Anal. Chem. 1998, 70, 1339-1345
Measurement of SDS Micelle-Peptide Association Using 1H NMR Chemical Shift Analysis and Pulsed-Field Gradient NMR Spectroscopy Laszlo Orfi,† Mengfen Lin,‡ and Cynthia K. Larive*
Department of Chemistry, University of Kansas, Lawrence, Kansas 66045
The binding of two simple tripeptides, glycyl-histidylglycine (GHG) and phenylalanyl-histidyl-phenylalanine (FHF) with SDS micelles was examined using 1H NMR chemical shift analysis and self-diffusion coefficients measured with pulsed-field gradient NMR spectroscopy. The presence of GHG or FHF did not appear to significantly affect the critical micelle concentration (cmc) or the average size of the SDS micelles formed. The chemical shifts of several of the GHG resonances change as a function of SDS concentration, indicating an interaction between the peptide and the micelles. In addition, the concentration-dependent decrease observed for the GHG diffusion coefficients suggests association of the peptide with SDS micelles. The free and micelle-associated GHG are in fast exchange on both the 1H chemical shift and diffusion time scales. The equilibrium constant for the binding of GHG to SDS micelles was determined from the analysis of the concentration dependence of the histidine C2 and C4 resonances to be 17 ( 5 and 24 ( 6 M-1, respectively. The precision of the equilibrium constants obtained by analysis of the chemical shift data is limited by the small chemical shift changes observed. Analysis of the concentration dependence of the diffusion coefficients produced an equilibrium constant of 17 ( 1 M-1. The more hydrophobic peptide, FHF is strongly associated with the SDS micelles. Because the fraction of free FHF is small in these solutions, it was not possible to determine a formation constant for the interaction of FHF with the SDS micelles by analysis of either the 1H chemical shift or diffusion coefficient data. The cmc of SDS in 0.10 M Na2C2O4 buffer was determined to be 5.4 ( 0.1 mM by analysis of the SDS diffusion coefficients in the absence of the peptides. The SDS cmc could also be extracted from the GHG and FHF diffusion coefficients measured as a function of the SDS concentration. The cmc determined from the GHG diffusion data, 5.7 ( 0.2 mM, is in good agreement with the value determined from analysis of the SDS diffusion coefficients in the 5.0 mM GHG solution, 5.2 ( 0.1 mM. The smaller cmc determined from the FHF diffusion data, 4.1 ( 0.1 mM, may reflect S0003-2700(97)01011-1 CCC: $15.00 Published on Web 02/28/1998
© 1998 American Chemical Society
some association of the SDS with the peptide prior to micelle formation in bulk solution. Micelles have become increasingly important in analytical chemistry as mobile-phase modifiers in chromatography and in spectrochemical analysis through their enhancement of fluorescence. Micelles of sodium dodecyl sulfate (SDS) are also often used to solubilize membrane proteins or to mimic the membrane environment in the conformational analysis of bioactive peptides.1-6 However, the association equilibria that describe peptide-micelle binding have not been extensively examined. The nature of peptide-micelle interactions is therefore an important area of research. In this work, the interactions of two simple tripeptides, glycyl-histidyl-glycine (GHG) and phenylalanyl-histidyl-phenylalanine (FHF), with SDS micelles have been examined using chemical shift analysis and self-diffusion coefficients measured with NMR spectroscopy. Both peptides carry a net single positive charge under the conditions of these experiments and therefore are attracted to the negatively charged SDS micelles by electrostatic interactions. In addition, the more hydrophobic peptide, FHF, forms stable adducts in which the aromatic side chains of the phenylalanine residues penetrate into the organic interior of the micelle. The aggregation number of a surfactant reflects the average number of monomers that are associated as micelles. For charged micelles, such as SDS, the aggregation number increases with increasing counterion concentration as evidenced by a lower critical micelle concentration (cmc) when an excess of counterions is present in solution.7,8 An aggregation number of 64 is reported for SDS at concentrations well above the cmc, and on average, † Permanent address: Institute of Pharmaceutical Chemistry, Semmelweis University of Sciences, Hogyes E. u.9. 1092, Budapest, Hungary. ‡ Permanent address: Central Research Division, Pfizer Inc., Eastern Point Road, Groton, CT 06340. (1) Parker, W.; Song, P.-S. Biophys. J. 1992, 61, 1435-1439. (2) McDonnell, P. A.; Opella, S. J. J. Magn. Reson. 1993, 102, 120-125. (3) Bruch, M. D.; Rizo, J.; Gierasch, L. M. Biopolymers 1992, 32, 1741-1754. (4) Kloosterman, D. A.; Scahill, T. A.; Friedman, A. R. Pept. Res. 1993, 6, 211218. (5) Young, J. K.; Anklin, C.; Hicks, R. P. Biopolymers 1994, 34, 1449-1462. (6) Battistutta, R.; Bisello, A.; Mammi, S.; Peggion, E. Biopolymers 1994, 34, 1535-1541. (7) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem. 1995, 99, 828-834. (8) Dingley, A. J.; Mackay, J. P.; Chapman, B. E.; Morris, M. E.; Kuchel, P. W.; Hambly, B. D.; King, G. F. J. Biomol. NMR 1995, 6, 321-328.
