The Lysozyme−Sodium Dodecyl Sulfate System Studied by Dynamic

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The Lysozyme-Sodium Dodecyl Sulfate System Studied by Dynamic and Static Light Scattering Ank Valstar,* Wyn Brown, and Mats Almgren Department of Physical Chemistry, Box 532, University of Uppsala, 751 21 Uppsala, Sweden Received September 14, 1998. In Final Form: December 11, 1998 The interaction between lysozyme and sodium dodecyl sulfate (SDS) was investigated by dynamic and static light scattering. The lysozyme-SDS system was studied at two different pH values (3.3 and 9.0), at which the net positive charges of lysozyme are 16 and 6, respectively. Furthermore, a comparison was made between the native lysozyme-SDS system and the reduced lysozyme (i.e., lacking its four disulfide bridges)-SDS system at pH 3.3. The concentration of SDS was varied from 0 to 0.55 M. The lowest molar SDS/lysozyme ratio was ≈55 because lower ratios result in a precipitate, making the samples unsuitable for measurement. Under the conditions used, (free) SDS micelles and lysozyme-SDS complexes coexist. Based on characteristic differences in the relaxation time distributions, the results obtained at low SDS concentration (0.25 M). At low SDS concentration, the hydrodynamic radii for the lysozyme-SDS complex in the three different systems are 3.23 ( 0.04 nm (native lysozyme-SDS, pH 3.3), 3.0 ( 0.1 nm (reduced lysozyme-SDS, pH 3.3), and 2.61 ( 0.06 nm (native lysozyme-SDS, pH 9.0). The hydrodynamic radius of (native) lysozyme at pH 3.3 is 1.82 ( 0.01 nm, and that of reduced lysozyme is slightly smaller (i.e., 1.79 ( 0.01 nm). The rather small hydrodynamic radii of the complexes cannot be accounted for by an unfolded lysozyme molecule. Reducing the disulfide bridges does not result in an increase, but a small decrease of the hydrodynamic radius. The small size can possibly be explained by a complex containing a micelle-like aggregate bound to the protein. At high SDS concentrations, two relaxation modes exist, both representing diffusional species and both containing lysozyme. It is assumed that two different complexes coexist: complex 1 is similar to that obtained at low SDS concentrations and has a compact structure, and complex 2 is a larger complex in which lysozyme probably has a more open, expanded structure, presumably caused by the binding of a greater amount of SDS. The hypothesis of a more expanded lysozyme molecule corresponds well with the change in the observed refractive index increment (∂n/∂clyz) values. The number of lysozyme molecules in the complex does not seem to depend on the SDS concentration and is determined, for the three systems studied in this article, to be ∼1.

I. Introduction Many industrial, biological, pharmaceutical, and cosmetic systems contain both proteins and surfactants.1 In analytical biochemistry, sodium dodecyl sulfate-polyacrylamide gel electrophoresis (SDS-PAGE) is a routinely used technique to estimate the molecular weight of proteins. Because the combination protein-surfactant is a feature of many systems, their interactions have been much studied (see ref 1 for a review). One of the globular protein-anionic surfactant systems frequently studied is the lysozyme-SDS system. Using X-ray diffraction, Blake et al.2 determined the three-dimensional structure of lysozyme, which is a small globular protein with a molecular weight of 14 350 g mol-1. It contains 129 amino acids and four disulfide bridges between residues 6-127, 30-115, 64-80, and 76-94. Some difference of opinion exists concerning the conformation of lysozyme in the lysozyme-SDS complex. Jones et al.3 concluded from enthalpy measurements that lysozyme unfolds when the number of bound SDS molecules increases from ∼20-35 (pH 3.2, 25 °C). Lysozyme has 18 positive charges at this low pH. The specific binding of ∼18 SDS molecules does not result in any major * To whom correspondence should be addressed. E-mail: [email protected]. (1) Ananthapadmanabhan, K. P. In Interactions of Surfactants with Polymers and Proteins, 1st ed.; Goddard, E. D., Ananthapadmanbhan, K. P., Eds.; CRC Press: London, 1993; p 319. (2) Blake, C. C. F.; Koenig, D. F.; Mair, G. A.; North, A. C. T.; Phillips, D. C.; Sarma, V. R. Nature 1965, 206, 757. (3) Jones, M. N.; Manley, P. In Surfactants in Solution; Mittal, K. L., Lindman, B., Eds.; Plenum Press: London, 1984; Vol. 2, p 1403.

conformational change in the protein structure. However, binding of even more SDS molecules (∼20-35) gives an endothermic contribution to the overall enthalpy, and this is interpreted as the unfolding of the native structure. Murata et al.,4 on the other hand, found that lysozyme does not unfold on binding with SDS. They based their conclusions on the appearance of the binding isotherms, determined by a potentiometric method utilizing an SDSselective electrode (at pH 5.8). Results of circular dichroism measurements also show that the effect of adding SDS to a lysozyme solution has no5 or little effect6,7 on the conformation of lysozyme. Fukushima et al.6 obtained a small increase of the R-helix content at the expense of the β-structure (the different fractions for R-helix, β-structure, and random coil changed, respectively, from 0.3, 0.1, and 0.6 for native lysozyme to 0.35, 0.05, and 0.6 for the SDSlysozyme complex). The published studies3-6 concern the complex formation between SDS and lysozyme in its native form (i.e., with the disulfide bridges intact), whereas the last-mentioned study7 also describes the interaction of SDS with reduced lysozyme. As summarized by Guo et al.,8 different models have been proposed to describe the protein-SDS complex: (1) (4) Murata, Y.; Okawauchi, M.; Kawamura, H.; Sugihara, G.; Tanaka, M. In Surfactants in Solution; Mittal, K. L., Bothorel P., Eds.; Plenum Press: London, 1986; Vol. 5, p 861. (5) Visser, L.; Blout, E. R. Biochemistry 1971, 10, 743. (6) Fukushima, K.; Murata, Y.; Nishikido, N.; Sugihara, G.; Tanaka, M. Bull. Chem. Soc. Jpn. 1981, 54, 3122. (7) Mattice, W. L.; Riser, J. M.; Clark, D. S. Biochemistry 1976, 15, 4264. (8) Guo, X.-H.; Chen, S.-H. Chem. Phys. 1990, 149, 129.

