehE3

ABS276. Once this approximate value was ob-tained, the nonlinear parameters (except fr of the 10.1 to 50-Ssegment) were also allowed to refine. The final value of ehE3

ABS276 re-fined to 137,764 AU M�1 cm�1. The quality of the fits is good(Fig. 3A and B), with a root mean square deviation (rmsd) of the fit-ted line from the data of approximately 0.008 fringes for the IF dataand approximately 0.008 AU for the A276 data. For the optics on ourcentrifuge, we ordinarily expect rmsd values between 0.004 and0.01. The chE3(s) distribution is shown in Fig. 3C. It has a dominantpeak at 5.7 S. As noted previously, there is also a minor peak havinga sedimentation coefficient of 7.8 S [10,24]. This material is pre-sumably an uncharacterized tetrameric form of hE3.

Fig. 3. Data used to determine signal increments for hE3 and XDD1. (A) IF data, fit, and residuals for hE3 alone. For this and all other IF data in this article, only every thirdscan and every 12 data point are shown. (B) A276 data, fit, and residuals for the same sample as in panel A. For this and all other absorbance data in this article, only every thirdscan and every fourth data point are shown except where noted. (C) The chE3(s) distribution used to model the data in parts A and B. The inset in this panel shows thedistribution used to model the aggregates. Note the change in scale for the y axis. (D) IF data, fit, and residuals for XDD1 alone. (E) A276 data, fit, and residuals for the samesample as in panel C. Owing to the lower signal-to-noise ratio in this experiment, only every sixth scan is shown for the sake of clarity. (F) The cXDD1(s) distribution used tomodel the data in panels D and E.


A similar analysis was performed for the sedimentation ofXDD1 alone (Fig. 3D–F). In this case, the eXDD1

IF of the XDD1 mono-mer (18,664 Da) was calculated to be 51,326 fringes M�1 cm�1.Again, the menisci for both the IF and A276 data sets were allowedto refine freely, and aggregation was modeled by species with svalues from 4.5 to 20 S. XDD1 sedimented mostly as a monomerwith an s value of 1.4 S (Fig. 3D–F). Other peaks in the cXDD1(s) dis-tribution occur at 2.1 and 3.1 S. These peaks could be dimeric andtetrameric forms of the protein, respectively. The value of eXDD1

ABS276

refined to 9453.73 AU M�1 cm�1. Again, the overall quality of thefits is good, with rmsd values of approximately 0.007 fringes and

0.007 AU for the IF and A276 data, respectively. From the analysisto this point, we notice that the eIF-to-e276 ratios for the two pro-teins are significantly different (2.1 and 5.4 for hE3 and XDD1,respectively; Table 2).

With the refined values of ehE3ABS276 and eXDD1

ABS276 in hand (Table 2),we turned to the analysis of the mixture of the two proteins. Forthis exemplary analysis, we chose a sample that had large molarexcess of XDD1 over hE3 (�13:1). The data (Fig. 4A and B) weremodeled with two overlapping distributions: a chE3(s) distribution,which reported only the presence of hE3, and a cXDD1(s) distribu-tion, which was specific for XDD1 (Fig. 4C). Three segments of s

Table 2Refined signal increments for the hE3/XDD1 experiments.

Protein e276 (AU M�1 cm�1) eIF (fringes M�1 cm�1) eIF/e276

hE3 137,764 289,759a 2.10XDD1 9453.73 51,326a 5.43

a Fixed in this analysis; calculated using the known amino acid composition andEq. (10).