Analytical Chemistry, Vol. 70, No. 7, April 1, 1998 1339
approximately 47 counterions are associated with each micelle.9 Diffusion coefficients measured as a function of surfactant concentration can be used to determine surfactant aggregation numbers. SDS diffusion coefficients measured by a variety of methods including sedimentation equilibrium,10 interferometry,11 surface tension,12 and NMR13 have been reported. Above the cmc, SDS molecules exist in a dynamic equilibrium between monomeric and micellar species; therefore, the diffusion coefficients measured with PFG NMR can be treated as a weighted average of the monomeric and micellar values. Pulsed-field gradient (PFG) NMR measurements of diffusion coefficients have been used to characterize large protein-SDS micelle complexes, by focusing on the SDS diffusion.7,8 The high information content of NMR spectroscopy offers an advantage in the study of the interactions of peptides with SDS micelles since the chemical shifts and diffusion coefficients of SDS and the peptide are measured simultaneously. An additional advantage is that, as a noninvasive methodology, the positions of the SDS monomer-micelle and peptide-micelle equilibria are unaffected by the NMR measurements. EXPERIMENTAL SECTION Materials. Glycyl-histidyl-glycine was obtained from Sigma. Phenylalanyl-histidyl-phenylalanine was synthesized by the Kansas State University Biotechnology Facilities Microchemical Core Laboratory. Both peptides were used as supplied without further purification. D2O (99.96% d, Cambridge Isotope Laboratories) was used as the solvent in these studies. DCl (Cambridge Isotope Laboratories) and NaOD (Isotec Inc.) were used to adjust the solution pH. All pH measurements were made with a Fisher Scientific Acumet 10 pH meter using a 3-mm Ingold combination microelectrode calibrated with aqueous pH buffers. The pD values reported for D2O solutions have been corrected for the isotope effect using the relationship pD ) pH meter reading + 0.4.14 A 0.10 M solution of sodium oxalate (Fluka) buffer in D2O, pD 5.40, was used to prepare the SDS/peptide solutions. Stock solutions of SDS (Aldrich), 200.0 mM, and GHG, 20.0 mM, were prepared by dissolving the appropriate weights of the solids in the sodium oxalate buffer solution. Because of its lower solubility, the FHF stock solution was prepared at a concentration of 10.0 mM in sodium oxalate buffer containing 40.0 mM SDS to enhance the solubility of the peptide. The peptide/SDS ratio of a sample was adjusted prior to analysis by diluting the appropriate volumes of the peptide and SDS stock solutions with sodium oxalate buffer. This procedure maintained constant pD and counterion concentration in the solutions studied. NMR Spectroscopy. NMR spectra were measured using a Bruker AM500 spectrometer at 298 K. One-dimensional 1H NMR spectra were acquired with a 6024-Hz spectral width and 16 384 data points. Proton chemical shifts are reported relative to (9) Moroi, Y. J. Colloid Interface Sci. 1988, 122, 308-314. (10) Doughty, D. A. J. Phys. Chem. 1979, 83, 2621-2628. (11) Sasaki, T.; Hattori, M.; Sasaki, J.; Nukina, K. Bull. Chem. Soc. Jpn. 1975, 48, 1397-1403. (12) Mikati, N.; Wall, S. Langmuir 1993, 9, 113-116. (13) So¨derman, O.; Stilbs, P. Prog. Nucl. Magn. Reson. Spectrosc. 1994, 26, 445482. (14) Bates, R. G., Ed. Determination of pH: Theory and Practice; Wiley: New York, 1964; pp 219-220.
