Size and Shape of Fast-tumbling Bicelles as Determined by

In this study, the size and shape of an isotropic bicelle have been determined by measuring the translational diffusion as a function of the volume fr...
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Langmuir 2006, 22, 2447-2449

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Size and Shape of Fast-tumbling Bicelles as Determined by Translational Diffusion August Andersson and Lena Ma¨ler* Department of Biochemistry and Biophysics, The Arrhenius Laboratories, Stockholm UniVersity, S-106 91 Stockholm, Sweden ReceiVed NoVember 23, 2005. In Final Form: January 18, 2006 In this study, the size and shape of an isotropic bicelle have been determined by measuring the translational diffusion as a function of the volume fraction of the lipids. A linear relation between the diffusion coefficients is obtained for both DMPC and DHPC in the bicelles. The slope of this linear function, which is strongly shape-dependent, is found to be different for the two molecules. This difference is direct evidence that the two molecules are not fully mixed in the bicelle. The shape- combined with the size-dependence of the diffusion coefficient allows us to calculate both the size and shape of the bicelle.

Introduction During the past decade, it has been shown that small fasttumbling lipid-detergent mixtures, so-called bicelles, are excellent model membrane systems for investigating peptide-membrane interactions by high-resolution NMR.1-3 The versatility of this system has been examined by introducing lipids with different physical properties but also by investigating several bicellebound peptides.4-6 The small isotropic bicelle has been shown to form disk-shaped aggregates, where the lipids form a central disk and a detergent circumference.7,8 The most well-examined bicelle mixture is the dimyristoylphosphatidylcholine/ dihexanoylphosphatidylcholine (DMPC/ DHPC) case, for which a proper phase diagram is starting to appear. A typical parameter in defining the bicelle is the q ratio, which can be defined as q ) [DMPC]/[DHPC]. For bicelles with q values above ∼3, a very complex phase diagram is obtained.9 Below that, typically, isotropic mixtures are obtained. The strict phase-separation of the lipids and the detergents in the bicelles has lately been debated, especially for bicelles with q values below 1, which are typically used for high-resolution NMR purposes. It has even been argued that bicelles with q values below 0.5 are not disk-shaped at all but form spherical aggregates.10,11 In the present work, we have examined the size and shape of a q ) 0.5 bicelle by measuring translational diffusion as a function of the volume fraction of the bicelles. Our findings indicate that DMPC and DHPC to a large extent are separated in these bicelles. * To whom correspondence should be addressed. Phone: +46 8 162448. Fax: +46 8 155597. E-mail: [email protected]. (1) Andersson, A.; Ma¨ler, L. J. Biomol. NMR 2002, 24, 103-112. (2) Chou, J. J.; Kaufman, J. D.; Stahl, S. J.; Wingfield, P. T.; Bax, A. J. Am. Chem. Soc. 2002, 124, 2450-2451. (3) Vold, R. R.; Prosser, R. S.; Deese, A. J. J. Biomol. NMR 1997, 9, 329-335. (4) Struppe, J.; Whiles, J. A.; Vold, R. R. Biophys. J. 2000, 78, 281-289. (5) Ellena, J. F.; Moulthrop, J.; Wu, J.; Rauch, M.; Jaysinghne, S.; Castle, J. D.; Cafiso, D. S. Biophys. J. 2004, 87, 3221-3233. (6) Ellena, J. F.; Burnitz, M. C.; Cafiso, D. S. Biophys. J. 2003, 85, 24422448. (7) Glover, K. J.; Whiles, J. A.; Wu, G.; Yu, N.; Deems, R.; Struppe, J. O.; Stark, R. E.; Komives, E. A.; Vold, R. R. Biophys. J. 2001, 81, 2163-2171. (8) Luchette, P. A.; Vetman, T. N.; Prosser, R. S.; Hancock, R. E.; Nieh, M. P.; Glinka, C. J.; Krueger, S.; Katsaras, J. Biochim. Biophys. Acta 2001, 1513, 83-94. (9) Katsaras, J.; Harroun, T. A.; Pencer, J.; Nieh, M. P. Naturwissenschaften 2005, 92, 355-366. (10) Triba, M. N.; Warschawski, D. E.; Devaux, P. F. Biophys. J. 2005, 88, 1887-1901. (11) van Dam, L.; Karlsson, G.; Edwards, K. Biochim. Biophys. Acta 2004, 1664, 241-256.

