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May 13, 2017 - consistent with previous studies.34,35 The solid and dashed. Figure 5. Zeta potential ζ distributions of BLG and BLG−SDS mixtures in...
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Complexation of a Globular Protein, β‑Lactoglobulin, with an Anionic Surfactant in Aqueous Solution Yan Li and Takahiro Sato* Department of Macromolecular Science, Osaka University, 1-1 Machikaneyama-cho, Toyonaka, Osaka 560-0043, Japan S Supporting Information *

ABSTRACT: The complexation of a globular protein, βlactoglobulin (BLG), and an anionic surfactant sodium dodecyl sulfate (SDS) in aqueous media was investigated using capillary zone electrophoresis, electrophoretic, static, and dynamic light scattering, and small-angle X-ray scattering in a considerably high protein concentration range (0.27 mM < CP < 3 mM). On increasing the molar concentration CR of the surfactant, cooperative binding of SDS to BLG starts at CR/CP ≈ 1; the BLG−SDS complex consists mainly of the BLG dimer and approximately 20 SDS molecules, where BLG takes a compact conformation similar to that of the native BLG up to CR/CP ≈ 20. At CR/CP higher than 30, the BLG dimer in the BLG−SDS complex dissociates into a unimer, but the dissociated BLG unimer still takes a compact conformation at least at 30 < CR/CP < 65.

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INTRODUCTION The complexation between a protein and a surfactant is applied in various fields from detergents to protein processing, separation, and characterization, and this has been studied since 1930s.1−7 Anson8 found the denaturation of globular proteins by complexation with surfactants. Pitt-Rivers and Impiombato9 were the first to report protein−ionic surfactant complexes of high surfactant binding ratios. Maizel et al.4 and Laemmli10 established the methodology of sodium dodecyl sulfate polyacrylamide gel electrophoresis (SDS-PAGE) for the separation and molecular weight determination of proteins. More recently, polymer scientists have been interested in the interaction of polymer surfactants with proteins because of their biological applications.11−14 The structure of the complex between the protein and the low-molar-mass surfactant is essential information to understand the protein−polymer surfactant interaction. Among the enormous structural studies of protein− surfactant complexes, the global conformation of the protein in the complex was investigated using scattering techniques.15−20 However, because the solution of the protein− surfactant mixture contains not only the protein−surfactant complex but also the free protein, free surfactant, and surfactant micelle components, and furthermore because the compositions of these components are strongly dependent on the concentrations of the protein and the surfactant in the solution, it is rather difficult to analyze the scattering data to extract information about the protein−surfactant complex. Moreover, precise scattering measurements need protein concentrations of test solutions much higher than the concentration usually studied using spectroscopic, chromatographic, and calorimetric techniques that give us information on the binding of the © 2017 American Chemical Society

surfactant to the protein. Therefore, little information is available on the surfactant binding to the protein under the condition of scattering measurements. Takeda and Moriyama21 were concerned about the spread of the misunderstood necklace model for protein−surfactant complexes through the repeated uncritical citations, which misrepresents the essential nature of the protein−surfactant interaction and causes other misunderstandings. Such a spread of misunderstanding mainly comes from the difficulty in scattering measurements. In this study, we have investigated the structure of the protein−surfactant complex not only using static and dynamic light scattering (SLS and DLS) and small-angle X-ray scattering (SAXS) but also using capillary zone electrophoresis (CZE) and electrophoretic light scattering (ELS) in similar concentration ranges of the protein and the surfactant. We have chosen β-lactoglobulin (BLG) as a globular protein and sodium dodecyl sulfate (SDS) as an anionic surfactant. In this study, we have made not only scattering but also CZE measurements at protein concentrations considerably higher than those examined in previous studies. As a result, we can directly compare the scattering and CZE results to rigorously analyze the scattering data for the complex multicomponent system. This work is the first to make such a rigorous lightscattering data analysis for the protein−surfactant complexation. Furthermore, under such conditions, we can examine the binding of the surfactants to the protein at relatively low Received: March 20, 2017 Revised: May 13, 2017 Published: May 13, 2017 5491

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Figure 1 shows the relaxation time spectra A(τ) at θ = 45° of buffer solutions of BLG−SDS mixtures at CP = 1.09 mM (cP = 0.02 g/cm3)

surfactant concentrations more precisely from the CZE results, and we found a cooperative binding of SDS to BLG.