1340 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998
external 3-(trimethylsilyl)propionic acid-2,2,3,3-d4 sodium salt (TSP, Aldrich). No correction for magnetic susceptibility effects was applied. The proton resonances of the peptides in 90% H2O/10% D2O solution at pH 3 were assigned using homonuclear decoupling and two-dimensional NMR spectra measured by use of the standard experiments COSY and NOESY. All one- and twodimensional NMR spectra measured in 90% H2O/10% D2O employed selective saturation for suppression of the solvent resonance. The chemical shift assignments in D2O solution at pD 5.4 were then derived by NMR pH titration of the peptide solutions. For FHF at pD 5.4, the aromatic resonances, although well resolved, were sufficiently complex that they could not be directly assigned from the homonuclear 2D spectra. The 1H13C HMQC spectrum was used in conjunction with the NOESY spectrum to complete the assignments of the aromatic proton resonances. Diffusion Coefficient Measurements. Diffusion coefficients were measured by PFG NMR spectroscopy using the bipolar pulse pair longitudinal encode-decode (BPP-LED) sequence.15 In this experiment, a longitudinal eddy current delay, Te (20 ms in our experiments), is used to minimize spectral artifacts resulting from residual eddy currents. The BPP-LED spectra were measured using a Bruker AM500 MHz spectrometer specially modified to accommodate pulsed-field gradient experiments. The details of the gradient instrumentation have been described previously.16 A 5-mm Bruker inverse probe with an actively shielded z-gradient coil was used. The coil constant was calibrated with β-cyclodextrin, which has a diffusion coefficient of 3.23 × 10-10 m2 s-1.17 In the BPP-LED experiment, the attenuation of the NMR resonance depends on gradient area as shown in eq 1, where Io
I ) Io exp[-D(∆ - δ/3 - τ/2)γ2g2δ2]
(1)
is the intensity of the resonance in the NMR spectrum in the absence of gradient pulses, γ is the gyromagnetic ratio, ∆ is the time period during which diffusion occurs, g and δ are the amplitude and duration of the bipolar gradient pulse pair, respectively, and D is the self-diffusion coefficient. The delay, τ, between the bipolar gradient pulse pair was 1.2 ms. Typically, in each PFG-NMR experiment, a series of 27 1H spectra were collected with the BPP-LED pulse sequence as a function of gradient amplitude. In our experiments, the gradient duration time, δ was 2 ms, the gradient amplitude varied from 0.024 to 0.4 T m-1 and the diffusion delay time, ∆, was either 0.2 or 0.35 s. All of the diffusion measurements were performed at 298 K. The individual free induction decays were transferred to a Silicon Graphics Indigo workstation and processed using Felix 95 software (Biosym). Following Fourier transformation, the series of spectra obtained as a function of gradient amplitude were processed using diffusion ordered spectroscopy (DOSY) methodology with computer programs generously provided by Dr. Charles S. Johnson, Jr., as described previously.16,18,19 Diffusion (15) Wu, D.; Chen, A.; Johnson, C. S., Jr. J. Magn. Reson. 1995, 115, 260-264. (16) Lin, M.; Jayawickrama, D. A.; Rose, R. A.; DelViscio J. A.; Larive, C. K. Anal. Chim. Acta 1995, 307, 449-457. (17) Uedaira, H.; Uedaira, H. J. Phys. Chem. 1970, 74, 2211-2214. (18) Morris, K. F.; Johnson, C. S., Jr. J. Am. Chem. Soc. 1993, 115, 4291-4299. (19) Morris, K. F.; Stilbs, P.; Johnson, C. S., Jr. Anal. Chem. 1994, 66, 211215.