Fig. 4. Stoichiometry of hE3 and XDD1. (A) IF data, fit, and residuals for the mixtureof XDD1 and hE3. (B) A276 data, fit, and residuals for the same sample as in panel A.(C) The chE3(s) and cXDD1(s) distributions used to model the data in panels A and B.As in Fig. 3C and F, the chE3(s) distribution is represented by a solid line, whereas thecXDD1(s) distribution is shown with a dashed line. The inset in this panel shows thedistribution used to model the aggregates. Note the change in scale for the y axis.


values were evaluated: 0.2 to 4 S, 4.5 to 10 S, and 10.5 to 60 S. Thetwo most prominent peaks in the cXDD1(s) distribution are at 1.5 S(free XDD1) and 6.0 S (complexed XDD1). In the chE3(s) distribu-

tion, there is a single prominent peak at 6.0 S. By modeling the datawith two ck(s) distributions, we arrived at a high-quality fit (Fig. 4Aand B); the rmsd values of the IF and A276 data sets were0.008 fringes and 0.008 AU, respectively. We conclude that hE3and XDD1 are cosedimenting in a complex that has a sedimenta-tion coefficient of 6 S. To arrive at the stoichiometry of this com-plex, the distribution was integrated over the range of 5 to 7 S.The resulting concentrations, 2.9 lM for XDD1 and 3.3 lM forhE3, indicate that the ratio of XDD1 to hE3 in the XDD1/hE3 com-plex is approximately 0.9 to 1. This result suggests that equal num-bers of XDD1 and hE3 molecules are present in the complex. Thus,possible stoichiometries are 1:1, 2:2, and the like. However, a com-plex harboring two or more molecules of hE3 would have a sedi-mentation coefficient significantly greater than 6 S. As weconcluded previously [10], the most likely stoichiometry of thecomplex, therefore, is 1:1.

The concentrations of hE3 and XDD1 in the complex are verysimilar, and it is a reasonable hypothesis that all species sediment-ing between 4.5 and 10 S are a 1:1 complex of the two proteins. Totest this hypothesis, we fixed the stoichiometry of the two proteinsto 1:1 in this range of s values (see Eq. (4)). Therefore, for this s va-lue range, the data are modeled with a single cXDD1:hE3 (s) distribu-tion with the built-in assumption of unitary stoichiometry (seeFig. 5 and ‘‘general features of the analysis” section above). Usinga confidence level of 0.683 (1r), we find that the quality of thefit with the constrained 1:1 molar ratio in the range of 5.1 to10 S (v2

t ¼ 1:206414) is not statistically worse than the originalunconstrained fit (v2

b ¼ 1:202899, v2c;lr ¼ 1:206784). Other

researchers had concluded that the complex between a proteinsimilar to XDD1 and hE3 was 2:1 [24]. We used the same method-ology described above to constrain the ratio of XDD1 to hE3 to 2:1,but no optimization with this constraint arrived at a v2

t that wasless than v2

c;lr. The best v2t value we could obtain with this stoichi-

ometric constraint was 1.451225. This value is well above v2c;2r

(1.216374), indicating that the 2:1 stoichiometric constraint isnot consistent with our data. These two results further buttressour contention that stoichiometry between the two proteins is 1:1.

Ligand-induced extinction changes

In a previous report, we established, using MSSV and isothermaltitration calorimetry, that two molecules of the treponemal proteinrTp34 could bind to the human mucosal protein apo-hLF [8]. In thesame report, we demonstrated that divalent metal ions induce thedimerization of rTp34 in solution. Given these results, one mayhypothesize that as many as four copies of rTp34 may bind tohLF in the presence of metal ions. To test this hypothesis, we stud-ied these proteins in the presence of 300 lM Zn2+ using MSSV.

As noted above, because of the glycosylation on apo-hLF, wecould not follow the method employed above (i.e., calculatingeapo-hLF

IF directly from the molar mass implied by its known aminoacid sequence). Instead, in our previous work [8], we determinedthe eABS280 for both apo-hLF and rTp34 using the method of Paceand coworkers [18]. The eABS280 values determined in this waywere fixed, and the eIF values were refined [8]. Adding Zn2+ to asolution containing both rTp34 and apo-LF poses significant exper-imental challenges. The most relevant problem in the current con-text is that hLF binds to divalent cations, and metal-bound hLFoften has a different eABS280 from apo-hLF [25,26]. At the beginningof the experiment, we did not know the extent to which ehLF

ABS280

would change in the presence of Zn2+. For this reason, we collectedSV data using three different signals for this experiment: IF, A280,and A250. Previously, we had used just IF and A280; it was surmisedthat the added signal could help if spectral resolution becamedifficult due to the addition of the cation.

