Buffer Dependence ofRefractive Index Incrementsof Protein Solutions

Vincent Ball1,2

Jeremy J. Ramsden2

1 Laboratoire deSpectrometrie

de masse bio-organique,1 rue Blaise Pascal,

67008 Strasbourg, France

2 Department ofBiophysical Chemistry,

Biocentre of the University,Klingelbergstrasse 70,

4056 Basel, Switzerland

Received 21 November 1997;accepted 6 July 1998

Abstract: The refractive index increment of a protein solution is a property not only of the protein,but also of the solvent. This is demonstrated theoretically and confirmed experimentally usinganalytical interferometry. © 1998 John Wiley & Sons, Inc. Biopoly 46: 489–492, 1998

Keywords: refractive index increment; proteins; solvent

INTRODUCTION

The refractive index increment is an essential param-eter when one wishes to evaluate quantitatively thesurface concentrations of adsorbed biopolymers as inexperiments aimed at understanding the fundamentalsof the adsorption mechanism,1 or optimizing or re-ducing adsorption with respect to a desired applica-tion (e.g., biomaterials). When assuming the forma-tion of a homogeneous and isotropic adlayer of con-centration cA within a layer of thicknessdA, thesurface concentration of the adsorbed biopolymer canbe obtained from the definition of the Gibbs surfaceexcess (assumingcA @ cB, the concentration in thebulk) according to

G 5 cA dA (1)

Usually, optical measurements such as ellipsom-etry or optical waveguide lightmode spectroscopy al-low both the thickness and the refractive indexnA ofthe adsorbate to be measured.2 The latter is propor-tional to cA:

nA 5 nC 1 ~dn/dc!cA (2)

wherenC is the refractive index of the buffer solution(C denotes the cover medium) at a given wavelengthand dn/dc is the refractive index increment of theadsorbate. Equation (1) then becomes

G 5~nA 2 nC!dA

dn/dc(3)

Hence an exact knowledge of dn/dc is necessary inorder to precisely quantify the surface concentration

Correspondence to:Jeremy J. RamsdenContract grant sponsor: Ciba-Geigy-Jubila¨ums-Stiftung

Biopolymers, Vol. 46, 489–492 (1998)© 1998 John Wiley & Sons, Inc. CCC 0006-3525/98/070489-04

489

of the adsorbate from the measured optical parame-ters. For proteins, many dn/dc values have been tab-ulated3 and show a wavelength dependence as ex-pected from the dispersion laws. Looking at thesedata, one has the impression that there is also somesolvent dependence even in the absence of any sys-tematic investigation. Some buffer dependence hasbeen observed for albumins in aqueous solutions con-taining sodium salts (chloride, phosphate, barbiturate)by means of a differential prism method at a wave-length of 578 nm.4

Most protein adsorption experiments reported re-cently have been carried out using the He-Ne laserline at 632.8 nm, and most researchers in the field usea dn/dc value of 0.186 0.03 cm3/g, regardless of theidentity of the protein and the actual electrolyte orbuffer ions in the solution. Yet this value was ob-tained in white light, using an Abbe´ refractometer,and for just a few proteins, including the popular henegg white lysozyme, dissolved in water.5 More re-cently, Jian et al. found values around 0.17 cm3/g at awavelength of 632.8 nm for serum albumin and im-munoglobulin G dissolved in phosphate buffered sa-line.6

It is the aim of this paper to demonstrate, both froma theoretical and an experimental point of view, thatthe value of the refractive index increment of a givenprotein is, in fact, buffer dependent.

THEORETICAL SECTION

Assuming that an aqueous solution contains a volu-metric fractionu of protein, then if the solution isnearly ideal one can write

nsol 5 npu 1 nC~1 2 u! (4)

where np is the refractive index of the dehydratedprotein andnsol that of the whole solution. The valueof u is related to the protein concentrationcA and thepartial specific volumev# of the protein according to

cA 5 u/v# (5)

Then, combining Eqs. (2), (4), and (5) yields

dn/dc 5 ~np 2 nC!v# (6)

In general, one sees from equation (6) that the proteinrefractive index increment should be buffer depen-

dent. For a solution in whichnC 5 nP, dn/dc equalszero.

EXPERIMENTAL

To investigate the buffer dependence, we measured therefractive indexes of hen egg white lysozyme (HEL) solu-tions (Sigma, L-6876, lot 65-H 7025, used without furtherpurification) at a wavelength of 632.8 nm. All solutionswere prepared in Nanopure water (Barnstead, resistivity. 17.8 MV cm) and using analytical grade salts (Merck orFluka). The pH of the 10 mM HEPES buffer (pKa 5 7.5)was adjusted with 1M NaOH and the 1:1 electrolyte con-centration was also 10 mM. In the case of 10 mM NH4HCO3

solutions, the pH was just brought to 8.0 with NaOH and noother electrolyte was added. The HEL concentration wasdetermined both by weighing, taking into account the per-centage of almost pure protein in the lyophilized powder,7

and by absorbance measurements at 280 nm (Uvikon 860,Kontron Instruments) using an extinction coefficient of 2.6cm2/mg. For all solutions investigated, the differences inconcentration values between the two methods never ex-ceeded 3%* Immediately after preparation the solutionswere diluted, their concentration measured by uv spectros-copy, and their refractive index measured with an LI3 (CarlZeiss) Rayleigh interferometer,9 calibrated at a wavelengthof 632.8 nm, using Nanopure water as the reference me-dium. During a measurement, the temperature of the solu-tions was kept within60.05°C. The refractive index ofwater was corrected for its temperature variation using theinterpolation formula of Tilton and Taylor.10 All the exper-imental data were collected within the temperature range22–24°C.