coefficients were extracted using the program SPLMOD.20,21 In each case, the results of our experiments were fit by a single diffusion coefficient. Determination of Solution Concentration. If the SDS concentrations were calculated on the basis of dilution from the stock solution, the concentration dependence of the diffusion coefficients measured for solutions just below and above the cmc deviated from the expected values. Similar observations have been reported in the literature.12 Therefore, the concentrations of SDS and GHG were determined experimentally from the relative integrals of the NMR resonances of the TSP external chemical shift standard, the histidine β-protons of the peptides, and the SDS methyl protons in quantitative 1H NMR spectra acquired for these solutions immediately prior to the diffusion measurements. Over the concentration range of 3-8 mM, the NMR-derived SDS concentrations were significantly lower than the value calculated by dilution. The deviation of the NMR-derived SDS concentrations from the value expected based on dilution from a stock solution most likely results from adsorption of SDS onto the glassware.11 An advantage of NMR analysis is that, in addition to measurement of diffusion coefficients, this nondestructive method can also be used for the quantitative determination of each analyte using the same solutions and an external concentration standard.22 RESULTS AND DISCUSSION The peptides examined in this study were chosen to probe the role of charge and hydrophobic interactions in micelle binding. Under the conditions of our experiments, both peptides carry a net positive charge. The carboxy termini of the peptides are deprotonated while the N-terminal amino groups and histidine imidazole moieties are protonated at pD 5.4. The ionic strength and controlled sodium ion concentration provide both constant dispersity for the surfactant and constant ionization state for the peptides. The interactions between the peptides and SDS were examined by systematically changing the SDS concentration from 0.4 to 60.0 mM while maintaining constant concentrations of GHG (5.0 mM) or FHF (1.0 mM). The cmc of SDS in 0.10 M sodium oxalate buffer was determined by plotting the diffusion coefficient as a function of SDS concentration. A cmc of 5.4 ( 0.1 mM was calculated from the breakpoint determined by linear least-squares analysis of the two segments of the curve, similar to that shown in Figure 1. The differences in the diffusion coefficients of SDS in D2O and in sodium oxalate buffer at the same pD, summarized in Table 1, illustrates the dependence of the cmc on the counterion concentration. Our results are consistent with the well-established literature for this surfactant.10 GHG-SDS Binding Interaction. The chemical shifts of the proton resonances of GHG and FHF in aqueous solution at pH 5.4 in sodium oxalate buffer are listed in Table 2. Table 3 summarizes the chemical shifts of the glycine R and histidine C2 and C4 protons of GHG as a function of the SDS concentration. (20) Provencher, S. W.; Vogel, R. H. In Numerical Treatment of Inverse Problems in Differential and Integral Equations; Dueflhard, P., Hairer, E., Eds.; Birkhauser: Boston, MA, 1983; pp 304-319. (21) Vogel, R. H. SPLMOD Users Manual Technical Report DA06; European Molecular Biology Laboratory, Heidelberg, 1983. (22) Larive, C. K.; Jayawickrama, D. A.; Orfi, L. Appl Spectrosc. 1997, 51, 15311536.
Figure 1. Concentration dependence of the SDS diffusion coefficient (O) measured for solution SDS in 0.1 M Na2C2O4 buffer and 5 mM GHG. A cmc of 5.2 ( 0.1 mM was determined from the point of intersection of the straight lines fit through the data points in each region of the curve.
The R-proton resonances of the GHG glycine residues, which are nonequivalent in D2O solution, become more equivalent as the SDS concentration is increased. The glycine R-proton chemical shifts and coupling constants were calculated using the equations for an AB spin system for solutions with SDS concentrations up to 50.0 mM. At concentrations greater than 50.0 mM, the HA and HB protons of glycine were neither resolvable nor identical and their chemical shifts could not be determined. These results suggest that, in the presence of the SDS micelles, the peptide backbone assumes a less rigid conformation than in aqueous solution. Because of the relatively low hydrophobicity of this simple peptide, stabilization of the GHG-micelle complex most likely results from charge interactions between the negatively charged micelles and the positively charged histidine imidazole and N-terminal ammonium moieties of the peptide.23 Chemical shift analysis as a function of the surfactant concentration can be used to quantitatively interpret peptide-micelle association. Because exchange of the free and micelle-associated GHG is fast on the NMR time scale, the measured chemical shift can be expressed as a weighted average of the free and bound chemical shifts:
δobs ) ffreeδfree + fbdδbd
(2)
where δobs is the observed chemical shift of the resonance of interest and δfree and δbd are the chemical shifts of the free and (23) Carlsson, I.; Edlund, H.; Persson, G.; Lindstrom, B. J. Colloid Interface Sci. 1996, 180, 598-603.