Fig. 6. Analysis of A280 and IF data for rTp34 and hLF in the presence of Zn2+. Thedashed line depicts the crTp34(s) distribution, and the solid line represents the chLF(s)distribution. The bar shows the s value and concentration of a discrete species thatwas also modeled in these data. Unlike the distributions, the unit of the height ofthe bar is micromolar (lM). It is noteworthy that the true concentration isunknown; the quantity given in the chart is based on an arbitrary signal increment.

Fig. 5. Analyzing the hE3/XDD1 mixture data with a fixed stoichiometry. (A) IFdata, fit, and residuals for the mixture of hE3 and XDD1. (B) A276 data, fit, andresiduals for the same sample as in panel A. (C) Distributions used to model the datain panels A and B. At low and high (inset) s values, chE3(s) and cXDD1(s) distributionswere used. But in the range of 4.5 to 10 S, a cXDD1:hE3(s) distribution (dotted line)was modeled with a fixed stoichiometry of 1:1.


We started the current analysis with the naive assumption thatthe eABS280 values of Zn2+-bound hLF (Zn–hLF) and Zn2+-boundrTp34 (Zn–rTp34) were unaffected by the cation (Table 1). There-

Table 3Refined signal increments for the Zn–rTp34/Zn–hLF experiments.

Protein e280 (AU M�1 cm�1) e250 (AU M�1 cm�1)

Zn–hLF 101,218 72006.8Zn–rTp34 32844.6 11292.6

a Fixed in this analysis; refined by Deka and coworkers [8].

fore, the eABS280 values were fixed and the eIF values were allowedto refine to their optimal values. We obtained eZn—hLF

IF ¼ 205;018fringes M�1 cm�1 and eZn—rTp34

IF ¼ 62;815:6 fringes M�1 cm�1. Thelatter value was approximately 4% less than that obtained previ-ously, but the former value differed from eapo-hLF

IF by approximately9% (Table 1). Moreover, these refined values resulted in signalincrement ratios that were very close to one another: eZn—hLF

IF =

ehLFABS280 ¼ 2:2 and eZn—rTp34

IF =eZn—rTp34ABS280 ¼ 2:0 (Table 3). In our previous

report, these ratios had been 2.5 and 2.1, respectively. Finally,the cZn–hLF(s) and cZn–rTp34(s) distributions calculated using therefined signal increments appeared to be incorrect (Fig. 6). First,given the concentrations of both proteins derived from the exper-iments with the proteins alone, we expected a higher concentra-tion of Zn–rTp34; the observed concentration was 5.5 lM, butthe anticipated concentration was 7.5 lM. This error was quitelarge even considering the pipetting errors that could haveoccurred. It is outside the range of concentration error that we usu-ally observe (±10% [data not shown]). Next, a significant amount ofZn–rTp34 was found to sediment at 8.4 S with no cosedimentingZn–hLF; there was no precedent for uncomplexed Zn–rTp34 sedi-menting that fast. Finally, the peak corresponding to the knownsedimentation coefficient of dimeric Zn–rTp34 was contaminatedwith more signal for Zn–hLF than observed in this s range withZn–hLF alone (not shown). All of these observations indicate a lackof sufficient spectral discrimination between Zn–hLF and Zn–rTp34for the two signals IF and A280.

Gaining spectral resolution of the two zinc-bound proteins re-quired a different strategy. It was clear that eZn—hLF

ABS280 had changedsignificantly from eapo-hLF

ABS280 and that eZn—rTp34ABS280 also could have been al-

tered. It seemed unlikely, however, that the IF signal incrementsfor the two proteins would change greatly with the addition of afew bound zinc cations. Therefore, we elected to use the IF signalincrements derived from the previous work [8] and fix them inour current analyses. Furthermore, we used all three signals (IF,A280, and A250) in the analyses, allowing the eABS280 values andeABS250 values to refine to their optimal values. Finally, we noted

eIF (fringes M�1 cm�1) eIF/e280 eIF/e250

226,612a 2.23 3.1565276.3a 1.99 5.78


that the IF system detected a small sedimenting species that wasnot present in the A280 or A250 data sets. It is very likely that thisphenomenon was due to a buffer imbalance between the referenceand sample sectors and that this species was a non-UV-absorbingbuffer salt. We modeled this sedimenting material as a discretespecies with a high arbitrary signal increment in the IF data set(100,000 fringes M�1 cm�1) and signal increments of 0 AU M�1

cm�1 in both the A280 and A250 data sets. This discrete species isshown as a bar in our distributions; its position on the x axis rep-resents its refined s value, and its height represents its refined‘‘concentration” based on the arbitrary signal increment.

