Analytical Biochemistry 381 (2008) 254–257

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Analytical Biochemistry

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Automated measurement of the static light scattering of macromolecularsolutions over a broad range of concentrations

Cristina Fernández, Allen P. Minton *

Section on Physical Biochemistry, Laboratory of Biochemistry and Genetics, National Institute of Diabetes and Digestive and Kidney Diseases,National Institutes of Health, US Department of Health and Human Services, Building 8, Room 226, NIH Bethesda, MD 20892, USA

a r t i c l e i n f o

Article history:Received 3 June 2008Available online 27 June 2008

Keywords:Rayleigh scatteringNonideal solutionsConcentrated protein solutionsBovine serum albuminOvalbuminOvomucoid

0003-2697/$ - see front matter Published by Elsevierdoi:10.1016/j.ab.2008.06.032

* Corresponding author. Fax: +1 301 402 0240.E-mail address: minton@helix.nih.gov (A.P. Minton

a b s t r a c t

A method and apparatus for automated measurement of the concentration dependence of static lightscattering of protein solutions over a broad range of concentrations is described. The gradient of proteinconcentrations is created by successive dilutions of an initially concentrated solution contained withinthe scattering measurement cell, which is maintained at constant total volume. The method is validatedby measurement of the concentration dependence of light scattering of bovine serum albumin, ovalbu-min, and ovomucoid at concentrations up to 130 g/L. The experimentally obtained concentration depen-dence of scattering obtained from all three proteins is quantitatively consistent with the assumption thatno significant self-association occurs over the measured range of concentrations.

Published by Elsevier Inc.

Characterization of protein interactions in concentrated solution(>�30 g/L) is complicated by significant contributions from weaknonspecific protein–protein interactions that lead to significantdeviations from thermodynamic ideality [1–3]. Conventional analy-ses of the concentration dependence of colligative properties of pro-tein solution—osmotic pressure, sedimentation equilibrium, andstatic light scattering—have been limited to first-order deviationsfrom thermodynamic ideality or so-called second viral coefficientcorrections [4]. However, such corrections cannot account quantita-tively for the behavior of solutions at concentrations exceedingapproximately 50 g/L [5,6]. A semiempirical treatment of nonidealbehavior referred to as the effective hard particle model [1,7] hasproven to be useful in accounting quantitatively for the concentra-tion dependence of all three colligative properties of protein solu-tions at concentrations up to several hundred grams per liter [5,8].

Although the measurement and analysis of static light scatter-ing of protein solutions has long been a standard method for char-acterization of the molar mass and self-association of proteins [9],studies of the light scattering of highly concentrated protein solu-tions [10,11] are quite rare due to technical difficulties associatedwith sample preparation, conventional techniques of batch mea-surement, and limitation of conventional analyses to treatmentof first-order deviations from thermodynamic ideality. We recentlypresented an extension of multicomponent light scattering theorythat is applicable in principle to solutions of multiple species ofproteins at arbitrary concentration, taking into account both

Inc.

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attractive interactions leading to self- and/or hetero-associationand nonspecific repulsive interactions leading to thermodynami-cally nonideal behavior [5]. To test the applicability of this theoryto real solutions of real proteins, we have developed a novel meth-od for automatically and rapidly performing a measurement of theconcentration dependence of light scattering over an extremelybroad range of concentrations. The purpose of the current articleis to describe this method in detail and to validate it by means ofmeasurements performed on single nonassociating proteins whoseproperties are documented in the literature. A second manuscript,currently in preparation, will present results and analysis of dataobtained from more complex solutions containing protein mix-tures and self-associating protein.

Materials and methods

Materials

Monomeric bovine serum albumin (BSA)1 was obtained fromSigma–Aldrich (cat. no. A1900, St. Louis, MO, USA). Ovalbumin fromegg white and ovomucoid were obtained from Worthington Bio-chemical (cat. nos. LS003048 and LS003087, respectively, Lakewood,NJ, USA). Before use, proteins were dialyzed against phosphate buffer(0.05 M phosphate and 0.15 M NaCl at pH 7.2). Dialysis for bufferexchange was performed against excess solvent overnight using10,000-MWCO (molecular weight cutoff) Slide-A-Lyzer Dialysis

1 Abbreviations used: BSA, bovine serum albumin; MWCO, molecular weight cutoff;NMWL, nominal molecular weight limit; w/v, weight/volume.