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1341
Table 1. Diffusion Coefficients × 1010 (m2 s-1) of SDS, GHG, and FHF as a Function of SDS Concentration in D2O Solution of 0.10 M Sodium Oxalate Buffer DSDS [SDStot] (M) 0 0.0004 0.001 0.002 0.003 0.004 0.005 0.006 0.008 0.010 0.016 0.020 0.030 0.040 0.050 0.060 a
in D2O
in GHGa
in buffer
in FHFb
DGHG in GHGa
DFHF in FHFb
5.57
5.09 5.62
5.82 4.90 3.25 5.00
4.52 2.91 2.40 2.05 1.78 1.73 1.62 1.46
2.16 1.92 1.47
2.26 1.46 1.11 1.04 0.91
1.18 1.07 1.06
1.62 1.46 1.22 1.18 1.04 0.97
1.22 1.12 1.12 1.08 0.87
0.91
5.23 5.16 5.14 5.09 5.00 4.89 4.79 4.68
2.97
4.18 3.85 3.62 3.29 2.86
0.89
2.50 1.51 1.19 0.93 0.96 0.93 0.89 0.91
Concentration of GHG was 5.0 mM. b Concentration of FHF was 1.0 mM.
Table 2.
1H
NMR Parameters of GHG and FHF chemical shift, δ (ppm)
amino acid residue
NH
GHGa 1Gly
3.857 3.765 4.852
2His 3Gly
FHFb 1Phe
CRH
8.428
CβH
spin-spin coupling constants (Hz)
aromatic protons
3J NH-CRH
3J
CRH-CβH
2J 2 CRH-CRH JCβH-CβH
24.3 3.260 3.304
C2H 8.541 C4H 7.329
3.889 3.829
6.6 6.0 5.5
4.179
3.087 3.012
2His
4.586
3.136
3Phe
4.393
3.230 2.954
C2,6H 7.109 C3,5H 7.233 C4′H 7.268 C2H 8.453 C4H 7.209 C2,6H 7.324 C3,5H 7.387 C4H 7.300
15.5 17.3
7.1 7.6
14.1
6.3 7.4
4.6 9.3
14.1
a Conditions: H O, pH 5.4, 25 °C. b Conditions: H O, pH 5.0, 25 °C, except for the His R-proton resonance of GHG, which was determined in 2 2 D2O, pD 5.0 using the WEFT experiment.
micelle-bound peptides, respectively. Assuming only two peptide species, free and micelle-bound, the sum of the mole fractions of free, ffree, and micelle-bound, fbd, peptide must equal 1 by definition. Because the GHG proton chemical shifts in SDS solutions below the cmc differed from those reported in Table 2 in the absence of SDS, the value of δfree was calculated from the average of the chemical shifts measured for SDS solutions below the cmc. However, the determination of the value of δbd was less straightforward. The chemical shift of the bound peptide was estimated from the Y intercept of the line obtained by plotting chemical shift vs reciprocal SDS concentration for solutions from 40.0 to 60.0 mM SDS. Assuming that the only interaction that occurs is between the peptide and micellar SDS, the equilibrium expression describing peptide-micelle binding, is
K ) [GHGbd]/([GHGfree][SDSmic]) 1342 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998
(3)
where [GHGfree] and [GHGbd] are the concentration of the free and micelle associated peptide, respectively. The micellar SDS concentrations, [SDSmic], were determined from the diffusion measurements as described in the subsequent section and are reported in Table 4. Solving eq 2 for the fractions of the free and bound peptide in terms of chemical shifts and substituting for the concentrations of the free and bound peptide in eq 3 results in the following expression for the binding constant:
K ) (δobs - δfree)/((δbd - δobs)[SDSmic])
(4)
The equilibrium constants for GHG-SDS micelle binding, summarized in Table 4, were calculated from the chemical shifts of the C2 and C4 protons of the histidine imidazole moiety to be 17 ( 5 and 24 ( 6 M-1, respectively. The relatively small chemical shift change over the concentration range studied and the determination of δbd by extrapolation contribute to the high errors
Table 3. Chemical Shifts (ppm) of Selected GHG Resonances as a Function of SDS Concentration [SDStot] (M)
1GlyCRH
none
3.857 3.765 3.847 3.764 3.844 3.761 3.840 3.761 3.841 3.763 3.841 3.764 3.840 3.763 3.836 3.767 3.832 3.770 3.830 3.777 3.825 3.776 3.820 3.777 nda
0.002 0.003 0.004 0.005 0.006 0.008 0.010 0.020 0.030 0.040 0.050 0.060 δfree δbd a
2
δHA, δHB
2His δC2H
2His δC4H
8.541
7.329
8.593
7.352
8.589
7.349
8.592
7.351
8.595
7.355
8.588
7.352
8.594
7.354
8.597
7.362
8.602
7.373
8.612
7.382
8.618
7.389
8.622
7.397
8.632 8.592 8.663
7.403 7.352 7.431
3GlyCRH
2
δHA, δHB 3.889 3.829 3.882 3.843 3.880 3.841 3.881 3.842 3.881 3.840 3.882 3.840 3.881 3.838 3.888 3.849 3.894 3.850 3.898 3.864 3.902 3.867 3.905 3.871 nd
nd, not determined.