As a result of the above strategy, we were able to gain excellentspectral resolution between the two proteins (Fig. 7). We followedan identical strategy to that outlined above for XDD1 and hE3, ex-cept that three signals were used in this analysis. First, the signalincrements were refined for an experiment containing only Zn–rTp34. The presence of Zn2+ in solution causes the protein to favorits dimeric form (3.5 S), although, under these conditions there isalso some monomer (2.2 S). It was not necessary to model aggre-gates for this protein. Second, the same type of analysis was per-formed for a sample containing only Zn–hLF. Three prominentpeaks appear in this distribution, at 5.1, 6.7, and 8.1 S (see Supple-mental Fig. 1 in supplementary material). The 5.1-S peak (which isdominant) is monomeric Zn–hLF, the 8.1-S peak is likely a dimer ofhLF, and the 6.7-S species is probably a subpopulation of Zn–hLFdimer that has sedimented at a lower time average s value becausesome of it has dissociated during the SV experiment. There are also

Fig. 7. Three-signal analysis of the interaction of rTp34 and hLF in the presence of Zn2+.same sample as in panel A. (C) A250 data, fit, and residuals. (D) Distributions used to mwhereas the solid line describes the cZn–hLF(s) distribution.

small species (2–3 S) that may be degradation products of hLF. Adistribution of species from 10.1 to 40 S was used to model aggre-gates of Zn–hLF. The signal increments obtained by analyzing thesefirst two experiments are found in Table 3. Third, the mixture ofthe two proteins was analyzed using the signal increments refinedin the previous two steps. These data were modeled with one dis-crete species (0.54 S) and distributions spanning 1 to 5 S, 5.5 to9.6 S, and 9.8 to 40 S. Excellent fits to the data (Fig. 7A–C) are ob-tained in this analysis (local rmsd values are 0.007 fringes,0.004 AU, and 0.005 AU for IF, A280, and A250, respectively). Onlytwo peaks are present in the range of 5.5 to 9.6 S, indicating thatthe presence of Zn–rTp34 has slowed the off-rate of the Zn–hLF di-mer such that little of the Zn–rT34-bound Zn–hLF dimer dissoci-ates during the SV experiment. Also, the spectral resolution issuperior to the two-signal Zn–hLF/Zn–rTp34 experiment describedabove (Fig. 7D). The observed concentrations are within approxi-mately 10% of those expected, both proteins are found in the 8.6-S material, and very little Zn–hLF contaminates the peaks for theexcess Zn–rTp34. Integrating the distributions at the dominant6.7-S peak shows that the molar ratio of Zn–rTp34 to Zn–hLF isapproximately 2 ([Zn–Tp34] = 3.8 lM, [Zn–hLF] = 2.0 lM).

The strategy delineated above for restricting certain s ranges tohypothetical stoichiometries can also be used in this case. For thisexample, we modeled the material sedimenting at 5.5 to 9.6 S as2:1 Zn–rTp34/Zn–hLF complexes. By comparing the v2

t of this fitto the data (0.573871) with the v2

c;1r (0.575228), we conclude thatthe data are consistent with the 2:1 assumption.

(A) IF data, fit, and residuals for the mixture. (B) A280 data, fit, and residuals for theodel the data in parts A to C. The dashed line denotes the cZn–rTp34(s) distribution,

Fig. 8. The interaction of VCA* with Arp2/3. (A) IF data, fit, and residuals for themixture of a large molar excess of VCA* with Arp2/3. (B) A496 data, fit, and residualsfor the same sample as in panel A. (C) Distributions used to model the data shown inpanels A and B. The dashed and solid lines depict the cVCA� ðsÞ and cArp2/3(s)distributions, respectively.