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EXPERIMENTAL SECTION

Materials and Test Solutions. BLG and SDS used in this study were purchased from Sigma-Aldrich Japan and Wako Pure Chemical Industries, respectively. BLG and SDS were dissolved in pH 7 sodium phosphate buffer that was prepared using 50 mM Na2HPO4 and 50 mM NaH2PO4. All reagents were used without further purification. In what follows, the composition of the aqueous solution of the surfactant (R) and the protein (P) is expressed in terms of the molar concentrations of R (CR) and P (CP) or the mass concentrations of R (cR) and P (cP), which are related to each other by

C R = c R /MR ,

C P = c P/MP

(1)

where MR and MP are the molar masses of R (MR = 288 g/mol) and P (MP = 18 400 g/mol), respectively. Furthermore, in the light-scattering experiment, we also use the total mass concentration c of the solute and the weight fraction wR of R in the solute defined by

c = cR + cP ,

cR wR = cR + cP

Figure 1. Relaxation time spectra A(τ) of buffer solutions of BLG− SDS mixtures with CP = 1.09 mM and changing CR, at θ = 45°.

(2)

′ is calculated from eq 5. For and changing CR, where the abscissa RH,app all solutions in Figure 1, A(τ) is bimodal, and the peaks of the slow ′ = 100 nm. The slow relaxation mode are located around RH,app relaxation component may be regarded as random aggregates of the fast relaxation component. If so, the relaxation strength ratio Aslow(τ)/ Afast(τ) of the slow to fast relaxation components is related to the hydrodynamic radius ratio RH,slow/RH,fast by22

SLS and DLS. Simultaneous SLS and DLS measurements were recorded at 25 °C using an ALV/DLS/SLS-5000 light-scattering system with vertically polarized incident light of 532 nm. The excess Rayleigh ratio Rθ over that of the solvent and the intensity autocorrelation function g(2)(t) were measured as functions of the total solute concentration c, the weight fraction wR of R in the solute (see eq 2), and the scattering angle θ. The light-scattering system was calibrated using toluene as the reference material. The optical constant K was calculated by 4π 2nS2 ⎛ ∂n ⎞ 2 ⎜ ⎟ K= NAλ 0 4 ⎝ ∂c ⎠av

2 A slow (τ ) wslow ⎛ 1.4RH,slow ⎞ ⎜⎜ ⎟⎟ = A fast (τ ) 1 − wslow ⎝ RH,fast ⎠

where wslow is the weight fraction of the slow relaxation component. Because Aslow(τ)/Afast(τ) ≈ 1 and RH,slow/RH,fast ≈ 20, wslow is as small as 10−3, so that we neglect the slow relaxation component in what follows, despite its scattering power being strong as a result of its high molar mass.22 By analyzing the experimental results of SLS and DLS for buffer solutions of SDS, the aggregation number m, the critical micelle concentration CR,cmc, and the hydrodynamic radius RH,Rm for SDS micelles were determined. The results are shown in Figure S1 and Table S1, which are consistent with the literature data.23−28 ELS. ELS measurements were recorded at 25 °C using an Otsuka ELSZ-1RZ zeta potential and particle size analyzer. The test solution was put in the flow cell after filtering with a 0.20 μm filter. The spectrum A(ζ) of the zeta potential ζ was obtained from the scattering intensity auto-correlation function of ELS. The average zeta potential ζ̅ was calculated using the equation

(3)

where nS is the refractive index of the solvent, NA is the Avogadro constant, λ0 is the wavelength of the incident light in vacuo, and (∂n/ ∂c)av is the average specific refractive index increment defined by