10.1021/la981234n CCC: $18.00 © 1999 American Chemical Society Published on Web 03/11/1999

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the ‘rodlike particle model’,9,10 which was proposed on the basis of viscosimetric measurements, describes the complex as a rigid rod with a cross-sectional radius of about 18 Å and a length proportional to the protein molecular weight; (2) the ‘flexible helix model’,11 which describes the complex as a flexible cylindrical micelle formed by the SDS molecules, on the surface of which hydrophilic segments of the protein are bound; and (3) the ‘necklace model’,12 which is based on results from the free-boundary electrophoresis technique and proposes an unfolded protein with SDS-micelle-like clusters bound to it. In addition to this summary by Guo, the ‘R-helix/random coil model’7 may be mentioned. This model is based on circular dichroism measurements that indicate that the protein-SDS complexes are constituted of the R-helix and the random coil. Of the models just mentioned, the necklace model seems to have the highest support. Results from small-angle neutron scattering (SANS),13,14 viscometry,15 and nuclear magnetic resonance (NMR)16 also confirm this model. Recently, Turro et al.,17 in a study combining fluorescence, electron spin resonance (ESR), and NMR and using the necklace model, concluded that the unfolded protein wraps around the micelles. The necklace model is similar to the structures reported for complexes formed between surfactants with polymers18 and polyelectrolytes,19 respectively. This work is an extension of a light scattering study done by Gimel et al.20 on the SDS-lysozyme system in 0.1 M phosphate buffer, pH 6.9. In this work the conformation of lysozyme in the complex was studied in two additional buffers (i.e., 0.1 M glycine/HCl buffer pH 3.3 and 0.1 M glycine/NaOH buffer pH 9.0). Furthermore, the role of the four disulfide bridges on the conformation of lysozyme in the complex was studied. The study was done at pH 3.3, where a comparison was made between the complex formation of SDS and lysozyme in its native form and in its reduced form (i.e., disulfide bridges broken). Because dynamic light scattering (DLS) provides information on the hydrodynamic radius of the complex, it gives indirect information on the conformation of lysozyme in the complex.

pure grade SDS was obtained from BDH. All other materials used were of analytical grade. Sample Preparation. The SDS was dissolved in the buffer, and a small amount of this SDS in buffer was used to prepare the lysozyme-SDS buffer solution. This lysozyme-SDS buffer solution, to which an extra amount of SDS (i.e., molar ratio SDS/ lysozyme ) 80) was added to accelerate the equilibrium process, was dialyzed for 24 h at room temperature against a large volume (i.e., 1 L) of the SDS buffer solution. Dialysis is performed to be able to determine the refractive index increment (∂n/∂clyz) at constant chemical potentials of the added electrolytes. The multicomponent system can now be considered as a twocomponent system (i.e., the SDS buffer is regarded as the solvent for lysozyme), and the molecular weight of lysozyme in the complex can be determined.22 Spectra Por cellulose ester membranes with a cutoff mass of 5000 g mol-1 were used. Lysozyme concentrations were determined by ultraviolet (UV) absorption measurements at 281.5 nm using the molar extinction coefficient 37 600 M-1 cm-1.23 β-Mercaptoethanol was used as the reducing agent. An SDS buffer was prepared as already described, and β-mercaptoethanol was added (0.1%). Again, a small amount of this buffer was used to prepare the lysozyme-SDS buffer solution. The amount of β-mercaptoethanol in the lysozyme-SDS buffer solution was increased to 1%, and the sample was incubated at 37 °C for 2 h.24 After cooling, the sample was dialyzed against the SDS buffer containing 0.1% β-mercaptoethanol. Dilutions were made using the dialysate, and the samples were filtered through 0.1-µm pore size Anotop filters into 10-mL cylindrical glass ampules. Static and Dynamic Light Scattering Measurements. Static light scattering (SLS) and DLS measurements were performed using a frequency-stabilized Coherent Innova Ar ion laser emitting vertically polarized light at 488 nm. The signal analyzer was an ALV-5000 digital multiple-τ correlator (Langen GmbH) with 288 exponentially spaced channels. The measurement temperature was 25 °C, which was controlled to within (0.02 °C. Toluene was used as a reference in static measurements, with a value of 3.1 × 10-5 cm-1 for the Rayleigh ratio Rtol.25 Data Analysis. This section is a brief review on the light scattering theory. More information is available in several textbooks.26,27 In DLS, the intensity-intensity autocorrelation function is measured and is related to the normalized electric field autocorrelation function, g1(t), by the Siegert relation:

II. Experimental Section

where β is a factor that accounts for deviations from ideality. The parameter g1(t) can be written as the Laplace transform of the distribution of relaxation rates, G(Γ):

Materials. Egg white lysozyme (Sigma no. L-6876) was used as supplied. The glycine/HCl buffer (pH 3.3; ionic strength, 0.009 M), the glycine/NaOH buffer (pH 9.0; ionic strength, 0.009 M), and the acetic acid/CH3COONa buffer (pH 5.0; ionic strength, 0.1 M) were prepared as described by Dawson et al.21 The ionic strengths of the glycine/HCl and glycine/NaOH buffers were adjusted to 0.1 M by adding NaCl. To avoid bacterial growth, NaN3 (200 ppm) was added to the buffer solutions. Especially (9) Reynolds, J. A.; Tanford, C. J. Biol. Chem. 1970, 245, 5161. (10) Reynolds, J. A.; Tanford, C. Proc. Natl. Acad. Sci. 1970, 66, 1002-1007. (11) Lundahl, P.; Greijer, E.; Sandberg, M.; Cardell, S.; Eriksson K.-O. BBA 1986, 873, 20. (12) Shirahama, K.; Tsujii, K.; Takagi, T. J. Biochem. 1974, 75, 309319. (13) Guo, X. -H-; Zhao, N. M.; Chen, S. -H-; Teixeira, J. Biopolymers 1990, 29, 335. (14) Ibel, K.; May, R. P.; Kirschner, K.; Szadkowski, H.; Mascher, E.; Lundahl, P. Eur. J. Biochem. 1990, 190, 311. (15) Shinagawa, S.; Kameyama, K.; Takagi, T. BBA 1993, 1161, 79. (16) Oakes, J. J. Chem. Soc., Faraday Trans. 1 1974, 70, 2200 (17) Turro, N. J.; Lei, X.-G.; Ananthapadmanabhan, P.; Aronson, M. Langmuir 1995, 11, 2525. (18) Cabane, B.; Duplessix, R. J. Phys. 1982, 43, 1529. (19) Hansson, P.; Almgren, M. J. Phys. Chem. 1995, 99, 16684. (20) Gimel, J. C.; Brown, W. J. Chem. Phys. 1996, 104, 8112. (21) Dawson, R. M. C.; Elliot, D. C.; Elliot, W. H.; Jones, K. M. Data for Biochemical Research; Clarendon Press: Oxford, 1969.

g2(t) - 1 ) β|g1(t)|2

g1(t) )

∫

∞

0

G(Γ)exp(-Γt) dΓ

(1)

(2)

where Γ is the relaxation rate. For relaxation times, τ, g1(t) will be expressed as

g1(t) )

∫

∞

0

τA(τ)exp(-t/τ)d ln τ

(3)

where τA(τ)≡ΓG(Γ). To obtain τA(τ), the DLS data were analyzed using the inverse Laplace transform routine REPES.28 The mutual diffusion coefficient, Dm, was calculated from the average relaxation rate (22) Eisenberg, H. In Photon Correlation and Light Beating Spectroscopy; Cummins, H. Z., Pike, E. R., Eds.; Plenum Press: New York, 1974; p 551. (23) Imoto, T.; Johnson, L. N.; North, A. C. T.; Phillips, D. C.; Rupley, J. A. The Enzymes, third ed.; Academic Press: London, 1972; Vol. 7. (24) Weber, K.; Osborn, M. J. Biol. Chem. 1969, 244, 4406. (25) Moreels, E.; Ceuninck, W. D.; Finsy, R. J. Chem. Phys. 1987, 86, 618. (26) Berne, B. J.; Pecora, R. Dynamic Light Scattering; John Wiley & Sons: New York, 1976. (27) Kratochvil, P. Classical Light Scattering from Polymer Solutions; Elsevier: Amsterdam, 1987. (28) Jakes, J. Czech. J. Phys. 1988, B 38, 1305.

2368 Langmuir, Vol. 15, No. 7, 1999 Dm ) Γ h /q2

(q f 0)

Valstar et al. (4)

where q ) 4πns/λ0 sin (θ/2), and ns is the refractive index of the solution, λ0 is the wavelength of the radiation in a vacuum, and θ is the scattering angle. According to their q2 dependence, the particles represent diffusional species. Because the hydrodynamic radius was not dependent on the scattering angle, most measurements were done at one angle (i.e., θ ) 90°). The diffusion coefficient, D0, can be calculated from

Dm(c) ) D0(1 + kdc)

(c f 0)

(5)

where c is the particle concentration and kd is a constant. The parameter D0 is related to the hydrodynamic radius, Rh, through the Stokes-Einstein relation

D0 )

kbT 6πηRh

(6)

where kb is the Boltzmann constant, T is the absolute temperature, and η is the viscosity of the solvent. The parameter kd can be expressed as

kd ) 2MA2 - kf - 2ν2

(7)

where A2 is the second virial coefficient, M is the molar mass, kf is the coefficient of the linear term in the development of the friction coefficient factor, and ν2 is the partial specific volume of the particle. The SLS data were analyzed using the classical Zimm equation:

Kc 1 ) + 2A2c Raθ Mw

(c f 0, θ f 0)

(8)

where A2 is the second virial coefficient, Raθ is the Rayleigh ratio at angle θ, and K is a constant depending on the apparatus and on the particles analyzed:

K)

4πns2 ∂n NAλ40 ∂c

2

( )

(9)

where ns is the refractive index of the solution, ∂n/∂c is the refractive index increment, NA is Avogadro’s number, and λ0 is the wavelength of the incident light in a vacuum. Because of the small size of the particles there is no angular dependence of the scattered intensity, and measurements can be done at only one angle (i.e., θ ) 90°). Surface Tension Measurements. Surface tension was measured with a KSV Sigma 70 instrument using a Du Nou¨y ring. The Zuidema-Waters correction for the ring was used.