Using labeled protein

The heteroheptameric Arp2/3 complex binds to actin filamentsand nucleates new filaments in a characteristic branched confor-mation. WASP family proteins are defined by a C-terminal VCA do-main that binds to and activates the Arp2/3 complex. Previously, ithad been assumed that only one VCA-containing protein couldbind to Arp2/3 at a time [27–31]. However, recent evidence hassuggested that two such proteins might bind simultaneously [9].We used MSSV to address this issue.

The experimental approach was to study the interaction of asmall, VCA-containing protein construct (called VCA hereafter)and bovine Arp2/3. The very large size difference between VCAand Arp2/3 complex posed a significant difficulty. The molar massof VCA is approximately 13,500 Da, whereas that of Arp2/3 isapproximately 224,000 Da. Given the calculated eABS280 values ofthe proteins, we anticipated that the absorbance and mass changesin Arp2/3 on VCA binding would be quite small, hampering accu-rate detection of VCA bound to Arp2/3. Therefore, we labeledVCA with the fluorophore Alexa 488, yielding VCA*. This expedientgave VCA* a unique absorption maximum at approximately496 nm, well into the visible range of the spectrum. Furthermore,the eABS496 for VCA* was high, providing a strong signal for thissmall protein. We collected data sets from two signals: IF and A496.

Unlike our above analyses, only two steps were required to as-sess the VCA*/Arp2/3 data. In the first step, we held the calculatedeVCA�

IF constant at 37,185.5 fringes M�1 cm�1 and refined eVCA�ABS496 (re-

fined value = 64,629.9 AU M�1 cm�1). The fitted cVCA� ðsÞ distribu-tion (not shown) describes the VCA* alone data well, with localrmsd values of 0.005 fringes and 0.005 AU for the IF and A496 datasets, respectively. Ordinarily, there would be a second step inwhich eArp2=3

ABS496 was refined. However, eArp2=3ABS496 was known to be 0

and eArp2=3IF (615,516 fringes M�1 cm�1) was calculated using Eq.

(10); refinement was unnecessary. In the last step, the knownand refined signal increments were used to analyze a mixture ofthe two proteins in which [VCA*] is approximately fifteen times[Arp2/3].

The results of this analysis are shown in Fig. 8. In the mixtureanalysis, excellent fits were achieved (Fig. 8A and B). Two segmentsof distributions were used to describe the data: one from 0.2 to 4 Sand the other from 4.1 to 15 S; separate fr values were refined foreach segment. The cVCA� ðsÞ distributions show two peaks: one at1.4 S and the other at 9.4 S. The cArp2/3(s) distributions have onlya single significant peak at 9.4 S. Arp2/3 alone has a sedimentationcoefficient of 9.0 S (not shown), indicating that complex formationwith VCA causes a 0.4-S shift in the sedimentation of Arp2/3. Inte-grating the 9.4-S peaks in the distributions results in[VCA*] = 1.1 lM and [Arp2/3] = 0.5 lM. Therefore, we concludethat two copies of VCA* bind to a single Arp2/3 complex. This resulthas been replicated many times with differing molar excesses ofVCA* (not shown). At very high molar excesses of VCA*, the absor-bance at 496 nm fell out of the linear range of the on-board spec-trophotometer. Instead, we capitalized on an absorption minimumof VCA* at 312 nm, which had roughly fivefold less absorbance thanat 496 nm.