Table 4. Equilibrium Constants for the Association of GHG with SDS Micelles Calculated by Analysis of 1H Chemical Shift (δ) and GHG Diffusion Coefficients as a Function of SDS Concentration Kchem shift (M-1) 2His-HC4
KGHG diffusn coeff (M-1)
[SDStot]
[SDSmic]
2His-HC2
0.0100 0.0200 0.0300 0.0400 0.0500 0.0600
0.0088 0.018 0.028 0.038 0.048 0.056
9 21 20 14 15 23
16 19 25 23 27 32
17 17 17 16 17 17
17 (5
24 (6
17 (1
mean SD
in the equilibrium constants calculated from these data. Although concentration-dependent changes in chemical shift are also observed for the glycine protons, the magnitude of these changes was too small to produce reliable values for the equilibrium constant. In addition, because of strong coupling between the inequivalent glycine protons, the chemical shifts of the glycine HA and HB protons must be calculated rather than measured directly from the spectrum, reducing the precision of these chemical shifts. NMR Diffusion Measurements. The interaction between GHG and SDS micelles can also be quantified by examination of the GHG diffusion coefficients as a function of the SDS concentration, summarized in Table 1. Because the concentrations of the SDS solutions varied slightly between trials, the values reported in Table 1 are rounded to one significant figure; however, exact concentrations with two or three significant figures were used in
all calculations and in the preparation of the figures. For comparison of the two peptides, the diffusion coefficients of both GHG and FHF are plotted as a function of SDS concentration in Figure 2a. The diffusion coefficients of GHG in solutions of constant peptide concentration (5.0 mM) decrease dramatically with increasing SDS concentration, confirming a binding equilibrium as hypothesized from the chemical shift data. To evaluate whether the changes in the GHG diffusion coefficients could be explained simply by crowding or viscosity changes over the range of SDS concentrations examined, the diffusion coefficient of the nonassociating molecule, β-mercaptoethanol, was measured in 0.10 M sodium oxalate buffer in D2O (1.01 × 10-10 m2 s-1) and in 60.0 mM SDS solution (1.06 × 10-10 m2 s-1) and was found to be in good agreement with the literature value.24 Therefore, the decrease in the GHG diffusion coefficient as a function of SDS concentration results from an interaction of the peptide with SDS micelles and not from a change in the physical properties of the solutions. The effect of solution conditions on the SDS diffusion coefficient for solutions in D2O, 0.10 M sodium oxalate, 5.0 mM GHG in 0.10 M sodium oxalate, and 1.0 mM FHF in 0.10 M sodium oxalate can be discerned from analysis of the results given in Table 1. The noticeable effect of counterions on SDS diffusion can be observed by comparison of the diffusion coefficients of SDS in D2O and in sodium oxalate buffer. Under the conditions of our experiments, the presence of 5.0 mM GHG had no significant effect on SDS diffusion coefficients. However, small deviations in the SDS diffusion coefficients at concentrations below 20 mM are observed in the presence of 1.0 mM FHF. Similarly to the averaging of NMR chemical shifts in the presence of fast exchange, exchange averaged diffusion coefficients are also observed in the fast exchange limit for the association of molecules with significantly different diffusion coefficients, although the chemical shift and diffusional time scales are not necessarily equivalent.13,16,25-27 In the fast-exchange limit, the measured diffusion coefficient is a weighted average given by
Dobs ) ffreeDfree + fbdDbd
(5)
In the application of this general equation to aggregation of SDS to form micelles, Dobs is the observed SDS diffusion coefficient, Dfree is the diffusion coefficient of monomeric SDS, Dbd is the diffusion coefficient of micellar SDS, and ffree and fbd are the mole fractions of the monomeric and micellar SDS, respectively. The concentration of micellar SDS, [SDSmic], in Table 4, is calculated by multiplication of the fraction of the bound SDS from eq 5 and the total SDS concentration. The monomeric SDS diffusion coefficient, 5.82 × 10-10 m2 s-1 was measured for a 0.4 mM SDS solution in 0.10 M sodium oxalate buffer in D2O. The micellar diffusion coefficient, 0.86 ( 0.04 × 10-10 m2 s-1 (R ) 0.99, N ) 6) used in our calculations was obtained from the Y intercept determined by linear least-squares analysis of the graph of SDS (24) Chen, A.; Wu, D.; Johnson, C. S., Jr. J. Phys. Chem. 1995, 99, 828-834. (25) Johnson, C. S., Jr. J. Magn. Reson. A 1993, 102, 214-218. (26) Lin, M.; Larive, C. K. Anal. Biochem. 1995, 229, 214-220. (27) Waldeck, A. R.; Kuchel, P. W.; Lennon, A. J.; Chapman, B. E. Prog. Nucl. Magn. Reson. Spectrosc. 1997, 30, 39-68.