III. Results and Discussion In Figures 1a and 1b, SLS and DLS results for lysozyme at three different pH values are compared. The net positive charges of lysozyme at pH 3.3, 5.0, and 9.0 are 16, 10, and 6, respectively.29 These values were determined at an ionic strength of 0.15 and depended only slightly on the ionic strength29 (small changes were observed in the titration curves for ionic strengths 0.03, 0.15, and 1.0, respectively). At pH 3.3, a positive second virial coefficient A2, representing a net repulsion, is observed. Increasing the pH, results in a smaller value for A2. At pH 9.0, A2 is negative, representing a net attraction, which indicates a tendency to form association products.30 Lysozyme is known to be subject to dimer formation in alkaline solution.31-33 Nevertheless, the weight average molar mass Mw calcu(29) Tanford, C.; Wagner, M. L. J. Am. Chem. Soc. 1954, 76, 3331. (30) Tanford, C. Physical Chemistry of Macromolecules; John Wiley & Sons: New York, 1961.

Figure 1. (a) Kc/Raθ as a function of the lysozyme concentration in 0.1 M glycine/HCl buffer pH 3.3 (open circles), in 0.1 M glycine/ HCl buffer pH 3.3 in the presence of β-mercaptoethanol (solid circles), in 0.1 M acetic acid/CH3COONa buffer pH 5.0 (crosses) and in 0.1 M glycine/NaOH buffer, pH 9.0 (triangles). (b) The mutual translational diffusion coefficient as a function of the lysozyme concentration (symbols as in a).

lated from the intercept (Figure 1a) at the different pH values approximates the mass of a single lysozyme molecule. As for A2, kd (eq 7) decreases with increasing pH. The hydrodynamic radius Rh of 1.82 ( 0.01 nm is (31) Sophianopoulos, A. J.; Holde, K. E. V. J. Biol. Chem. 1961, 236, PC82-PC83. (32) Sophianopoulos, A. J.; Holde, K. E. V. J. Biol. Chem. 1964, 239, 2516. (33) Bruzzesi, M. R.; Chiancone, E.; Antonini, E. Biochemistry 1965, 4, 1797.

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identical at the three pH values and is comparable to the values reported earlier in the literature.34,35 The critical micelle concentration (cmc) of SDS in the glycine/HCl buffer was determined by surface tension measurements (the Du Nou¨y ring method; result not shown), to be 1.25 ( 0.05 mM. The weight average molar mass Mw ) (2.8 ( 0.2) × 105 g mol-1 corresponds to an aggregation number of ∼97 molecules of SDS per micelle, and Rh of the micelle is 2.29 ( 0.04 nm (results not shown). The native lysozyme-SDS system at pH 3.3 will be described first, and then comparisons will be made with the reduced system at pH 3.3 and the system at pH 9.0 (native lysozyme). Finally, comparisons with the native lysozyme-SDS system at pH 6.9 as studied by Gimel et al.20 will be made. The Native Lysozyme-SDS System at pH 3.3. The positively charged lysozyme will be neutralized by the negatively charged SDS molecules to form a complex. The complex becomes progressively less soluble with increasing SDS concentration and finally precipitates. The binding isotherm of SDS in a 0.125% lysozyme buffer solution at pH 3.3 and ionic strength, I, of 0.1119 was determined by Jones et al.3 (Figure 7) in this reference shows the precipitate region and the point at which free SDS micelles first occur; i.e., at a SDS/lysozyme molar ratio ≈ 50). At SDS/lysozyme molar ratios higher than ∼60, the chargereversed complex becomes soluble and a clear solution is observed. This ratio does not seem to depend much on the lysozyme concentration: a 1% lysozyme buffer solution is clear at SDS/lysozyme molar ratios higher than ∼55. Because of the occurrence of the precipitate, light scattering measurements are confined to SDS/lysozyme molar ratios of g55. Static Light Scattering. Static light scattering data provide information on the molar mass of the protein in the protein-SDS complex,20,36 which means that the number of lysozyme molecules in the complex can be determined. The system is considered a binary system. The SDS buffer solution (i.e., the dialysate) is regarded as the solvent when the refractive index increment ∂n/ ∂clyz and the excess scattered intensity are measured relative to the SDS buffer solution. As described in ref 20, the molar mass of lysozyme in the complex can be determined using the following Zimm relation:

( )

K′

∂n 2 c 2A2c ∂clyz lyz 1 ) + 2 clyz Raθ Mlyz R

(clyz f 0, θ f 0) (10)

where K′ ) K/(∂n/∂cc) , A2c is the second virial coefficient of the complex, Mlyz is the weight-averaged molar mass of lysozyme in the complex, R ) (∂n/∂cc)/(∂n/∂clyz), and cc and clyz are the concentration of complex and the concentration of lysozyme, respectively. Fifteen series of different constant SDS concentrations (Table 1) between 0.017 and 0.55 M were measured. The number of lysozyme molecules in the complex does not seem to depend on the SDS concentration. The average value is 1.4 ( 0.1, which indicates a mixture of complexes containing, respectively, one and two lysozyme molecules per complex. A complex containing one lysozyme molecule is expected because lysozyme is predominantly monomeric at pH 3.3 (Figure 1). Figure 2 shows the second virial 2

(34) Skouri, M.; Munch, J.-P.; Lorber, B.; Giege, R.; Candau, S. J. Crystal Growth 1992, 122, 14. (35) Muschol, M.; Rosenberger, F. J. Chem. Phys. 1995, 103, 10424. (36) Takagi, T.; Miyake, J.; Nashima, T. BBA 1980, 626, 5.