Two signals, three proteins

In the VCA*/Arp2/3 system described above, it was of interest tointroduce a third protein, the NtA domain of cortactin. This domainis known to compete with VCA domains for binding to the Arp2/3complex [9,31], but it was unknown whether NtA domains com-pete with one or both VCA-binding sites on Arp2/3 (Fig. 9A). To ex-plore this competition, we again turned to MSSV. We used thesame materials as above, namely unlabeled Arp2/3 and VCA*. TheNtA construct was unlabeled and consisted of residues 1 to 36 of

human cortactin. Sedimentation was monitored using IF and A496

as before.Theoretically, to establish the stoichiometry of a three-compo-

nent complex, at least three signals are needed. We monitored onlytwo signals. However, our experiment was designed to track onlythe VCA*/Arp2/3 stoichiometry as NtA was titrated in. Therefore,two modifications to our VCA*/Arp2/3 strategy were required. First,excess NtA was modeled as a discrete species with an eNtA

IF of11,281 fringes M�1 cm�1 and a eNtA

ABS496 of 0 AU M�1 cm�1. Second,the assumption was made that the binding of NtA to Arp2/3 didnot alter eABS496

IF . In essence, the fact that NtA was binding toArp2/3 was spectrally ignored. Using this assumption, we could

Fig. 9. Interaction of VCA* with Arp2/3 in the presence of NtA. (A) Scheme of the competition of VCA* and NtA for binding to Arp2/3. Arp2/3 (black, labeled ‘‘A”) has twodifferent binding sites (1 and 2). In this experiment, we added VCA* (gray ovals marked ‘‘V”) and NtA (white circles marked ‘‘N”) and allowed the system to come toequilibrium. It was known (Fig. 8) that VCA could bind to both binding sites; the purpose of this experiment was to test whether NtA could effectively challenge VCA* forArp2/3 binding at one or both of the sites. Two scenarios are considered. In scenario 1, shown in the upper part, a large excess of NtA will effectively compete for only one ofthe VCA* binding sites and the limit of VCA/Arp2/3 stoichiometry at high [NtA] will be 1. In scenario 2, shown in the lower part, NtA effectively competes for both of the VCA*

binding sites and the limit of VCA/Arp2/3 stoichiometry at high [NtA] will be 0. (B) IF data, fit, and residuals for the VCA*/NtA/Arp2/3 mixture. (C) A496 data, fit, and residualsfor the same sample as in panel B. (D) Species and distributions used to model the data in panels B and C. Free VCA* and free NtA are modeled as single species correspondingto the gray and black bars, respectively. The cVCA� ðsÞ and cArp2/3(s) distributions are shown as dashed and solid lines, respectively.


calculate cVCA� ðsÞ and cArp2/3(s) distributions without accounting forthe third protein. Strictly speaking, the assumption of unalteredeArp2=3

IF cannot be true. The added mass of NtA will cause the signalincrement of the NtA/Arp2/3 complex to be more than that of apo-Arp2/3. However, a single molecule of our NtA construct has only1.8% of the molecular mass of Arp2/3. Therefore, we hypothesizedthat NtA binding to Arp2/3 would have a negligible effect on eArp2=3

IF

and, thus, that its binding could be ignored for the purposes ofspectral discrimination.

We followed the same methodology as described above forVCA*/Arp2/3. The only difference was that a discrete species wasadded to model free NtA. The analysis was performed on five sam-ples having the following concentrations of NtA: 0, 3.5, 7.7, 13.9,and 23.2 lM. The concentrations of Arp2/3 and VCA* were heldconstant at 0.5 and 9.6 lM, respectively.

Here we present the analysis of the sample with 7.7 lM NtA.Two discrete species (one for free VCA* and one for free NtA) andtwo ck(s) distributions (ranging from 3 to 12 S) were used to glob-ally model the two SV data sets. The data, resulting fits, and ck(s)distributions resulting from this analysis are shown in Fig. 9. Thequality of the fits was excellent; the rmsd values were0.004 fringes and 0.005 AU for the IF and A496 data, respectively.We found that the concentrations of free VCA* and free NtA were

8.9 and 7.4 lM, respectively. Integrating the peaks at 9.2 S, wefound that the 0.7 lM VCA* cosedimented with 0.5 lM Arp2/3,making the molar ratio of these two proteins 1.4 to 1. The presenceof NtA has lowered the molar ratio, indicating that NtA effectivelycompetes for at least one of the VCA*-binding sites on Arp2/3. Thesmaller sedimentation coefficient of the presumed Arp2/3/VCA*/NtA complex compared with the Arp2/3/VCA* complex is in keep-ing with its expected smaller size. In Fig. 10, we show the full re-sults of the complete titration experiment. We found that evenwith a large molar excess of NtA over Arp2/3 (46:1), the molar ratioof VCA*/Arp2/3 was still greater than 1. This result suggests thatNtA competes with VCA* for only one of the two VCA*-binding siteson Arp2/3.