⎛ ∂n ⎞ ⎛ ∂n ⎞ ⎛ ∂n ⎞ ⎜ ⎟ = ⎜ ⎟ w + ⎜ ⎟ (1 − wR ) ⎝ ∂c ⎠av ⎝ ∂c ⎠R R ⎝ ∂c ⎠P

(4)

with the specific refractive index increments of P (∂n/∂c)P and R (∂n/ ∂c)R. The specific refractive index increments at 532 nm for 50 mM sodium phosphate buffer solutions of BLG and SDS were determined to be 0.190 and 0.113 cm3/g, respectively, using a differential refractometer. In our analysis of SLS data, both BLG and SDS were regarded as the solute, and the phosphate buffer was regarded as the solvent, which was an analysis different from that studied in ref 16. The scattering intensity auto-correlation function g(2)(t) obtained through DLS was analyzed using the CONTIN program to obtain the relaxation time spectrum A(τ), where the relaxation time τ was ′ of the converted to the apparent hydrodynamic radius RH,app component that is defined by22 ′ RH,app ≡

kBT 2 kτ 6πηS

ζ̅ =

τ

τ

(6)

and the mutual diffusion coefficient Dm was calculated from A(τ) by

Dm = lim Γ/k 2 k→0

i

(9)

CZE. CZE measurements were recorded at 25 °C using an Agilent 7100 capillary electrophoresis system using a cartridge equipped with a bare fused silica capillary (Restek, i.d. = 50 μm) of length 33 cm. The applied electric voltage was 10 kV, 50 mM sodium phosphate buffer was used as run buffer, and 32 mM TX-100 in 50 mM sodium phosphate buffer was chosen as the neutral marker. The sample signal was detected by UV absorption at 214 nm. The capillary was conditioned by flushing 0.1 M HCl, 0.1 M NaOH, and water successively and by washing the run buffer before use. Sample volumes of 10 nL were injected hydrodynamically (50 mbar, 4 s); then, the pressure was removed, and the capillary inlet end was transferred to the run buffer reservoir at the applied voltage of 10 kV. The inner glass wall of the capillary has silanol groups, and the countercations flow by the applied electric field. The solute molecule flows along with this electro-osmotic flow. For the negatively charged solute, the electrophoretic mobility decreases with increasing zeta potential (by the electric force directed oppositely toward the electro-

(5)

∑ τ −1A(τ) ∑ A(τ)

∑ ζiA(ζi) ∑ A(ζi) i

where kBT is the Boltzmann constant multiplied by the absolute temperature, ηs is the viscosity coefficient of the solvent, and k is the amplitude of the scattering vector. The first cumulant Γ was calculated from A(τ) by

Γ=

(8)

(7) 5492

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Langmuir osmotic flow) and increases with increasing molecular size (because of the stronger frictional force).29,30 Electrophoretic mobility μ was calculated as30

μ=

lL ⎛ 1 1⎞ ⎜ − ⎟ V ⎝ ts t0 ⎠

inactive, we did not observe the peaks for the SDS unimer and the micelle. Electrophoretic mobilities μ of P and PR are plotted against CR/CP in Figure 3 by unfilled and filled circles, respectively.

(10)

where l is the length of the capillary between the anode and the detector (=24.5 cm), L is the total capillary length (=33 cm), V is the applied voltage, and ts and t0 are the migration times for the sample and the neutral marker, respectively. SAXS. SAXS measurements were conducted using the method described previously.31 In brief, synchrotron radiation SAXS experiments were conducted at 25 °C on a BL40B2 beamline system, SPring-8, Hyogo, Japan. The incident X-ray was polarized, and the wavelength was 0.1 nm. The camera length and the accumulation time were 4.17 m and 180 s, respectively. The BLG molar concentration was 1.63 mM, and the SDS molar concentration was 16 mM.

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RESULTS CZE. Figure 2 shows the CZE chromatogram for buffer solutions of BLG with SDS with CP (cP) fixed at 1.63 mM (0.03 Figure 3. Electrophoretic mobilities μ of P (unfilled circles) and PR (filled circles) obtained using CZE and the average zeta potential ζ̅ (unfilled squares) obtained using ELS, plotted against CR/CP.