The estimated thickness of the bicelle furthermore agrees well with that of DMPC vesicles. Methods Sample Preparation. Phospholipids, DMPC and DHPC, were obtained from Avanti lipids. 2H2O and KCl were bought from Sigma Aldrich. A q ) 0.5 bicelle sample was produced by vortexing DMPC in a small amount of 2H2O and KCl (final concentration 50 mM) until a homogeneous slurry was obtained. Subsequently, DHPC was added from a 1 M stock-solution, dissolved in 2H2O. This mixture was vortexed for 1 min and was set to equilibrate at 50 °C for 30 min. The concentration of DMPC was calculated to be 150 mM, and the concentration of DHPC was 300 mM, even though a small increase in volume was observed in the sample. The density of DMPC and DHPC has been estimated to be 1 kg/L.12,13 The volume fraction of DMPC + DHPC in the sample is approximately 23%. This sample was subsequently diluted by adding 50 mM KCl in deuturated buffer to obtain different volume fractions. NMR Spectroscopy. All spectra were recorded using a Varian Inova spectrometer, operating at 14.09 T, using a triple-resonance probe head. The temperature was calibrated to 37 °C by monitoring chemical shift differences for the two 1H signals in ethyleneglycol. 1H translational diffusion experiments were carried out using the modified Stejskal-Tanner spin-echo with a gradient prepulse.14,15 The pulsed field gradients were used with a maximum power of 60 G/cm. A total of 16 transients were typically recorded to achieve a good signal-to-noise ratio. The PFG measurements were carried out using fixed time intervals and 30 linearly incremented power levels from 1/30 to maximum power. A T1-relaxation delay of 0.35 s was used in all measurements. The effects of nonlinear gradients were accounted for according to Damberg et al.16 Since all samples were recorded in 100% 2H2O, no special attention was given to water suppression. The methyl signals for the acyl chains for DMPC (0.88 ppm) and DHPC (0.93 ppm) were used as markers for the two molecules.17

Results and Discussion: The translational diffusion of a particle is related to molecular size, shape, and viscosity. These relations are described by the (12) Kucerka, N.; Liu, Y.; Chu, N.; Petrache, H. I.; Tristram-Nagle, S.; Nagle, J. F. Biophys. J. 2005, 88, 2626-2637. (13) Lin, T. S.; Chen, S. H.; Gabriel, N. E.; Roberts, M. F. J. Am. Chem. Soc. 1986, 108, 3499-3507. (14) Callaghan, P. T.; Komlosh, M. E.; Nyden, M. J. Magn. Reson. 1998, 133, 177-182. (15) Stejskal, E. O.; Tanner, J. E. J. Phys. Chem. 1965, 42, 288-292. (16) Damberg, P.; Jarvet, J.; Gra¨slund, A. J. Magn. Reson. 2001, 148, 343348. (17) Andersson, A.; Ma¨ler, L. Langmuir 2005, 21, 7702-7709.

10.1021/la053177l CCC: $33.50 © 2006 American Chemical Society Published on Web 02/14/2006

2448 Langmuir, Vol. 22, No. 6, 2006

Letters

Figure 1. NMR-signal intensity corresponding to DMPC diffusion as a function of gradient power in a diffusion experiment for to φ ) 0.14 sample (D ) 1.8 × 10-11 m2/s). Data points are shown as circles and the solid line is calculated from the fitted parameters.