Automated measurement of static light scattering / C. Fernández, A.P. Minton / Anal. Biochem. 381 (2008) 254–257 255

cassettes from Pierce (Rockford, IL, USA). To prepare concentratedprotein solutions, proteins were dissolved at low concentrations(<30 g/L), dialyzed, and then concentrated using Centricon filter de-vices (Ultracel YM-10 membrane, 10,000 NMWL [nominal molecularweight limit], Millipore, Billerica, MA, USA) up to different final con-centrations determined from the absorbance at 280 nm using thefollowing values of A (280 nm, 1 g/L): BSA, 0.65; ovalbumin, 0.75;and ovomucoid, 0.41 [12]. Buffer and protein were prefilteredthrough 0.02-lm Whatman Anotop filters. Immediately prior tomeasurement of light scattering, protein solutions were centrifugedat 80,000g for 30 min to remove residual particulates and micro-scopic bubbles and then were transferred via pipette to the lightscattering cuvette described below.

Methods

A Wyatt MiniDAWN Tristar light scattering detector from WyattTechnology (Santa Barbara, CA, USA) was modified as follows. AVariomag Mini cuvette stirrer (Variomag-USA, Daytona Beach, FL,USA) was mounted in the base of the MinDAWN read head andconnected to a Variomag Mini 20 P controller. Wratten neutraldensity filters of the appropriate optical density (typically 1 or1.5 OD) were placed over the photodiode scattering detectors toattenuate light scattered from highly concentrated protein solu-tion, and the instrument was recalibrated using a freshly prepareddilute solution of monomeric BSA (MW 70,000). The light scatter-ing flow cell provided as standard equipment with the MiniDAWNdetector was replaced by a square cuvette holder, supplied as partof the Wyatt Micro-batch accessory. A square fluorescence cuvette(internal cross section 10 � 10 mm) containing 2 ml of a proteinsolution of predetermined concentration and an 8-mm-long mag-netic stirring bar is inserted into the cuvette holder. The cuvetteis connected to a liquid handling system, shown schematically inFig. 1, consisting of a Microlab 541C syringe pump (Hamilton,Reno, NV, USA) with dual 1000-ll syringes under computer con-trol. The cuvette is then stoppered with a Teflon cap containingtwo 21-gauge stainless-steel tubes, for the addition of buffer andthe removal of solution, and an opening for an IT-18 thermocoupleprobe (Physitemp Instruments, Clifton, NJ, USA).

SYRINGE A S

BUFFER INLINEFILTER

Fig. 1. Schematic diagram of the

An automated concentration gradient experiment proceeds un-der computer control as follows. In step 1, the magnetic stirrer isturned on, and a volume of filtered buffer calculated to dilute thesolution by a user-selected fraction is added to the solution usingthe left-hand syringe of the Hamilton pump. Added buffer passesthrough a Whatman Anotop 0.1-lm filter prior to entering the scat-tering cell. After mixing is complete (typically within a few seconds),the stirrer is turned off. In step 2, the 90� scattering intensity is readfor a period of time sufficient to obtain a precise average value, typ-ically 3 to 4 min. In step 3, a volume of solution identical to thatadded in step 1 is removed using the right-hand syringe of the Ham-ilton pump to restore the initial volume of fluid in the cuvette. Steps 1through 3 are repeated until near baseline levels of scattering are ob-tained. The cuvette is then automatically rinsed several times withlarge volumes of buffer, and the baseline scattering intensity is mea-sured precisely. A typical dilution run requires approximately 1 h. InFig. 2, the relative intensity of 690-nm light scattered at 90� recordedin a typical experiment is plotted as function of time.

Because the Wyatt MiniDAWN detector is not equipped withtemperature control, the temperature of solution in the cuvette ismeasured continuously by means of the aforementioned thermo-couple probe connected to a Physitemp BAT-12 thermocouplethermometer. Scattering and temperature data are recorded to-gether using Wyatt ASTRA software (version 4.9.08), and it is ver-ified that the temperature remains essentially constant (26 ± 1 �C)throughout the dilution experiment. Although the temperature ofthe unstirred solution rises slowly under the influence of laser illu-mination, it is restored to near room temperature on dilution andmixing with buffer.