The mobility of PR is lower than that of P and decreases with increasing CR. In CZE, the solute flows with the electro-osmotic flow of the solvent, and the flow speed slows down on increasing the number of negative charges and decreasing the size of the solute. Because the size of PR must not be smaller than the size of P, the smaller μ of PR is due to the increase in the negative charges of the complex PR. Figure 4 shows the peak areas of P ( fA,P) and PR (fA,PR) relative to the total peak area in Figure 2, plotted against CR/CP.

Figure 2. CZE chromatograms for mixtures of BLG (CP = 1.63 mM; cP = 0.03 g/cm3) and SDS (different CR) in 50 mM sodium phosphate buffer.

g/cm3) and changing CR. The peak of BLG in the CZE chromatogram separates into two peaks at 2 mM < CR < 16 mM. The position of the fast migrating peak is almost identical to that of the peak of the native BLG at CR = 0, whereas the slowly migrating peak shifts to the longer time region, and its area increases with increasing CR. The fast and slowly migrating peaks are assigned as the free BLG (P) and the complex of the BLG and SDS (PR), respectively. (A similar peak separation in electrophoresis was reported in aqueous BLG by the addition of an anionic surfactant many years ago.32) The long tail of the slowly migrating peak may come from the partial dissociation of the complex during electrophoresis. However, we can estimate the concentration of the complex PR in the prepared solution from the area of the long tailed peak because the peak does not overlap the peak of the free protein P. Because SDS is UV-

Figure 4. SDS concentration dependence of the peak areas of the uncomplexed BLG (fA,P, unfilled circles) and the BLG−SDS complex ( fA,PR, filled circles) in 50 mM sodium phosphate buffer. Solid curves indicate the theoretical values calculated using eq S14 with mP = nP = 2, n′ = 15, and n″ = 100.

The surfactant does not interact with BLG at CR/CP < 1.2 but abruptly forms PR at CR/CP ≈ 1.2, and almost all BLG forms PR at CR/CP ≈ 10. ELS. Figure 5 shows the zeta potential ζ distribution of BLG−SDS mixtures at different surfactant concentrations. It is seen that the peak of BLG appears at ζ close to 0 mV because 5493

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Figure 5. Zeta potential ζ distributions of BLG and BLG−SDS mixtures in 50 mM sodium phosphate buffer. Figure 7. CR/CP dependences of Mw,av (unfilled circles) and RH,av (filled circles) for BLG−SDS mixtures in 50 mM sodium phosphate buffer. Solid, dotted, and dash-dot curves indicate the theoretical values for nP = 2, nP = 1, where PR takes the globular conformation and nP = 1 where PR takes the random coil conformation, respectively.

pH (=7) of 50 mM sodium phosphate buffer is close to the isoelectric point of BLG (=5.2) and slightly shifts toward negative ζ with increasing CR, and a new peak appears around ζ = −25 mV at CR ≥ 16 mM, where the peak for the uncomplexed BLG (P) disappears in the CZE chromatogram (see Figure 2). The CR/CP dependence on the average zeta potential ζ̅ of the BLG−surfactant mixtures is shown in Figure 3 by unfilled squares. With increasing CR/CP, ζ̅ gradually decreases because more SDS molecules with the negative charge are adsorbed on BLG. SLS and DLS. Figure 6 shows the total solute mass concentration c (=MPCP + MRCR) dependences of (Kc/R0)1/2 and Dm for the fast relaxation component of aqueous BLG− SDS mixture solutions with different wR [=1/(1 + MPCP/ MRCR)] (MP and MR being the molar masses of P and R) values. By extrapolation to zero c at a fixed wR, we have determined the average molar mass Mw,av and the average hydrodynamic radius RH,av defined by M w,av −1/2 =

RH,av

−1

=

lim

c → 0 at fixed wR

6πηS kBT

lim

(Kc /R 0)1/2

c → 0 at fixed wR

Dm

CP, both Mw,av and RH,av first increase, then decrease, and finally increase again. The solution of BLG−SDS mixtures contains multiple scattering components, so that we have to consider the structural and composition changes of all components with CR/ CP to explain the unique CR/CP dependences of Mw,av and RH,av. For the multicomponent solution containing the component i with the weight fraction (in the total solute) wi, the molar mass Mi, and the hydrodynamic radius RH,i, we can write Mw,av and RH,av as22,33 M w,av =