Discussion

In all three of the experimental systems explored in this article,MSSV has proven to be a useful method for the determination ofthe stoichiometry of proteins that cosediment as a complex in anSV experiment. In two of these cases (hE3/XDD1 and rTp34/hLF),the stoichiometry established here comports with that measuredwith another biophysical method, ITC, which is known for its

Fig. 10. NtA titration. The x axis shows the total [NtA] calculated from the fittingsession in SEDPHAT. The y axis shows the ratio of VCA* to Arp2/3 in thecosedimenting complex.


ability to determine the stoichiometries of protein–proteinassociations [32].

In general, the MSSV method demands that at least as manysignals be collected as there are proteins in the complex understudy. The analyses presented above illustrated two interestingdepartures from this rule. First, the Zn–rTp34/Zn–hLF interactionwas studied with one more signal than was thought to be neces-sary. The inclusion of three signals (IF, A280, and A250) in the anal-ysis afforded spectral resolution, whereas an analysis with justtwo of those signals (IF and A280) failed (Figs. 6 and 7). Furtheranalyses (not shown) demonstrate that two signals, IF and A250,would have sufficed. As may be deduced from Tables 1 and 3,the IF/A250 extinction ratios for the two proteins are significantlydifferent. Most of the spectral discrimination, then, came from thedifference in these ratios. However, the inclusion of the A280 datalikely added to the hydrodynamic resolution of the experimentbecause exclusion of these data would have introduced time gapswhere no information on the sedimentation of the several specieswas available. Obviously, if it were known beforehand that theA280 signal would not contribute to the spectral discrimination,the optimal data collection strategy would be to collect only IFand A250 signals.

The other exception to the ‘‘one signal per component” rule wasin the VCA*/NtA/Arp2/3 study (Fig. 9). It is important to note thatthis method succeeded only because the molar mass of NtA wasa small fraction of that of Arp2/3 and also because only the stoichi-ometry of VCA* and Arp2/3 was monitored. These two conditionsmust be met before attempting an experiment of this type.

In principle, the MSSV experiment and analysis could accom-modate more than the two-protein analyses described above. Gi-ven the current capabilities of the Beckman XL-I analyticalultracentrifuge, there is the possibility of spectrally distinguishingfour cosedimenting components. One of the signals in such anexperiment is necessarily IF. It is possible that the UV absorbanceof proteins would provide the second and third signals (A280 andA250). For most proteins, there is no other convenient peak of UVabsorbance; the peptide chain absorbs too strongly in the far UVto be of general use. Consequently, a visible wavelength would berequired for a four-signal experiment. Some proteins containcoenzymes that have peaks in the visible region of the spectrum,but most do not. Therefore, labeling at least one protein with achromophore, as was accomplished for VCA in our example,would be required. Importantly, the choices of chromophoreand of the position at which to modify the protein are not trivial.If IF is to be used, the chromophore should not absorb the lightemitted by that optical system’s laser. Its signal increment shouldprovide sufficient signal to noise yet should not overwhelm thecapabilities of the on-board spectrophotometer (see above). Fur-

thermore, the site of modification obviously should be distal fromthe protein’s interaction surface. Our choice of Alexa 488 cova-lently attached to VCA at its amino terminus met all of thesecriteria.

Of course, there is no reason why only protein–protein interac-tions can be studied. Any interacting molecule with a measurablesignal could be studied. Protein–nucleic acid interactions seemparticularly well suited to the method because these macromole-cules have distinctive UV absorption signatures. The study of car-bohydrates (e.g., in a protein–carbohydrate interaction), shouldbe amenable so long as the size of the carbohydrate and the signalincrements of the carbohydrate are known. In such a case, anexperiment analogous to those of le Maire, Salvay, and coworkerscould be performed [33,34]. These researchers were concernedwith the amount of detergent bound to their protein, but the sameprinciple holds for protein–carbohydrate interactions.