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1343
the SDS-buffer solution, indicating that binding of the peptide does not significantly affect micelle formation. Because the free and micelle-bound GHG are in fast exchange on both the chemical shift and diffusion time scales, the equilibrium constant for the binding of the peptide with SDS micelles can be calculated from eq 5 in a manner analogous to that used in the analysis of SDS aggregation. This equation can be used to analyze peptide-micelle interactions by defining the parameters as follows: Dobs is the observed peptide diffusion coefficient, Dfree is the diffusion coefficient of the unbound peptide, Dbd is the diffusion coefficient of micellar SDS, and ffree and fbd are the mole fractions of the free and micelle-bound peptide, respectively. The diffusion coefficient of GHG in 0.10 M sodium oxalate buffer in the absence of SDS, Dfree, was determined to be 5.26 × 10-10 m2 s-1 by extrapolation of the experimental diffusion data to zero SDS concentration. The micellar diffusion coefficient was calculated as described earlier from the analysis of SDS diffusion coefficients. Because the micellar SDS diffusion coefficient is not dependent on the presence of the peptide and because the size of the peptide is small compared to that of the micelle, the assumption that the diffusion coefficient of the micelle-bound peptide is equivalent to the micellar diffusion coefficient is probably reasonable. The GHG-SDS micelle binding constant can be calculated by substitution of the fractions of the free and bound peptide solved in terms of diffusion coefficents into the expression for the equilibrium constant:
K ) (Dobs - Dfree)/((Dbd - Dobs)[SDSmic])
Figure 2. (a) Diffusion coefficients of 5 mM GHG (O) and 1 mM FHF (b) in 0.1 M Na2C2O4 buffer as a function of SDS concentration. A cmc of 4.1 ( 0.1 mM SDS was determined from the point of intersection of the straight lines fit through the data points in each region of the FHF curve. (b) Expansion of the GHG diffusion data from 2 to 10 mM SDS. A cmc of 5.7 ( 0.2 mM SDS is determined from the sigmoidal fit of these data.
diffusion coefficients against the reciprocal SDS concentration above the cmc. The diffusion coefficients of micellar SDS in concentrated SDS solutions calculated for the GHG solutions were equivalent within experimental error to the value calculated for 1344 Analytical Chemistry, Vol. 70, No. 7, April 1, 1998
(6)
This treatment of the peptide-micelle equilibrium is exactly analogous to the chemical shift analysis in the fast-exchange limit except that the experimental data is now based on changes in molecular size resulting from binding rather than changes in the local environment of the nuclei as reflected in the chemical shift. The binding constants determined from analysis of the diffusion data are summarized in Table 4. The average binding constant determined with this method, K ) 17 ( 1 M-1, is in good agreement with the values obtained by chemical shift analysis. The precision of our diffusion measurements is, on average, 1% of the measured diffusion coefficient based on multiple measurements of the same solutions. However, a 1% error in the diffusion coefficient translates to a 4% error in the binding constant. In addition, because the SDS micelle and the GHG concentrations are known only to two significant figures, the imprecision of the diffusion measurements is probably a minor contribution to the overall error in K. No trend is observed in the binding constants reported in Table 4 that would indicate competition of GHG for micelle binding sites. Although more rigorous methods have been used for the analysis of micelle binding,13 in this case, the agreement between the equilibrium constants calculated using chemical shifts and diffusion coefficients demonstrates that a simple single-site binding model can be used to characterize the interaction between SDS micelles and GHG. FHF-SDS Binding Interaction. The 1H NMR parameters of FHF in aqueous solution at pH 5.4 are listed in Table 2. Although the chemical shifts of the GHG glycine R and histidine imidazole protons change as a function of the SDS concentration, the chemical shifts of the resonances of the FHF phenylalanine
Figure 3. Dependence of the FHF aromatic proton resonances on SDS concentration for a solution of 1 mM FHF in 0.10 M Na2C2O4 buffer: (a) 0, (b) 1, (c) 4, (d) 16, and (e) 60 mM SDS.