Table 1. Static Light Scattering Data for the Native Lysozyme-SDS System at pH 3.3 [SDS], M

10-4 Mw, g mol-1

# lysozyme/complex

0.017 0.026 0.043 0.052 0.069 0.076 0.083 0.087 0.12 0.15 0.17 0.26 0.35 0.45 0.55

2.65 ( 0.06 2.35 ( 0.06 2.22 ( 0.01 1.96 ( 0.01 1.85 ( 0.06 2.03 ( 0.03 1.91 ( 0.02 2.15 ( 0.06 1.54 ( 0.02 1.56 ( 0.02 2.28 ( 0.07 2.03 ( 0.03 1.86 ( 0.03 1.80 ( 0.02 1.85 ( 0.04

1.8 1.6 1.5 1.4 1.3 1.4 1.3 1.5 1.1 1.1 1.6 1.4 1.3 1.3 1.3

Figure 2. The second virial coefficient of the complex, A2c as a function of the SDS concentration in 0.1 M glycine/HCl buffer pH 3.3 (open circles), in 0.1 M glycine/HCl buffer, pH 3.3, in the presence of β-mercaptoethanol (solid circles), and in 0.1 M glycine/NaOH buffer, pH 9.0 (triangles). Error bars are shown if the error exceeds the size of the symbol.

coefficient of the complex, A2C, as a function of the SDS concentration. These numbers have to be considered with care. Because the SDS buffer solution is considered as the solvent (binary system), the solvent will change with the SDS concentration. However, it is still possible to compare the three different lysozyme-SDS systems (i.e., at pH 3.3, at pH 3.3 + β-mercaptoethanol, and at pH 9.0) containing the same amount of SDS. This topic will be discussed in the sections concerning the other two systems. It should also be mentioned that in the determination of the number of lysozyme molecules in the complex it is assumed that the composition of the complex does not change with the lysozyme concentration. Figure 3 shows the refractive index increment ∂n/∂clyz of lysozyme as a function of the SDS concentration. (The maximum lysozyme concentration used in the determination of ∂n/∂clyz was 1.1 × 10-3 M). In the absence of SDS, ∂n/∂clyz ) 0.184 ( 0.001 mL g-1; however, ∂n/∂clyz increases considerably if a small amount of SDS is present (for example, ∂n/∂clyz ) 0.340 ( 0.002 mL g-1 at an SDS

2370 Langmuir, Vol. 15, No. 7, 1999

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Figure 3. The refractive index increment ∂n/∂clyz as a function of the SDS concentration in 0.1 M glycine/HCl buffer pH 3.3 (open circles), in 0.1 M glycine/HCl buffer, pH 3.3, in the presence of β-mercaptoethanol (solid circles) and in 0.1 M glycine/NaOH buffer, pH 9.0 (triangles).

concentration of 0.017 M). The refractive index increment ∂n/∂clyz is approximately constant up to an SDS concentration of ∼0.12 M, but then decreases to 0.266 ( 0.003 mL g-1 at 0.17 M and becomes approximately constant again. These high ∂n/∂clyz values are in good agreement with literature values.37 The refractive index increment ∂n/∂clyz is a measure of the average dielectric constant of lysozyme in solution. Changes in ∂n/∂clyz should thus reflect conformational changes of lysozyme in the presence of SDS. Dynamic Light Scattering. Because of the characteristically different appearance of the relaxation time distributions at different SDS levels, the results obtained at SDS concentrations 0.1 M will be discussed separately. [SDS] < 0.1 M. Figure 4a shows relaxation time distributions for a series of measurements at constant SDS concentration (0.017 M) and varying lysozyme concentration. The distributions show only one peak. In the absence of lysozyme, this component represents the relaxation of the SDS micelles. The peak position changes slightly to longer times when a small amount of lysozyme is also present, and the distribution becomes slightly broader. This mode consists of overlapping peaks describing the relaxation of the (free) SDS micelles and of a lysozyme-SDS complex. Because the relaxation times of these two species are of similar magnitude, it is impossible to resolve them. The free SDS micelles will be the dominant species at low lysozyme concentrations and will dominate the value of the mean relaxation time. A higher lysozyme concentration results in fewer free SDS micelles. In the interval of SDS/lysozyme molar ratio of ≈100 to ≈55, the SDS-lysozyme complex dominates the relaxation time distribution. In this interval, the mean relaxation time is approximately constant; that is, independent of the lysozyme concentration. (37) Jones, M. N.; Manley, P. J. Chem. Soc., Faraday Trans. 1 1979, 75, 1736.

Figure 4. (a) Relaxation time distribution for a series of measurements at constant SDS concentration (0.017 M) and varying lysozyme concentrations (shown in figure) in 0.1 M glycine/HCl buffer, pH 3.3. (b) The translational diffusion coefficient as a function of the lysozyme concentration for several SDS concentrations in 0.1 M glycine/HCl buffer, pH 3.3.

