Effect of Nonadditive Repulsive Intermolecular Interactions on the

ARTICLE pubs.acs.org/JPCB

Effect of Nonadditive Repulsive Intermolecular Interactions on the Light Scattering of Concentrated Protein-Osmolyte Mixtures Cristina Fern
andez and 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, U.S. Department of Health and Human Services, Bethesda, Maryland 20892 ABSTRACT: The static light scattering of three globular proteins, bovine serum albumin, ovalbumin, and ovomucoid, and binary mixtures of each protein and trimethylamine oxide (TMAO) containing between 10 and 70% protein, were measured as a function of total weight per volume concentration up to 100 g/L. The observed dependence of scattering upon concentration may be accounted for quantitatively by an effective hard sphere model incorporating an extension that takes into account the nonadditive nature of the repulsive intermolecular interaction between protein and TMAO.

’ INTRODUCTION The effects of a class of small organic compounds termed “osmolytes” upon the structure and stability of proteins has been the subject of intensive study because of the physiological significance of those effects. One of the most strongly stabilizing osmolytes is trimethylamine N-oxide (TMAO), (CH3)3NO, which is accumulated at high concentration by marine organisms to protect proteins under stress conditions and to regulate cell volume.1 In the pH range 6-8 the molecule is almost uncharged.2 TMAO has been referred to as a “chemical chaperone” because of its ability to maintain enzyme structure and function under otherwise denaturing conditions.3 It has been proposed that the stabilizing effect of TMAO is due to preferential exclusion of the osmolyte from the immediate vicinity of the protein backbone, thus destabilizing unfolded conformations of a protein relative to the compact native state.4,5 The concentration dependence of the static light scattering and other colligative properties of solutions of each of several proteins has been shown to be quantitatively accounted for over a broad range of concentration (up to ca. 100 g/L) by a simple semiempirical model, according to which each protein is treated as a hard convex particle, the dimensions of which reflect the magnitude of intermolecular interactions resulting from a combination of “hard” steric repulsion and “soft” electrostatic repulsion.6-10 More recently, it has been shown that the osmotic pressure and static light scattering of solution mixtures of similarly charged proteins at very high concentration can be quantitatively described by the same model.11,12 However, it is questionable whether an effective hard particle model can describe the behavior of mixtures of solutes in which self-interaction and heterointeraction are not additive or approximately additive, such as mixtures of charged and uncharged solutes.7,8 The present study was carried out to investigate the properties of nonadditive mixtures at high concentration and to determine whether the effective hard particle r 2010 American Chemical Society

model or some modification thereof can provide a useful description of these properties. We have measured the concentration-dependent static light scattering for mixtures of charged protein molecules and a nearly neutral osmolyte (TMAO) at total weight per volume concentrations of up to 100 g/L. The experimental data were obtained using the recently developed method of automated sequential dilution for measuring the concentration dependence of the static light scattering of protein solutions at high concentration.6 A simple extension of the effective hard particle model is proposed to account for the experimental results obtained, according to which the size of the effective hard sphere representing protein depends on the composition of the mixture.

’ MATERIALS AND EXPERIMENTAL METHODS Materials. Trimethylamine N-oxide (TMAO) and monomeric bovine serum albumin (BSA) A1900, batch 127K7406, were obtained from Sigma-Aldrich (St. Louis, MO). Albumin (chicken egg white) and ovomucoid (trypsin inhibitor) were obtained from Worthington Biochemical Corporation (Lakewood, NJ) (LS003048 and LS003087, respectively). TMAO and proteins were used without additional purification. All proteins eluted from a size exclusion chromatography column (Superdex 200 10/300 GL, GE Healthcare) as a single peak corresponding to the monomer, except for BSA, which shows a small additional peak corresponding to the covalent dimer (∼3% of total protein). Before use, BSA, ovalbumin, and ovomucoid were dialyzed against phosphate buffer, 0.005 M phosphate, 0.15 M NaCl Received: October 27, 2010 Revised: December 2, 2010 Published: December 22, 2010 1289