R and histidine imidazole protons in SDS solutions are not significantly different from their values in D2O. The largest changes in FHF chemical shifts in the presence of SDS are observed in the aromatic region of the spectrum as shown in Figure 3. Taken together, the chemical shift behavior suggests that the FHF aromatic rings probably penetrate the interior of the micelle with the peptide backbone and histidine side chain residing on the exterior of the micelle. Although significant changes in chemical shift are observed for the FHF aromatic resonances in going from D2O to 4.0 mM SDS solution, higher concentrations of SDS produce only subtle changes in the chemical shifts of the FHF resonances, as shown in Figure 3. This behavior of the chemical shifts of the FHF aromatic protons is consistent with a much larger micelle binding constant for FHF than for GHG. This difference is not surprising, since FHF should have strong hydrophobic interactions with SDS micelles while the GHG-micelle interactions are primarily electrostatic. Diffusion coefficients measured for 1.0 mM FHF in 0.10 M sodium oxalate buffer at pD 5.4 as a function of SDS concentration are listed in Table 1. The diffusion coefficient measured for 1.0 mM FHF in 0.10 M sodium oxalate buffer at pD 5.4 is 5.09 × 10-10 m2 s-1 compared with the diffusion coefficient of 5.57 × 10-10 m2 s-1 measured for 5.0 mM GHG under identical experimental conditions, reflecting the larger hydrodynamic volume of the FHF molecule. Comparison of the diffusion data for SDS and FHF in Table 1 shows that once the SDS concentration reaches the cmc,
the fraction of free FHF is so small that the observed diffusion coefficients are simply those of the micelle-bound peptide. Except at the highest SDS concentrations examined, the FHF diffusion coefficient is always significantly less than the SDS diffusion coefficient measured for the same solution. Therefore, FHF is almost entirely micelle-bound while the SDS diffusion coefficient is a weighted average of the free and micellar SDS. The strong association of FHF with SDS micelles as evidenced by both the chemical shift and diffusion data is also consistent with the physical behavior of the peptide; FHF has very low solubility in aqueous solution in the absence of SDS. The dramatic decrease in FHF diffusion coefficients can be used to calculate the SDS cmc. A cmc of 4.1 ( 0.1 mM for SDS in the presence of 1.0 mM FHF was determined from the intersection of the lines defined by the linear least-squares fit of the FHF diffusion coefficients above and below the cmc as shown in Figure 2a. This value is somewhat less than the cmc of 5.4 ( 0.1 mM calculated from analysis of the SDS diffusion data and may reflect some association of the peptide with SDS prior to micelle formation in bulk solution. However, the behavior of the GHG diffusion coefficients near the cmc is much different. Figure 2b shows an expansion of the GHG diffusion data over the SDS concentration range of 1-10 mM. The SDS cmc calculated from a sigmoidal fit of the GHG diffusion coefficients over this concentration range is 5.7 ( 0.2 mM, in excellent agreement with that determined from the SDS diffusion data. The cmcs determined from the diffusion coefficients of peptides in SDS solutions reflect both the high information content of the PFG NMR experiment and the sensitivity of even simple peptides, such as those examined here, to the physical properties of the solution. CONCLUSIONS The chemical shift assignments of the peptides in aqueous solution and in the presence of SDS micelles are reported. PFG NMR spectroscopy and chemical shift analysis were used to analyze the extent of association of the peptides with SDS micelles. In the case of GHG-SDS binding, the NMR chemical shift and diffusion data could be analyzed to determine the association constant for the binding equilibrium. The results are consistent with relatively weak electrostatic interactions for GHG and stronger hydrophobic interactions for FHF with the SDS micelles. ACKNOWLEDGMENT The authors gratefully acknowledge the support of the National Science Foundation through Grants EHR 92-552223 and CHE 9502389. We also thank Dr. Charles Johnson, Jr., for the gift of the computer programs used in processing the DOSY data. Received for review September 12, 1997. January 24, 1998.
Accepted
AC971011M
Analytical Chemistry, Vol. 70, No. 7, April 1, 1998
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