Figure 4b shows the corresponding diffusion coefficients for SDS concentrations between 0.017 and 0.087 M. Because the complex precipitates at molar ratios of SDS/ lysozyme smaller than ∼55, the measurements at low SDS concentrations are confined to a rather small range of lysozyme concentrations. The curves are similar in appearance: at SDS/lysozyme molar ratios between ≈100 and ≈55, diffusion coefficients independent of the lysozyme concentration are obtained. The diffusion coefficients obtained at SDS/lysozyme molar ratios between ≈100 and ≈55 have been extrapolated to zero lysozyme concentration (as shown for [SDS] ) 0.017 M in Figure 4b). These diffusion coefficients, Dlyz ) 0, are plotted versus the SDS concentration in Figure 5. Extrapolating to zero SDS concentration gives the diffusion coefficient Dlyz)0, SDS)0 of the SDS-lysozyme complex. Using the Stokes-Einstein (eq 6), the hydrodynamic radius of the complex, Rh, is determined to be 3.23 ( 0.04 nm. A few comments

Study of Lysozyme-SDS System

Figure 5. The extrapolated diffusion coefficient Dlyz)0 as a function of the SDS concentration in 0.1 M glycine/HCl buffer, pH 3.3 (open circles), in 0.1 M glycine/HCl buffer, pH 3.3, in the presence of β-mercaptoethanol (solid circles), and in 0.1 M glycine/NaOH buffer, pH 9.0 (triangles). The Dlyz)0 values for both the fast and slow mode at SDS concentrations >0.1 M are shown. The diffusion coefficients of pure SDS are included for comparison (squares).

concerning the assumptions made in the determination of Rh are in order. First of all, it is assumed that the composition of the complex does not change with the SDS nor with the lysozyme concentration. Second, the increase of Dlyz)0 with increasing SDS concentration is assumed to depend solely on the thermodynamic and hydrodynamic interactions between the complexes and the SDS micelles, characterized by k′d in Dlyz)0 ) Dlyz)0,SDS)0 (1 + k′d [SDS]); that is, the contribution of complex-complex interactions is not included in Dlyz)0. However, Dlyz)0 will also depend on conformational changes of the complex. Two extremes can be considered: (1) changes in Dlyz)0 depending only on the interactions between the particles (as just described), and (2) changes in Dlyz)0 caused only by conformational changes (k′d ) 0). Combinations of (1) and (2) also exist. The hydrodynamic radius changes from ≈1.8 nm for lysozyme to ≈3.2 nm for the lysozyme-SDS complex. Such a small increase cannot account for an unfolded and extended lysozyme molecule. A complex consisting of one lysozyme molecule and one SDS micelle can be imagined (note that complexes containing two lysozyme molecules may also exist). This interpretation corresponds to some extent to the ‘necklace model’12 (unfolded protein with SDS micelle-like clusters bound to it). However, because probably only one micelle-like cluster is bound, lysozyme is unlikely to expand much. [SDS] > 0.1 M. As already mentioned, the relaxation time distributions observed at SDS concentrations >0.1 M are different from those observed at lower SDS concentrations. Figure 6 shows relaxation time distributions for three series of measurements at constant SDS concentration (0.17, 0.26, and 0.35 M) and varying lysozyme concentration. At low lysozyme concentrations, the relaxation time distribution looks similar to that of

Langmuir, Vol. 15, No. 7, 1999 2371

Figure 6. Relaxation time distributions for three series of measurements at constant SDS concentration (0.17, 0.26, and 0.35 M) and varying lysozyme concentrations (shown in figure) in 0.1M glycine/HCl buffer, pH 3.3.

Figure 7. The normalized scattering intensities of the fast and slow modes at constant SDS concentration (0.26 M) as a function of the lysozyme concentration in 0.1 M glycine/HCl buffer, pH 3.3.

the lysozyme-SDS system at low SDS concentrations (Figure 4a); that is, the distribution is single peaked. However, at higher lysozyme concentrations, two different modes can be resolved. According to their q2 dependence, both modes represent diffusional species. The contributions of the fast and the slow modes to the intensity of the scattered light (If and Is, respectively) can be deduced from the relaxation spectrum. The normalized intensities, If/ Itol and Is/Itol, both increase with increasing lysozyme concentration (Figure 7), which means that both diffusing species contain lysozyme.

2372 Langmuir, Vol. 15, No. 7, 1999

Valstar et al. Table 2. Static and Dynamic Light Scattering Data for the Reduced Lysozyme-SDS System at pH 3.3 [SDS], M

10-4 Mw, g mol-1

# lysozyme/ complex

0.043 0.069 0.087 0.17 0.26 0.35 0.45 0.55

1.92 ( 0.04 1.58 ( 0.07 1.26 ( 0.08 2.01 ( 0.04 2.08 ( 0.08 2.12 ( 0.07 2.1 ( 0.1 2.11 ( 0.09

1.3 1.1 0.88 1.4 1.5 1.5 1.5 1.5

a

102 kd,M-1a 2.6 ( 0.3 2.6 ( 0.5 2.8 ( 0.1 -1.5 ( 0.1b -2.5 ( 0.1b -2.8 ( 0.4b -3.8 ( 0.6b

kd in D ) Dlyz)0 (1 + kd [lyz]). b Slow mode.