⎛ ∂n ⎞ −2 ⎛ ∂n ⎞ 2 ⎜ ⎟ ⎜ ⎟ wM , ∑ ⎝ ∂c ⎠av i ⎝ ∂c ⎠i i i

RH,av −1 =

(11)

−1 ∑i (∂n/∂c)i 2 wM i iR H, i

∑i (∂n/∂c)i 2 wM i i

(13)

At wR = 0, Mw,av and RH,av are identical to the true weightaverage molar mass and the true hydrodynamic radius of BLG, respectively. The true weight average molar mass of BLG is 2.93 × 104 g/mol at wR = 0, indicating that BLG exists mostly as the dimer in 50 mM sodium phosphate buffer. This is consistent with previous studies.34,35 The solid and dashed

(12)

The results of Mw,av and RH,av obtained are plotted against CR/CP = wRMP/(1 − wR)MR in Figure 7. With increasing CR/

Figure 6. Total concentration dependences of (Kc/R0)1/2 and Dm for the fast relaxation component of BLG−SDS mixtures with different wR values investigated in 50 mM sodium phosphate buffer. 5494

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R may interact by the hydrophobic interaction in aqueous solution. Because the native P takes a globular conformation where the hydrophobic amino acid residues exist inside of the globule, the hydrophobic interaction with R needs some conformational change of P. This conformational change may need to adsorb many R molecules on P simultaneously, being accompanied by the molar Gibbs energies Δμconf ° of the conformational change of P and Δμassoc ° of the association of R. The aggregation number of R molecules at this cooperative binding is denoted as n′, and a further non-cooperative binding of R may follow the cooperative binding. (Strictly speaking, Δμassoc ° at the cooperative and non-cooperative bindings may not be identical, but we ignore this difference in Δμ°assoc in the following.) In what follows, the uncomplexed protein is denoted as PmP, the complex formed by the cooperative binding is denoted as PnPRn′, the complex formed by the further non-cooperative binding is denoted as PnPRn′+n″, and the micelle of R is denoted as Rm. Here, mP, nP, n′, n″, and m are the aggregation numbers in each component. Then, the association−dissociation equilibria among the components are written as

curves in Figure 7 indicate the theoretical values, as explained in the Discussion section. SAXS. Excess scattering intensities Iθ obtained using SAXS for BLG, SDS, and BLG−SDS mixture (CP = 1.63 mM and CR = 16 mM; wR = 0.133; and c = 0.0346 g/cm3) in 50 mM sodium phosphate buffer are plotted against the magnitude of the scattering vector k in Figure 8. It can be seen from Figure 2

⎧ K cK a n ′ ⎪(nP /mP)PmP + n′R HoooooI PnPR n ′ ⎪ ⎪ Ka ⎨P R + R ⇌ PnPR n ′+ i (1 ≤ i ≤ n″) ⎪ nP n ′+ i − 1 ⎪ ⎪ mR HKoomI R ⎩ m

Figure 8. Excess scattering intensity Iθ obtained using SAXS for buffer solutions of BLG (CP = 1.63 mM; ○), BLG−SDS mixture (CP = 1.63 mM and CR = 16 mM; ●), and SDS (CR = 16 mM; △) plotted against the magnitude of the scattering vector k. The solid, dashed, and dotted curves indicate the theoretical values for the prolate with the shorter axis of 1.9 nm and the axial ratio of 2, the prolate with the shorter axis of 2.15 nm and the axial ratio of 2, and the double-layered sphere with the inner and outer radii of 1.4 and 2.3 nm, respectively (see the Supporting Information).