Previously, other authors have used sedimentation equilibrium(SE) or multisignal SE (MSSE) to establish the stoichiometry ofprotein–protein or protein–nucleic acid interactions [35–39].Two approaches are commonly employed. In the SE approach,several SE experiments are performed with different ratios ofthe interacting components. In this approach, it is helpful if oneof the components dominates the data at one of the signals[37,38]. The radial concentration profiles in the centrifugationcells are monitored using a signal that is dominated by one ofthe components. The several experiments are analyzed individu-ally, and a signal average buoyant molar mass is derived for eachone. A plot of this mass versus the component ratio should reacha plateau at the buoyant molar mass of the maximal complex.This mass should coincide with the theoretical buoyant molarmass of a complex of a certain stoichiometry, thereby establishingthat quantity (e.g., see Ucci and Cole [38]). In MSSE, a stoichiom-etry is assumed and the data are fit to this experimental model.The goodness of the fit is taken as confirmation of the stoichiom-etry [35,36,39]. Often in such analyses, other information aboutthe associating proteins is known. This information may be builtinto the analysis; for example, the buoyant molar masses of thecomponents may be known, or the number of components andtheir approximate buoyant molar mass may be known from anSV experiment. MSSV represents a complementary approach tothe problem with distinct advantages. First, an SE experimentgenerally takes days to perform, whereas MSSV can be done inhours (overnight). Second, SE and MSSE do not give the experi-menter information regarding the hydrodynamic properties ofthe complex (scomplex and fr), whereas MSSV does. Third, the databasis of the MSSV experiment is significantly larger than SE orMSSE and so may lead to better spectral resolution of species[1]. Fourth, SE data analysis requires that an interaction modelbe imposed, whereas MSSV is model free in that regard. It shouldbe noted that short-column SE experiments may be performed inhours [37], mitigating the first point above, at the expense ofmaking the data basis of those experiments smaller. Therefore,SE, MSSE, or MSSV may be used to determine stoichiometry; forquick and accurate determination of stoichiometry only, a singleMSSV experiment should suffice.

As pointed out by Balbo and coworkers [1], MSSV is best suitedto experimental systems that have a slow koff relative to the timetaken to perform an SV experiment (koff < 10�3 s�1). By simulatingdata for fast interactions, these authors found that they may becharacterized by MSSV but that one of the components must bepresent at a large molar excess over the other. For the hE3/XDD1and Zn–rTp34/Zn–hLF systems, the koff values are likely to be slow;they do not dissociate when subjected to size exclusion chroma-tography (not shown). Furthermore, the molar excesses used inthese experiments ensure a high degree of occupation of the com-plex. The koff of the VCA/Arp2/3 [9] interaction is fast by the above


criterion, but the presence of large molar excesses of this proteinensures full occupation in our experiments.

In conclusion, MSSV has proved to be a dependable method todetermine the stoichiometry of proteins in a hetero-associatingcomplex. In addition to the experiments presented above, severalother groups (see, e.g., Refs. [1,40–43]) have successfully used thistechnique. The multisignal approach has also been used to charac-terize protein/detergent complexes [34]. MSSV adds a new tool tothose tools already available to the biophysicist to answer one ofthe fundamental questions that arises from studying protein–pro-tein interactions in detail, and it should be applicable to a widevariety of experimental systems.

Acknowledgments

Portions of this research were supported by National Institutesof Health (NIH) Grants R01-AI056305 (to M.V.N.), R01-GM056322(to M.K.R.), R01-DK026758 (to D.T.C.), R01-DK062306 (to D.T.C.),and F32-GM06917902 (to S.B.P.). Also, support was received fromWelch Grants I-0940 (to M.V.N.), I-1544 (to M.K.R.), and I-1286(to D.T.C.).

Appendix A. Supplementary data

Supplementary data associated with this article can be found, inthe online version, at doi:10.1016/j.ab.2010.07.017.

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