Table 3. Static and Dynamic Light Scattering Data for the Native Lysozyme-SDS System at pH 9.0 [SDS], M

10-4 Mw, g mol-1

# lysozyme/ complex

102 kd, M-1a

0.017 0.043 0.087 0.26 0.35

1.16 ( 0.05 1.16 ( 0.02 1.03 ( 0.02 1.81 (0.06 2.13 ( 0.05

0.81 0.81 0.71 1.3 1.5

4.6 ( 0.2 3.0 ( 0.1 2.3 ( 0.2 -1.4 ( 0.1b -0.86 ( 0.07b

a

Figure 8. The translational diffusion coefficients of the fast and slow modes at several constant SDS concentrations as a function of the lysozyme concentration in 0.1 M glycine/HCl buffer, pH 3.3.

It is assumed that the fast mode corresponds to that obtained at low SDS concentrations (Figure 4); that is, it is a combination of the relaxation of the free SDS micelles and a lysozyme-SDS complex. The slow mode represents a slower diffusing species also containing lysozyme. The number of lysozyme molecules in the complex can be deduced from SLS measurements (Table 1). This number (1.4 ( 0.1) does not seem to depend on the SDS concentration and thus does not explain the appearance of the slow mode at high SDS concentrations. Because the slow mode seems to represent a different complex, it will be called complex 2 to distinguish it from the complex corresponding to the fast mode (complex 1). The slower diffusion of complex 2 may be caused by a higher number of bound SDS molecules, for example, a lysozyme molecule binding two micelle-like clusters can be imagined. To accommodate more SDS molecules, a conformational change will have to occur. This change corresponds well with the changes observed for the ∂n/∂clyz values (Figure 3). The decrease of ∂n/∂clyz correlates with the changes in the relaxation time distributions. As shown in Figure 7 both modes contain lysozyme, although the distribution of lysozyme over these modes cannot be estimated. Figure 8 shows the diffusion coefficients of the two modes plotted versus the total lysozyme concentration for several SDS concentrations. From these data, the Dlyz)0 of complex 2 at the different SDS concentrations can be determined, and these results are shown in Figure 5. Data obtained at low SDS concentrations are also included. The fast mode will be dominated by the diffusion of the free micelles, when the SDS concentration is high and no information concerning complex 1 can be extracted. The diffusion coefficients of pure SDS at pH 3.3 are included for comparison. The Dlyz)0 of complex 2 decreases with increasing SDS concentration. This behavior could depend on several factors: (1) because the Dlyz)0 values are not extrapolated to zero SDS concentration, the interaction between the complexes and the SDS micelles will contribute to the value of Dlyz)0; (2)

kd in D ) Dlyz)0 (1 + kd [lyz]). b Slow mode.

Dlyz)0 decreases when the complex becomes larger (a greater amount of bound SDS, causing a greater conformational change of lysozyme); or (3) Dlyz)0 will decrease with increasing kf (eq 7). As the SDS concentration increases, the first appearance of the slow mode is obtained at progressively lower lysozyme concentrations. This phenomenon is shown in Figure 6. At an SDS concentration of 0.17 M, two overlapping modes are obtained for a lysozyme concentration of 1.1 × 10-3 M, whereas in an [SDS] ) 0.35 M solution the two modes readily are resolved at a lysozyme concentration of 7.0 × 10-5 M. The Reduced Lysozyme-SDS System at pH 3.3. In Figures 1a and b, native and reduced lysozyme are compared (in the absence of SDS). No significant differences are observed for either Mw or A2. The DLS results indicate a slightly smaller Rh for reduced lysozyme (i.e., 1.79 ( 0.01 nm compared with 1.82 ( 0.01 nm for native lysozyme). [However, it should be mentioned that treating lysozyme (in the absence of SDS) with β-mercaptoethanol as described in the Experimental Section causes aggregation. The contribution of the aggregates to the scattered light can be deduced from the relaxation spectra and the SLS data were corrected for their contribution]. Static Light Scattering. The average number of lysozyme molecules in the complex is similar to that found for the native lysozyme-SDS system (i.e., 1.3 ( 0.1; Table 2). However, (much) higher A2c values for reduced lysozyme are obtained (Figure 2). Thus, two systems that are nearly identical (i.e. equal pH, equal ionic strength, equal amounts of SDS), except for the presence of the reducing agent β-mercaptoethanol, differ a lot in A2c. The value of A2c depends on the volume of the complex + solvation shell and, because the complex is charged, on electrostatic interactions. The volume of the reduced lysozyme-SDS complex is somewhat smaller (as can be deduced from the DLS measurements discussed later), resulting in a lower A2c rather than a larger one. It can be concluded that the difference in A2c is mainly caused by a difference in electrostatic interactions (i.e. electrostatic repulsion because the A2c values are positive). Differences in electrostatic interaction will result from differences in the charge of the complex; that is, the number of SDS molecules bound to lysozyme. However a fluorescence study done on the

Study of Lysozyme-SDS System

Figure 9. The translational diffusion coefficient as a function of the lysozyme concentration for several SDS concentrations in 0.1 M glycine/HCl buffer, pH 3.3, in the presence of β-mercaptoethanol.