As described previously [13], excess scattering intensity is con-verted to values of the Rayleigh ratio R normalized to units of theoptical constant Ko, given by [5]

Ko ¼4p2~n2

0ðd~n=dwÞ2

k40NA

; ð1Þ

where ñ denotes the refractive index of solution and ño denotesthat of solvent, w denotes the weight/volume (w/v) concentrationof scattering solute, ko denotes the wavelength in vacuum of

YRINGE B

SOLUTIONCOLLECTION

THERMOCOUPLETHERMOMETER

automated dilution system.

Fig. 2. Light scattering (90�, 690 nm) of a solution of BSA (initial concentration 118 g/L), plotted as a function of elapsed time through a dilution gradient. Each stepcorresponds to a 20% reduction in protein concentration. The dashed line represents the baseline. RU, relative units.

0 50 100 1500

500

1000

1500

2000

w (g/L)

R/K

o

BSA

OVALBUMIN

OVOMUCOID

Fig. 3. Experimentally obtained values of normalized scattering intensity (R/Ko)plotted as a function of protein w/v concentration w. Different symbol types representexperiments starting at different initial concentrations. The solid curves werecalculated according to Eqs. (2)–(5) with the following best fit parameter values: BSA,M = 68,700 ± 1600, veff = 1.81 ± 0.06 cm3/g; ovalbumin, M = 45,500 ± 1000,veff = 1.68 ± 0.05 cm3/g; ovomucoid, M = 28,100 ± 800, veff = 1.65 ± 0.07 cm3/g. Indi-cated uncertainties correspond to ±1 standard error of estimate.

3 We note that veff is defined as equal to the specific volume of a hard sphericalparticle whose interparticle interactions best mimic those of the actual protein under

256 Automated measurement of static light scattering / C. Fernández, A.P. Minton / Anal. Biochem. 381 (2008) 254–257

scattered light (690 nm in the current experiments), and NA de-notes Avogadro’s number. The value of dñ/dw is taken as0.185 cm3/g for all three proteins [14]. The protein concentrationat each dilution step is calculated from the prior concentration(or initial concentration) and current dilution factor. Because thedetermination of concentration calculated in this fashion is subjectto compound error with increasing number of dilution steps, wehave verified the accuracy of our calculated concentration in twoways. First, the concentration is checked by spectrophotometricmeasurement of protein concentration after a large number ofdilution steps. Second, the scattering of a protein solution of spec-trophotometrically determined concentration is compared withthat of a solution whose nominally near identical concentrationis calculated following a substantial number of dilution steps(�10). Raw data are processed using user-written scripts done inMATLAB (MathWorks, Natick, MA, USA) to create secondary datasets consisting of tables of the Rayleigh ratio normalized to theoptical constant Ko as a function of protein concentration.2

Results

The concentration dependence of light scattering of three pro-teins—BSA, ovalbumin, and ovomucoid—at concentrations up toapproximately 130 g/L is plotted in Fig. 3. The concentrationdependence for each protein was measured several times, startingat different loading concentrations. Each measurement is plottedwith a different symbol type. The superimposability of these multi-ple determinations is a measure of the accuracy with which we cancalculate the concentration of a sample after multiple dilutionsteps. We have fitted to the data for each protein to the followingrelation for the concentration dependence of light scattering of asingle nonassociating species at arbitrary concentration [5]:

RKo¼

~n~n0

� �2 Mw

1þw dIncdw

ð2Þ

where M denotes the molar mass and c denotes the thermodynamicactivity coefficient of the scattering solute. The dependence of solu-tion refractive index on protein concentration is given by [15]

~n ¼ ~n0 þd~ndw

w ð3Þ

The concentration dependence of the logarithm of the activitycoefficient is obtained by modeling the protein molecule as aneffective hard spherical particle [7]:

2 Scripts are available on request.

wdIncdw¼ 8/þ 30/2 þ 73:4/3 þ 141:2/4 þ 238:5/5 þ � � � ð4Þ

where / denotes the fraction of volume occupied by protein, givenby

/ ¼ meff w; ð5Þ

and veff denotes the specific volume of the effective hard sphericalparticle.3 The infinite power series indicated in Eq. (4) is truncatedafter five terms because test calculations indicated convergence overthe measured range of concentrations. According to this model, thecontribution of repulsive nonideal interactions to the light scatteringat all protein concentrations is determined by the value of the singleparameter veff [16]. The best fit of Eqs. (1)–(5) to each of the proteindata sets is plotted together with the data in Fig. 3, and the valuesand uncertainties of the best fit values of M and veff for each proteinare given in the figure caption.

a particular set of experimental conditions. When protein molecules interact viarepulsive electrostatic interactions, the effective hard particle appears to be largerthan the actual molecule [1,7,16].