(14)

where Kc [≡exp(−Δμconf ° /RT)], Ka [≡exp(−Δμassoc ° /RT)], and Km are the equilibrium constants of the conformational change of P, of the association of R to P, and of the micellization of R, respectively, being defined by

that the scattering component is mostly the BLG−SDS complex at CP = 1.63 mM and CR = 16 mM. The scattering function for the BLG−SDS mixture is slightly different from that for BLG in a high k region, indicating that the local structure of BLG is slightly changed by complexation with SDS. Circular dichroism demonstrated that the β-sheet structure in the native BLG changes to the α-helix in the BLG−SDS complex (see Figure S2). The SDS micelle formed in aqueous solution possesses a hydrophobic core of a low electron density formed by dodecyl chains, which is reflected on the minimum of the SAXS scattering function,36 as shown in Figure 8. The scattering functions for the solution of the BLG−SDS mixture exhibit no such minimum, indicating that the BLG−SDS complex does not possess any hydrophobic core of low electron density formed by dodecyl chains. The scattering functions for BLG and SDS are fitted to the theoretical curves for a prolate and a double-layered sphere (see the caption of Figure 8). The scattering function for the BLG− SDS mixture is also fitted to a prolate slightly larger than the BLG dimer (the dashed curve in Figure 8), but the fitting is not so good. The scattering function for SDS has an upswing at low k, indicating the existence of a small amount of large aggregates, which corresponds to the slow relaxation component observed using DLS (see the filled triangles in Figure 1).

KcK a n ′ =

[PnPR n ′]

Ka =

, [PmP]nP / mP [R]n ′

(1 ≤ i ≤ n″),

Km =

[PnPR n ′+ i] [PnPR n ′+ i − 1][R]

[R m] [R]m

(15)

with the gas constant multiplied by the absolute temperature RT. Furthermore, from the mass conservation law, we have the following relations n″

C P = mP[PmP] + nP∑ [PnPR n ′+ i], i=0 n″

C R = [R] + m[R m] +

∑ (n′ + i)[Pn R n′+ i] P

0

(16)

Eqs 15 and 16 are simultaneous equations to obtain the molar concentration of each component. The calculation method is given in the Supporting Information. The above-mentioned theory contains five aggregation numbers, mP, nP, n′, n″, and m, and three equilibrium constants, Kc, Ka, and Km. The SLS result at CR/CP = 0 in Figure 7 indicates that BLG exists mainly as the dimer in 50 mM sodium phosphate buffer, that is, mP = 2. The aggregation number m and the association constant Km for the SDS micelle have been determined to be m = 70 and log(Km/M1−m) = 175 using SLS (see Table S1). Here, we first assume that BLG in the complex is also the dimer. Then, by choosing nP = 2, the fraction fA,PR of the BLG−

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DISCUSSION Model for the Complexation of the Globular Protein and the Surfactant. The globular protein P and the surfactant 5495

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Figure 9. CR/CP dependences of the population fA,PR of the complex PR and of the weight-average aggregation number nw of R in the complex PR, calculated from eqs S14 and S12 using several sets of adjustable parameters (εR = 0). All curves except for the thin solid curve in panel b, calculated with nP = 2, Kc = 200, and n″ = 100, along with Ka = 320 M−1 and n′ indicated in the panels for the solid, dashed, and dot-dashed curves, and with Ka = 250 M−1 and n′ = 15 for the dotted curve. The thin solid curve in panel b, calculated with nP = 1, n′ = 7.5, Ka = 360 M−1, Kc = 4, and n″ = 100.