RESULTS AND DISCUSSION

The measured refractive indices (Figure 1) are a linearfunction of the protein concentration as expected fromEq. (2) and the slopes of the straight lines are equal tothe refractive index increment of HEL in each givenenvironment. From Table I one clearly sees that in thepresence of Nanopure water, NH4HCO3 and NaSCN,the dn/dc values differ significantly from the 0.186cm3/g given by de Fejter et al. for HEL in pure waterand using white light,5 although this “universal” valuedoes hold for the NaCl, NaNO2, NaCH3COO, andN(CH3)4Cl solutions. Table I also shows that thedifferences between the HEPES buffer without addi-tional salt and HEPES plus NaCl (at 10 and 100 mM)are insignificant.

* Changes in the physicochemical parameters of the solutionare able to change the value of the extinction coefficient, as exem-plified in the case of bovine fibrinogen.8

490 Ball and Ramsden

Equation (6) implies that dn/dc is expected to varyupon changing the nature of the ions or their concen-tration, but the lack of correlation between dn/dc andnC in this range of salt concentrations (see Table I forthe case of NaCl) implies changes innP or v# due to theenvironment of the protein. However, the partial spe-cific volume of proteins remains essentially un-changed upon folding or unfolding at low pressuredue to a cancellation of opposite effects: a reductionof the volume of aliphatic and aromatic side chains isbalanced by a volume increase for polar and charged

side chains upon folding.11 Moreover, NaSCN andNH4HCO3, which display the most significant devia-tions from the expected value of 0.186 cm3/g, areknown to be destabilizing (salting in) and stabilizing(salting out), respectively.12 At present, we have noclear explanation for this surprising behavior. But ifthe different dissolved salts do not then affectv# , butmerely change the anions around the positivelycharged protein, we suspect the dn/dc variations to becorrelated with changes in the refractive index of theprotein [nP in Equation (6)]. The molar refractivity ofthe positively charged amino groups in the protein,and thus their index of refraction, could be charged bythe presence of these counterions characterized bydifferent polarizabilities. Measurements of dn/dc indifferent water/water soluble solvent mixtures shouldyield important information in this respect, since sig-nificant solvent-dependent perturbations in the sec-ondary and/or tertiary structure of the protein areexpected to occur.13,14

CONCLUSIONS

These results emphasize the need to measure therefractive index increment of the protein one wishesto adsorb in order to calculate true surface concentra-tions using Eq. (2). However, this is not always pos-sible with some biological samples that can be verydifficult to purify and hence are only available insubmicrogram quantities. The present example ofHEL illustrates that one should bear in mind thatoptical measurements yield only relative surface con-centrations when the dn/dc value is not preciselyestablished.

FIGURE 1 Refractive index increments of protein solu-tions in different aqueous solutions, measured at a wave-length of 632.8 nm. The dotted lines represent the limits ofthe 95% confidence interval.Dn is defined asnprotein solution

2 nwater. E: HEPES (10 mM) 1 NaSCN (10 mM); ■:NH4HCO3 (10 mM); ‚: HEPES (10 mM) 1 NaCl (10 mM);}: H2O (Nanopure).

Table I Values of dn/dc for HEL in Different Aqueous Solutions

Solution Conditions pH Dnc/1026 adn/dc

(60.002)bLinear Correlation

Coefficientc

H2O ; 6 0 0.153 0.978NH4HCO3 10 mM 8.0 906 10 0.260 0.995NaSCN 10 mM HEPES 10 mM 7.4 5406 8 0.272 0.986NaCl 10 mM HEPES 10 mM 7.4 4786 4 0.188 0.992NaCl 100 mM HEPES 10 mM 7.4 14706 10 0.186 0.998NaNO2 10 mM HEPES 10 mM 7.4 4566 8 0.186 0.981NaCH3COO 10 mM HEPES 10 mM 7.3 4976 5 0.184 0.998N(CH3)4Cl 10 mM HEPES 10 mM 7.4 5986 8 0.188 0.994

a Dnc is defined asnpure buffer2 nwater and represents the values of they axis intercept of the straight lines in Figure 1.b Obtained from the slope of straight lines like those in Figure 1. Units are cm3/g.c Linear correlation coefficient obtained from least squares analysis of the data.

Refractive Index Increments 491

We thank the Ciba-Geigy-Jubila¨ums-Stiftung for financialsupport, and E. K. Mann for some encouraging and illumi-nating remarks.

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