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at pH 7.4. Dialysis for buffer exchange was performed against excess solvent overnight using Pierce 10000 MWCO Slide-ALyzer Dialysis cassettes (Thermo Scientific). When stock solutions of TMAO were prepared, the pH of the solution in buffer was adjusted to a final pH 7.4. Protein final concentrations were determined from the absorbance at 280 nm using the following standard values for absorbance in optical density units per centimeter path length for 1 g/L solution: BSA, 0.65;13 ovalbumin, 0.75;13 and ovomucoid, 0.446 (extinction coefficient was derived from ExPASY, accession no. P01005). The buffer, proteins, and TMAO were prefiltered through 0.02-μm Whatman Anotop filters (Whatman, Florham Park, NJ). Immediately prior to measurement of light scattering, protein and TMAO were mixed and centrifuged at 60000g for 20 min at 10 °C to remove residual particulates and microscopic bubbles. Refractive Increments of TMAO and Proteins. The specific refractive increment of TMAO was determined experimentally by differential refractometry at 589 nm, using an Arias 500 Abbe refractometer (Reichert Instruments, Buffalo, NY). A calibration curve of refractive index versus TMAO concentration was constructed; we measured four different TMAO concentrations in phosphate buffer at pH 7.4. The calibration curve gave a best fit value of d~n/dw = 0.148 ( 0.005 cm3/g at 589 nm. Using the relation of Perlmann and Longsworth,14 the specific refractive increment of TMAO at 690 nm, the wavelength of light utilized in the scattering experiments, was estimated to be 0.146 cm3/g. The refractive increment d~n/dw of all three proteins was taken to be equal to 0.185 cm3/g.15 Measurement of Concentration-Dependent Scattering of Mixtures. Measurements of concentration-dependent scattering

were carried out via automated sequential dilution as described previously.6 A MiniDAWN Tristar light scattering detector (Wyatt Technology, Santa Barbara, CA) was modified by the addition of a Variomag Mini cuvette stirrer (Variomag-USA, Daytona Beach, FL) mounted in the base of the MiniDAWN read head. The light scattering flow cell was replaced by a thermostated cuvette holder to keep the temperature constant during the experiment (25 ( 2 °C). Measurements are made in a square fluorescence cuvette containing 2.3 mL of solution. The gradient of protein concentration was created by sequential dilution of an initially highly concentrated solution. During each dilution step, after the addition of buffer, the sample was mixed with the buffer for 40 s using a 7 mm long magnetic stirring bar. Scattering data were collected in ASTRA (v4.9, Wyatt Technology, Santa Barbara, CA) and exported as text files for subsequent analysis using user-written scripts in MATLAB (R2009a, Mathworks, Natick, MA), available upon request from the authors. The raw scattering data were converted to composition-dependent values of the Rayleigh ratio for solute scattering at 90°.6 Calculation of Concentration-Dependent Static Light Scattering for Nonideal Mixtures of Protein and TMAO. The three proteins used in the present study were selected because we have shown previously that, under the conditions of these experiments, they do not self-associate to a significant extent over the range of concentrations studied.6 We shall assume that TMAO neither self-associates nor heteroassociates with protein over the range of compositions studied. We therefore employ formalism appropriate for two scattering species denoted by subscripts 1 (for protein) and 2 (for TMAO). According to multicomponent scattering theory16,17



 D ln γ2 D ln γ1 D ln γ1
2 G1 2 M1 2 c1 1 þ c2 þ G2 2 M2 2 c2 1 þ c1 - 2G1 G2 M1 M2 c1 c2 R ~n Dc2 Dc1 Dc2 ¼


2 K ~n0 D ln γ1 D ln γ2 D ln γ1 1 þ c1 1 þ c2 - c1 c2 Dc1 Dc2 Dc2 where R/K denotes the Rayleigh ratio in units of an optical constant calculated according to 4π2 ~n0 ½ðd~n=dwÞ2 λ0 4 N A 2

K ¼

ð2Þ

In eqs 1 and 2, ~n denotes the refractive index of solution, ~n0 denotes the refractive index of solvent, λ0 denotes the wavelength in vacuum of incident light, NA denotes Avogadro's number, and wi, ci, Mi, and γi denote respectively the weight/volume concentration, molar concentration, molar mass, and thermodynamic activity coefficient of species i . (d~n/dw)* denotes a “standard” specific refractive increment common to most proteins (0.185 cm3/g), and Gi  (d~n/dwi)/(d~n/dw)*. The refractive index of the solution is calculated according to18 ~n ¼ ~n0 þ

X d~n wi dwi i

ð3Þ

The concentration derivatives of the activity coefficients of the scattering species are evaluated using an extension of the effective hard particle model.9 According to this model each

ð1Þ

scattering species is represented by an equivalent hard convex particle, in the present instance a hard sphere. Given the molar mass Mi and radius reff,i of each species of equivalent sphere, or equivalently, the specific volumes veff,i of each species of sphere, where 4πNA ½reff , i ðÅÞ3 =Mi veff , i ðcm3 =gÞ ¼ 3  1024 ¼ 2:52½reff , i ðÅÞ3 =Mi the activity coefficients and concentration derivatives of the activity coefficients may be estimated via the scaled particle theory of hard particle mixture fluids19,20 using explicit relations for d ln γi/dcj provided in the appendix to ref 21. It has been demonstrated that the effective hard sphere model can account quantitatively for the composition-dependent scattering of binary mixtures of globular proteins with similar iso-ionic pH values at total protein concentrations of up to 100 g/L.12 In the present case, the assumption that effective hard sphere radii (or specific volumes) of each species are independent of composition is unrealistic, because at the pH of our experiments, all three proteins bear significant negative charge,22,23 while 1290