bovine serum albumin (BSA)-SDS38 system showed that the number of SDS bound to BSA does not depend on the presence of the disulfide bridges. Assuming an equal number of bound SDS molecules, differences in A2c might be caused by a different conformation of lysozyme in the complex resulting in the higher A2c values. The decrease in A2c values between [SDS] ) 0.012 M to 0.017 M, followed by a plateau value is also seen for the reduced lysozymeSDS system (Figure 2). Figure 3 includes data for the refractive index increment ∂n/∂clyz of reduced lysozyme as a function of the SDS concentration. The changes in ∂n/∂clyz are similar to those observed for the native lysozyme-SDS system. The values for ∂n/∂clyz are somewhat higher at low SDS concentrations, and somewhat lower at high SDS concentrations. Dynamic Light Scattering. [SDS] < 0.1 M. In Figure 9 the diffusion coefficients of the complexes at constant SDS concentrations (0.017 - 0.087 M) are shown. The kd values (Table 2) are greater than those observed in the native lysozyme-SDS system (kd ≈ 0, Figure 4b). The higher kd values agree with the higher A2c values. Extrapolations to zero lysozyme concentration are made to obtain Dlyz)0. These diffusion coefficients are plotted in Figure 5. The hydrodynamic radius of the reduced lysozyme-SDS complex, Rh ) 3.0 ( 0.1 nm, is somewhat smaller than that of the native lysozyme-SDS complex, Rh ) 3.23 ( 0.04 nm. This result is somewhat surprising because it might be expected that breaking the disulfide bridges creates more available sites for SDS to bind, which would result in a more unfolded conformation of lysozyme (i.e., a larger complex). However, as already mentioned, a fluorescence study done on the BSA-SDS38 system revealed that the number of SDS bound to BSA does not seem to depend on the presence of the disulfide bridges. Assuming an equal number of bound SDS molecules, a large increase in size is not expected because the protein (38) Vasilescu, M.; Angelescu, D.; Almgren, M.; Valstar, A., submitted to Langmuir.

Langmuir, Vol. 15, No. 7, 1999 2373

Figure 10. The translational diffusion coefficient as a function of the lysozyme concentration for several SDS concentrations in 0.1 M glycine/NaOH buffer, pH 9.0.

molecule is wrapped around a micelle with a constant aggregation number. [SDS] > 0.1 M. The change from a relaxation time distribution showing only one mode to one showing two modes is also seen in the reduced lysozyme-SDS system. Again, similar features are observed: both modes represent diffusional species and both contain lysozyme. The extrapolated diffusion coefficients Dlyz)0 are shown in Figure 5. The Native Lysozyme-SDS System at pH 9.0. Static Light Scattering. The average number of lysozyme molecules in the lysozyme-SDS complex is 1.0 ( 0.2, which is somewhat smaller than that found at pH 3.3 (1.4 ( 0.1). Rather high values for the second virial coefficient A2c at low SDS concentration are observed. By increasing the pH from 3.3 to 9.0, the net positive charge of lysozyme decreases from 16 to 6. If an equal amount of bound SDS is assumed, the higher value of A2c will reflect the higher net negative charge of the complex. As derived from DLS measurements (discussed later), the volume of the complex is smaller at pH 9.0. The increase of A2c at high pH is probably due to electrostatic interactions. Different conformations of lysozyme in the complex might also result in differences in A2c. The refractive index increment of lysozyme ∂n/∂clyz decreases with the SDS concentration after an initial increase (Figure 3). Unlike the results obtained at pH 3.3, no plateau value is observed at low SDS concentrations (i.e. below 0.1 M). The ∂n/∂clyz values at high SDS concentrations (∼0.25 M) are comparable to the value for lysozyme in the absence of SDS. Dynamic Light Scattering. At low SDS concentrations, a single relaxation mode is found, similar to the other two systems described. Figure 10 shows the diffusion coefficients for different constant SDS ( 0.1 M) SDS concentrations. The lowest SDS/ lysozyme molar ratio in both regions is ∼55, and lower ratios result in a precipitate. The division into two regions is mainly based on characteristic differences in the relaxation time distributions. However, changes in ∂n/∂clyz correlate with those in the relaxation time distributions. The hydrodynamic radius of the native lysozyme-SDS complex at pH 3.3 at low SDS concentrations is 3.23 ( 0.04 nm. (As described earlier, several assumptions are made in the determination of Rh.) The hydrodynamic radius of lysozyme itself is 1.82 ( 0.01 nm, which indicates that lysozyme in the complex has a compact conformation. Reducing the disulfide bridges does not result in a larger complex, on the contrary, a somewhat smaller complex is obtained (Rh ) 3.0 ( 0.1 nm). At high SDS concentrations, two relaxation modes exist, both representing diffusional species and both containing lysozyme. It is assumed that two different complexes coexist: complex 1 is similar to that obtained at low SDS concentrations and has a compact structure, complex 2 is a larger complex and lysozyme probably has a more open, expanded structure, presumably caused by the binding of a greater amount of SDS. The hypothesis of a more expanded lysozyme molecule corresponds well with the changes observed in ∂n/∂clyz (Figure 3). The decrease of ∂n/∂clyz correlates with the changes in the relaxation time distributions. The number of lysozyme molecules in the complex does not seem to depend on the SDS concentration and is, for the three systems studied in this article ∼1. Complementary techniques are needed to describe the system more completely, for instance, NMR could be used to assist in the interpretation of the two relaxation modes. It would also be interesting to study the interaction between other proteins, both in their native and reduced form, with SDS. Both fluorescence studies38 as well as light scattering studies on the interaction between BSA and SDS and different surfactants are being undertaken in our laboratory. Acknowledgment. We thank Dr. Taco Nicolai for his interest and valuable comments and Britta Folmer (Institute for Surface Chemistry, Stockholm, Sweden) for her help with the surface tension measurements. LA981234N