Automated measurement of static light scattering / C. Fernández, A.P. Minton / Anal. Biochem. 381 (2008) 254–257 257

Discussion

We have introduced an experimental method for automaticallyand rapidly performing a measurement of the concentrationdependence of light scattering over a wide range of concentrations.This method allows the maximum amount of information to be ex-tracted from the concentration dependence of light scattering dueto the acquisition of data at equal logarithmic increments of con-centration, so that data obtained at both very low and very highconcentrations receive equal statistical weight [5].

The method has been validated by measuring the concentrationdependence of three proteins: BSA, ovalbumin, and ovomucoid. Itwas shown that the concentration dependence of each may be ac-counted for quantitatively over a wide concentration range by asimple model, according to which each protein molecule interactswith other protein molecules only via short-range repulsive inter-actions that may be approximated as hard particle interactions anddoes not self-associate to any significant extent over the concen-tration range examined. Molecular weights obtained for all threeproteins agree well with literature values [4,17].

Our finding that the concentration dependence of scattering forBSA at high concentrations may be accounted for by an effectivehard sphere model without significant self-association at concen-trations below 100 g/L agrees well with the results of earlier mea-surements of the light scattering, osmotic pressure, andsedimentation equilibrium of concentrated BSA solutions [18].Our finding that the concentration dependence of the scatteringof ovalbumin may be accounted for by an effective hard spheremodel without significant self-association at concentrations below130 g/L agrees with a previous interpretation of the concentrationdependence of osmotic pressure [19]. However, an earlier mea-surement of sedimentation equilibrium of concentrated ovalbumin[20] was interpreted as evidence of equilibrium monomer–trimeror monomer–dimer–tetramer self-association. The automateddilution system developed here provides a significant improve-ment in the experimental precision of measurement over a widerange of concentrations, especially at high concentrations. At-tempts to fit our data to a nonideal monomer–trimer or mono-mer–dimer–tetramer model [5] were unsuccessful. Hence, theorigin of the discrepancy between light scattering and sedimenta-tion equilibrium results remains unresolved. We are unaware ofprevious characterizations of the colligative properties of ovomu-coid at high concentrations, although it has been used as an ‘‘inert”cosolute at high concentrations to study the quantitative effect ofmacromolecular crowding on protein aggregation [21].

Analytical methods that are used to characterize proteins insolution generally require dilution to solvent conditions that arevery different from those in which the protein functions in vivo[2,3] or in a biopharmaceutical formulation [22]. In contrast, theapparatus and experimental technique introduced here provide arelatively inexpensive and moderately high-throughput tool forprecise quantitative characterization of the state of association ofproteins in solution at all concentrations up to the solubility limit.In a future manuscript, we will describe how data derived frommeasurements like those described here may be used to detectand quantitatively characterize weak equilibrium self-associationsin a highly nonideal solution.

The new method presented here may be compared with thebest current automated method for measuring the concentrationdependence of light scattering in solutions of proteins and othermacromolecules, where a stock protein solution is automaticallymixed with buffer in varying ratios prior to introduction to lightscattering and concentration detection flow cells [13,23,24]. Themethod presented here is easier to implement for very concen-trated protein solutions because no transport of concentrated solu-

tion through narrow bore tubing or filters is required. Moreover, noseparate concentration flow detector is needed because the proteinsolution being measured remains in the measurement cellthroughout and the extent of dilution is determined precisely bythe high-resolution stepping motor-controlled syringe pumps.

Acknowledgments

We thank Peter McPhie (National Institutes of Health) for help-ful comments on a draft. This work was supported by the Intramu-ral Research Program of the National Institute of Diabetes andDigestive and Kidney Diseases.

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