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TMAO is nearly neutral.2 The effective radius of the hard particle representing TMAO (r2) is presumed to be unaffected by electrostatic interactions and does not depend upon whether it is interacting with itself or with protein. The effective volume of the hard sphere representing a protein molecule as sensed by a second similarly charged protein molecule reflects a contribution from electrostatic repulsion between the two molecules in addition to steric exclusion, and is consequently larger than the hard core volume of the molecule.9,10,24 However, the effective volume of the hard sphere representing protein as sensed by a neutral TMAO molecule has little or no contribution from electrostatic interaction, and hence would be expected to be smaller.25 We denote the effective specific volume of the protein with respect to self-interaction by v(self) eff,1 and the effective specific volume with respect to interaction with TMAO by v(other) eff,1 . The question then arises, how may one calculate the compositiondependent activity coefficients and concentration derivatives of the activity coefficients of both species using hard particle fluid theory when the effective volume of protein is not constant? We propose an empirical approximation: ðself Þ

ðotherÞ

veff , 1  f1 veff , 1 þ ð1 - f1 Þveff , 1

ð4Þ

where f1 denotes the mass fraction of protein in the mixture. We know that this expression is correct in the limits f1 f 0 and f1 f 1,25 so the test will be to see if an effective hard particle model incorporating eq 4 can account for scattering of mixtures with intermediate compositions. This approximation requires only one parameter, v(other) eff,1 , in addition to those used in the previous model for scattering of additive protein mixtures.12

Figure 1. Concentration dependence of normalized scattering intensity for BSA and TMAO mixtures. Circles represent experimental data. Pure BSA, black; 70% BSA, blue; 50% BSA, red; 25% BSA, green; 10% BSA, magenta. The solid curve for BSA was calculated using the effective hard sphere model for a single species with best-fit parameter values of M1 and v(self) eff,1 given in Table 1. Solid curves for the mixtures were calculated using the effective hard sphere model for two species with a composition-dependent effective specific volume of protein, as described in the text. Dashed curves for the mixtures were calculated neglecting proteinTMAO interaction. Dotted curves for the mixtures were calculated neglecting nonadditivity of protein-TMAO interaction. The calculated scattering intensity of pure TMAO, plotted in cyan, is almost indistinguishable from zero on the scale of this figure.

’ RESULTS AND ANALYSIS The experimentally measured normalized scattering intensity of solutions containing mixtures of each of three proteins (BSA, ovalbumin, and ovomucoid) and TMAO in varying proportion are plotted in Figures 1, 2, and 3. The data were analyzed as follows. For the case of a single species of hard sphere, eq 1 reduces to6
2 R ~n G2 Mw ð5Þ ¼ K ~n0 1 þ wðd ln γ=dwÞ where
 d ln γ ¼ 8φ þ 30φ2 þ 73:4φ3 þ 141:2φ4 þ ... w dw

ð6Þ

and ðself Þ

φ ¼ veff w

ð7Þ

First, the scattering of pure TMAO was calculated as a function of concentration modeling TMAO as an effective hard sphere of molar mass M2 = 75 and radius r2 = 3.0 Å (D. P. Goldenberg, personal communication). The calculated normalized scattering intensity reaches a maximum of 2.5 (g2/mol cm3) at 100 g/L and is therefore nearly indistinguishable from zero on the scale of these figures. Next, eqs 5 and 6 were fitted to the experimentally measured concentration dependence of R/K for each of the three pure protein solutions to obtain the best-fit values of M1 and v(self) eff,1 for each protein, presented in Table 1. Given fixed values of

Figure 2. Dependence of normalized scattering intensity upon total concentration of ovalbumin and TMAO mixtures. Circles represent experimental data. Pure ovalbumin, black; 55% ovalbumin, blue; 25% ovalbumin, red; 10% ovalbumin, green. Solid, dashed, and dotted curves as described in the caption to Figure 1.

M1, M2, v(self) eff,1 , and r2, eqs 1, 3, and 4 and the scaled particle theory equations given in the appendix to ref 21 were globally fit to the data for all mixtures of each protein with different mass fractions of TMAO to obtain a best-fit value of the single remaining undetermined parameter, v(other) eff,1 , given in Table 1. The solid curves in each figure were calculated using these equations together with the best-fit parameter values.