binding of SDS to BLG at such a low CR/CP. We have neglected this initial binding39 at CR/CP < 1 because the mobility change of P at CR/CP < 1 is much smaller than that of PR, indicating that the number of SDS molecules interacting with BLG is so small at the initial binding. Using the parameters determined above, we can calculate Mw,av, as explained in the Supporting Information. The result is indicated by the solid curve for Mw,av in Figure 7. The theoretical curve almost agrees with the experimental results at CR/CP ≲ 20 but appreciably overestimates at CR/CP ≳ 20, indicating that the BLG dimer in the PR complex dissociates into the unimer at a high CR/CP. Thus, we have calculated fA,PR and Mw,av, assuming nP = 1. Choosing the parameter values listed in the third row of Table 1 (nP = 1), we obtain almost the same solid curve for fA,PR in Figure 4 at CR/CP ≳ 5 and the dashed curve for Mw,av in Figure 7. The latter curve agrees with the experimental results of Mw,av at CR/CP > 30. The increase in Mw,av at CR/CP > 30 corresponds to the increase in nw. The thin solid curve in Figure 9b shows nw at nP = 1 and other parameters listed in the third row of Table 1. (Although the thin solid curve shows nw only at CR/CP < 20, it keeps increasing at CR/CP > 20.) Again, n″ and Kc in the third row of Table 1 (nP = 1) are not so decisive because they are not sensitive to fA,PR and Mw,av, especially at CR/CP > 20. The calculation of RH,av needs the values of the hydrodynamic radii of the uncomplexed P (RH,P), the complex PR (RH,PR), and the micelle of R (RH,Rm) in eq S19. From the results of RH,av at CR/CP = 0 in Figure 7 and of DLS for aqueous SDS solution (see Table S1), we can choose RH,P = 2.9 nm and RH,Rm = 2.2 nm. The solid and dashed curves for RH,av in Figure 7 indicate the theoretical values for nP = 2 and 1, respectively, using parameters listed in the second and third rows of Tables 1 and 2. The former and latter curves agree with the experimental results at CR/CP ≲ 20 and CR/CP ≳ 30, respectively. Tanford et al.38 reported the sedimentation coefficients of various proteins, including BLG, taking the random coil conformation in concentrated aqueous guanidine hydrochloride. According to their results, RH of the single BLG chain taking the random coil conformation is estimated to be 3.5 nm. When this value is used as RH,PR for the PR complex with nP = 1, we obtain the dash-dot curve in Figure 7, which

SDS complex determined using CZE (see Figure 4) and the weight-average aggregation number nw of R in the complex PR are simulated from eqs S14 and S12, respectively, using several sets of adjustable parameters n′, n″, Kc, and Ka (Figure 9). In panel a, fA,PR increases more gradually with increasing n′, and the asymptotic value of fA,PR at high CR/CP decreases with decreasing Ka. Because the sum of the finite series S0(x) given by eq S10 rapidly approaches asymptotic values with increasing n″, fA,PR is insensitive to n″ for sufficiently large n″. The variation in Kc within ±100 does not essentially change fA,PR. As shown by the solid, dashed, and dot-dashed curves in Figure 9b, nw increases with increasing CR/CP in two steps, corresponding to the cooperative binding and the subsequent non-cooperative binding. However, the dotted curve for Ka = 250 M−1 does not show the increase in the second step. This is because of the weak non-cooperative binding, and R forms the micelle rather than adsorbing to P with increasing CR/CP. As a result, fA,PR did not attain unity in panel a. (The thin solid curve in panel b will be explained later.) Comparison with Experimental Results. The solid curve for fA,PR in Figure 4 is identical to the solid curve in Figure 9a, and the solid curve for fA,P in Figure 4 is obtained by 1 − fA,PR. These theoretical curves agree satisfactorily with the experimental data. The fitting parameters chosen are listed in the second row of Table 1 (nP = 2). As mentioned above, the values of n″ and Kc are not so decisive. Table 1. Parameters Used in the Fitting of the CZE and SLS Results for the BLG−SDS Mixture in 50 mM Sodium Phosphate Buffer Shown in Figures 4 and 7 mP

nP

n′

n″

Kc

Ka/M−1

m

log (Km/M1−m)

2 2

2 1

15 7.5

100 100

200 4

320 360

70

175

Circular dichroism measurements demonstrated the secondary structural change from the β-sheet to the α-helix of BLG at C R /C P ≈ 0.5 at C P = 0.054 mM (see Figure S3). Correspondingly, the mobility of P shown in Figure 3 (unfilled circles) slightly decreases at CR/CP < 1. These results indicate some interaction between BLG and SDS even at CR/CP < 1. The fitting parameters listed in Table 1 do not predict any 5496