Stokes-Einstein equation:

D0 )

kT 6πηrh

(1)

where D0 is the translational diffusion coefficient, k is Bolzmann’s constant, T is the absolute temperature, η is the viscosity, and rh is the radius of hydration. This formula assumes that the object is spherical and that the diffusion is unobstructed, i.e., not dependent on concentration. Corrections for shape and obstruction factor have been described analytically, especially in the case of ellipsoids. The Perrin shape factor for an oblate object is given by

fp )

xp2 - 1 p2/3 arctanxp2 - 1

(2)

where p is the ratio between the long and the short axes.18,19 The dependence of the diffusion coefficients on solute volume fraction (φ) is to a first approximation given by

D ) D0(1 - kφ)

(3)

where k is a shape dependent factor and D0 is the unobstructed diffusion coefficient.20 Diffusion coefficients for the two components in the bicelle were measured for samples containing different amount of lipid. The attenuation curve for a sample with φ ) 0.14 is shown in Figure 1. The experimentally measured diffusion coefficients for DMPC and DHPC are plotted against the volume fraction of the lipids in Figure 2. From these plots, it is clear that the data for both DMPC and DHPC sufficiently well can be described by a linear expression like eq 3. The fitting parameters for DMPC are D0 ) 2.68 × 10-11 m2/s and k ) 2.91, and for DHPC we have D0 ) 12.06 × 10-11 m2/s and k ) 3.40. It is thus evident that DHPC moves much faster than DMPC, and that DHPC experiences a rather different shape, as seen from the different k values. The effect of the volume fraction of the lipids on the diffusion on 2H1HO in the sample is less pronounced as compared with DMPC and DHPC. For φ ) 0.23, the diffusion coefficient for the water was DH2O ) 232 × 10-11 m2/s and increased until φ ) 0.14 giving a DH2O ) 260 × 10-11 m2/s. At lower volume (18) Perrin, F. J. Phys. Radium 1936, 7, 1-11. (19) Perrin, F. J. Phys. Radium 1934, 5, 497-511. (20) Cantor C. R.; Schimmel P. R. Biophysical chemistry Part II: Techiques for the study of biological structure and function; W H Freeman and Company: San Francisco, 1980.

Figure 2. Translational diffusion coefficients of DMPC (a) and DHPC (b) as function of volume fraction. The solid lines are fitted to the data points using eq 3.

fractions the diffusion time of the water diffusion remained unchanged. This plateau is not expected from theory, for which the relation 2/(2 + φ) is expected for the solvent in a mixture of oblate objects.21 It is well-known that a small fraction of the DHPC in the bicelle sample is free in solution, and this accounts for the faster diffusion observed in the bicelle samples.22-24 The physical interpretation of the difference in shape factor between the two molecules is, however, not self-evident. DHPC has a larger shape factor, indicating a more obstructed diffusion. This is somewhat surprising since one would expect a lower dependence due to the large fraction of DHPC in solution. The general opinion about bicelle shape is that DMPC forms a disk-shaped center with flanking DHPC molecules. The two are separated due to the different chain lengths of the molecules (14 carbons versus six carbons) and due to their different physical properties. Thus, the DHPC molecules would reside in a more toruslike than disklike three-dimensional distribution. A different location of the two species in the bicelle would result in different apparent obstruction factors for DMPC and DHPC, since these factors are greatly affected by the shape of the aggregate. The observed difference in obstruction factors for DHPC and DMPC clearly indicates that the two species are indeed separated in the bicelle. It is not obvious that the shape-factor of a torus could account for the observed data, but it is nevertheless clear that DMPC and DHPC are not fully mixed in the bicelle. Several groups22,25-27 have used translational diffusion to calculate the fraction of bicelle-bound molecules (x), e.g., peptides, using the relation

xD0bicelle + (1 - x)D0peptide ) D0complex

(4)

Using expression 3 and neglecting the obstruction effect for the (21) Johannesson, H.; Halle, B. J. Chem. Phys. 1996, 104, 6807-6817. (22) Andersson, A.; Ma¨ler, L. FEBS Lett. 2003, 545, 139-143. (23) Ottiger, M.; Bax, A. J. Biomol. NMR 1998, 12, 361-372. (24) Struppe, J.; Vold, R. R. J. Magn. Reson. 1998, 135, 541-546. (25) Chou, J. J.; Baber, J. L.; Bax, A. J. Biomol. NMR 2004, 29, 299-308. (26) Wang, J.; Schnell, J. R.; Chou, J. J. Biochem. Biophys. Res. Commun. 2004, 324, 212-217. (27) Marcotte, I.; Dufourc, E. J.; Ouellet, M.; Auger, M. Biophys. J. 2003, 85, 328-339.