’ DISCUSSION To estimate the effect of the net repulsive interaction between TMAO and protein upon the scattering intensity, the total 1291

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Figure 3. Dependence of normalized scattering intensity upon total concentration of ovomucoid and TMAO mixtures. Circles represent experimental data. Pure ovomucoid, black; 50% ovomucoid, blue; 25% ovomucoid, red; 10% ovomucoid, green. Solid, dashed, and dotted curves as described in the caption to Figure 1.

Table 1. Best-Fit Values of Parameters for Mixtures of Proteins and TMAOa

BSA

a

M1

3 v(self) eff,1 (cm /g)

v(other) (cm3/g) eff,1

68 900 ( 1 150

1.79 ( 0.04

1.37 (þ0.05, -0.10)

ovalbumin

43 800 ( 850

1.52 ( 0.05

0.88 (þ0.05, -0.16)

ovomucoid

27 500 ( 330

1.66 ( 0.04

1.04 (þ0.05, -0.10)

v(self) eff,1

For each protein, M1 and were determined by modeling the experimental data for pure protein using a non-self-associating equivalent hard sphere model. The best fit value of v(other) was then determined eff,1 by globally modeling the data for all mixtures of that protein with TMAO using the nonadditive binary mixture model with the values of M1 and v(self) eff,1 constrained to the best-fit values previously determined, as described in the text.

scattering of each mixture was recalculated using eq 1 assuming that total scattering is equal to the sum of scattering of each solute in the absence of the other. The resulting scattering profiles are plotted as dashed curves in Figures 1-3. It is evident that repulsive interactions between TMAO and each protein are responsible for a significant reduction in the total light scattering of mixtures at high concentration. To estimate the effect of nonadditivity of the protein-TMAO interaction upon scattering intensity, the total scattering of each mixture was recalculated using eq 1, assuming that the effective volume of the hard sphere representing protein is independent of concentration; i.e., veff,1 = v(self) eff,1 . The resulting profiles are plotted as dotted curves in Figures 1-3. It is evident that neglect of nonadditivity results in a significant overestimate of the effect of protein-TMAO interaction at intermediate compositions, and consequent underestimate of total scattering intensity. The values of specific exclusion volumes used to parametrize the repulsive interaction of each protein with itself and with TMAO given in Table 1 may be seen to be significantly larger than the partial specific volume of each protein (ca. 0.73 cm3/g). The difference reflects the fact that the partial specific volume of a protein is a measure of the volume excluded by that protein to water, which is a lower bound to the volume excluded by the same protein to any cosolute molecule that is larger than a water molecule.

By using eq 4, a simple linear composition-dependent inter(other) polation between the limiting values of v(self) eff,1 and veff,1 , we are able to account for the observed dependence of scattering of mixtures of all three proteins with TMAO to within experimental precision over a broad range of compositions. The mean field approximation embodied in eq 4 is comparable in degree to the overall level of approximation inherent in the effective hard particle model, which, although clearly semiempirical, has proven capable of accounting quantitatively in a self-consistent, physically reasonable, and parsimonious fashion for the experimentally measured values of several colligative properties of macromolecular solutions and solution mixtures over a broad range of composition.8-12,24,25 It should be noted that the value of v(other) eff,1 , the sole additional parameter required to provide the comprehensive description of the composition dependence of scattering in nonadditive mixtures reported here, need not be treated as an independently variable fitting parameter, as it may be measured experimentally via the technique of nonideal tracer sedimentation equilibrium.25 The general applicability of eq 4 and other mean-field approximations to the description of other properties of nonadditive solution mixtures will be the subject of future study.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT The authors thank Dr. Peter McPhie, NIH, for critical review of a preliminary draft of this report. This research was supported by the Intramural Research Program of the National Institute of Diabetes and Digestive and Kidney Diseases. ’ REFERENCES (1) Yancey, P. H.; Clark, M. E.; Hand, S. C.; Bowlus, R. D.; Somero, G. N. Science 1982, 217, 1214. (2) Qu, Y.; Bolen, D. W. Biochemistry 2003, 42, 5837. (3) Bennion, B. J.; Daggett, V. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 6433. (4) Bolen, D. W. Protein stabilization by naturally occurring osmolytes. In Protein Structure, Stability and Folding; Murphy, K. P., Ed.; Humana Press: Totowa, NJ, 2001; Vol. 168, p 17. (5) Bolen, D. W.; Baskakov, I. V. J. Mol. Biol. 2001, 310, 955. (6) Fern
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