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Table 2. Hydrodynamic Radii Used in the Fitting of the DLS Results for the BLG−SDS Mixture in 50 mM Sodium Phosphate Buffer Shown in Figure 7 CR/CP

mP

nP

RH,P/nm

RH,PR/nm

RH,Rm/nm

≲20 ≳30

2 2

2 1

2.9 2.9

3.2 2.45

2.2 2.2

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b00941. SLS and DLS for the aqueous SDS solution; circular dichroism spectra; method for calculating compositions and light-scattering quantities in the protein−surfactant solution; and the calculation method of SAXS profiles of the globular protein and the surfactant micelle (PDF)

appreciably overestimates the experimental result of RH,av at CR/CP ≳ 30. When the native BLG dimer is viewed as a dumbbell, the hydrodynamic radius of the constituent sphere is calculated to be 2.15 nm by (3/4)RH,P,37 which is rather close to the RH,PR value (=2.45 nm) giving the dotted curve for RH,av in Figure 7. Thus, the BLG unimer in the PR complex at CR/CP ≳ 30 still takes a compact conformation rather than the “necklace” model for protein−surfactant complexes,21,40 although approximately 40 SDS molecules are adsorbed on the BLG unimer. The SAXS scattering function for BLG in 50 mM sodium phosphate buffer can be nicely fitted by the prolate with the shorter axis (the equatorial radius) of 1.9 nm and the axial ratio of 2, as shown by the solid curve in Figure 8. The hydrodynamic radius for this prolate is calculated to be 2.5 nm,37 which is slightly smaller than RH,P (=2.9 nm) obtained using DLS, being affected by the hydration of BLG. The dashed curve in Figure 8 is the theoretical curve for the prolate with the shorter axis of 2.15 nm and the axial ratio of 2, which is close to the experimental profile of the BLG−SDS complex at CR/CP = 10. The hydrodynamic radius for this prolate is calculated to be 2.8 nm,37 which is close to but somewhat smaller than RH,PR (=3.2 nm) obtained using DLS for the PR complex at CR/CP ≲ 20. In the PR complex, approximately 20 SDS molecules are adsorbed on the BLG dimer, which make the global size of the complex slightly larger than RH,P. The change in the secondary structure of the BLG dimer in the complex (see Figure S3) may also contribute to the difference between RH,PR and RH,P.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Takahiro Sato: 0000-0002-8213-7531 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS CZE measurements were taken with the support of Otsuka Electronics Co., Ltd. We thank Dr. K. Terao and Dr. R. Takahashi for helping with the SAXS measurements and Prof. A. Hashidzume for his comments on CZE measurements. The SAXS data were acquired at the BL40B2 beamline in SPring-8 with the approval of the Japan Synchrotron Radiation Research Institute (JASRI) (Proposal No. 2015B1674 and 2016A1053).

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REFERENCES

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CONCLUSIONS We have investigated the complexation between BLG and SDS in 50 mM sodium phosphate buffer by combining CZE, SLS, DLS, ELS, and SAXS. The fractions of the free BLG and the BLG−SDS complex were determined, using CZE combined with ELS, as functions of the molar concentration ratio CR/CP of SDS to BLG. The binding of SDS to BLG starting at CR/CP ≈ 1 is cooperative, followed by independent binding at higher CR/CP. SLS and DLS data for the aqueous solutions of the BLG− SDS mixture were analyzed by using the fractions of the free BLG, the BLG−SDS complex, and the SDS micelle determined using CZE. The analyzed results revealed that the BLG−SDS complex formed by the cooperative binding consists mainly of the BLG dimer and approximately 20 SDS molecules and takes a compact conformation, the size of which is close to the native BLG dimer at CR/CP ≲ 20. The compact conformation of the BLG−SDS complex is supported by the SAXS experiment. At CR/CP higher than 30, the BLG dimer in the BLG−SDS complex dissociates into the unimer. Although approximately 40 SDS molecules are adsorbed on the dissociated BLG unimer, the BLG unimer still does not take the random coil conformation (the “necklace” model) as illustrated in the literature23,40 but a compact conformation at least at 30 < CR/ CP < 65. 5497

DOI: 10.1021/acs.langmuir.7b00941 Langmuir 2017, 33, 5491−5498

Article

Langmuir

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DOI: 10.1021/acs.langmuir.7b00941 Langmuir 2017, 33, 5491−5498