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Langmuir, Vol. 22, No. 6, 2006 2449

solvent, eq 4 can be reformulated as

Dobs Dobs bicelle complex + (1 - x)Dobs x ) peptide 1 - kφ (1 - kφ)

(5)

The fraction of bicelle-bound molecules can then be calculated as

x)

obs Dobs complex - Dpeptide(1 - kφ)

Dobs bicelle

-

Dobs peptide(1

- kφ)

(6)

Using this equation one can reexamine previous results. As an example, the difference in interaction of the peptide hormone motilin with neutral and acidic q ) 0.5 (φ ) 0.14) bicelles has been studied previously.22 The diffusion of motilin in partially acidic bicelles (30% DMPG) was found to be 4.7 × 10-11 m2/s, and in the corresponding zwitterionic bicelles the diffusion was 6.1 × 10-11 m2/s.22 The diffusion for the pure bicelles was 2.2 × 10-11 m2/s, and the diffusion of motilin in buffer was 21.1 × 10-11 m2/s. Using eq 6 and k ) 2.91, we find that x ) 0.80 for acidic bicelles and x ) 0.66 for neutral bicelles, compared to the earlier findings x ) 0.90 for acidic bicelles and x ) 0.84 for zwitterionic ones. The present formulation thus predicts a larger difference in the interaction between the different bicelles. Because of difficulties in making a homogeneous concentrated sample with φ ) 0.23 (which was the starting value for the present investigation) due to the high viscosity of the mixture, markedly lower diffusion coefficients were observed as compared with earlier findings.22 However, when making φ ) 0.14 bicelles directly a similar value to the previously reported was obtained, DDMPC ) 2.4 × 10-11 m2/s (compared to 2.2 × 10-11 m2/s found previously). By using the obstruction shape factor, k, calculated above and DDMPC ) 2.4 × 10-11 m2/s, we get D0 )4.1 m2/s. The shape-dependence of the obstruction factor has been described theoretically for ellipsoids.28,20 By assuming an oblate shape, we thus get a long axes to short axis ratio of approximately 2. This corresponds to a Perrin shape factor (eq 2) of fp ) 1.14. Using T ) 310 and η ) 10-3 kg/s, we can use eq 1 to calculate (28) Simha, R. J. Phys. Chem. 1940, 44, 25-34.

Figure 3. q ) 0.5 DMPC/DHPC bicelle dimensions based on the translational diffusion results.

the radius of hydration for the bicelle, which becomes rh ) 48.6 Å. This value can, together with the ratio between the long and short axes in the bicelle, be used to estimate the size of the bicelle. If the short axis of the bicelle is a, then the long axis of the bicelle is 2a, and according to the relation between the volume of an oblate object and a sphere, given by Biverståhl et al.,29 we get a ) 30.4 Å, corresponding to half of the bicelle thickness, which is in good agreement with the value for the hydrated bilayer thickness of a DMPC vesicle (62.6 Å).12 A model of the q ) 0.5 DMPC/DHPC bicelle size based on the results presented here is shown in Figure 3. The observation that the shape factor and the obstruction factor are different for DMPC and DHPC has very interesting implications. When investigating the positioning of peptides within bicelles, little attention has been given to resolve whether the peptides reside in the DMPC rich region or in the DHPC region, or if the peptide increases/decreases the mixing of these two components. By measuring the volume-fraction dependent diffusion of peptide, DMPC and DHPC, information on these effects is, at least in theory, obtainable. This clearly emphasizes the importance of the present work. Acknowledgment. This work was supported by grants from the Swedish Research Council and the Carl Trygger Foundation. LA053177L (29) Biverståhl, H.; Andersson, A.; Gra¨slund, A.; Ma¨ler, L. Biochemistry 2004, 43, 14940-14947.